I. An Attempt to Prepare Antibodies to Histamine In Vitro. II. An Investigation of a Possible Method for Preparing Large Single Crystals of Aluminum Orthophosphate. III. Investigations of the Crystal Structures of Amino Acids by X-Ray Diffraction: A. An Investigation of the Space-Group and Lattice Constants of dl-Serine. B. An Investigation of the Crystal Structure of ℓ-Threonine Citation Shoemaker, David Powell (1947) I. An Attempt to Prepare Antibodies to Histamine In Vitro. II. An Investigation of a Possible Method for Preparing Large Single Crystals of Aluminum Orthophosphate. III. Investigations of the Crystal Structures of Amino Acids by X-Ray Diffraction: A. An Investigation of the Space-Group and Lattice Constants of dl-Serine. B. An Investigation of the Crystal Structure of ℓ-Threonine. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/a036-nq76. https://resolver.caltech.edu/CaltechTHESIS:04222025-154900081 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry and Physics) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Minor Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Pauling, Linus (advisor) Corey, Robert B. (advisor) Thesis Committee: Unknown, Unknown Defense Date: 1 January 1947 Record Number: CaltechTHESIS:04222025-154900081 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:04222025-154900081 DOI: 10.7907/a036-nq76 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17167 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 30 Apr 2025 16:28 Last Modified: 30 Apr 2025 16:35 Thesis Files PDF - Final Version See Usage Policy. 50MB Repository Staff Only: item control page

I AN ATTEMPT TO PREP.All ANTIBODIES TO HISTAMINE,!! YlTRO II AN INVESTIGATION OF A POSSIBLE METHOD FOR PREPARING LARGE SINGLE CRYSTALS OF ALUMINUM ORTHOPHOSPHATE III INVESTIGATIONS OF THE CRYSTAL STRUCTURES OF .AMINO ACIDS BY :X...RA.Y DIFFRACTION A. AN INVESTIGATION OF THE SPACE-GROUP AND LATTICE CONSTANTS OF dl-SERINE :B. AN INVESTIGATION OF THE CRYSTAL STRUCTURE OF l ~THREONINE Thesis by David Powell Shoemaker In Partial. ]fulfilment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California TABLE OF C01"TENTS Page I. An Attempt to Prepare Antibodies to Histamine 1. 2. Introduction 1 The general method 4 5 5 3. Experimental (c) Materials Partial denaturation in the presence of histamine Schultz-Dale tests (d) (e) Preliminary experiments Tests for antibody-like activity (a) (b) 4. Results An Investigation of a Possible Method for Preparing Large Single Crystals of Aluminum Orthophosphate Introduction Previous work Apparatus and materials Preparation of aluminum orthophosphate crystals 5. Variations in the cond.i tions of crystallization 6. Solubility of crystals 7. Growth of large crystals from seeds 8. Properties of the crystal£ 9. Discussion of the technique 10. Acknowledgements 11. Summary 1. 2. t References Investigations of the Crystal Structures of Amino Acid.s by X-Ray Diffre.cti.on 1. Introduction An Investigation of the 14 15 15 16 19 21 21 ~a 25 27 28 29 30 31 34 Space Group and Lattice Constants of 9.J..-Serine l. 2. g 31 References A. 7 12 References III. 6 6 9 5. Discussion and summary II. 1 Introduction Preparation of crystals 35 35 36 Page 3. Optical examina,tion 4. 5. 6. 7. Density Cleavage Laue symmetry Layer-line measurements S. Precise determination of lattice constants 9. Weissenberg photographs 10. Laue photographs 11. Summary of work on &-serine 12. Acknowledgements References E. An Investigation of the Crystal Structure of L-Threonine 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Introduction Discussion of previous crystallographic work Materials Growth of crystals Morphological study Cleavage Density Laue symmetry Determination of lattice constants (a.) Layer...line measurements (b) Precise determination of lattice constants Systematic extinctions Summary of data on the space group and lattice constants Collection of intensity data (e.) Weissenberg photography (b) Estimation of intensities (c) Correction and correlation of intensities (d) Revision of the film factor (e) Powder photography (f) Reduction to an absolute basis Application of a three-dimensional Patterson synthesis (a.) Introduction (b) Theoretical discussion (c) The mechanics of the synthesis for )-threonine (d) Interpretation of the Patterson distribution (1) General considerations (2) Examination of peaks close to the origin (3) Determination of some atomic parameters The determination of the approximate structure Conclusions Acknowledgements References APPElIDIX 37 ~ 4o 4o 4o 43 45 46 47 48 49 49 51 53 54 54 56 56 56 57 57 58 61 62 65 65 66 68 70 11 73 75 75 77 89 93 93 99 101 105 115 117 119 122 ACKNOWLEDGEMENT Elsewhere in this thesis I have acknowledged the cooperation and assistance given me by those who have supervised my research and by those who have made contributions to its progress. I wish here to emphasize my gratitude to Professor Linus Pauling for his interest in my work and for his va1uable advice and suggestions, and to Dr. Robert B. Corey for his continued advice and ~ncouragement and especially for the very friendly association that existed between us in the amino acid work. I also wish to thank Dr. Corey and Professor Verner Schomaker for many helpful criticisms during the prepar~tion of this thesis. I AN ATTEMPT TO PREPARE ANTIBODIES -- TO HISTAMINE IN VITRO 1. Introduction The object of the investigation here described is to prepare antibodies to histamine in vitro, by a method suggested by Professor Linus Pauling. Although the experiments failed to give evidence of · anti- body formation, a description of the work will be given here. 1 In 1940 Professor Pauling published a theory of the structure of antibodies and of the mode of their formation. He assumed that antibody molecules differ from molecules of serum globulin only in the way the ends of the polypeptide chain are coiled, and suggested that in the formation of an antibody in a living organism the ends of a polypeptide chain similar to that of globulin coil in contact with the antigen molecule in such a way that the completed antibody, which is not significantly different in stability from the related globulin molecules, has over part of its surface a shape complementary to that of some region or regions of the antigen molecule. The close mechanical fit that is possible between an antigen and the related antibody makes possible bonding of adequate strength, though the bonding forces consist only of weak van der Waals forces and hydrogen bonding forces, and accounts for the great specificity of antibody-antigen interactions. As each polypeptide chain is double-ended, the antibodies may be bivalent, and precipitates consisting of three dimensional networks may form when the antibodies interact with multivalent antigens. Professor Pauling also suggested1 that the necessary conditions 1 for antibody formation might be obtained in vitro as i..rell as in vivo. As a partial uncoiling of the polypeptide chain may be expected to occur when a protein is subjected to conditions that tend to denature it, antibodies might be formed by partially denaturing globulin in the presence of the antigen, subsequently removing the denaturing agent or condition under circumstances favoring a re-coiling of the chains in contact with the antigen molecule s, and finally dissociating the antibody-antigen complexes in order to enable the removal of the antigen from the preparation. Ex- periments which were carried out along these lines by Professor Pauling and Professor Dan H. Campbell 2 indicated that this method may be a feasible one for the artificial production of antibodies. In 1942 Professor Pauling suggested that the in vitro method be used in an attempt to prepare antibodie s to histamine, HC = C-CH -CH -NH I I HN N 2. ). 2. \I C H ' which is the decarboxylation product of the amino acid histidine. Histamine is a metabolic _produci of living organisms which ordinarily is destroyed rapidly by the organisms. When injected into an animal it produces a shock- like response, and many of the characteristics of anaphylactic and trau~ matic shock are ascribed to the produce of histamine by the organism3 . .Antibodies capable of binding and inactivating histamine and histamine-like substances may be of therapeutic value in the treatment of shock and allergy, and investigations involving their use may aid in the elucidation of the 2 relation of histamine to shock. The in vitro method was chosen for this work in part because of the difficulty of preparing a suitable antigen for injection into animals by coupling histamine, as a hapten, to a protein molecule. After the investigation described below was completed Fell, Rodney, and }~rshall4 reported that antisera to histamine azoprotein (histamine azo-despicatedhorse-serum-globulin) and histamine carbamido protein had been prepared and that these preparations inhibited anaphylaxis in vivo and ill vitro, precipitated the corresponding antigens, and gave positive hapten inhibition tests. These workers, however, coupled the histamine molecule to the protein molecule through the aliphatic amino group; a much better procedure would be to couple at the ring in order to leave virtually unchanged the molecular fragment that is believed to give the molecule its physiological activity 5 . Additional work is being carried out along these lines by Professor Carl Niemann and coworkers. Further discussion of the ill n.Y2 method is beyond the scope of this report. I devoted three months in the summer of 1942 to an attempt to prepare an antibody to histamine by the i n ~ method. out under the supervision of Profe ssor Carl Niemann. This was carried It was recognized at the outset that probability of success was not high, as the general method was very novel and the best conditions had not been established. The investigation was nevertheless carried out because of the high importance of obtaining information regarding the relation of histamine to shock, and because of the therapeutic value that antibodies to histamine might possess. 3 2. The general method In these experiments, preparations to which we will refer as histamine-treated globulin (filG) were prepared by heating bovine serum globulin with a molar excess of histamine at 56°c, which is about ten degrees below the temperature of irreversible denaturation, in order to allow the polypeptide chains to uncoil partially. The mixtures were slowly cooled in order to favor the re-coiling of the chains at the surfaces of the histamine molecules and dialyzed to dis sociate the complexes and remove the histamine. As the histamine molecule is very small in comparison to antibody molecules its irrnnunological valence is at most two. Accordingly we would not expect an antibody-antigen precipitate to form on addition of histamine to the HTG preparation. As a pr ecipitation test with hista- mine would not be expected to be useful, it is necessary to use some other method of evaluating the anti-histamine activity of the fil.Q preparations. For this purpose we used smooth muscle protection tests with guinea pig ileic strips 6 in a Schultz-Dale apparatus. The applicability of this test for this purpose derives from the fact that in the presence of histamine, even in very low concentrations, strips or lengths cut from the ileum of the guinea pig undergo a contraction sufficient to activate a recording device, and that under the optimu.~ conditions the magnitude of the response is an approximately linear function of the histamine content at low concentractions. If an filQ preparation ha s antibody-like activity against histamine, the addition of the preparation to a hi s t amine solution should reduce the effect 0£ the solution on the smooth muscle, at le ast relative to t he control experiment s . 4 3. Experimental (a) Materials Histamine was obtained in the form of histamine phosphate, in which two molecules of phosphoric acid are combined with each molecule of histamine. For use in assay work aqueous solutions containing one gamma of histamine, calculated as t he free base, per ml. were prepared. I1ore concentrated solutions were used in the preparative work. Bovine ~-globulin* was obtained from the laboratories of Armour and Company. This material (Q.) was used for most of our experi- ments in a two-percent aqueous solution. In an attempt to remove sub- stances having histamine-like activity against smooth muscle, a part of our supply was dialyzed in a two-percent solution against 0.9-percent sodium chloride solution for several days and dried by the lyophil procedure to obtain a product which we shall designate dialyzed~ lyophiled globulin (£9). In later experiments the dialysis was carried out against a phosphate buffer at pH 7.5 in order to obtain a product (BG) with higher pH stability. assumed 7 The molecular weights of these materials were to be about 160,000. Smooth muscle for the assay work was obtained from guinea pigs which weighed about 200 to 400 grams. Each a..'1.imal was killed by a blow on the head and the ileum was removed and flushed with nutrient solution until clean, The ileum was then stored in a refrigerator between cotton pads saturated with nutrient solution, and was cut into one-inch lengths as needed. * Run 21, Fraction II% III. 5 Tyrode's solution 8 was us ed as the nutrient solution in all of t his wo r k. (b) Partial denaturation in the presence of histamine. Solutions containing two percent of the untreated globulin (Q) or of the dialyzed and lyophiled globulin (DG or BG)and 0.0015 to 0.003 percent of histamine (calculated as the free base) were heated at 56°c. in vaporstats over boiling acetone for pe riods ranging from two ' days to a week. The solutions, together with any precipit ates that formed, were then placed in Dewar flasks and set aside to cool. They were then dialy zed in cellophane bags against 0.9-percent sodium chloride solutions for four to eight days at 4°c. with daily changes of the dialysates. was then centrifuged off. Any precipitate that was present The solutions are designated HTG, HTDG, or HTBG, depending on the protein preparation used. Corresponding control preparations, designated CTG, Q..TI2Q, and CTBG, wer e prepared by a similar procedure but without the addition of histamine. were made in this procedure; To obtain additional controls other variations the most important one is the omission of the dialysis operation. (c) Schultz-Dale tests The apparatus used in this work is similar to th at designed by Dr. Gordon Alles of this Institute. In a single all-glas s unit are provided a muscle bath ,.Jith a capacity of 20 ml., a reservoir for storage of nutrient solution, a stopcock for draining the contents of the muscle bath and refilling the bath fro m the reservoir, and a jacket through which water is pumped from a thermostat to maintain the contents of the bath and reservoir at J7°C. The contents of the bath and the reservoir are continually aerat ed by a stream of air bubbles from a hypodermic needle or glass capillary tube. 6 In each run a one-inch length of the smooth muscle was tied at both ends with a silk thread and mounted in the muscle bath. One end was tied to a kymograph lever by means of which the contractions of the muscle could be amplified and recorded on a kymograph drum. hour in the bath the muscle was ready for use. After an Its response was cali- brated with known amounts of histamine, 0.05 to 0.25 gamma, at the beginning of the run and frequently during the run. In each test about 1 ml. of the solution to be assayed was introduced into the bath with a hypodermic syringe, and when the response became steady the bath was drained, rinsed three times with nutrient solution, and refilled. Tests were made in cycles in which solutions to be tested for antibody activity were alternated with the controls. In each cycle four or more different solutions were tested. Very erratic behavior was often observed; the calibration usually changed considerably with time, and consecutive runs were often quite unreprod~cible. , For this reason it was neces s ary to make several tests with each solution and to compare the results for different solutions only within a single cycle of tests. (d) Preliwinary experiments Measurements of pH were made on the protein solutions at various stages of their treatment. The untreated solutions of raw pro- tein were found to have pH values of about 7.2. The addition of histamine and two days of heating at 56°c usually did not significantly affect the pH value, although in a few cases pH values as low as 6.1 were observed. After dialysis the pH value dropped often as low as 4.8. Similar results were obtained duri ng the treatment of DG, but in the experiments with BG 7 the pH value remained at 6.9 to 7.2 during the entire procedure. The amounts of precipitate that formed during heating and especially during dialysis were smallest in the experiments carried out with BG and largest in those with DG. Some experiments were carried out to determine the histaminelike activities of the unheated and heated protein preparations. We found that one milliliter of the two-percent globulin solution (.Q) is equivalent to about 0.15 or 0.16 gamma of histamine. The activity was found to decrease to about 0.12 on he ating at 56°c. for several hours. The DG had an activity equivalent to about 0.11 gamma of histamine. As these activities are of the order of the activity of histamine in the amounts used in the assay work, the need for controls is clear. To esti- mate the degree of non-specific binding of histamine by protein, mixtures of histamine with heated ~~d unheated globulin were compared with undialyzed lIT,g preparations and with histamine itself. No positive indication of non-specific binding was obtained. (e) Tests for antibody-like activity A total of 229 solutions was prepared for tests of antibody- like activity. Most of these were prepared by mixing the histamine stock solution (one gamma per milliliter) with the various protein preparations (HTG, 1:IT!ill, HTBG, and the coDresponding control preparations). On the assumption that all of the protein molecules in each preparation had been converted into bivalent antibodies, one milliliter of the antibody solution is calculated to be equivalent to 28 ml. of the histamine solution. The proportion of antibodies in the preparations is not expected to be large, however; therefor e many of the mixtures tested were prepared with a much 8 larger ratio of protein solution to histamine solution. The mixing ratios that we employed ranged from 9: 1 to 1: 99. Some of the solutions tested were: undialyzed 1-ITG preparations, solutions of histamine that had been heated at 56°c. under conditions similar to those of the treatment of the protein preparations, mixtures of untreated protein with histamine solution, and water controls similar in composition to the other test solutions but with water substituted for protein solution. . These solutions were tested in groups of four to six by the Schultz-Dale technique as described above. Each group was selected to represent a particular set of conditions determined by the choice of starting material, the conditions of treatment of the protein, a.~d the ratio of the protein preparation to the histamine solution in the solutions to be tested. Each group usually contained one mixture prepared from lIT.Q, one prepared from undialyzed lIT.Q, one prepared from CTG, a solution of the untreated protein, a water control, often a heated histamine 9 control, and sometimes others that we will not mention here. 4. Results The amplitudes of the contractions were measured with a milli-, meter scale. The results for each testing cycle were judged as a group, and on a relative basis. When, through the group, the solutions to be tested for antibody activity as ,, ayed less than the corresponding controls (except for the water control which was virtually always low), the result of the group was designated a positive antibody response ( + ). When they were consistently above the controls, the result was designated an anomalous an'tibody 9 response ( - ) . Intermediate designations ( ±, O, =t= ) were as signed to groups that gave inconsistent or inconclusive results. The criterion for positive antibody response may be, for example, the satisfaction of all of the inequalities R ( HTG ➔ .W < R (CTG ➔ ID' R (HTG + ,!!) < R (HTG) + R(ll), R (HTG -t: .tl) < R (g.) R (!:ITQ undialyzed) + R(H), and < R (QTii) + R (!:fil) , where E designates smooth muscle response and where corresponding total quantities of protein and of histamine (assuming no decomposition of the latter) are the same on both sides of each inequality. The results of these te sts are presented in Table 1. The sym- bols used in this table and el sewhere in the text may be sum.m ari zed as follows: Q = globulin (usually in a 2% aqueous solution), DG: dialyzed and lyophiled globulin, fill:: globulin dialyzed against a buff er and then lyophiled, ll = histamine (usually in a solution containing one gamma per ml.), prefix fil = histamine-treated (Sec. 3b), prefix QI =· dontrol-treated (Sec. 3b), and HH = heated histamine (H heated at 10 56°c.). ,Table 1 Results of Tests for .Antibody Activity Ratio of protein preparations* to histamine solution** in mixtures tested 9 1 7 1 .1 1 . .3 1 1 7 1 9 1 19 3 97 1 49 1 99 Ma jor groups of test solutions HI'G HI'DG HTG HTDG G CTG HTG HTBG CTG G CTBG HH BG HH G + ---o oo-- +o- +ooooo--T -o--+-o ---o oo+-1-0 ++ -0--00 -o + oo+oo+ Experiments with undialyzed preparations -oo-+oo 000-000- * 2% aqueous solution. ** Aqueous solution containing one garmna of histamine per ml. 11 0000 5. Discussion and su."lllllary It is apparent from the results given in the table that the preparations possessed no ability to protect smooth muscle against histamine. The preponderance of anomalous (-) results ( 11 probody 11 response) is very difficult to explain, for it is hard to see any mechanism whereby any of these preparations could enhance the activity of histamine when it is introduced into the muscle bath in a mixture with histamine. A simple explanation of these results might be that the histamine molecules are so bound by the modified protein molecules that their activity toward smooth muscle is not decreased, and that the histamine-protein complexes are absorbed by ~he smooth muscle. This hypothesis is an extremely tenuous one for it is almost inconceivable that the histamine molecule could be bound bY, an antibody without losing its activity through blocking of an es sential part of the active molecular fragment. We must conclude that the results of this experiment indicate that this method of preparing antibodies to histamine was unsuccessful, and that otherwise the r esults are inconclusive. It is possible that because of the comparatively small size of the histamine molecule a.s an antigen, the histamine molecules were completely surrounded or enclosed by the re-coiling polypeptide chains in such a way that the complexes could not be dissociated by dialysis. experiments in which the antigen molecules comprise ,Ill ill!:2 histamine molecules as haptenic groups coupled by azophenyl li.nkages to protein molecules or to resorcinol molecules might be more successful; in vivo work along these 4 lines has already been done • The use of antigens of this kind would permit the use of precipitation tests and possibly hapten inhibition tests. 12 I am very grateful to Professor Linus Pauling for suggesting this problem, and to Professor Carl Niemann for valuable guidance and suggestions. 13 References 1. 2. Linus Pauling, iL.. Am, Chem, Soc. g, 2343 (1940). Linus Pauling and D. H. Campbell, Science 95, 440 (1942); .,,..... L. Exper. Med. 76, 221 (1942). 3. C. H. Best and E.W. McHenry, Physiol, Rev. g, 371 (1931). 4. N. Fell, G. Rodney, and D. E. Marshall, J..,_ Immunal. 47, 237, 251 (1943). - 5. Carl Niemann and J. T. Hayes, L. Am. Chem, Soc. 64, 2288 (1942). 6. M. Guggenheim, and W. Loffler, Biochem, i,_ 7. E. J. Cohn and J. T. F.dsall, "Proteins, .Amino Acids, and Peptides", A.C.S. Monograph. New York: T. Sollman, -72, 303 (1916). -- Reinhold Publishing Corp., 1943. p 428. 8. A Manual of Pharmacology". Co., 1942. p. 854. 9. For details see a report by D. P. Shoemaker, "An Attempt to Prepare an Antibody to Histamine", submitted to Professor Carl Niemann, September 23, 1942. 11 14 Philadelphia: W. B. Saunders II AN INVESTIGATION OF A POSSIBLE METHOD FOR PREPARING LARGE SINGLE CRYSTALS OF ALUMINUM ORTHOPHOSPHATE 1. Introduction Large native crystals of o -quartz constitute a very important raw material in the electronics and communications industry where these crystals are used in the manufacture of piezoelectric elements for frequency controls and filters. They are also important in the chemical industry for the manufacture of clear fused silica, and they have uses in the optical industry as well. The usefulness of quartz for piezoelectric elements arises from the lack of a center of symmetry, a crystal structure that results in a piezoelectric effect of appreciable magnitude, a degree of hardness that enables the crystals to withstand severe mechanical vibrations of very high frequencies, am the high degree of homogeneity, purity, and perfection that can be found in native crystals of this substance. A large proportion of the crystals that are used in the electronics industry are imported from Brazil. Although .~he supply was adequate for many years, the additional demands imposed by the recent war made native quartz crystals of satisfactory size and quality a critical material. As no means existed for preparing suitable crystals of quartz synthetically, it became very desirable to search for a suitable substitute. In the spring of 1943 Professor Linus Pauling pointed out that crystals of aluminum orthophosphate (AlP0 ) might serve as a satisfactory 4 substitute for quartz. This suggestion was based on the close structural similarity of crystals of this compound to those of quartz and on the ., 15 apparent feasibility of growing them from a solution. At Professor Pauling's suggestion, and with the approval of Dr. J.B. Conant, then Chairman of the National Defense Research CoI!h~ittee, I undertook to study the conditions by which such crystals could be prepared, with the hope that if the results showed promise the work would become the subject of an NDRC contract. I carried out this work under the supervision of Dr. Reuben E. Wood. My preliminary work on this problem is described below. Although crystals up to 8 mm. in length and 4 mm. in diameter were prepared, and although the method appeared to be promising for the preparation of larger crystals, the work was abandoned after two and one-half months on receipt of word from Dr. Conant that the major problem had been solved by other methods. 2. Previous work Aluminum orthophosphate (AlP0 ) appears to have been first pre- 4 pared in the anhydrous crystalline state by de Schulten1, who in 1884 reported that he obtained crystals by adding concentrated phosphoric acid in excess to a saturated aqueous solution of sodium aluminate and heating the mixture in a sealed tube for several hours at 250° C. The crystals appeared as hexagonal prisms at most 2 mm. in length and 0.1 mm. in diameter. Examination with the polarizing microscope showed them to be optically uniaxial and positively birefringent. Strada2 obtained powder photographs of both the orthophosphate and the orthoarsenate- (A1Aso4 ) of aluminum, and indexed them on the basis of a tetragonal cell. is s2 4 He concluded that the space-group of both compounds - 14 and that the crystals are similar in structure to crystobalite. 16 The orthoarsenate was reinvestigated by Machatschki3, who found the conclusions of Strada with regard to this compound incorrect. From compari- sons of powder photographs of this substance with photographs of q-quartz Machatschki concluded that aluminum orthoarsenate, and probably aluminum orthophosphate which was claimed to be isomorphous with the orthoarsenate, are rhombohedral in symmetry and similar to d.-quartz in structure. A similarity to the quartz structure should not be surprising, for the crystallographic properties of Al+J, P~ 5, and As~ 5 are in some ways analogous to those of Si~4, particularly with regard to the tendency for oxygen atoms to coordinate tetrahedrally around these kernels. Huttenlocher4 undertook to verify this conclusion for the orthophosphate. By a method similar to that of de Schulten he obtained small crystals with prismatic and rhombohedral faces similar to those of quartz. The angle between adjacent prismatic and rhombohedral faces in the zone of a two-fold axis was found by goniometric measurements to be 21°05'; this is very close to the angle (2021)/(1010) for quartz, which is 21029•. The lattice constants were determined from powder photographs. These and other properties of this substance as determined by Huttenlocher are compared in the following table with the cell constants and properties of ~-quartz as determined by Wyckoff5 and others, and with the cell constants and density of aluminum orthoarsenate as determined by MachatschkiJ. Table i Lattice Constants and Physical Properties of Aluminum Orthophosphate, Aluminum Orthoarsenate, and <ll -Quartz AlPO 4 4 ~-Quartz Lattice constants, i a C c/a c/a (x-ray) (optical) 4.93 2 X 5.47 2 X 1.11 2 X 1.123 Density, g./cm. 3 Hardness 5.03 2 X 5.61 2 X 1.11 4.90 3.34 2.65 5 5.39 1.10 Considerable 7* 1.524 1.544 1.553 .009 Indices of refraction Ordinary ray Extraordinary ray Double refraction * On Mohs' 1.530 .006 scale It may be inferred from the data given in this table that the two aluminum compounds are very similar in structure to (A -quartz. The similarity is further borne out by comparisons, made by Huttenlocher and Machatschki, of intensities of x-ray reflections with those of quartz. In accordance with the doubled £-axis found for the aluminum compounds, it is probable that positions corresponding to those of silicon atoms in quartz are occupied alternately in the £-direction by atoms of aluminum and phosphorus or arsenic. Huttenlocher also observed that aluminum orthophosphate undergoes a transition at high temperaturestoaform which is very nearly optically isotropic. In order to determine whether this transition is analogous to 18 6 the transition between~- and ,0-quartz, Professor J. H. Sturdivant in an unpublished investigation carried out an x-ray investigation of aluminum orthophosphate at room temperature and at high temperatures. His work substantiated the conclusions of Huttenlocher regarding the structure of the low temperature form and indicated that the high temperature form is similar in structure to fi-;-quartz. The method employed by Professor Sturdivant for preparing crystals of aluminum orthophosphate is similar to that of de Schulten and is the one which was adopted as the basis of the present investigation. His best crystals, which ranged in size up to one or two millimeters, were obtained by dissolving 1/3 mole of aluminum turnings in a solution of 0.5 mole of sodium hydroxide in 100 ml. of water, mixing the filtered solution with 3 to 5 mDles of phosphoric acid (used as the 85% solution), and heating the mixture at 250° C. in sealed tubes. In the experiments described below solutions of the same kind were used, and the compositions of the solutions and the conditions of crystallization were varied in order to determine the compositions and conditions which favor the growth of the largest and best formed crystals of aluminum orthophosphate. 3. Apparatus and materials In this work it was necessary to heat aqueous solutions at temperatures as high as 250° C. in sealed glass tubes. Accordingly some attention was given to the design of tubes which are able to withstand internal pressures as high as 50 atmospheres at this temperature without bursting. Tubes with inside diai:ooters as large as 20 mm. were prepared from pyrex combustion tubing of 2-mm. wall thiclmess. 19 These had body lengths of about 2.5 inches, were closed at one end, and were tape~ed ',at the other end to a junction with a length of 7-mm. pyrex tubi~ of 1-mm. wall thickness. In addition, many tubes of smaller dian:eter were made from stock pyrex tubing with a wall thickness of about 1 mm. All tubes were carefully annealed. Since the surface of the glass becomes etched during contact with the hot solution, each tube could be used only once. In use, each tube was filled about two-thirds full, and the open end sealed off. It was then enclosed in a length of steel pipe to minimize hazards due to bursts, and placed horizontally in an electric furnace. The electric furnace used in these experiments was lined on the inside with a copper pipe 2.5 inches in diameter and 24 inches long. The ends of the furnace were stopped with copper and asbestos plugs which were provided with holes or notches to accomodate a thermometer and a specially constructed mercury thermoregulator. By means of this thermoregulator the . furnace temperature could be maintained at any desired temperature up to 3006 C. within one or two degrees. The solutions that were heated in the furnace were prepared in the following way. A solution of sodium aluminate was prepared by adding 27 g. of aluminum turnings to a solution of 60 g. of sodium hydroxide in 300 ml. of water. The reaction vessel was cooled under the cold water tap until the reaction was complete. The solution was then filtered and made up to 300 ml. by the addition of water to replace that lost by evaporation. This stock solution was designated solution,!. A stock solution desig- nated as solution~ was prepared by adding 75 ml. of 85% phosphoric acid to 30 ml. of solution Jt and stirring until the precipitate of aluminum 20 hydroxide, which first formed on the addition of acid, redissolved to give a solution which contained aluminum ions and primary phosphate ions (¾P0 -) as well as sodium ions, water, and excess phosphoric acid. 4 Another solution,~' which contained aluminum and phosphate in the same total concentrations but no appreciable amount of sodium ion, was prepared by dissolving a well washed precipitate of aluminum hydroxide in an excess of 85% phosphoric acid and diluting the resulting solution with water. Best results were obtained when these solutions were freshly prepared before each experiment. 4. Preparation of aluminum orthophosphate crystals In order to obtain a stock of crystalline material to be used in solubility studies and as seeds for the growth of larger crystals, glass tubes were charged with solution] or solution~, sealed off, and placed in the furnace where they were maintained at 200°- 250° C. for a day or more. The tubes were then removed from the furnace, cooled, and opened. The crystals were washed into a Buchner funnel where they were further washed with water and dried with alcohol and ether. Crystals prepared in this way ranged in size from microscopic particles to rhombohedra 2 mm. or 3 mm. long and large multicrystalline clumps. Many of the crystals had white surfaces which apparently resulted from etching by the solution. 5. Variations in the conditions of crystallization It was desired to determine the effect of composition, water content, and temperature on the rate of production of crystals and on the size and quality of the crystals obtained. In parallel experiments in which stock solutions~ and Q were 21 heated at 220° C. for 15 hours, solution~ gave a 15% yield of wellformed crystals which ranged in size up to n2arly 3 mm., while solution Q gave a 60% yield of somewhat smaller crystals. The reason for the dif ference in behavior may be that in solution~, which contains an excess of primary phosphate ions, the aluminum ions are more completely complexed with primary phosphate ions than in solution Q.. This hypothesis must be taken as tentative, however, for the results of this experiment would not be much different if solution Q contained a much larger number of nuclei on which crystals can grow, either by accident or as a fundamental result of some step in the preparation of the solution. In the absence of other evidence the results of this experiment may be taken to indicate that the use of sodium aluminate rather than aluminum hydroxide in the preparation of the crystallizing solution is favorable for the growth of large, well-formed crystals. Other experiments showed that the addition of water to solution~ increases the yield of crystals and the rate of their growth, , but decreases their size. Reduction of the water content by the addition of phosphorus pentoxide considerably reduced the rate of crystal growth. In the short time available, no radical changes in the com- position of the crystallizing medium were tested. 22 In the remaining experiments solution~ was used without alteration, except in some cases in which the concentration was increased by dissolving previously prepared crystals in the solution. Reduction in the rate of crystallization by addition of phosphorus pentoxide appeared to be inadvisable because over the long period of time that would be required to grow a large crystal many additional centers of crystallization are likely to appear. Experiments with solution~ at different temperatures showed that no crystals form below about 1900 c. Above 1900 crystals were found to grow at a rate which increased with the temperature. crystals that appeared were usually small in size. At 250° C. the Moreover, at this temperature the glass tubes were strongly etched by the solution. From the standpoint of size and perfection of the crystals the optimum temperature appeared to be in the range 195o to 200° C. 6. Solubility of crystals At room temperature the crystals are apparently insoluble in water or phosphoric acid, but at temperatures between 100° and 180° C. they dissolve in phosphoric acid or in solution] at an appreciable rate. Hence the successful use of a seed crystal requires that the crystallizing solution be heated rapidly to temperatures above 190° C. and that the seed not be too small. Moreover, tubes containing finished crystals should be cooled rapidly to prevent etching of the crystal faces. Experiments showed that at 110° C. solution~ is capable of dissolving powdered crystals of aluminum orthophosphate to the extent of about 0.2 g. per ml. It may therefore be possible to grow crystals of this compound at temperatures below 180° C. by the simple expedient of 23 first saturating the crystallizing solution with it at still lower temperatures. 7. Growth of large crystals from seeds Several experiments were carried out in which seed crystals were placed in tubes charged with solution~ and the tubes heated at 196° C. for periods ranging from four days to several months. In one experiment three tubes were charged with solution Band with respectively no seed crystal, one seed crystal, and several seed crystals. These were heated at 196° C. for two weeks. At the end of this time each of the tubes contained a large number of small crystals, which were for the most part well formed. No crystals larger than 3 mm. in size were found in the unseeded tube, one large crystal 8 mm. long and about 4 mm. in diameter was found in the tube to which a single seed had been added, and three or four crystals having maximum dimensions of 5 nnn. to 8 mm. were found in the tube to which several seeds had been added. The crystals were rhombohedra of varying degrees of perfection; their lengths were approximately twice their diameters. The results indicate that the growth of large crystals from seeds is feasible, but that care must be taken to eliminate other possible centers of crystallization. It is apparent from the relative sizes of the crystals that the small crystals in each tube must have begun to grow only after several days of heating; during this time the glass walls of the tubes may have been etched by the solution to such an extent that they provided unwanted centers of crystallization. In another experiment a tube was charged with 35 ml. of solution 24 ~ and with one seed crystal, and was heated at 196° C. for two months. At the end of that time there were many crystals present in the tube and it was impossible to determine which of them had grown on the seed. 8. Properties of the crystals The crystals are similar in shape and features to those prepared by Professor Sturdivant, though many of them were much larger in size. The largest single crystal was 8 mm. in length and 4 mm. in diameter. The crystals are rhombohedral in form, though few of them approached perfection. Prismatic faces were not observed. The faces are etched in varying degrees, and the etch patterns on the rhombohedral faces of well formed crystals indicated that the crystals have the point-group symmetry n - 32, as does quartz. 3 A crystal about 4 mm. long and in shape a very nearly perfect rhombohedron was mounted on an optical goniometer with its three-fold axis vertical, and the latitude and azimuthal angles for five of the faces were measured. The results are given in the following table. Table 3 · Goniometric Examination of a Crystal of Aluminum Orthophosphate Indices Character of reflection Hex. axes Rhomb. axes 1011 100 Good 1101 OlO Rather fuzzy 0111 001 * 1011 100 Very fuzzy** 25 Azimuth Latitude 21° 24 1 120° 00 1 179° 48' 21° 25 1 Table 3 (continued) Indices Character of reflection ·~zi:inuth Latitude Hex. axes Rhomb. axes 1101 010 Excellent 300° 04 1 - 21° 25 1 0111 001 Rather fuzzy 60° 08' - 210 221 * Only a blur was observed; this face apparently was in contact with the wall of the tube. ** This poor reflection was not used in orienting the crystal. The average absolute value of the latitude angle, which corresponds to the angle between rhombohedral and prismatic faces in the zone of a twofold axis, is 21° 24 1 if the data for (0111) and (1011) are excluded. is to be compared with the value 21° 05 1 reported by Huttenlocher4. This With the use of hexagonal axes the azial ratio c/a is found to be 2.210, in good agreement with the values previously found by x-ray measurements and listed in Table 2. The density of the crystals at 20° C. was measured by displacement of water in a pycnometer, and was found to be 2.61, in rough agreement with the value 2.56 given by Huttenlocher. The hardness of the crystals was found to be about 4 on Mohs' scale. They are accordingly considerably softer than quartz, which has a hardness of 7. This result appears to contradict that of Huttenlocher, who did not, however, refer the hardness of his crystals to Mohl scale. On heating strongly in a gas-oxygen flame the crystals usually turned white and crumbled. When the crystals were fused, small bubbles 26 were observed in the melt, and on resolidifying the product did not have a glass-clear appearance. Lack of time prevented the study of the piezoelectric properties of the crystals. Moreover, quantitative piezoelectric studies would require crystals larger in size than those that were available. Qualitative or semi-quantitative measurements might be carried out with the present crystals by one or more of the methods outlined by Wooster 7 • 9. Discussion of the technique The results of this study indicate that it is feasible to grow crystals of aluminum orthophosphate that are large enough to use for piezoelectric purposes. The following conclusions may be drawn with regard to method: (a) The crystals may be grown from a concentrated mixture of sodium aluminate and phosphoric acid in excess. The use of sodium aluminate rather than aluminum hydroxide appears to give better results, possibly due to better complexing of the aluminum ions. The solutions should be at least as concentrated as those used in the present investigation, but the results of these studies do not appear to suggest radical changes in their composition. (b) Large crystals may be best grown from seeds. Great care should be exercised to exclude additional centers of crystallization. If glass tubes are to be used, the experimental conditions may require modification to permit work at temperatures low enough so that etching of the glass does not take place. It may be desirable to use tubes of fused silica, or to carry out the crystallization in a fused silica beaker within 27 an autoclave. (c) The temperature at which the crystals are grown should not be much higher than that of incipient crystallization. If further experiments are attempted, variations in the experimental arrangement should be · tested. For example, the crystals might be grown in a tube that is heated non-uniformly in order to obtain stirring by convection. If a considerable amount of the crystalline material is placed in the cool end of the tube, this material may continuously replenish the solution as it is depleted by the growth of a larger crystal at the warmer end of the tube. If an autoclave is to be used in the way mentioned above, the bottom of the beaker might be covered with small crystals, and an electrically heated finger, dipping into the solution and holding a seed crystal, could serve as the site for the growth of a large crystal. It should be pointed out that the relative softness of the aluminum orthophosphate crystals (4 on ~bhs~ scale) may be a barrier to their use as a general substitute for quartz in piezoelectric applications. If the crystals are found to have piezoelectric properties comparable to those of quartz, they may nevertheless find application in electronic circuits that do not subject them to mechanical vibrations of high amplitude. 10. Acknowledgements I am indebted to Dr. Reuben E. Wood, who supervised this work, for many valuable suggestions. I am very grateful to Professor James H. Sturdivant for information concerning his previous work, and to Professor Verner Schomaker for several valuable discussions. I wish to thank Professor Linus Pauling for suggesting this study. 28 11. Swnmary A method of preparing crystals of aluminum orthophosphate has been tested with a view to the development of a procedure for growing large single crystals of this substance for possible use as a substitute for quartz in the manufacture of piezoelectric elements. In this method, a mixture of sodiu.~ aluminate and phosphoric acid is heated in a sealed tube at about 200° C. This work was dropped before completion on receipt of information that other methods were being used to solve the problems caused by the wartime scarcity of large quartz crystals, and the effort which might otherwise have been spent in continuing this investigation was directed to war work of higher priority. Enough work was done to indicate that the preparation of large single crystals of aluminum orthophosphate is feasible. 29 References -- 1. A. de Schulten, Compt. Rend,·98, 1583 (1884). 2. M. Strada, Gazz, Chimica ital, 64, 653 (1934). 3. F. Machatschki, L Krist, ....... 90, 314 (1935) . 4. H.F. Huttenlocher, .!:. Krist, ,-.; 90, 508 (1935). 5. R. W. G. Wyckoff,''The Structure of Crystals" (Second F.dition), ACS Monograph No. 19. New York: Chemical Catalog Co., 1931. p 239. 6. Handbook of Chemistry and Physics (Twenty-ninth Edition). Cleveland, Chemical Rubber Publishing Co., 1945. p 452. 7. W. A. Wooster, Crystal Physics. Cambridge: At the University Press, 1938. Chapter VI. """'- 30 III INVESTIGATIONS OF THE CRYSTAL STRUCTURES OF AMINO ACIDS BY X-RAY DIFFRACTION 1. Introduction The work presented in this section will be discussed under two headings: (A) An Investigation of the Space-Group and Lattice Constants of dl-Serine, and (B) An Investigation of the Crystal Structure of !-Threonine. Information regarding the structure of amino acids and simple peptides is of considerable interest in connection with the study of the structure of protein molecules, a study which is the subject of a research program of the Gates and Crellin Laboratories of Chemistry of 1 2. this Institute' X-Ray diffraction investigations of amino acids and simple peptides are undertaken primarily to obtain knowledge of the structures of the amino acid residues as they probably exist in the protein molecule, of the manner of combination of these residues ip peptide chains, and of possible modes of packing of the peptide chains in the protein molecule. The structural information given by an x-ray diffraction study of an amino acid concerns bond distances and bond angles among the atoms of the amino acid molecule, and the manner of packing and hydrogen bonding among the molecules that make up the crystal. Information of this kind has been given by the few complete structure determinations that have been carried out in the amino acid field; this information should be' supplemented by 31 thorough studies of many other amino acids and simple peptides which represent a wi?e variety of modes of packing and of intermolecular bonding, substituent groups, spacial relations among residues in peptides, and so forth. Needless to say these investigations are only a part of the work which must be done on the problem of protein structure; this work must also include x-ray studies of protein molecules in crystals and fibers, physical measurements of the shapes, molecular weights, and properties of these molecules, chemical analysis for amino acid residues, and perhaps electron microscopy. The structures of only two amino acids have been investigated in detail by x-ray diffraction methods. The crystal structure of dl-glycine has been determined by Albrecht and Corey3, and the structure of nickel glycine dihydrate has been determined by Stosick4. The crystal structure of fil-alanine has been determined by Levy and Corey5. Quantitative work on peptides is limited to the determination by Corey6 of the crystal structure of diketopiperazine, which is a cyclic dipeptide of glycine, and the work (still in progress) by Hughes and Moore 7 on p-glycylglycine. Preliminary work has been done by Bernal8 and by Albrecht and coworkers9 on a number of other amino acids. This work includes determinations of space-groups, lattice constants, densities, and in many cases cleavage and optical properties. The amino acids studied by Bernal are i-glycine, @-glycine, g-alanine, fil-alanine, g-phenylalanine, J-cystine, asparagine monohydrate, i.-aspartic acid, {-glutamic acid, and diketopiperazine; those studied by Albrecht and coworkers are dl-valine, dl-threonine, dl-serine, dl-norleucine, and dl-methionine2 • The space-group reported for dl-thneorine by Albrecht and coworkers is apparently incorrect, and will be discussed 32 further in a later section. The occurrence of this error indicates the need for a careful review of the preliminary work on some of the other amino acids. I had originally planned to undertake a reinvestigation of the space-groups and lattice constants of some of the amino acids mentioned above, as well as to carry out similar studies of some amino acids for which data on space-groups and lattice constants are inadequate or lacking. The latter group includes tyrosine, iodogorgoio acid, thyroxine, leucine, isoleucine, hydroxyglutamic acid, arginine, lysine, histidine, praline, hydroxyproline, and tryptophane. It soon became apparent that it would be impossible for me to carry out a complete investigation of a single amino acid if I were to make studies of space-groups and lattice constants of any significant number of compounds. The work described in this section is therefore limited to a determination of the space-groups and lattice constants of gl-serine and J-threonine, and to a more detailed investigation of the structure of i-threonine. 33 Reference s 1. R. B. Corey, Chem. Rev, 26, 227 (1940). 2. R. B. Corey, Advances ,;tn Protein Chemistry (to be published). 3. Gustav Albrecht and R. B. Corey,~ Am. Chem. Soc. 61, 1087 (1939). 4. A. J. Stosick, ~Arn.Chem. Soc, 67, 365 (1945). 5. H. A. Levy and R. B. Corey, J. Am. Chem, Soc, 63, 2095 (1941). 6. R. B. 7. E. W. Hughes and W. J. Moore, l:. Am. Chem. Soc, 64, 2236 (1942). 8. J. D. Bernal, iL Krist. 78, 363 (1931). 9. Corey, l.:_ Am. Chem, Soc, 60, 1598 (1938). G. Albrecht, G. W. Schnakenberg, M. S. Dunn, and J. D. McCullough, Chem, 47, 24 (1943). ~ Phys, 34 A. Ai~ INVESTIGATION OF THE S?ACE-GROUP AND 1, LATTICE CONSTANTS OF dl-SERINE Introduction This section is a description of a redetermination of the spacegroup and lattice constants of dl-serine: H HO - CH2 - C - COOI NH3 .f. This compound is of frequent occurrence in proteins, notably silk-fibroin. It may be regarded as a hydroxyl derivative_of alanine. Its study by x-ray diffraction is an attractive problem because of the relatively small number of atoms in the molecule. The space-group and lattice constants of dl-serine crystals were first determined by Albrecht and coworkers1 . These investigators found the crystals on goniometric examination to be monoclinic holohedral, with axial ratios a:b:c. 1.194: 1: 0.522 and with~. 73°47'. The authors found that their results may be reconciled with those reported by Groth2 who made a different choice of~ ands axes*. From measurements of layer-lines of rotation photographs and from measurements of high-order pinacoid reflections Albrecht and coworkers obtained the following values for the lattice constants: 0 a 0 • 10.74 A bo • 9.15 0 c 0 • 4.78 A ( R, = 73°47') i By the usual convention the supplement of the reported value of~, 106°13 1 , * The authors •· assertion that Groth made different choices of both the axis and the s axis is apparently incorrect; chosen differently. ~ 35 only the£! axis was would be given. It is not clear whether this angle was calculated from the x-ray data; the mode of presentation of the results suggests that this angle was merely taken from the optical data. The density value of 1.537 g. per cm3. indicates that there are four (4.00 calculated) molecules in the unit cell. The systematic absences of odd order QkQ reflections and of loi reflections with the space-group C~h - b odd led the authors to assign "P2,/a to fil-serine. A quantitative investigation of the structure of dl-serine was begun in these laboratories by Dr. Chia-Si Lu. Dr. Lu subsequently moved to Amoy, China, where he plans to complete this work. His data are not immediately available to us, but he has recently informed me (in a private communication) that his results for the space-group and lattice constants agree with those of Albrecht. In view of the importance of this amino acid I undertook to make a redetermination of its space-group and lattice constants, with a view to the possibility of carrying out a complete structure determination at a later date. The work which I have completed is described below. Ad- ditional work on this amino acid in these laboratories has been postponed, and will probably be undertaken if Dr. Lu is unable to complete the work in China. 2. Preparation of crystals The dl-serine used in this work was prepared by Roland N. Icke, and was kindly made available to us by Professor Carl Niemann. Crystals of dl-serine were prepared in the following way. A solution saturated with the amino acid at about 50° C. was prepared by 36 adding finely ground crystals in small portions to about 30 ml. of water. The solution was then divided into two or three portions in 50-ml. beakers. Each beaker was covered with a watch glass and immersed in a water bath consisting simply of a one-liter beaker filled with water heated at 500 C. The water baths were allowed to cool for one to three days; as a result of the cooling, and also of the accompanying loss of water from the solutions by evaporation, amino acid crystals of a wide variety of sizes and degrees of perfection appeared. Promising crystals were removed from the beakers with an eye-dropper, dried on filter paper, and transferred to a circular paper pillbox for storage. Each beaker was then warmed to 500 C. in its water bath, enough water was added to obtain complete solution, and the bath was again allowed to cool; this process was repeated until a sufficient number of satisfactory crystals was obtained. Selected crystals of dl-serine were mounted on stiff glass fibers with the aid of clear lacquer. The crystals that were mounted for x-ray work were usually less than 0.5 mm. in their longest dimension; frequently it was necessary to resort to cleavage to obtain crystals of suitable shape and size because of the plate-like character of the virgin crystals. Larger crystals were mounted with goniometer wax for optical work. 3. Optical examination dl-Serine crystallized in monoclinic tablets; a drawing of a typical crystal is present.ed in Figure 1 . as that of Albrecht1 • Our choice of axes is the same The faces in the zone [OOU possessed many striae in the zone direction; this was especially true of (100) and (ioo). Two crystals about 1 mm. in size and several 0.5 mm. or less in 37 size were examined with the optical goniometer. tained from all faces not in the zone [po~. Good reflections were ob- Most of the faces in the zone [oo'J] gave streaky reflections. Faces (110), (110), (110), and (llO), however, gave fair reflections. The face development and the characteristics of the individual faces indicate that the crystals have the point-group symmetry C 2h(monoclinic prismatic). In Table 4 are presented the averaged results of the most important goniometric measurements for three crystals and the values of the axial ratios calculated from them. 38 Table 4 Optical Goniometry of dl-Serine Crystals Crystal faces Number of measurements* 100/001 Angle between face normals Data of Groth2,3,4 Average value Mean deviation 14 73°29' 5' 011/001 6 26°51 1 91 110/100 5 48°40 1 28 1 100/110 430161 111/101 8 27040 1 12 1 011/001 27°27 1 10I/100 9 80°10 1 10 1 001/100 79°16 1 Computed values of axial ratios and monoclinic angle: a1 : a2 : a a3 3 = 1.176 al• 0.449 \j 2 - 106°31 1 1: 0.528 (= a 0 :b0 :c0 ) 1 ( - (3 ) * Number of equivalent pairs of crystal face s measured among the three crystals examined. Groth2 , in summarizing studies of serine by Erlenmeyer and Stoop3 and by Haushofer4, reports that crystals of dl-serine are monoclinic prismatic, with axial ratios of 1.141: 1: 0.5235 and a monoclinic angle 8 = 100°44 1 • These results correspond to a choice of ~2 and 2 3 similar to ours, but ~l is along [Lo_:f\ with respect to our axial system. By our choice of axes, axial ratios of 1.163 : 1: 0.5235 and a monoclinic angle of 105°30 1 may be derived from Groth 1s data. 4. Density The density of serine was determined approximately by displacement of 60°-700 ligroin in a small pycnometer, and was found to be 1.52 g./ml. 39 5. Cleavage The crystals were found to give good cleavage parallel to the £ face. Attempts to cleave the crystal in other orientations gave un- satisfactory results. 6. Groth2 reports cleavage parallel to the~ face. Laue symmetry A Laue photograph taken with~ parallel to the incident beam indicated the presence of a two-fold axis; several Laue photographs taken with a2 perpendicular to the incident beam indicated the presence of a mirror plane. The Laue symmetry is therefore c2h, and the crystal must belong to this point group or to one of the subgroups c2 or Cs. 7. Layer-line measurements Rotation photographs were taken with each of the three principal crystal axes in turn oriented parallel to the rotation axis. was used. CuK radiation Approximate values of the lattice constants were obtained from layer-line measurements. The results are presented in Table 5 . Table .5 Results of Layer-Line Measurements on dl-Serine a1 = 10.0 .i 0 a2 = 9.1 A a2 = 4.4 i 8. Precise determination of lattice constants Precise values of the unit cell dimensions were obtained from oscillation and rotation photographs; the results are presented in Table 6. CuK radiation filtered through nickel foil was used. 40 The effective film-radius of the camera was calibrated by means of powder photographs of sodium chloride. Table 6 Precise Determination of Lattice Constants for dl-Serine A. Calculation of b1 Reflection 2 sin J Weighting factor ) 200 400 10.0.0 12.0.0 801 801 10.0.1 10.0.1 12.0.1 0.1954 ki"" 1 .3895 .9738 1.1682 0.8654 .7474 1.0554 0.9397 1.1254 0.09770 kt.... , .09738 .09738 .09735 .09733** .09744,f* .097J3H .09780** .09730** 1 2 5 X 2* 6 X 2* 4 4 5 X 2i~ 5 6 Average value of h1oo= bl= 0.09740 Mean deviation .00009 * The dl °"2 doublet was resolved in the indicated reflections; hence these reflections were weighted doubly. ** These values were calculated with the aid of the value given below for b3 and with a preliminary value of B. 2 (73°30 ) . 1 Calculation of b 2 Reflection 2 sin J. .A 020 040 060 061 051 062 0. 2195 lclf~I .4381 .6571 .6925 .589.3 . 7874 ho10 Weighting factor 0.1093 kX.;.. 1 .1095 .1095 .1096* .1096* .1096* 1 2 3 3 2 3 Average value of h010 • b2 - 0.1096 Mean deviation .00005 * These quantities were calculated with the aid of the value given below for b . 3 41 Table 6 (continued) c. Calculation of b 3 Reflection 002 003 004 005 2 sin J ,A 0.4432 .6505 .8658 1.0824 ,x-, h 001 Weighting factor 0.2166 .A"X -' .2168 .2164 .2165 2 J 4 5 Average value of hool = bJ • 0.2165 .. Mean deviation .0001 D. Calculation of {!> 2 from b1, b3, and ho.i Reflection 2 sin JJ_ reflections cos f32 Weighting factor 0.28327 . - • 1 .28357 3 "I\ 605 201 402 603 804 403 604 404 803 802 404 1.0748 0.2466 .4933 .7405 .9880 .8454 .8978 .8424 .8616 .9922 1.0454 1x-' .27846 .28216 .28496 .28327 .28119 .28305 Average value of cos B2- 0.28318 Mean deviation .00059 Calculated values of P 2 Mean deviation (not incltrled in average) 1 1 1 1 1 Table 6 (continued) E. Summary =0.1096 b3 =0.2165 ;J: -1 .0001 kX -1 .00005kX 1 .0001 02 - 73°33' ± 2' ± b1 • 0.0974 b2 1:: u- Adding an uncertainty of 0.1% for error in camera calibration and reading of fiducial mark, we obtain for the unit cell dimensions: a1 = 10.70 ± .02 a2 • 9.12 ± .02 kX a3 • 4.815 :!- .006 kx ~2 • 106°27' ::1:: 4' kX 9. Weissenberg photographs Well exposed equatorial Weissenberg photographs were taken with each of the three crystal axes in turn oriented parallel to the axis of rotation. Unfiltered CuKo(.. radiation was used. In addition, equi- inclination Weissenberg photographs were taken of the first and second layer-lines with ~3 parallel to the rotation axis and of the first layer line with ~2 parallel to the rotation axis. The photographs were examined by means of an indexing chart and the reflections and extinctions were noted; these are tabulated below. 43 Table 7 Systematic Extinctions from Weissenberg Photographs Orders of OkO observed 020, 040, 060, 0.10.0 Orders of OkO absent 030, 050, 070, 090; 080 Orders of hO) observed 200, 201, 202, 203, 205, 201, 202, 203, 204, 205, 400, 402, 403, 404, 40I, 402, 403, 40~, 40~, 600 (?), 601, 602 (?), 604, 6oI, 602, 603, 60;, 801, 802, 802, so3, 804, 10.0.0, 10.0.1, 10.0.2, 10.0.I, 10.0.2, 10.0.3, 10.0.4, 12.0.0, 12.0.1, 12.0.2, 1o T Orders of hO ,€ absent 10~, 100 103, 104, 102, 102, 103, 104, 105, 300, 301, 302, 303, 304, 30~, 302, 303, 304, 305, 500, 501:, 503._, 502,. 504, 501, 5oz, 503", 501;, 502_, 700, 701, 70~, 703, 704, 701, 702, 703, 704, 705, 900, 901, 902, 901, 902, 903, 904, 11.0.0, 11.0.1, 11.0.1, 11.0.2; 204, 401, 603, 604, 800, 803, 805 Observed OkO reflections with k odd: none Observed hOJ reflections with h odd: none These data indicate that the symmetry elements of dl-serine include a twofold screw axis parallel to ~2 and an ~-glide plane perpendicular to it; the first demands that no OkO reflections with k odd should appear, and the second demands the absence of hOJ reflections with h odd. Although the number of reflections permitted by the use of CuK~ radiation is not large, it is felt that the generality of the extinctions is reasonably certain. 41,, It is apparent that the lattice is primitive as the extinctions required by centered lattices are violated. It may be concluded that the space group is C~h - P21 /a, as none of the other primitive space groups ·1somorphous with c2h or its subgroups C2 or C5 show the above systematic extinctions. This space group is in agreement with the previous finding of Albrecht and coworkers1 . 10. Laue photographs Four Laue photographs of dl-serine have been indexed by means of gnomonic projections on the basis of the lattice constants given above, and the value of n A was calculated for each reflection from the measured value of sinJ.. and the (relatively prime) indices of the reflection. The results of this work are summarized in Table 8. Table 8 Summary of Laue Photographs of dl-Serine Number of first order reflections Orientation of crystal Total number of observed reflections s !-1 JI "'0 85 252 s 62 233 ,a.,3 II zo 207 449 103 297 ~2 ti f "'0 £,3,20 'Ill 6°55 ' .,._~ .l ...s 0 1 Only three first order reflections were observed for which the apparent value of nA was less than 0.24 i, the short wavelength limit of the x-ray • tube, and of these the lowest value found for n/\ was 0.214 45 t We may conclude that within experimental error all of the values of n) are greater than the short wavelength limit of the x-ray tube, and that the lattice constants given above are correct within the experimental error of their determination. 11. Stuunary of work on dl-serine The results of the redetermination of the space-group and lattice constants of dl-serine are summarized in Table 9, where they are 1 compared with the results of .Albrecht's original determination . Table 9 Summary of Work on dl-Serine Present investigation Space group 5 Results of Albrecht 5 c2h - P21/a 02h - P21/a a1 10.70 ± .02 kX 10. 74 A a2 9.12 :I: .02 _kX 9.15 2 a3 4.815 ± .006 kX 4.78 A Lattice constants o{ 2 Density in g. per cm. .3 at 25°0. Number of molecules per unit cell 106°27 1 ±. 4' 0 0 (106°13') 1.52 1.537 4 4 (4.00 calc.) (4.14 calc. ) Table 9 (continued) Present investigation Results of Albrecht Axial ratios (x-ray) 1.173: 1 a1 : a2 : a3 0.450 a3: a1 0.528 1 1.174: 1: 0.5224 0.445: 1 Axial ratios and monoclinic angle (optional) 1.176: 1: 0.528 0.449 1 1.194: 1: 0.522 0.437: 1 1060l3 ' Because of the precision of the x-ray data from which the unit cell was determined, and because of the surprisingly good agreement with the data obtained optically, it may be concluded that the values found in the present investigation for the axial lengths and the monoclinic angle are at least as accurate as those of Albrecht. 12. Acknowledgements I am indebted to Professor Carl Niemann for the sample of dl-serine used in this work. I am happy to acknowledge the assistance given by Miss Lillian Casler in the preparation of the gnomonic projections, and to acknowledge the generous cooperation and valuable suggestions given by Dr. Robert B. Corey, under whose guidance this work was done. 47 _References 1. G. Albrecht, G. W. Schnakenberg, M. S. Dunn, and J. D. McCullough, ~ Phys. Chem, £, 24 (1943). 2. Groth,~Chemische Krystallographie; Vol. 3. Liepzig, Wilhelm Engelmann, 1910. p. 221. 3. Erlenmeyer and Stoop,_ Ann. 5L_ Chemic. 11.'.?, 257 (1904). 4. Haushofer, !,_ Krist. 3, 74 (1879). -- 48 B. AN INVESTIGATION OF THE CRYSTAL STRUCTURE OF f-THREONINE 1. Introduction In this section, work that has led to the determination of the space group, lattice constants, and approximate structm~e of crystals of l-threonine is described. Threonine, or tl-=amino-f?, -hydroxy-g~butyric acid, has the molecular structure OH I H CH3 - C - C - COO H I NH3 with a ~ configuration of the amino and hydroxyl groups with respect to the extended aliphatic chain (similar to threose). The diastereoisomer, allothreonine, was not studied in the present investigation. Threonine was probably first isolated from a protein hydrolysate by Schryner and Buston1 , who isolated from a hydrolysate of glutenin (from oats) an amino acid C4Hc)03N which gave a dibenyoyl derivative and a phenylisocyanate derivative. Later McCoy, Meyer, and Rose 2 isolated from commercial fibrin an amino acid of the same empirical formula, which was found to stimulate growth of rats and to be an essential amino acid. They showed that this amino acid is one of the four isomeric ot=amino= /3-hydroxy-11-butyric acids. In a later investigation3, Meyer and Rose found that treatment of the natural product with nitrous acid yields the dihydroxy-n-butyric acid that corresponds to d(-)-threose. nine. Accordingly they named the naturally occurring isomer g(-)-threo- The diastereoisomer allothreo~ was so named by West and Carter5. In a series of investigations West and Carter prepared mixtures of 49 the four isomers (g- and !_ -threonine, and g- and !. -allothreonine) 4, separated the isomers 5, and found that g(-)-threonine is the only one of the four isomers that stimulates the growth of rats 6 • as follows. Their method of synthesis was Crotonic acid was mercurated with mercuric acetate in hot methanol to form anhydro- 0( -hydroxymercuri- p-methoxy-u-butyric acid" The potassium salt of this compound was treated with bromine and potassium bromide in the presence of light, and the ~ -bromo-~-methoxy acid obtained was aminated by treatment with a'11Ill.onia. thereby The methoxy group was re- moved by refluxing with hydrobromic acid to give a mixture containing all four CX. -amino- ~ -hydroxy-n-butyric acids. In order to obtain ell-threonine free from J.1. -allothreonine, the methoxy precursors were formylated or benzoylated and the acylated 0-methylthreonine was crystallized or precipitated from the solution. The acyl group and the methyl group were removed by refluxing with hydrobromic acid. Threonine was resolved into its optical isomers by treatment of N-formyl-0-methylthreonine with brucine, separating the salts by crystallization, and removing the brucine and the formyl and methyl groups in the usual manner. H. B. Milne 7 of the laboratories of this Institute has prepared J. -threonine by the foll owing method. From an aqueous solution of N-benyoyl- 0-methyl- &}_ -threoni ne, the phenylhydrazide of the J -isomer was enzymatically precipitated. The precipitate was hydrolyzed with hydrobromic acid and i -threonine was pre~ipitated from the neutralized solution by the addition of ethanol. The material that he prepared was used in our x-ray investigation. 8 According to Cohn and F<lsa11 , threonine has been found in the following proteins: fibroin (1.36%). insulin (2.66%), casein (3.5%), gelatin (1.4%) , and silk Brand9 reports that it is also present in (3 -lactoglobulin (5.85%), egg albumin (4.0%), 50 lactalbumin (5.1%), bovine serum albumin (6.5%), human serum albumin (5.0%), and human j -globulin (8.4%). Hence threonine is a protein constituent of considerable importance. It is, moreover, comparatively simple in molecular structure, and is therefore an attractive subject for an x-ray crystallographic study. The )-isomer was chosen for x-re.y wor k instead of the g.-isomer because the former is more easily prepared. There is no doubt that the crystal structures of the two isomers are identical except for the enantiomorphic difference; indeed, much of the work described below was done on crystals grown from the racemic mixture, with results that were identical to those obtained with f-threonine. The work described below was done under the supervision of Dr. Robert B. Corey. 2. Discussion of previous crystallographic work Preliminary crystal structure work on ·threonine was reported by Albrecht and coworkers 10 in 1943. From an aqueous solution of Jl.-threonine they obtained flat, six-sided plates which they found on goniometric examination to be orthorhombic hemimorphic hemihedral ( c2 7l'-mm) with axial ratios 1.675: 1: 0.6644. From layer-line measurements on rotation photo- graphs these authors obtained the lattice constants 13.64 i, 7.75 i, 5.16 i. The density was found to be 1.437 g./cm.3; this value indicates that there are four molecules per unit cell (3.99 calculated). Laue photographs that were taken along the three axes showed that the cell constants are correct 51 and revealed no systematic (hkl), (Okl), (hOl), or (hkO) absences. With the assumption of two molecules of each optical isomer in the unit cell, these results lead uniquely to the space-group c½v - Pmm2. On the basis of our present-day knowledge of the principles governing crystal structures it is immediately apparent that the spacegroup assigned by these workers is incorrect. As the individual molecules can have no planes of symmetry, no molecule can extend through a mirror plane. Hence with the proposed space-group each molecule must be confined within a region bounded by mirror planes and of rectangular cross-section only 6.82 i by 3.87 i in size. It is hard to see how a non-planar molecule like threonine can be confined between mirror-planes only 3.87 i apart. It is even more difficult to see how a structure can exist in which groups of the same electrical charge are as close together as they would have to be with this space-group, or how two adjacent molecules touching each other only at a mirror plane are prevented from sliding or rotating against each other to produce a better fit and to fill the holes in the structure. The authors' assertion that crystals of threonine are orthorhombic hemimorphic hemihedral is not borne out by our morphological studies of crystals of this substance, nor in any obvious way by the microphotograph that they published. In all other respects we have verified the data on which their space-group assignment was based: the Laue symmetry (D2n), the size of the unit cell and the number of molecules in it, the primitive character of the lattice, and the absence of glide planes. If we reject the space group c;v - Pmni2 and accept the other results, we are led uniquely to the four primitive space-groups of the orthorhombic enantiomorphic hem.ihedry ( D2 - 222), and 52 to the corollary that the crystals which these authors studied were not crystals of A,-threonine but were instead crystals of g-threonine and of }-threonine which either formed separately or grew together as twins. Their examination of Laue photographs alone for evidence of systematic extincti ons due to glide planes gave these authors no opportunity to observe possible systematic extinctions of the type (hOO), (OkO), and (OO!). The only apparent alternative to the acceptance of an enantiomorphic space group is the assumption that the crystals are twins of pseudo-orthorhombic individuals having a true symmetry lower than orthorhombic. This al- ternative cannot easily be rejected with certainty, but the work described later makes it appear very improbable. The enantiomorphic character of the space group can be tested, however, by an x-ray investigation of one of the isomers alone. We have carried out such an investigation and have obtained x-ray photographs identical with those obtained with crystals grown from the racemic mixture. This evidence, together with additional evidence from systematic extinctions and from the interpretation of our .intensity data, has led us to the assignment of the space-group D'2,4 - n 121 21 to crystals of _g.., or J-threonine. 3. Materials The preparations of J) -threonine and ;Q-threonine that were used in this investigation were kindly supplied by Professor Carl Niemann. threonine was prepared by Dr. P. L. Nichols, Jr. The JJ..- The method of preparation was essentially that of West and Carter4,5. The) -threonine was prepared by H.B. Milne as described above. Determinations of the optical activities of these two preparations were made 53 with small samples; J.l-threonine showed no significant notation, and }-threonine showed a rotation of ~D • 27' in rough agreement with the previously reported value of 28.4° at 26° c.11 4. Growth of crystals Crystals of both preparations were obtained by crystallization from water by the method described above in connection with the investigation of serine. 5. Morphological study Examination of the crystals with the microscope and the optical goniometer indicated that the crystals are orthorhombic. No morphological characteristics that would indicate symmetry less than that of the holohedry were observed. Crystals grown from the two preparations were very similar; they differed only in that the crystals prepared from Ji-threonine were usually long needles whereas those prepared from)-threonine had much more pronounced (100) faces and were lath-like in shape. Drawings of typical crystals of the two preparations are given in Figure 2. It is very difficult to evaluate the axial ratios precisely from our goniometric data because of the very poor agreement among the datao Discrep- ancies of one degree or more were observed among measurements of a given interfacial angle, but no systematic tendencies indicative of lower symmetry were observed. The crystals of }-threonine gave results of somewhat greater consistency than did crystals grown from the racemic miA-ture. Goniometric data obtained from the best crystals are given in the following table. value enclosed by parentheses was not included in the average. 54 The Table 10 Goniometr ic Data for Threonine A.Crystals prepared from »-threonine Crystal 7 Crystal 5 100/210 (39°41') 100/210 410251 100/210 41°05 1 100/210 410131 100/210 41°16 1 J.00/210 410171 Crystal 5 Crystal 1 Crystal 15 011/010 56°12 1 011/010 56006 1 011/010 56°30 1 011/010 56°10 1 011/010 56°06 1 011/010 56°43' 011/010 56021 011/010 56°12 1 011/010 56011 B. Crystals prepared from 1-threonine Crystal 2 100/210 41°00 1 100/210 40°51' loo/2io 40°53 I Ioo/210 41°13 1 C. Summary Crystal 1 Crystal 2 Average value of 100/210 etc. 41°09 1 Average value of 011/010 etc. 56°14' Axial ratios: al: a 2 : a 3n 1. 748 55 1 o.669 We may note that Albrecht's values of the axial ratios correspond to the following values of the two most important angles: 100/210 39°57' 011/010 While the last is in agreement with our results, the first is not. Angles as small as 3cp57• were, however, not infrequently observed for 100/210 in our crystals. 6. Cleavage Good cleavage parallel to (100) was observed, and good cleavage faces were obtained. Attempts to cleave crystals on (010) were unsuccessful. When attempts were made to cleave crystals parallel to (001) conchoidal fractures usually resulted, with slight indications of (001) cleavage in some instances. 7. Density The density of the crystals was determined by flotation. Two crystals grown from the two respective threonine preparations were suspended together in a vial containing a mixture of methylene iodide and benzene, and the composition of the mixture was adjusted until the crystals showed no significant tendency to rise or fall. A very slight indication of a difference in density between the two crystals was observed; the J -threonine crystal tended to rise very slowly while the other remained stationary, but the difference was smaller than the probable error due to changes in the temperature during the experiment. The density of the final mixture was measured with a pycnometer, and was found 3 to be 1.464 g. per cm .• 8. Laue symmetry Laue photographs of crystals of the first preparation, taken with 56 the three principal axes in turn oriented parallel to the x-ray beam, showed in each case t he presence of two mirror planes. fore D2h• The Laue symmetry is there- Because of the possibility that the crystals may be twins of monoclinic or triclinic individuals, many crystals and fragments of crystals were examined in this way; all showed the D2h Laue symmetry. No evidence of twinning was obtained from Laue photographs of this preparation. Laue photographs of crystals of the ) -threonine preparation were substantially identical to those of the first preparation in the positions and relative intensities of the spots, and differed from them only in that some of the photographs of ) -threonine showed streaky or elongated spots indicative of bending or twinning. The character of these spots was not such as to suggest that their peculiarities resulted from interpenetrating of individuals of symmetry lower than orthorhombic. In view of the very good evidence of the identity of the two preparations from the point of view of x-ray diffraction, no dis tinction has been made between them in the selection of crystals for the remaining work, and no differences were observed between them in this work. 9. Determination of lattice constants (a) Layer-line measurements Well exposed rotation photographs taken around the three principal axes with copper K~ radiation gave well-defined layer lines. From measurements of the positions of the layerlines the following values of the lattice constants were calculated: 7.71 5.13 57 1 These values are in agreement with those of Albrecht within the limits of experimental error. (b) Precise determination of lattice constants Equatorial reflections on several oscillation and rotation photographs taken around the three principal axes with copper K~ radiation were indexed and their positions measured. Preliminary values of the reciprocal lattice constants b1 and b2 were obtained from orders of (100) and (010). These values were used in the calculation of b_3 principally from (10)) and (20)) reflections, as only one order of (001), namely (002), has been found to have appreciable intensity. With the aid of this value of b3 and the preliwinary values of b and b additional reflections were used in the 2 1 calculation of final values of bi and b2• In averaging the results for a given reciprocal lattice vector bi, the value obtained from each reflection was weighted with a factor equal to the product of the index hi by the number of individual measurements made on that reflection (counting ot measurements as separate). 1 and 0( 2 The lattice constants are given in both kX units 0 and Angstrom units, and the reciprocal lattice constants are given in reciprocal kX units. 58 rable 11 ~recise Determination of Lattice Constants for }-Threonine (a) Determination of b 1 ~eflection 2 sin J A 600 800 10•0•0 12•0•0 14• 0•0 16•0•0 0.4411 . 5879 . 7359 .8842 1.0314 1.1774 - 1?1 Weighting ·factor 0.07.352 .07.349 .07.359 .07.368 .07.367 .07.359 6 8 10 24 28 64 Preliminary value of b (weighted mean of above deterin.inations) 0.07.362 1 810 8 0.6042 0.07377 10•1•0 (omitted from mean) .07390 .750.3 ' 10·0·1 20 .7617 .07.364 11·1·0 (omitted from mean) .8226 .07.384 11 11·0·1 .07367 .8335 12·0·1 .07.358 24 .90~ 13•1·0 .9672 13 . 07.37.3 14•0·1 1.0491 .07363 42 16·0·1 .32 1.1938 .07361 Final value of b1 (weighted mean of all determinations) Mean weighted deviation (b) Determination of b2 Reflection 2 sin .J 0.0736.3 .00004 Weighting factor A 020 040 060 080 0.1.300 .1295 .1295 .1294 0.2599 .5180 . 7769 1.0.356 !omitted from mean) 8' 6 8 Preliminary value of b2 (weighted mean of above determinations) 061 071 081 190 091 0.8018 .9268 1.05.38 1.1678 1.1810 0.1296 .1294 .1295 .1295 .1294 Final value of b2 (weighted mean of all determinations) Mean weighted deviation 59 0.1295 12 7 8 18 18 0.1295 .00005 Table 11 (continued) (c) Determination of b 3 Reflection 2 sin & Weighting factor ~ 002 105 205 106 206 0.3900 .9758 .9852 1.1713 1.1786 0.1950 2 .1946 .1948 5 5 30 12 .1948 .1949 Final value of b3 (weighted mean of all determinations) Mean weighted deviation (d) 0.1948 .00005 Summary; calculation of a1, a2, a3 (ai c l/b1)* b1 = 0.07363 b2 = 0.1295 b3 = 0.1948 kX-l kX-l kX-l 0 al= 13.58 ± .02 kX = 13.61 :l: .02 A (cgs) a2 = 7.72 ± .Ol kX = 7.74 ± .01 X a3 = 5.13 ± .Ol kX = 5.14 ± .01 R a3 m 1.759: 1: o.665 * 1 kX = 1.0020 i (cgs) 3 From the volume of the unit cell (541 .8 i ), the density of the crystal (1.464 g. per cm. 3 ), and the molecular weight of threonine (119.12) it was found that there are four molecules per unit cell (4.01 calculated). (c) Verification by means of gnomonic projections Four Laue photographs of ) -threonine have been successfully indexed, by means of gnomonic pro jections, on the basis of the lattice constants given above. This work is summarized in the following table. Table 12 Gnomonic Projections of Laue Photographs of )-Threonine No. Orientation Number of first-order reflections Total number of reflections 1 t1 I( - s o * 125 391 2 ~2 I( 2o 133 308 3 !3 II 170 338 -415 779 4 ! i i) 2-1 J_ ~o ; {.. !J,~o = 7°55' 1816 843 * "'o s denotes a unit vector in the direction of the incident beam The value of n ~ was calculated for each reflection. Only two values of nA appeared to be lower than 0.24 i, the short-wavelength limit of the x-ray tube; (561) and (561), on the fourth film, gave n A values of 0.227 i and 0.229 i. 0 As these are lower than 0.24 A by an amount that is within the experimental error of the measurement of small angle reflections, we may conclude that the indexing is correct and that the unit cell has been correctly chosen. 10. Systematic extinctions Well-exposed Weissenberg photographs have been taken around the three principal axes with copper Ko( radiation. No systematic extinctions of the types (hki), (Oki), (hOj), and (hkO) were observed. Reflections of the type (hOO), (OkO), and (OOi) were examined with the following results. 61 Table 13 Observed and Unobserved Reflections for j -Threonine (hOO) observed: 200, 400, 600, 800, 10•0•0, 12·0•0, 14•0•0, 16•0•0 (hOO) not observed: 100*, 300, 500, 700, 90oi~*, 11.0.0, 13.0.0, 15.0.0 (OkO) observed: 020, 040, 060, 080 (OkO) not observed: 010, 030, 050, 070, 090 (ooi) observed: 002, (004) (ooi) not observed: 001, 003, 005, 006 * The reflection angle of (100) is too small for observation of this reflection on Weissenberg photographs, as the beam stop interferes; however, this reflection was not observed on rotation and oscillation photographs. ** A CuK /1 reflection from (10•0•0) lies at the expected position for (900) on Weissenberg photographs; no (900) reflection was observed, however, on a well exposed oscillation photograph. Five-degree oscillation photographs were taken with copper Kot radiation in an attempt to obtain some of the odd order reflections. No such reflections have yet been found, with the single exception of a spot obtained at the expected position for (700) on oscillation photographs taken around the ~2 axis. The spot is of a very remarkable character and is unquestionably not a (700) reflection; it may be a Laue spot. Photographs taken with molybdenum K~ radiation, in an attempt to obtain higher orders of (001), were not sufficiently well exposed to be useful. 11. Summary of data on the space-group and lattice constants The crystal morphology and the Laue symmetry indicate that the crystals are orthorhombic. As there can be no symmetry plane in a crystal 62 containing only 1 -threonine molecules, the space-group must be of the orthorhombic enantiomorphic hemihedry (D2 - 222). All of the atoms must lie in general positions because the molecule does not have a two-fold symmetry axis. As there are no systematic absences of the type (hkl), the lattice must be primitive and the number of molecules must be equal to the order of the point group, which is four, or to some integral multiple of this number. As a value of four is given by experiment, there can be only one set of crystallographically equivalent molecules in the crystal. The systematic absence of odd order (hOO) and (OkO) reflections strongly indicates that there are two-fold screw axes parallel to !land £,2 • The existence of a third screw axis parallel to ~3 is also indicated by the extinctions but with less certainty; with copper K~ radiation the only odd orders of (OO}) that can be examined are (001), (003), and (005). From the apparent absences it was concluded that the space-group is probably D24 - P21 21 21 , though there still remained the possibility that the absences of odd order (OOi) reflections is accidental and that the space-group is accordingly D£ - P21 21 2. It is of course also possible that the (hOO) and (OkO) extinctions are accidental but the likdihood is small. Accordingly, pending verification by the analysis of intensity data, the space-group was assumed to be D24 - P212121. As will be shown later, the analysis of the intensity data has confirmed this space-group beyond reasonable doubt. The data on the space-group and lattice constants are summarized in Table 14 , where these results are compared with those of Albrecht10 • 63 Table 1/., Data on the Space-Group and Lattice Constants for ,£-Threonine Crystal Form P-Threonine, this investigation M-Threonine, AlbrechtlO Orthorhombic Orthorhombic Hemimorphic Hemihedry Laue Symmetry Axial ratios, optical al :a2 :a.3 Cleavage 1.748: 1: o.669 (100) Density, g.per cm •.3 1.4.37 Lattice constants 0 0 1.3.61 ± .02 A 7. 74 !:- .01 i 1.3.64 A 7 .. 75 j 5.16 i 5.14 :1: .01 i Axial ratios, x-ray 1.160 Number of molecules per unit cell Systematic extinctions 4 (4.01 Cale.) (hOO), h odd (OkO), k odd (00 ), J. odd(?) 1 o.666 4 (3.99 Cale.) None observed. 1 0 2v - Prnm2 Space-group 64 12. Collection of intensity data (a) Weissenberg photography Three crystals were used in the collection of intensity data. They were mounted, respectively, with the three principal axes parallel to the axis of rotation of the Weissenberg x-ray goniometer. They may be described as follows: ~• ,,j. -threonine. The crystahto be mounted on this axis was prepared from It was shaped into a cylinder (with its axis parallel to ~ ) 1 about 0.3 mm. high and 0.3 mm. in diameter by dissolving away excess material with a camel's-hair bruch moistened with water. ~• This crystal was also prepared from )-threonine,' and was shaped roughly into a cylinder 0.4 mm. high and 0.24 mm. in diameter. ~ . 3 This crystal is a needle about 1 mm. in length, 0.25 mm. in its largest cross-sectional dimension, and 0.18 mm. in its smallest such dimension. The crystal was grown from a solution of elf-threonine and was used without any fur·t her treatment. It is similar in shape to the crystal shown in Figure J c;t,. The crystals were mounted on stiff pyrex fibers with the use of flake shellac, which was melted with an electrically heated wire. They were oriented by means of the optical goniometer or with Laue photographs. The reasons for the use of crystals as small as this are that we desired to obviate the necessity for applying absorption corrections a.~d that we wished also to reduce the effect of extinction. As the calculated linear absorption coefficient to threonine for copper KC{ radiation is 1.04 mm. -l, the absorption is approximately 22% for a cylindrical crystal 0.3 nun. in diameter and is very nearly the same for all scattering angles in the equatorial plane 12 • The deviations from average absorption that are encountered in crystal,.g , which 3 65 Ls not cylindrical, are of the order of ¾ 3% of the intensity of the scattered Jeam. These approximations may be expected to hold for the layer lines to a Jrecision adequate for our work. Equatorial and equi-inclination Weissenberg photographs were taken :,f the following layer lines with copper K O<. radiation: o, 1, 2, 3, 4, 5, 6, 7, 8 a1: h1 • a2: h2 • o, 1, 2, 3, a3: h3 = o, 1, 2, 3 4, 5 rhese are all of the layer lines that can be photographed with an equi-inclination 9.ngle of less than 30°, which is the limit of the capacity of the Weissenberg goniometer that we used. to 1.20 On each layer line reflections may be obtained out ~t1 in reciprocal space (sin .J..,,_. ,... 0.925); the limiting circumstance is in this case geometric interference by the pinhole system. With the use of the three crystals all of the 618 reflections in an octant of a sphere of radius 1.20 i-l in the reciprocal latice were made available for estimation of intensity. All but 70 of these reflections occur on two or more layer lines (around different axes), and 191 reflections occur on three layer lines. To facilitate the estimation of intensities, a multiple film technique similar to that of deLange, Robertson, and Woodward13 was employed in obtaining these photographs. The camera of the Weissenberg goniometer was modified to permit the simultaneous use of four or five films. Eastman No-Screen Duplitized Safety X-Ray Film (Code No. 5133) was used throughout. (b) Estimation of intensities The intensities of all of the 1357 reflections on 19 sets of photographs were estimated visually. A novel scheme, which turned out to be 66 very successful, was employed. Instead of being estimated directly, the in- tensities were estimated first on a logarithmic scale which had as its base of logarithms the so-called film factor. The film factor is the reciprocal of the factor by which the intensity of the reflected x-ray beam is decreased by absorption in passing through a single film. with this method, is as follows. The most convenient procedure, First a single strong reflection spot is chosen as a primary standard and arbitrarily assigned a number, or intensitx index, say 6.00. A number of secondary standards with intensity indices of 5.00, 4.00, 3.00, etc., are then found by intercomparison of the films in the set; use is here made of the fact that the intensity index of a given reflection decreases by 1.00 on going from one film to the next. As the film factor is approximately equal to 4, it is possible to find tertiary standards with intensity indices of 5.50, 4.50, etc., by superposition of primary standards, for a doubling of intensity corresponds approximately to an increase of 0.5 in the intensity index. The tertiary standards may be checked by superposing them and comparing with secondary standards. The intensity indices of the remaining reflections may be obtained by interpolation among these standards, and by making use of the decrement of 1.00 from film to film. It is convenient in this work to cut a piece of tracing paper to the shape and size of the first film of the multiple-film set, draw on it an indexing net, and write the intensity indices directly on the paper. A minor difficulty which was experienced when the number of spots on a film was comparatively small was the scarcity of spots suitable for use as standards. This difficulty was often removed by making use of spots on other sets of films. More serious difficulties, which are independent of the method 67 of estimation, were the variations in the shape ·and character of the spots due to the resolution of the~ 1 OC 2 doublet, compression or extension of spots close to the base-line of layer line photographs, and the splitting which often resulted from backlash of the camera drive screw on the Weissenberg goniometer. The relative intensity, i, of each reflection on the film was determined from the intensity index,~, by use of the relation (1) in which R is the film factore This was at first assumed to be equal to 4; this value was determined several years ago by Dr. Chia Si Lu of these laboratories and has been in general use in this laboratory. (c) Correction and correlation of intensities For a set of films that represents a given layer line or reciprocal lattice net, the values of i determined visually are assumed to be proportional to the integrated intensities of the respective reflections . The constant of proportionality is not known, and is in general different for each set of films. It is possible, however, to put the intensities obtained from all of the films on the same relative basis, for reflections from a given plane were usually obtained with more than one orientation of the crystale From the in- 2 tensities for each set of films, values of Ehkl (the square of the structure factor) corresponding to a given net in the reciprocal lattice may be calculated on a relative basis peculiar to that net. As each point of the reciprocal lattice may lie on two or three such nets, scale factors may be obtained which may be applied to the different nets in order to tie all of the data on these nets to a common relative basis. 68 Because the absolute intensities are not known, all constant factors in the expression14 for scattering of unpolarized monochromatic x-rays by a small, rotating, ideally im:r:;erfect (mosaic) crystal may be absorbed into an unknown constant of proportionality k, and we may write i =k~kl 1 + coi· 2J • sin 219-- 1 (2) ' where we make use of the form developed by Tune11 1 5 for the Lorentz factor to be used in equi-inclination Weissenberg photography. In this equat ion J is 2 the Bragg angle, J) is the equi-inclination angle, and fhkl is the square of the absolute value of the structure factor for the (hkl) plane; we will hence2 forth refer to kEhkl as the corrected intensity. With this equation all of the data were converted into corrected intensities. To facilitate the computations, a plot of 1 against sin f cos2 2 ,.Q sin 21" J.. and a plot of 1 J against the ratio sin v / sin J- sin2 1/ 1 - - ..... ~ sin2 Jwere prepared. By making all possible comparison among the reciprocal lattice nets and averaging the scale factors obtained, a set of 19 scale factors for the 19 respective ne ts was· obtained. By applying these scale factors all of the corrected intensities were placed on the same relative basis. The corrected in- tensities were then averaged for each plane with weights based upon the quality of the reflections. 69 We now have an opportunity to observe the agreement that was obtained among the two or three determinations of the corrected intensity for each reflection. As the emp1rical procedure of establishing the relative bas~s determined only one parameter for each 50 to 100 spots, the individual intensity determinations are virtually independent. In Table 18 on page (10 the individual determinations are compared for each of several planes that are now being used in structure factor work. In quality of agreement these planes are represen- tative of the remaining reflections, except that the agreement for reflections of very low intensities or high indices is not quite as good, in general, as that shown in the table, but is certainly adequate for our work. The general agreement is surprisingly good and justifies considerable confidence in the intensity data. (d) Revision of the film factor The precision that can be obtained in visual interpretation of x-ray photographs appears to be high enough to suggest that other factors that influence the estimation of intensity should be brought under closer control. One of the most important of these is the film factor. A small error in the film factor has a negligible effect on reflections of comparable strengths but it may have a large effect when reflections of considerable different strengths are compared. Dr. Herman E. Seemann of the Eastman Kodak Co. has informed me 16 that the sensitivity of different lots of No-Screen film may depart as much as 10% from the mean; a similar departure may be expected for the film factor. For intensities that differ by a factor of only four, this deviation would produce a 10% error in the intensity ratio. It is therefore desirable to determine the film factor for each lot of film, or at least to determine the average film 70 factor to an accuracy much better than 10%. The latter course is the only practical one available to us in our study of J -threonine. During the collection of intensity data for ,R -threonine it be:came apparent that the accepted value of 4 is too high. Measurements made with a densitometer on multiple film oscillation photographs indicated a film factor of about 3.5, and microphotometric measurements of a set of powder photographs indicated a factor of only 3.2. These methods are, of course, of limited precision. Dr. Seemann16 made direct measurements of the transmission of NoScreen film with K fluorescence radiation from copper and molybclenum15. The measurements were made with an air ionization chamber, and included estimates of the magni tude of scattering by the film. His results for per centage trans- mission are as follows: With scattered radiation Without scattered radiation Copper 26.7 Molybdenum 72.7 These results are claimed to be good to within ± 3% for the sample tested. The film factor indicated for copper K~ radiation by the se results is 3.7. This value is probably the best so far obtained, and was used subsequently in our work. 2 All of our values of kFhkl are now being corrected in accordance with the new film factor. (e) Powder photography In order to determine the effect of extinction on the intense reflections, a multiple-film powder photograph was prepared. 71 A few crystals were ground to an extremely fine powder in an agate mortar. A thin-wall py-~ex capillary tubing about 0.25 mm. in inside diameter was loaded with the powder and mounted vertically on a goniometer head by means of a close-fitting glass fiber which was inserted into one end of the tube. By pulling the capillary tube downward the fiber was made to extrude from the top of the tube a compressed cylindrical rod of powder. This rod was placed in the path of an x-ray beam of low divergence and was rotated during the exposure. The lines on the films were indexed and equatorial photometric tracings of the films were made with a Fred Henson microphotometer. As the resolved lines were not widely different in half-width, the optical density of each line in comparison to the background was taken as a measure of the integrated intensity. Comparisons among the data obtained from the first three films of the set showed that the density is a very nearly linear function of the intensity over the density range encountered (the maximum density was O.J). The integrated intensity, per unit length of the line at the equator, . given . l? by the equat·ion is (3) where 1 is an unknown constant, and Bis the number of planes of identical type that belong to the form (hkl) and thereby contribute to the powder line. 2 The calculated values of! Ehkl for the well resolved lines were multiplied by a scale factor in order to bring the values for all except the very strongest reflections into correspondence with the values of k ~ obtained from single-crystal photographs. The results are sho~m in Table 15. 72 Table 15 Comparisons of Strong Reflections on Single Crystal and Powder Photographs hkl Corrected Intensities Single crystal Powder 480 430 1600 3270 320 221 1350 2500 2090 990 3270 1850 1800 620 1550 210 101 011 120 211 121 2730 1030 3580 1920 2000 1390 It is evident that the effect of primary and secondary extinction is unusually small; indeed it does not greatly exceed the probable error of the intensity determinations. This is largely due to our use of small crystals, but it does nevertheless seem to indicate a high degree of imperfection in the crystals. 2 Small corrections were made in the values of~ Ehkl for the very strongest planes. As the magnitude of such small extinctions is practically independent of the scattering angle it is only necessary to multiply each 2 value of~ Ehkl by a factor (1 ~ g Q) where g is an empirically determined constant and g is proportional to the integrated intensity of the reflection. (f) Reduction to an absolute basis The final reduction of structure factors to an absolute basis is best done at the later stages of the structure determination. 73 An approximate method, which does not depend on a lmowledge of the structure, was developed in order to b~ing the structure factors close enough to an absolute basis to facilitate the testing of trial structures. As will be shown later, the amplitude of the peak at the origin of a Patterson distribution is given by ':~ P.•• (o) ' -=- 1F ,, a. ~J JI (4) in which the summation on the right is taken over all atoms in the unit cell, and (5) The term Pjj(e) represents the contribution of atom l to the amplitude of the peak at the origin. In equation (5) H = 2 sin -iR (6) A ., and f ·' (H) is the atomic form factor combined with the temperature factor. For equation (5) to be strictly valid it is necessary that the temperature factor be isotropic. It is also required that there be no significant amount of interference from neighboring Patterson peaks. The heretofore unknown constant of proportionality is determined by requiring that equation (4) be satisfied. It is necessary to assU1lle a value for the temperature factor; the value chosen for all atoms was where A: 1.7 x lo-lb at room temperature. This is the value that was found in the determination of 74 the structure of glycine by .Ubrecht and Corey18 . The form factors that we used were those compiled by James and Brindley12h. The term F000 is, for 2 convenience, subtracted from both sides of equation (5); it is simply the square of the number of electrons in the unit cell. This method was applied to the structure factors that were used later for comparison with calculated structure factors. The application of the method to the new set containing the new value of the film factor is now in progress. 13. Application of a three-dimensional Patterson synthesis (a) Introduction Since the publication of Patterson's 1935 paper19 on the direct 2 Fourier inversion of Fhkl data, the method which he proposed has been widely used by workers in the field of crystal structure. It is possible, in principle, to carry out the Fourier inversion in three dimensions, but with the calculation aids available the computations have been heretofore regarded as much too involved. The method has been used almost entirely in one- or two-dimensional syntheses of all of the orders of a given plane or of all of the planes in a given zone; the Patterson pro jections obtained in this way are projections of all of the Patterson density in the unit cell onto a line or plane. These projections are very useful if the structure contains heavy atoms in special positions or if there are only a few atoms in the unit cell, but their interpretation may be extremely difficult if there are a large number of atoms of comparable scattering power in the unit cell. A closer approach to a three-dimensional synthesis is that of Harker20 , who showed that lines or planar sections of Patterson space which have, as their constant coordinates, the corresponding translation components 75 of symmetry elements have properties similar in some ways to Fourier projections. When the number of atoms in the unit cell is large the interpre- tation of these Harker sections may be difficult because many peaks may accidentally be present that are not due to the symmetry relations on which these sections are based. for A Ha:rker section which we prepared from the data i -threonine failed to give much useful information concerning the structure until it was examined in connecti on with other features of the three-dimensional Patterson distribution. The great reduction in calculation effort that was introduced by the use of punched-card methods with the International Business Machines21 suggested that it might be feasible to carry out Patterson computations in three dimensions without undue effort. The Hollerith punched-card method 22 has already been used in England for three-dimensional Fourier calculations. The development of the L cards, which correspond to the Beevers-Lipson strips, by Professor Verner Schomaker 23 has provided the most convenient means yet found for carrying out two-dimensional summations. Professor Schomaker sug- gested that these cards be used in the calculation of the three-dimensional Patterson distribution for )-threonine. These calculations have been carried out by Professor Schomaker and myself, and the Patterson distribution that we obtained proved to be of great value in the determination of the approximate structure of ).-threonine • .Although use has been made of Patterson sections by other worket:s, to our knowledge the work described below represents the first time that a complete three-dimensional representation of the Patterson function has been calculated and used in the determination of a crystal structure. As a background for this work we shall discuss the theory of the 76 Patterson distribution with special regard for its use in three dimensions. (b) Theoretical discussion It was shown by Patterson19 that a direct Fourier inversion 2 of the experimentally determined set of .!'hkl data~ "° L L Flv_ ~:z_tr(l..lL+kv-~,lw), '".I..=-- k • -o0i ,, _. - '°f(u ,v;w) =;2 o.:> (7) yields a density distribution i n ~ space which may be interpreted in terms of interatomic vectors in the crystal. A peak which has coordinates (y,y ,~) represents a vector between two atoms in the crystal; this vector is (8) P ~ ua1 ,..,, ,,.. + va2 "' + wa3 .., where !i, £2, and ..§.J are t he lattice vectors corresponding to the particular choice of the unit cell. As (9) each interatomic vector is represented in Patterson space (y 1 y,~ space) by two peaks related by a center of symmetry at the origin. All interatomic vectors that are related to a given vector by the operations of the space gr oup are represented by related peaks in Patterson space. The symmetry of the distributi on of Patterson peaks is related to that of the crystal. The Patterson distribution always has a center of symmetry in consequence of the double-ended character of the vectors, but the Patterson syrrn:netry is not simply that of the crystal space group plus a center of sy1IID1etry except in special cases. The addition of a center of symmetry to D24 - P212121, for 15 16 example, gives D2h - Pbca or D2h - Pruna, while the space group of the 1 Patterson distribution is n2h - Pmmm. There is also in the Pat terson distri- * .F h~ is written for convenience i nstead of f.fhkll 2; 77 ~ "'vo/1,1. .,-i e o ·r t..~ .v, if ,:.d i. bution a n ~ symmetry comprising the necessary relations that must exist among the coordinates of peaks representing various types of interatomic vector interacticms, for the non-equi val ent peaks are not independent in general. It can be shown 19 that the Patterson function E (Y, Y, H) written P (u, v,w ) where =Va J.' [,' Lp may be (x,y,z ) f"x~u,y+v, z+w) dxdydz1 (10) p (x, y, z) is the electron density distribution in the crystal, in terms of electrons per uni t volume. Fourier series in two ways: CW'> pc~,1,}) = ~ We may expand the electron density as a oD 00 f . :f f:_ (11) 00 and (12) When these expressions are multiplied together and integrated term by term in equaticn (10), aU terms for which h, k, and ! are not all equal r espectively to ~ i and t ' vani sh by orthogonality, and we obtain p {tA. 1v; w1 =I ~ ~ ~ v:' ,I.,::LL- L -- Jt :,..o .1 :-oO <0L which gives equation (7) because 2 n~ F* 21Ti {A.u.1- 1.. 1r+P~ (13 > ,,t..J...e.~ ,1 2 Fhkl = F nk! • The definition of E ( y, y, ~) given by equation (10) gives this quantity the dimensions of reciprocal volume, and E (y, y, ~)maybe interpreted as the number of electron-electron interactions per unit volume of Patterson space where the interactions to be considered are t hose between all of the electrons in a single unit cell of the crystal and all of the electrons in the entire crystal. 78 The electron density may be wr itten z c,, , ,}) 00 f (-,, -~ji'~) = fj J=' where f j represents the electron density to be ascribed to atom i, and where the summation is taken over all of the atoms in the crystal. On replacing the electron density functions in the integrand of equation (10) by the summations we obtain i' rp where both sums are taken over all of the atoms in the crystal, and v;; (' Jo J ,, (,}) ('/x+u. , -i+v,} + w} c>.,i. "-'I"'; . o o The only terms Eij that are significantly large are those representing i nteractions among the atoms that contribute significantly to the electron density in th~ _unit cell covered by the integration. Let us attempt to obtain this result in a more usefui form. In virtue of the _t ~3:-Dsl ati on ~roun of the ~rystal_ la_ttic_e , . 00 ~ j ~ o0 oo eo Al - p., l_(u. ,v;w) = LL Z.. Z. ~j cu.+ ...... , v-+-, w+ p) "'-=-co n •-cio r;::-co j co co~ l.. J .,,, .,. .,,, NJI. ' p (u, Uj t.,.J) == 2.. L. ~-.I (u, v;w) = LL LL L. f:- I· (u. -+,..., -v--t"',tu-t I') l't\ :,.-00 ~ 0 0 p~...o ;_ J Further (15a) where (15b ) and where we have again made use of the t r anslation group. The Pat terson function is represented in equation (15a) as the folding of the crystal l attice 79 with the distribution fN due only to the N atoms in a single unit cell. Now f ij is the contribution to the Patterson distribution made by the vector that extends from a single atom i and a single atom j in the same unit cell. The N terms of kind I~ ~ in the summation of equation (15b) represent the 2 interactions of each of the N atoms in the unit cell with itself, and the N- N terms of kind f ij represent the N (N-1) interactions of these atoms with each other. We shall now investigate the nature of P • -ij transform the coordinates of p1 and To do this we shall fir st f j to coordinates which have their origins at the centers of the respective atoms. Let (16) where (17) and ~i' Ji, ~i are the coordinates of the center of atom!. Now fj {;c·Hl,, "f+v--,}+W) ::: f:,C~j +~,1-ij4-lT,, )J•+w) =- f; (s,:+~i - l'.s +- U., •• • ) because etc. Now if we let Lt = '<q . +A,, , u. <J . . =- "'!- I. - "'!- c.. ' 'tr == V ci+~~ j , V-:·. (,O w.:; + >I i i , w.LI- = }; - )~' ~ then <~ C, ~ ; -~i , '\ } (18) and we can write ff ..., ""'""' t/j ( it, ,., -,w) = f?:j (A,r 1v) =1T.ts ?,:(S)-,,))fj(~t~;71t~,S-tlJ) lj"..t?~) (19) -oe, - 00 _.,. where for convenience we have dropped the subscripts on the coordinates. 80 If p1 and pj are monotonically decreasing functions of the distance I ~ + 11 ~~ + ) ~3) ~ I from the nucleus of the atom, it is evident that Pij monotonically decreases with the distance I A~,-+ 1-4-~~ -t V~31 from the point in Patterson space which has the coordinates (~ij' ~ij' ~ij), and that this point is the center, or at any rate the position of maximum density, of a peak. The i2 interactions of the atoms with themselves have in common that the peaks due to these interactions are alJ. superposed at the origin, and in fact at each lattice point. The B (~-1) interactions of atoms with one another give rise to peaks that are, in general, separated from one another. When peaks overlap or superpose, their amplituies are additive. It is possible to calculate the sha2~ of the peak, i.e. the variation of Patterson amplitude as a function of the vector distance from the center of the peak. transforms. 24 To do this we will make use of a theorem on Fourier If +c~>: 1_: and r- 1(~) = )..oQ G C-f.)..e. F(t)= z.ffi: t-,. "'° 1 "° -f fa) .t. 2.rri-t ~ -~~ {::r)--e lob M, 6- (t-) :: J: ffu.i G ( t )~;:f_: f 1 are two sets of Fourier transforms, then C:r) u. + ·t (:L)~ -'-"" . el/f- -irril-1- /4 ~~ The integral on t he left represents a type of folding of the functions E and Q, and the integral on the right provides the means of carrying out this folding by use of the Fourier transforms of _E and Q. easily generalized to three dimensions. In our case the Fourier transform of the electron density, f '- (~, 17 5), is the f.Q!'.l!! factor, 1 81 This may be !i (~, ~, ~), of atom J:.. We will here regard the Miller indices as continuous variables. We may assume that and accordingly so that we use the cosine transforms: (' d ~. n, r) • -k_ and r:c(-!J/, -4,1) ""'- ~ ,r-(1.. 3, J..-,, , -R;)dl..&,LR (20 l -L c,,e,,J,1) = ~ [ 1: [r,(~1,S') We now have 'f:J~,f-,1)~ l!,n,211 r1..r+--'1 .ff)ds,D,c1.r. (21 ) 4 .,,, "" ... l f f f {Oc,le))~{l,A,1)en2.TT(-1..).+/4,,._.,.J-»)di.Btdi. . (22) -o -o0 .... oo We may further assume that the atoms are spherically syrmnetrical in electron density and that the form factors accordingly have spherical symmetry. Let (23) where ,,e1 , 1'2, and l>J are the basic vectors of the reciprocal lattice, and let f.i (').,1-4-,11) =- 'Pi;s CR)J ii (1., -4,1) =- 1r~ ( H) where E and li are the scalar quantities corresponding to equations (23). (24) The quantity li is related to the Bragg angle of x-ray reflection by equation (6). The quantity R represents distance from the center of the Patterson peaK. Equation (22) may now be transformed into our final result 0() ~ j ( R) = 4 'll' [ tJH) t (H) ~11"-J.:: R 1-1 \1 fl by standard methods. (25) 0 If we assume that each atom has a spheric ally symmetrical temperature factor of known magnitude, we may multiply it into the form factor, 82 (26) and we may calculate for the shape of the Patterson peak ~: (R)= 41f[ohf tH) ½'(II) 7;;:R_ 112J.11 . (27) If the temperature factor is anisotropic, it is necessary to make use of a more general expression analogous to equation (22) . For the special case of B ~ 0 and!= l, equation (27) gives the expression that was used in putting the experimentally determined values of 2 lhkl on an absolute basis (equations (4) and (5)). Patterson19 has shown that the peaks may be sharpened by dividing 2 an average form factor out of the fhkl data before carrying out the Fourier summation. The coefficients used in the summation were When this is done, a Patterson distribution is obtained which corresponds to a crystal structure in which the atoms have an electron density distribution such that their form factors are equal to The peaks will therefore have a shape given by 0q:·(R) =11ir -1., 1.L ~"-1fffR. 2-rr fl R. i'd /.I . (28) - z.. () -f In the limit where f.if.jfr is a constant the peak assumes the characteristics of a three-dimensional delta function: infinite height and infinitesimal width. _P ractical limits are imposed on the attainable degree of sharpening by the limited accuracy of the data and, more importantly, by t he degree of convergence that can be obtained with the amount of data at hand. 8.3 In order to prevent the occurrence of large periodic variations in amplitude at appreciable distances from the center of the Patterson peak it is necessary -2 that fifj/f be rapidly converging toward zero at the maximum value of B for which data have been obtained. The problem of convergence is analogous to that which arises in electron diffraction work. Dr. Jurg Waser and Professor Schomaker have investigated the problems of convergence and of resolving power for the field of electron diffraction in a way that is more general than the simple method of Patterson, and van Reijen 26 has investigated these problems in a somewhat similar way for the field of crystal structure. Dr. Waser and Professor Schomaker intro- duced the modification function, which for our purposes we may write as !':J(,!!). This is a function that is multi plied into the experimental data before the Fourier synthesis is carried out. Its form is so chosen as to obtain a satisfactory compromise between convergence and resolving power. Both of these properties may be determined for a given modification function by calculating its Fourier transform, which is related to the shapes of the peaks that will be obtained in the electron diffraction radial distribution function or in the Patterson distribution obtained for a crystal. For use in the Patterson calculation we will assume that before 2 the modification function is applied the coefficients Ihkl have been divided by the square of an average value of the combined form factor and temperature factor to obtain new coefficients that show no systematic tendency to rise or fall in magnitude with increasing]. to that of Patterson. This is a sharpening procedure similar After the application of the modification function the coefficients are 84 After the Fourier synthesis (29) is carried out, the peaks are expected to have shapes given by the equation (30) , . ., ~X f 06 M(H) ~ ~rr HR II "'oJ_ H ,._ rrHR (30a) 0 It is assumed that the ratio is spherically symmetrical in H. If there is a marked anisotropy in the tem- perature factor, the anisotropy should be removed in the sharpening procedure. As an example of the type of modification function that could be used, the artificial temperature factQt, which is a Gaussian function, /11 {fl) = .R. might be cited. - ol.7..!f 2- (31) The Fourier transform of this function is likewise a Gaussian function (32) In the use of any modification functi on, allowance must be made for the fact that the integration in equation (28) can be carried out only to the limit of the data. The shape of the peak will contain the effect of the limit or cutoff, so the cutoff must be regarded as an essential part of the modification function unless the modification function itself goes to zero before the limit of the data is reached. In the use of the artificial temperature 85 factor the parameter tJ... must be taken large enough to obtain satisfactory convergence. On the other hand, as r,(_ is made larger in an effort to obtain good convergence, the Patterson peaks become broader and the resolving power accordingly becomes smaller. Although the artificial temperature factor may be a convenient modification function to use, it does not necessarily enable the best compromise between convergence and resolving power to be made. Professor Schomalcer has shown that functions of the type* ... 1.- M,,..__ CH) = fl ~,,,,(_ - oe,.., H ' ,M. >o (33) give, at comparable convergence, peaks that are sharper than those given by the artificial temperature factor. They have the somewhat objectionable feature, however, that each peak is surrounded by a shallow negative area of large extent. This may be less objectionable than the more slowly damped periodic variations due to non-convergence that arise when an artificial temperature function is used at the same resolving power. Another consideration that aff ects the choice of a modification function is the relative reliability of the data at different values of ]J; (34) (35) (36) where (37) \t.e may write if -f-i" fj 1/I'l- = ~ ~i (R) If (after Professor ?Chomaker) we - we take as the criterion of convergence the smallness of the 86 it is advantageous for the modification func tion to have its highest values where the data are most reliable. If the intensities of strong reflections at low Bare uncertain because of extinction, it may be desirable to choose a modification fu..'1.ction that is small at low B. Small values at high B are desired both to obtain good convergence and to take account of the greater uncertainty in the estimation of intensities for the weaker reflections. Finally, the use of a modification function which has small values at low B of may have the advantage 11considerably reduci ng the contributions due to hydrogen atoms, because the form ~actor for hydrogen decreases more rapidly with increasing li than do the form factors of carbon, nitrogen, and oxygen atoms. Before proceeding with an account of the calculation of the threedimensional distribution for threonine, we shall mention another contribution of Patterson that was of use in our work. Patterson showed that it is possible to carry out the calculation in such a way that the peak at the origin does not appear. In our case the elimination of the peak at· the origin was a matter of convenience in the calculations, for its presence would require f0 quantity 11_.,_ J:° H r--i ( H)J. H S ::: I 1-l MC H) c{ H and as the criterion for resolving powir the magnitude of the quantity T = - I -2- [ I 02... D N(D) c)R2. RN (R ] 47T " R =- D which is related to the curvature of the peak, we obtain, for modifications functions H,...,.Jl, - "'......_... H"-, n =0 So = To = •n ;; 2 s2 = T2 = 3 I z' • o<. L (38) (39) (40) if •f .. J_,J_ n =4 T4= S4 = 2o('L For two given values of the convergence .we obtain for the relative resolving 87 the handling of rather large numbers in the punched card calculations. To eliminate the peak at the origin it is only necessary to subtract the Fourier transform of the peak from the data. If the average form- temperature factor used for the sharpening operation is chosen in an appropriate way, _ -z_ _f N f (42) we need only subtract from the data a constant times the modification function. This may be done by subtracting a constant from the sharpengg, data before applying the modification function, so that the coefficients for the Fourier summation are = [ (43) The constant A is chosen to make "° 00 1 Pro, o,o) = ~?:~ f _'° ~- C,JJJ_ oc} 00 ;".J o If it is not necessary that the peak vanish quantitatively, satisfactory results may be obtained by equating,! to the arithmetic mean of all of the sharpened coefficients: A =It is important in this procedure to make sure that the data have been correctly sharpened; otherwise the shape of the peak subtracted from the Patterson distribution may be different from the natural shape of the peak, so that although the amplitude may be zero at the origin the r e may powers of the three modification functions: s0 • s2 • s4 a o.oJ, T0 T2 S0 = s2 = s4 = 0.01, T0 88 T2 1.09 1.18 1.15 1.25 (41) be enough over- or under-compensation in the neighborhood of the central peak to affect the heights and positions of nearby peaks. The characteristics of the Patterson distribution that are useful in the determination of the structure of a crystal are described later for the space-group P21 21 2i in connection with their application to ) -threonine. (c) The mechanics of the synthesis for _}.-threonine Because of the crystal syn:unetry P21 21 21 it was necessary to calculate the Patterson distribution only for one octant of the unit cell: l l l Y -- Qt0 2, ~ -- Qt O 2• Y : Q to 2, The data available for the Patterson synthesis for }.-threonine 2 were the 618 non-equivalent corrected intensities kFhkl' that had been calculated from the intensity data with a film factor of 4.0 and placed on the same relative basis. The new value (3. 7) of the film factor was not known at th9.t time, and the extent of extinction in strong reflections had not been determined. The limit of the data was sin -J... max Q-1 =O. 925, Rznax = 1.20 A • It was now necessary to decide what form of modific ation function to use. As the extent of the data is rather limited* we need to use the data in such a way that the maximum resolving power is obtained consistent with reasonable freedom from complications due to non-convergence. As the extent of extinction was not then known, we desired to suppress the strong reflections at low]. On the basis of these considerations, Professor Schomaker suggested that we use the modification function ,ff M{lf) = If~ - o(_ 2/{L * 1/Hmal" 0.83 i, which is an appreciable fraction of the interatomic distances in the molecule. 89 with 2 IX. 2 1¾na.x = 6. 97, corresponding to 5 = 0.03 in equation (38). This modification function has a linear resolving power about 18% greater than that of the artificial temperature factor at comparable convergence. In order to improve the convergence the modification o-1 function was reduced in magnitude near the cutoff at H • 1.2A. A plot of the modification function finally adopted is given in Figure 3, and the radial distributions of amplitude for oxygen-oxygen, nitrogen-nitrogen, and carbon-carbon peaks, as calculated from equation (JO) are given in Figure 4. The amplitude scale for the plots of peak-shapes is the same as the amplitude scale of the finished Patterson. 2 The corrected intensities k~l were first sharpened by dividing out the square of the combined form factor and temperature factor for nitrogeno In order to eliminate the peak at the origin, the sharpened intensities were averaged and the average value was subtracted . from each sharpened intensity. The modification function was applied to obtain the coefficients given by equation (43). The Patterson summation may be written as follows: 'i'cCA,v;w) -= -::- ~ ~ ~ ~ ~ C!c.L- 11r (J.1.1_-+A,,..-+..Qw) c.. -'--=- -""' ).::-.0 £-=-"" J<l, 1=-~ o6 ~-40 ~ laN. 1 ~ CJJJ_ ~2TTut - (IJp:Uf • -~:l.iT w . I The second form of writing follows from the fact that because of the orthorhombic symmetry the coefficients are even functions of h, k, and 1. Further, in virtue of this property,* I * The term C000 does not appear in the following equation because M(O) • O. 90 1. 0 0.5 \ Hmit of data Figure 3. ModificA.tion function used in the calculp.tion of the PFtt t ex·son functi on. P.(R) ll 0-0 ~ c-c N-N Figure 4. Amnli tude~ of t hree 0 0.5 1.0 A I.S z.o R, kind s of Pattereon ·peaks, as functions of the ra.dia l distpnces from the centers nf the pe13_ks . Ce.lcubted by mepM of equAt ion ( 30 ) from the moct i fic ::it ion function f',iven in Figure 3. 00 oO '9 v;_ P (u 1 rzr1 w) = 2 c'4. 00 ~ HT kt.<.. :2. l.= I 1 + ,. 2 C. OQ j :: I 1)1) I + ~ 00 ,Q 1r ).'),T- ~ 211,,;_ w ,, . + 8' / ' ,.>!~ ___.,.. ...... , .. ~-" '··- k ::::.1 C4 ,_ 1T /4 v- ,~ 2-, 2 ·o!kl'~~ -+ 4 "'::: ~=I 1_ _ _ £, c o-4.o ~1.rr..£w oC>c / C> ~.\ c~~~ / 4. ::::1 OD / (Zl.v...l &i}'k 2. .R. ::;, lL +- 4k=~ 12 cJ.,o,R, -, -, - Ji. 0000/ 1 C@llT 1A·4,17T. /,t) ~)J.. v- ~~ w (45) where II cit.DO I = 2 C lt,oO I ~ I = 4 C ",JJ. ,~ . c~ = 8 cj._,u._ .fl CoJd,. After taking account of th~ multipl icity, we were ready to carry out the summation with the L cards on the International Business Machines. Each card contains values of Aces 2 'ii'hx X: 0, or Asin 2'1'thx for 1/60, 2/60, •••, 15/60 91 and when it is run through the tabulator with each of' four different lead cards it provides values of the function from z u Oto_! e 1 in intervals of l/60e Cards are available for all combinations of the amplitudes A • :t.: 1, ± 2, .•• , 'i- 5, ± 10, ... , -:i: 50, ± 100, ± 200, ±500 with the frequencies h =0, 1, 2, • . • 20. Each value of the function is rounded off to the nearest integer. The am- plitudes of our coefficients ranged from - 57 to+ 367 but must of them were less than 50 in absolute magnitudes. The frequencie s ranged as follows: h: O, 1, 2, ... , 16 ... 9 1 = o, 1, 2, ... 6 . 2, k ::: 0' 1, We calculated the Patterson function over the follow:i.ng ranges in B, y, ~ and with the following intervals between points: u = 0 to J.. 2, Ll u =1/60, al~ u 0 =0.227 A, 0 = 0 to½ L) V = 2/60, a2 L1 V = 0.258 AJ w= 0 to½ b,w = 3/60, a3 iJ w = 0.257 AJ V 0 Number of points calculated 5 31 values 16 values 11 values 5456 . The calculations were done in the fol l owing way. A swnmation over the index J.. was carried out for each hk combination to obtain the function {;, ;E,_ chkl cos 2.rr .Rw. Bhk (w) = (46) 1 ;: 0 For each of eleven values of !! from O to ½ and for each value of h the ~ 1 s were summed over the index k: Cf Dh (v,w) = lo Bhk (w) cos 2 7T/4 V: Finally the 12' s were summed over ,h for each of the sixteen values of']:_ and 92 (47) the eleven values of~: ~ P,,_ ( u, V, W) ::: k =O nh (v, w) cos ::i..1r A-µ.. (48) There were 134 summations, of one to seven terms each, in the first step. In the second step there were 187 summations of one to ten terms each, and in the final step there were 176 summations of fifteen to seventeen terms each. The total number of surranations was 497 and the number of terms was estimated to be about 4500. cards. This necessitated the handling of more than ten thousand The cards were pulled from files containing three or more cards of each amplitude-frequency combination, and were checked once before putting them on the tabulator. The terms were then listed by the tabulator and checked again for errors. The sunmations were then carried out twice with the tabulator to guard against machine errors. Finally, the cards were sorted by machine back into the files to be used again. Professor Schomaker and I, working together, completed the operations with the punched cards in three and a half days of work; a total of 62 man-hours were spent in these operations. This is certainly less than the total time spent in other operations related to the Patterson synthesis: the preparatory operations of sharpening the data, eliminating the peak at the origin, and applying the modification function, and the final operations of plotting the results and drawing in contours. The completed Patterson distribution is presented in an appendix to this thesis. (d) Interpretation of the Patterson distribution (1) General considerations In the interpretation of the Patterson distribution two distinct types of vector interactions are recognized. 93 First, there are interactions among crystallographically equivalent atoms; these have characterist ics which depend upon the symme t ry elements in the crystal. The interactions of atoms interrelated by the translation group, for example, give peaks at the lattice points in Patterson space; these are similar to the peak at the origin due to interactions of atoms with themselves. Interactions among atoms interrel ated by symmetry planes and symmetr y axes give rise to peaks having special values for one or two of their coordinates; these peaks are restricted, therefore, to special lines or planes the constant parameters of which correspond to the constant translational components of the respective syrrrrnetry elements. As these interactions provided the basis of Harker 1 s methoa. 20 of determining atomic parameters, we shall refer to the corre sponding peaks as Harlli peaks. The lines or planes on which these peaks are constrained to lie are known as Harker lines and Harker sectio,n s. Second, if there are more than one set of equivalent atoms in the crystal, interactions between pairs of non-equivalent atoms will exist and will give rise to peaks that have no special values for their coordinates; these peaks will be referred to as !lQ!!-Harker peaks. Unless it accidentally lies on a Harker section, a non-Harker peak may be 1'rm1ediately recognized as such. If the symmetry axis is a two-fold screw axis or -.,. rotation axis, the Harker plane coincides with a mirror plane of the Patterson distribution, and any non-Harker peak that accidentally lies on the Harker section will superpose with the peak that is related to it by the mirror plane to give a peak twice as high as a generally situated peak due to a similar interaction. Since a Harker peak has a height equal to 94 that of a generally situated peak due to non-equivalent atoms of the same kind,. it may be possible to recognize Harker peaks by their height as well as by the apparent rigor of their constraint to the Harker plane. The heights of oxygen- oxygen, nitrogen-nitrogen, and carbon-carbon peaks that occur on our Patterson distribution (see Appendix) are given for both Harker and non-Harker peaks under various multiplicity conditions in Table 16. Table 16 Relative Heights of Patterson Peaks* Positions of Non-Harker Peaks Positions of Harker Peaks General Ydrror Two-fold Position Plane axis Center, of Symmetry Harker Plane Two-fold axis Center of Symmetry 0-0 109 218 436 872 109 218 436 N-N 69 139 278 555 69 139 278 0-C 47 95 190 380 47 95 190 * On the same relative scale as the contour heights for the Patterson distribution as given in the appendix From the symmetry of the crystal and the number fl of atoms in the unit cell it is possible to calculate the number of peaks of each kind to be expected in the Patterson cell. For the space-group n24-P21 21 21 , to which we will hereafter restrict our discussion, there are three Harker-sections, one of which corresponds to each of the three two-fold screw axes. Each of the atoms interacts* with the three other atoms crystallographically equivalent to it so as to give three Harker peaks, one on each section. There are * We use this term in the following sense: between atoms Xi and Xj there are two interactions Pij and Pji representing respectively the vectors xi~xj and Xj ~ Xi• 95 therefore on each section four equivalent peaks (of which, in the Harker method, one may be assigned to a given atom) for each of the N/4 kinds of non-equivalent atoms. the unit cell. There are NHarker peaks on each section, or 3N in Each of the N atoms in the uni t cell interacts with the 4(&4-l)=N-4 atoms that are not equivalent to it to give altogether N(N-4) non-Harker peaks. The total number of peaks, aside from the peak at the origin, is seen to be N(N-1) , in agreement with the r esult previously obtained. If these numbers agree with actual counts of the peaks obtained from the Patterson synthesis, the analysis of the Patterson distribution may be carried out with the assurance that each peak has a unique interpretation. For threonine, with 32 atoms in the unit cell, we expect a total of 992 peaks of which 896 are non-Harker peaks and 96 are Harker peaks. In each quadrant of each of the three Harker sections we expect to find eight Harker peaks and within the octant that we have cal culated we expect to find 112 non-Harker peaks; the total number of peaks for which we must account is 136. Approximately half that number of resolved peaks has been found; a considerable amount of overlapping and superposition of peaks has evidently occurred, and we must take this into account. The necessary relations, other than those given only by the operations of the space group on individual interatomic vectors, that exist among the positions of Patterson peaks are expected to follow a pattern, characteristic of the space group, that we may cal l the inner symmetry of the Patterson distribution. The essential principl e of the inner symmetry is: f or any closed circuit of interatomic vectors in the crystal, the vectors represent ed by the corresponding Patterson peaks must add vectorially to zero; i.e. the respective coordinates of the corresponding peaks must add to zero. 96 The features of the inner symmetry that are characteristic of the crystal space group arise when this principle is applied to vector circuits which contain Harker vectors, i.e. vectors between atoms that are equivalent by virtue of the operations of the space group. For example, the apparent symmetry of the Patterson distribution obtained for a crystal with any 1 primitive orthorhombic space group is D2h-Pmmm. The characteristic differences among the Patterson distributions for these space groups involve the existence and locations of Harker lines and sections, the relative positions of Harker peaks representing interactions between equivalent pairs of equivalent atoms, and the relations between Harker peaks and non-Harker peaks; differences in these features constitute differences in inner sym_metry. We shall discuss some of these features briefly in com1ection with the spacegroup n4 2-P21 21 21 . We may first examine the relations between Harker and non-Harker peaks in this space group. If two non-equivalent Harker peaks are to be ascribed to interactions between equivalent atoms in two respective non-equivalent pairs, then two non-equivalent non-Harker peaks must be found which correspond to the two kinds of interaction between non-equivalent atoms. The way in which the inner symmetry principle applies in the case of a two-fold screw axis is shown in Figure 5. 18 A special case, pointed out by Albrecht and Corey. is illustrated in Figure 6. If an interatomic vector between non-equivalent atoms is parallel to a Harker section, a non-Harker peak is found on the Harker section half way between the two Harker peaks. It will, moreover, be the super- position of two peaks (the limiting case of the overlapping of two peaks, one on either side of the Harker plane). Every peak on the section li=o, for example, must give rise to thi s phenomenon on the section wml. 97 • non-eauivl'\lent set!:' of atoms grouped around a two-fold screw a.xis. Tvrn ½ For convenience in presentPtion. all etoms .qre assumed to lie in a plane which includes the screw- axis. I / / 0 0 0 p / / Q / / ½. 0 I i I RA.rker sect ions \ \ 0 b 0 0 Figure 5, Relations between H8.rker and non-...Harb::er peaks. 0 0 0 Patterson distribution (same sct1le) I / / / 0 Atoms At Z -= i!:.o, 2o+- I t etc. 0 Atoms at i! = ;: +}_, etc. 0 Non-rfa.rke r peak nt -w--o. 0 I I / / / 1,(/: z . I Non-Harker -peak at / I 1/ }Ton-&:r1r:er intere.ction He.rker interact ion Two non-equivA.lent Reta of atoms grouned ~round a screw axis 0 I I Patterson di~tribution I o, ( same sea.le) I I' I Figm-e 6. Pa tterson distribution due to two non-equivalent ~ets of atoms wh i ch h~ve, by ~ccident , the same~ par,:imeter. Let us determine the inner sy.~rrnetry relations among Harker peaks. With the space-group D24-P21 21 21 , the position of a Harker peak due to a given pair of equivalent atoms depends on the vector distance between each atom and the screw axis; twice this distance gives the vector distance of the Harker peak from the origin of coordinates for the section. The atom is not, in general, equidistant from each of the screw axes; corresponding components of the vectors between an atom and three differently oriented screw axes have a sum or difference of (u/2 +¾)where n is an integer. This is obvious from Figure 7 in which a diagr~m of the symmetry elements of the space group is given. 12 b If Ha~ker peaks corresponding to a given atom on the three different Harker sections are given the coordinates ( l2, v..., , ·.W r) ' (u", ½, w"), and (u 11 ' , v"', ½), the necessary relations may be written u" ± u"' .. n' ± ½ n 1 , n", n 111 ~ integers v' :I:: Vlh • n" -+- l2 w' ±' w" (49) = n'" -+ l2 An important application of the inner symmetry was the confirmation of the space group of J -threonine. The small number (three) of odd orders of (001) that could be examined with copper Ko<. . radiation did not allow much certainty i n the conclusion that the symmetry axis parallel to ~3 is a two-fold screw axis. A search for peaks with the expected character of Harker peaks on the sections w 5 0 and w • ½, an examination of the relations among the peaks on the two sections, a test of the equations (49), and finally.the discovery of several other vectorial relations consistent with the inner symmetry of the space group n24-r2 1 21 21 , all verified the conclusion 98 4- J_ j 0 Figure 7. ~ 1 x---► l. 4- I 4 J ~. 4- .1 j I I to the plp,ne of the -op:per a nd is directed toward the reader. Symmetry elements of the ~na.ce group D - P2 1 2 1 2 1 . 2 Adauted from Interna.tionale Tabellen but with a change in the orientation of the axes. One unit cell is shown. The g. 3 axis is ,erpendicular ' g.1~-t---- I I 1 , 4- 4 I 4- I I that this space group is correct. We have by no means exhausted the study of the inner symmetry. With the background given above, however, we may proceed to the analysis of the Patterson distribution for information regarding the structure of ) -threonine; (2) Examination of peaks close to the origin In the octant we should expect to find seven peaks, due to pairs of atoms bonded with covalent bonds, within 1.6 j of the origin; nine, each due to a pair of atoms bonded indirectly through a third atom, in the range 2.2 i to 2.7 i; and in the range 2.7 i to J.O peaks corresponding to hydrogen bonds. i we expect to find some ' If the peaks for these short vectors can be identified, the orientation and configuration of the threonine molecule can be determined immediately. On inspection of the region within 1.6 i of the origin it is difficult to account for seven interactions due to bonded pairs of atoms. peak at (~y,bT) • (0.08, 0.12, 0.00) is about 1.5 i from the origin; A it has an extension in the !! direction and is high enough to account for two carboncarbon interactions. An elongated peak centered at (o.oo, 0.06, 0.25) is about 1.4 i from the origin and could accomodate two or three carbon-carbon, carbon-nitrogen, or carbon-oxygen interactions. We find in the range 2.2 A to 2.7 A a high peak at (~, y, !!_,) = (0.055, o.oo, 0.40) that is elongated in the :!t! direction, probably by over- lapping with the equivalent peak at (O.Q55, very symmetrical. o.oo, 0.60), but is otherwise Its center is 2. 25 i from the origin, and its height is about that expected for an oxygen-oxygen peak. 99 The only other peak centered 0 0 at 2.2 A to 2.3 A is a peak at (O.OO, 0.27, 0.00) which is much too low, in view of the multiplicity, to represent any interactions except those involving hydrogen atoms unless its small amplitude can be accounted for by negative contributions of other peaks. Other peaks in this range are 0 a high peak at (0.17, 0.13, 0.07), 2e7 A from the origin; a broad, moder- i from the origin; and an elongated peak of moderate strength at (0.09, 0.16, 0.35), 2.5 i from the ately strong peak at (0.10, 0.25, 0.20), 2.6 origin. Each of these is high enough to account for at least two inter- actions; together with the one good peak 2.2 i from the origin they can probably account for the nine indirectly bonded interactions expected in this region. When the calculation of a three-dimensional Patterson distribution was first contemplated it was thought that the peaks near the origin would be the most useful feature of the distribution. However, with a single exception which is discussed below, we were unable to make a clear-cut interpretation of these peaks without additional evidence. Perhaps the most useful single clue to the structure was provided by one of these peaks, however. Among the intramolecular interatomic inter- actions the ones which should give the strongest peaks are the three oxygenoxygen interactions. One of these, moreover, ha s a known distance that is unique among all of the possible interatomic distances in the structure; it is the oxygen-oxygen interaction of the carboxyl group; glycine 18 and alanine 27 have oxygen-oxygen distances very close to 2.20 i. No other pairs of atoms not directly bonded together can easily have interatomic distances less than 0 2.4 A. The peak at (O.~, o, 0.40) is the only peak, high enough to account 100 0 for an oxygen-oxygen interaction that occurs at a distance close to 2.2 A from the origin. This peak may therefore be identified with the carboxyl oxygen-oxygen interaction with fair certainty. (3) Determination of some atomic parameters With the assumption that our assignment of the peak (0.055, o.oo, 0.40) to the interaction of the carboxyl oxygen atoms is correct, we proceeded to look for the Harker peaks corresponding to these two atoms. In the analysis that follows, we shall take the non-Harker vector corresponding to these two atoms as = (-0.055, o.oo, 0.40) in which the negative sign for the first coordinate is arbitrarily chosen. The first requirements for the Harker peaks are that they have the re spe ctive vector separations ( <'.1 u, Liv, l\ w) : li Harker (Ozr~ Or )= ( ± 1.10, o.oo, o.oo) y_ Harker (O:ir ~ O.r ) = ( ± 1. 10, o. 00, ± O. 80) 1; Harker (0.1f ~ Or ) = ( o.oo, o.oo, ± 0.80) and that the peaks have coordinates that satisfy equations (49). After ex- haustive examination of the sections the only assignment of peaks which we found to be compatible with these requirements is as follows. The coordinates given are (~, ~, ~); the values given do not correspond exactly to the centers of the peaks but have been shifted slightly in the light of further developments. The reader may locate these peaks on the sections given in the ap- pendix. The prime marks represent atoms equivalent to the unprimed atoms by the respective screw axes. 101 l:! Harker y Harker ,,, 0r-'°'Or = (0.37, d'➔ o 'Jr '][ O.47, ½) ... (O.48, 0.47, ½) 0.40) d~- Or = (-0.13, l2, l (-0 .02, 2, o;-, o.J[ -0 .40) 1111 y Harker l O~➔ Or = ( 2, -0.03, 0.90) l o~~ O:ir = ( 2, -0.03, 0.10) This assignment may now be tested by calculating the expected coordinates of non-Harker vectors from the requirements of closure: '" o"'-z = (O.425, O.47, 0.10) o:r: = (O.425, O.47, O.9O) o'r· - Oa- = O~➔ O.1r Q"--7 1£ o.r:- :: (-0.075, o. 50, o.oo) (-0.075, o. 50, 0.00) o:~ 0.xr = (0. 555, --0.03, o. 50) 0~~ 0.r a (O.445, - 0.03, 0.50) To illustrate the closure of vecto::-s we may add the vectors in a typical circuit: (O.425, O.47, O.1O) o.n:- , o.:r - (-0.055, o.oo, 0.40) or ~ o"':r. = (-0.37, -0.47, -½) ff O W/ = Or ~ r (o.oo, o.oo, o.oo) All of these points lie on peaks in the Patterson distribution; hence the assignment conforms with the requirements of inner symnetry. The coordinates of the atoms are, from this assignment, X y z O_r O.435 0.235 O.45 0.1[ O.49 0.235 0.05 These are obtained by substituting the coordinates of the Harker peaks for the unprimed atoms into the relations 102 (50) 11 z-w - - . , .1.1.-w' 4 -- 2 2 ' which are consistent with equations (49). On examination of the section vaO we find peaks at (0.25, and at (0.195, O.OO, 0.40). o.oo, 0.00) As the vector connecting these peaks is just the o.oo, 0.40) it appears likely that these peaks re- vector (-0.055, present interactions of some other atom in the structure with 01 and O.Jf . This atom which we will designate J1, must be represented on they Harker section by a Harker peak, and on this same section there must be two non-Harker peaks involving atom Xr because the atom apparently has the same :z coordinate as the two oxygen atoms. We observe on they Harker section the phenomenon which we expect to find when three ato~~ have equal~ parameters: the three Harker peaks which represent these atoms lie at the vertices of a triangl e, the edges of which are bisected by non-Harker peaks. This i s illustrated in Figure Let us start wi th the assignment = (0.195, o.oo, 0.40). We may expect to find Harker peaks as follows: Xr " -'> XI = (0.37, ½, 0.40) XI 1 ➔ Xr = ( ½, -0.03, 0.90). We indeed find that these points lie on peaks. peaks are expected to be: 103 The positionsof non-Harker 8 • XI '" -'l> 0.I =(0. 62, 0.47, o. 50) , = (0.12, 0.50, 0.40) X ' ➔ 0 = (0.25, -0.03, 0.90) XI II ---;,, 0 r L Xr "4 x.r 11 '-7 0I[ J I O.rr= (0.675, 0.47, 0.10) = (o.175, 0.50, o.oo) ? All of these points lie on peaks, as the reader may verify. From equations (50) we obtain the parameters X xr o.685 y z o.235 0.90 In a similar way we find an atom X~ which has coordinates Xn: X y z 0.560 0.115 0.'90 by making use of Harker peak (0. 715, 0. 23, f ), and the non-Harker peaks (0.065, 0.13, 0) and (0.80, 0.37, 0.50) which relate it approximately to the !!! Harker peak for atom X.r (0.87, 0.47, ½). In this case·, the correspondence of the expected interactions with Patterson peaks is not as good as that We have established tentative coordinates for other atoms but have hesitated to rely on them as in some cases the agreement with observed peaks is poor. At this point we turned to examination of evidence of other kinds, which we shall discuss in the next section. Our analysis of the Patterson distribution is by no means complete. We expect that during the refinement of parameters, frequent checking of parameter changes against the Patterson distribution will be useful. We have already checked our promising trial structure, which is described in the next section, against the Patterson distribution by comparing the calculated and observed positions of peaks. The calculated points are plotted in red on 104 the sections given in the appendix. The result, which we will not discuss in detail here, was a promising fit in which nearly all of the expected peaks fell on or close to actual peaks although many of the peaks were not utilized in the determination of parameters. A few bad disagreements exist, but there is g-ood promise of obtaining a satisfactory fit eventually. 14. The determination of the approximate structure* From the analysis of the three-dimensional Patterson distribution we haye obtained parameters for four atoms. We must now attempt to inter- pret this information in the light of other evidence. This includes steric considerations, possible modes of hydrogen bonding, some requirements imposed by structure factors, and cleavage properties. We started with the assumption that the atoms for which we have parameters are all in the same molecule. This assumption is based partly on evidence obtained from structure factors which indicated that the molecule is strung out approximately in the a "" direction, and partly on the difficulty of obtaining a plausible mode of hydr ogen bonding between the amino groups and the carboxyl groups if the contrary assumption is made. The mutual electrostatic attraction of the carboxyl oxygen atoms and the amino group may tend to bring the nitrogen atom close to the plane of the carboxyl group. In the structures of alanine 27 and glycine 18 the nitrogen atom is not far out of the pla.~e of the carboxyl group. Placement of the nitrogen atom in approximately the position shown by Figure 9 in line with this argtnnent is not incompatible with the Patterson distribution and provides an excellent opportunity for hydrogen bonding to 0 .1[ of the * Frequent reference to Figure 9 may be of help in following this discussion. 105 I . / I - / . .• / ' X. \ \ \ 0-.,zs \ ( . I ' / / 4 • / 4 q J" ... / J_ \ j I I j 0 \ ........ • 0 I I I Y'',, ~ Om ' --- -.so~ -- ' .,., ' J.OC J.,s~ ,:. c.lll I:, -- \ -.... t I ,I 4 I j Jg, V\ "'~· f!:'1:t; -y '·'·' •--\ . ._ \ I ~ I --- --- _... I · 4 Probable aupro::x:imP.te structure of d- or 1-threonine. One unit cell is 1_:1ho,,.rn; the ~3 axis is perpendicular to the plP;e of the paner (toward the reader). In decreasing order of their sizes, thP circles renresent cFJrbon, nitrogen, and oxygen atoms. Hydrogen P.toms Hre not shown. Bonds between atom!; in a. molecule s.re shown as solid lines: h;vdrogim bonds A.re shown as dashed lines. See also Figure 9b. ~ r ~- Figure 9a. •---- • ~'f I I I 4 I 4 I Figure 9b. 4'~- - 1~······~ 4 I / I / / / / o:r / ~ / \ \ -- ~ • \ \ " "" " ' I ~ ---- ---~ , - - -- -- - - - - - -- - - - - - - X -------- _. \ •- - - - - - --- - I I 4 I 4 I 4 In this view of the annro:xima.te structure, the_ ~h . axis is normal to the r,l,cine of the nauer (away from the reader). ~ ~ t I Q-3 molecule abo7e (in the ~-direction) and to 0;ir of another molecule. V10re- over, with this placement of the nitrogen atom, Ca:- and Car can be made to occupy the atomic positions XE and X.z: respectively.* The position of Cr is now fixed, and we are left with the task of placing C.nz: and OJlI. • At this point we made an arbitrary assignment of parameters to these two atoms a.'1.d calculated structure factors for some of the low-index planes. The agreement between observed and calculated structure factors was extremely poor, but the results yielded a very useful piece of information: the calculated value of (200 ) was much too high. to this plane is made by the carboxyl group. A very large contribution In order to reduce the structure f ~ctor to the experimental value, it is necessary that the atoms Om and Ctt have ~ parameters as near as possible to 3/4 in order to cancel partially the contribution of the atoms near x = ½. This consideration, further, made it very unlikely that the molecule has a diagonal orientation with an appreciable component in the~ direction. The approximate structure shown in Figure 9 was then proposed. * The numbering of the atoms is as follows: 106 In this structure the ammonium group forms two good hydrogen bonds to 0:1T atoms in two different adjacent molecules and a third weaker bond to the oxygen atom, O..III , of the hydroxyl group in a third molecule . The hy- droxyl group has an opportunity to form a hydrogen bond to Or of another molecule. Thus all of the capacity of the amino group and the hydroxyl group for hydrogen bonding is utilized, and both carboxyl oxygen atoms are involved in the hydrogen bonding. The packing of the molecules appears to be good; a rather short intramolecular N- C.Ill distance (3.0 i) is the only obj ectionable feature, and there is considerable l iklihood that this distance will be lengthened in more refined models. The strong N-0..zr hydrogen bonds form a two-dimensional network of molecules that would resist cleavage on (001) and (010) planes; in addition, nearly all of the ionic bonding is confined to the virtually twodi mensional array of positively charged amino groups and negatively charged carboxyl groups. Cleavage on (100), however, would be resisted only by hydrogen bonds involving the hydroxyl group and by weak van der Waals forces. The cleavage properties expected for this structure are in agree- ment with experiment; good cleavage was obtained only on (100). After making small changes in the parameters predicted for the atoms by the Patterson distribution, we calculated the structure factors of low index (Oki), (h01 ), and (hkO) reflections for this trial structure. The structure factor may be written _ ~ r.'ci ) +-21ri(l.. ~-f.-'4.;+~J-) ~ - 4- ft ,1,J .£_ (51) t=I where the sum is taken over all of the atoms in the unit cell. In the , space group P21 21 21 the atoms occur in sets of four, which are crystallographically 107 equivalent and have the coordinates 12b, 1 xyz; The structure factor reduces t o 1 2-z. (52) t.1-ie form N/4 - L-... ~ F ., -hkl where 1 2'f'X, ;t;-y, Z; i -, [~ (hYcl) ... i Bhkl] 12b ~ l = 4 cos 2 '11' [ h(x-¼)~ } cos 2 t r [ k(y--!-1~}1 •cos 2 7 r[ i ( z - ¾ ) 1 ] (53) B h k l • -4 sin 2 7r [ h(x-¾).f.!} sin 2 7f [ k(y-¾){} sin 2 7 r[ i ( z - ¼ ) i _ ] It is now necessary to smn only over N/4 non-equivalent atoms, as for example those in a single molecule of threonine. For calculation of (Okl), (hOl), and (hkO) reflecti ons it is convenient to take the origin of each respective set of coordinates on the respective screw axis in order to make B vanish. We finally obtain A = Oki 4 cos 2 'ff ky1 cos 2 ?ri z1 , k+i even -4 sin 2 'lf kyl sin 27' !z1 , k.f.1 odd f 1 Y1 -- y~; 4 cos 2 Tr hx2 cos 2 'lriz 2 , h-,.1 even [ -4 sin 2 'Tr hx 2 sin 2 '/TJ..z , h-,.1 odd 2 z 2 = z-¼, ½ = x cos 2 "trky , 1.+.4 ~vn\ 3 sin 2 7r'ky , ,l,,. t )e odd 3 y 3 =y 108 (54) The parameters that were assigned to the atoms of the trial structure are given in Table 17, and the structure factors that were calculated with these parameters are compared with the experimentally determined structure factors in Table 18 • Table 17 Approximate Parameters of Atoms Atom X y z 0.433 0.233 0.450 0.492 0.233 0.050 0. 767 0.167 0.500 N. 0.588 0.025 0.625 0.508 0.21? 0.300 o. 608 0.117 0.425 ,., 0.675 0.250 0.450 V J![ o.658 0.367 o.675 109 Table 18 Corrected Intensities, and Observed a.~d Calculated Structure Factors 2 Relative Fhkl hkO ~ 1 110 1500 -Fcalc 1680 29 -24 1680 1750 30 14 2 310 F -obs 3 220 310 335 290 13 23 510 400 385 430 15 -18 420 4940 4950 5070 52 -42 130 50 48 5 6 330 2190 1980 2430 34 31 620 2140 2320 2720 36 25 1660 1660 30 -24 710 530 6 <4 ~9 ' 2 10 240 13~ 11.30 1510 27 -37 44D 87 107 80 7 2 820 <. 4 <7 .( 11 '- 2 -6 730 256 243 252 12 12 150 21 14 3 -6 200 1090 1080 24 -36 400 4030 4060 47 18 600 363 341 14 3 800 78 74 6 10 10.0 .0 615 578 18 -10 12·0•0 631 680 19 28 110 Table 18 (continued) Relative F~ hkO F F -obs -calc 1 2 3 210 690 630 750 19 15 120 3150 3420 42 -23 410 2990 3020 2970 /40 48 2840 2970 39 24 ODD 320 230 570 530 590 17 26 520 740 680 660 19 18 610 320 370 3/40 14 -27 430 2400 2220 2740 36 -30 140 1100 1060 24 9 340 2260 1890 2350 35 -21 720 580 680 690 19 3 630 82 75 59 6 0 38 36 5 -14 810 540 418 426 434 15 8 250 27 30 29 4 -4 111 Table 18 (continued) 2 hOl Relative Fhkl 1 2 2060 2090 F - obs fcalc 33 -20 3 m.N 101 301 24 22 1 -.30 202 7 <5 .3 2 .3 501 2760 2680 3010 .39 -18 402 650 680 630 19 -16 210 194 10 -8 23 20 701 103 920 1000 602 162 180 169 10 16 303 t.. 4 <. 8 <'. 5 <2 0 002 3260 3320 42 -53 004 3 1 8 006 < 2 ( 1 -2 < 7 112 Table 18 (continued) . hOl Relative F 2 hkl F . !obs -calc 1 2 3 201 470 480 420 16 -26 401 8 9 6 2 8 102 570 680 18 -8 302 3 5 4 1 -17 1850 1940 32 21 ODD 6ol 502 1040 950 930 23 -7 203 680 790 700 20 -17 ( 11 < 1.5 -14 801 702 73 77 67 6 4 403 1190 1200 1100 25 -5 113 Table 18 (continued) 2 Relative Fhkl Okl -obs F F -calc 1 2 3 011 3910 3740 4430 46 -62 031 11 14 8 2 2 022 3160 2610 3330 40 36 013 304 322 311 13 -4 042 80 98 91 7 14 033 18 ~ 26 23 3 -5 020 5020 5360 53 74 040 371 324 14 -46 060 189 174 10 9 080 52 44 5 -17 EVEN >/ ODD 021 63 69 63 6 23 012 11 7 11 2 1 032 1070 1110 1000 24 -22 041 198 180 171 10 15 023 237 234 243 11 6 Notes to Table 18 : Er¼2 (1) The values of relative were obtained with the film factor are given the values obtained with 4.0. Under the headings 1, _g, and crystals rotated around the axes 21, 2-2, and ~3 respectively. (2) Jhe values of ;[ b were obtained from averages of the value of relative Fhkl but were sca~e! to an absolute basis. 114 The general agreement between observed and calculated structure factors is sufficiently good to indicate that this trial structure is a promising one which deserves an exhaustive examination. Subsequent examination of these results with structure factor maps by Dr. Corey and Dr. Werner Nowacki has revealed that there is a promising degree of consistency among the shifts in atomic parameters that are indicated by the structure factors and the interatomic distances. A small shift in the carboxyl oxygen atoms that is not inconsistent with the Patterson distribution has materially reduced the disagreement in many of the planes. There is yet some uncertainty regarding the positions of Ctt' and Orrr and we feel that these atoms are responsible for much of the disagreement. Preparations are now being made for more extensive work with structure factors, and for a Fourier pro jection to be made with the hkO data with the signs established by structure-factor comparisons. 15. Conclusions On the basis of the evidence provided by the Patterson distribution, structure factors, cleavage, and the plausible modes of packing and hydrogen bonding, we feel that the approximate structure shown in Figure 9 is with high probability fairly close to the correct structure, and that it can serve as the starting point for the precise evaluation of the parameters by the usual refinement procedures. We may state our conclusions more specif- ically as follows. (a) It is hard to see how the conclusion regarding the relative orientation of the two oxygen atoms of the carboxyl group can be wrong. 115 (b) The proposed aDproximate parameters for the oxygen atoms are well supported not only by the agreement between the positions of expected and observed Harker and non-Harker peaks that we suppose to be due to these atoms, but also by the good agreement observed for their interactions with at least one other atom, and the fair agreement ob served with additional atoms. (c) The position of at least one atom in addition to the car- boxyl oxygen atoms is probably established. As we have been able to devise a plausible structure only by identifying this atom as C..:rrr in the same molecule, this identification appears very probable. (d) Evidence from structure factors indicates that the general orientation of the molecule in space cannot be radically different from that proposed. (e) The simultaneous satisfaction of the more obvious require- ments of cleavage, hydrogen bonding, and packing that occurred when a structure conforming to all of the above restrictions was constructed is impressive and would seem to be very far from accidental. (f) Comparisons of observed and calculated structure factors and of observed and calculated Patterson distributions showed promising systematic tendencies toward agreement and revealed no disagreement that appears impossible of resolution. The work may be carried on from its present point with considerable confidence in the intensity data, which I believe are as good as can be expected with the use of the visual method, and probably as good as any that 116 have been obtained by this method in this laboratory. The present investigation has also shown that the complete three-dimensional representation of the Patterson function can be an extremely useful tool in the determination of crystal structures. We have also shown that the calculation of the function by punched card methods does not require an excessive amount of labor. I would expect the three-dimensional Patterson method to be very useful in the determination of the structure of dt-serine. There is some question as to whether the modification function that we used materially aided the interpretation of the Patterson fu.i.,ction. The presence of a negative region associated with each peak has complicated the interpretation considerably. The integrated amplitude of a group of un- resolved or partially resolved peaks is difficu..lt to interpret in terms of the number of interatomic interactions involved. Preparations are now being made for a new Patterson calculation in which an artificial temperattITe factor may be used instead of the modification function described above. 16. Acknowledgements I am very deeply indebted to Dr. Robert B. Corey for his generous and valuable contributions of advice, encouragement, and friendly cooperation. I am also very grateful to Professor Schomaker for his collaboration in the calculation and interpretation of the three-dimensional Patterson distribution, and for many valuable discussions. I believe that all crystal structure workers are indebted to him for suggesting the use of a three-dimensional Patterson distribution and for demonstrating the feasibility of calculating such a distribution by punched card methods. 117 I wish to thank Dr. Werner Nowacki for taking over the problem at its present stage. I am grateful to Professor Carl Niemann arid l/;r. H. B. VJilne for making available to us samples of threonine for this work, and to Professor J. H. Sturdivant for his cooperation and suggestions with regard to the use of the facilities of the x-ray laboratory and of the machine shops of the Department. I wish to express my thanks for the large contributions made by Miss Lillian Casler in the prepar ation of gnomonic projection~ in the calculation of Lorentz and polarization factors,in the preparation of structure factor maps, and in assisting with a l arge amount of other calculation work. I am indebted to Miss J ean Dewey for considerable assistance of this kind, particularly in the calculation of structure factors, to tliss Maryellen Kates for preparation of some of the figures and for other graphical work, and to Miss Virginia Berry for assistance with some of the punched card work. I also wish to thank H~inz G. Pfeiffer for assist- ance in the calibration of one of the cameras. As also in connection with my work on other topics, I am grateful to Professor Linus Pauling for his valuable suggestions. * * * * The cost of this work was supported in part by a grant made by the National Foundation for Infantile Paralysis to the California Institute of Technology. I also wish to acknowledge the financial aid given to me by the National Research Council, of which I have been a Predoctoral Fellow since March 1946. 118 References 1. S. B. Schryuer and H. W. Buston, Proc. Roy. Soc. London, B92, 476 (1925-26). 2. R. H. McCoy, C. E. Meyer, and W. C. Rose, I... Biol, Chem, 112, 283 (1935-36). """""' 3. c. E. Meyer and w. C. Rose, L_ Biol, Chem, fil, 723 (1936). 4. H. D. West and H. E. Carter, L_ Biol, Chem, 119, 103, (1937). 5. H. D. West and H. E. Carter, .:L., Biol. Chem, ~1,2, 109, (1937). 6. H. D. West and H. E. Carter, L, Biol. Chem, ~ ' 611, (1937-38). 7. H. B. Milne, unpublished work. 8. E. J. Cohn and J. T. Edsall, "Proteins, Amino Acids, and Peptides". ACS Monograph No. 90. New York: Reinhold Publishing Corp., 1943. pp 358, 368. 9. Erwin Brand, Ann. New York Acad, Sci. fl (:Art.2), 187 (1946). 10. G. Albrecht, G. W. Schnakenberg, M. S. Dunn, and J. D. McCullough, L, Phys, Chem, 47, ...... 24 (1943) . 11. C. L. A. Schmido, "The Chemistry of Amino Acids and Proteins", Second Edition. Springfield, Ill.: Charles Thomas, 1944. p. 1177. 12. Internationale 'l'abellen zur Bestimmung von Y.ristallstructuren. Berlin: Gebrtider Borntraeger, 1935. a. Vol.II, p. 584 b. Vol. I, p. 120 13. J. J. deLange, J. M. Robertson, and I. Woodward, Proc, Roy. Soc, (London), ............... AJ..71, 398 (1939) . 14. W. fl. Zachariasen, "Theory of X-Ray Diffraction in Crystals". New York: John Wiley and Sons, 1945. p . 108. 15. G. Tunell, Am. Mineralogist~' 448 (1939). 16. Herman E. Seemann, private communication. ~ 17. W. H. Zachariasen, 2Ih cit., p. 110 18. G. Albrecht and R. B. Corey, L, Am. Chem, Soc. 61, 1087 (1939) . ..--; 119 References (continued) z. Krist,~' 517 (1935 ). 19. A. L. Patterson, 20. David Harker, 21. P. A. Schaffer, Jr., Verner Schomaker, and Linus Pauling, Phys, ,___ 14, 648, 659 (1946 ). 22. D. M. Crowfoot and B. W. Rogers - I.ow, a Monograph on penicillin, to be published. 23. V. Schomaker, unpublished investigation. 24. G. A. Campbell and R. M. Foster, "Fourier Integrals for Practical Applications". Bell Telephone System Monograph B-584, 1931. p. 39. See also E. C. Titchmarsh, "Introduction to the Theory of Fourier Integrals", Oxford, 19.37, p. 51. (Note that the form of the theorem given by these authors is different from that given in the text of this thesis; the form given here is obtained by a change of variables.) 25. Jurg Waser, Doctoral Thesis, California Institute of Technology, 1944, p. 70; Jurg Waser and Verner Schomaker, unpublished work. 26. L. L. van Rei jen, Physica 9, 461 (1942). 27. H. A. Levy and R. B. Corey, L. Am. Chem. Soc,~' 2095 (1941). L. Chem, Phys, b 381 (1936). - 120 L. Chem, SUMMARY An attempt ha s been made to prepare antibodies to his tamine in vitro by partially denaturing serum globulin in the presence of histamine. Controlled tests with ileic strips showed, however, that this attempt was unsucce ssful. A study was made of conditions suitable for the growth of large crystals of al11i'Ilinum orthophosphate. Crystals up to 8 mm. in length were prepared and the method that was tested appeared to be promising for the growth of larger crystals, but the work was abandoned in favor of war work of greater urgency. The space group and lattice constants of crystals of dl-serine wer e redetermined. The results of this study confirmed those of previous investigators. A more comprehensive x-ray study of )-threonine wa·s undertaken. The space group and lattice constants were determined and intensity data were obtained. An analysis of the intensity data by means of a three- dimensional representation of the Patterson function led to an approximate crystal structure for 1-threonine. Observed and calculated structure factors for this structure show promising general agreement. the refinement of this structure is in pro~ess. 121 Work toward APPENDIX THREE-DIMENSIONAL REPRESENTATION OF PATTERSON FUNCTION FOR l-THREONINE On the following pages are given eleven sections of the threedimensional Patterson distribution for /-threonine. These are given at intervals of 0.05 in the ~-parameter and cover the range~= 0.0 to J:l = 0.5 inclusive. On each section the origin of E and y coordinates is taken in the lower left hand corner. The coordinate y runs to the right from O. 0 to O. 5, and the coordinate y runs upward from O. 0 to O. 5. eleven sections constitute an octant of the Patterson cell. The The other octants are equivalent to this one by mirror planes at the surfaces, twofold axes at the edges , and centers of symmetry at the corners of the octant. If a parameter is given a negative value in the text, its sign may be changed; if its value is greater than 0.5, it may be subtracted from 1.0. Also given are the sections y = O, y = 0.5, ~ = O, and y = o. 5. The unit of amplitude is that which resulted from arbitrary scaling of the coefficients to magnitudes convenient for the punched card work. In terms of this unit the contour interval is 50. Zero and posi- tive contours are indicat ed by solid lines, negative contours are indicated by dashed lines. Minus signs are placed in some shallow negative r egions in order to avoid confusion. Expected positions of Patterson peaks for the probable approximate structure are plotted in red. Red dots indicate that the Ji 122 parameters of the peaks are eq_ual to those of the respective sections; red circles indicate that t~ey are greater by about 0.025 (i.e. half way to the next sectio~. All of these sections are plotted to a scale of four centimeters per in.gstrom unit. 123 PROPOSITIONS 1. (a) In the assignment of space groups to crystals prepared from racemic mixtures of enantiomorphic compounds, care should be exercised in rejecting space groups applicable to enantiomorphic structures, as the separation of isomers on crystallization from a solution of the racemic mixture is not a rare occurrence. (b) rnix-f-vre Any indication that an enantfomorphic ea:rer .m crystal- lizes to a structure containing mirror planes should be looked upon with considerabl e suspicion unless additional molecular or ionic species are present. (c) The erroneous assignment of the space gToup c:v- - Pmm to threonine by Albrecht and coworkers1 is an example of non-recognition of these principles. (d) The validity of the space groups reported by .Albrecht and coworkers1 for dl-methionine (c: - P2, Z = 4) and dl-ve.line (C~ - P21 , Z = 4) should be checked by examination of crystals prepared from the individual isomers. It has been proposed 2 that the critical tension (tensile strength) of a liquid is determined by the size of the smallest cavity in which vapor can exist in equilibrium with the liquid, and that such a cavity has a diameter equal to the average distance between molecules of the vapor at the vapor pressure of the liquid. Although this hypothesis appears to con-:i form to a (rather uncertain) experimental observation.., that the critical tension rises with the tempe rature to a maximum and then decreases, the assumptions involved in the hypothesis are not necessarily justified •. 124 Even if dust particles or other nuclei are absent and if absorption of high energy radiation is excluded as a cause of rupture, the conditions for the incipient rupture of a liquid must be treated by statistical methods without undue regard for the equilibrium concepts of surface tension and vapor pressure. 3. (a) A striking feature of the phenomenon of superconductivity is its apparent absence in the Group VIII and nearby transition elements and in the rare earth elements~ On the basis of the known effects of external magnetic fields on superconductors and theoretical limitations on internal magnetic fields I propose that perturbations due to the resultant magnetic moments of unfilled non-bonding atomic orbitals5 may inhibit superconductivity in these elements. (b) The method of valence-bond wave functions should be applied to the investigation of the electronic structures of metals •. 4. (a) In the visual method of estimating the intensities of x-ray reflections with multiple-film sets, a convenient scale for intensity interpolation is a logarithmic one, with the film factor taken as the base of logarithms. (b) A routine procedure for mea~uring the film factor should ' be developed and applied to the testing of all x-ray film used in intensity work. 5. A practical method for placing observed structure factors on the correct absolute sea.le is proposed. In this method, the structure factors 125 are so scaled that they satisfy the where fl--= The sunnnation on the right is taken over all of the atoms in the unit cell. fhe primed form fa.ctor contains an approxim13,te temperature factor, which is assumed to be isotropic. ~ The treatment may be modified to take account of anisotropy in the temperature factor if necessary. 6. (a) In the estimation of viscosities of concentrated solutions of nitrocelluloses and. other high polymers in volatile solvents with a capillary-type viscometer, errors resulting from evaporation of solvent may be practically eliminated by use of a viscometer which can be attached to the container in which the solution is prepared. can be used in this way has been described. (b) A viscometer which 6 In the argentometric titration of chloride with fluorescein or eosin as indicator, the silver chloride suspension 198-Y be stabilized near the end point by the addition of a small amount of a suitable wetting agent, such as Aerosol OT. 7. In the treatment of quantum mechanical problems by the per- turbation theory7, it is sometimes found that the first-order treatment fails to remove the degeneracy of a level; it has been recognized g that caution should be exercised in proceeding with the second-order treatment in this case. If by the first-order treatment zero-order wave functions 126 can be found for which all non-diagonal matrix elements of the perturbation vanish, I propose that a second-order secular equation where I' HI( = M1. j,t_ I LI 117"r:J_ !-1~1A- p(_ w .-1-t.. - J wo£ be used to obtain the energy correctio.ns '.: to second order. 8. Martin and Synge 9 have proposed a theory of chromatography for linear absorption isotherms which takes into account the effects of diffusion and non-attainment of equilibrium by a treatment analogous to the treatment. of fractionating columns with the concept of theoretical plates. This treatment ma.y be generalized to non-lin~ar isotherms and arbitrary initial adsorbate distribution by a method simila,r to that of DeVault10 to obtain t~e differential equation (~'):),,- + i {~)~ + [ I( + _._{'(c)) (~~_,, = 0 in which his analogous to the HETP of a fractionating column and other symbols are those used by DeVault. 9. (a) The three-dimensional representation of the Patterson function shows great promise of being a very useful tool in the determination of crystal structures of moderate difficulty. (b) The inner symmetry of the Patterson distribution should be systematized at least for the more commonly encountered space groups. (c) I propose that the three-dimensional Patterson function be applied to the determination of the crystal structure of &-serine at the earliest opportunity. 127 10. developed (a) ll A paramagnetic oxygen analyzer which has been recently depends for its operation on the transport of heat from a wire by magnetic convection in a non-homogeneous magnetic field. It should be pointed out that the response of this analyzer probably depends appreciably on factors other than the paramagnetic snsceptib:tlity of the gas mixture, among the most important of which are the viscosity and the heat capacity of the mixture. This analyzer should not be expected to have the general applicability of the Pauling Oxygen Meter. (b) A modification of the Pauling Oxygen Meter in which the test body is brought to a null position by rotating the fork on which the fiber supporting the test body is mounted should be tested. An instrument constructed in this way should give a strictly linear response and should. be capable of high precision. ' It may be an especially appropriate instrument for determining the magnetic susceptibilities of diamagnetic gases. 11. I propose that the method used by Stokes 12 for the preparation of a composite lens for the fiy 1 s eye camera can be considerably simplified. A possible simplification would be to make a direct impression of a sheet of plastic against an array of ball bearings, fill the depressions in the plastic sheet with a liquid of higher index of refraction, and cover the composite of liquid lenses with a glass plate. A hexagonal array of be ball bearings would lasier to obtain than a suitable square array and may give a composite lens almost as useful. 128 References l. G. Albrecht, G. W. Schnakenberg, M. S. Dunn, and J. D. McCullough, 2. Allen King, ~ - R,ev. ~' 38 (1944). l• ~ - ~ !±L 24 (1943). D. P. Shoemaker, Thesis, Reed College, 1942. p. 39. E. F. :Burton, :a:. G. Smith, and J. o. Wilhelm, 11 :Phenomena at the Reinhol~ Publishing Temperature of Lig:u,id Helium 11 • Corp., 1940. New York: p.92. 5. Linus Pauling, ~ Rev. fil!., 899 (1938) 6. D. P. Shoemaker, Earl Hoerger, R. M. Noyes, and R.H. Blaker, ~ - ~ - li, 131 (1947). Jr., Linus Pauling and E. B. Wilson,,. 11 lntroduction to ~tum Mechanics 11 • New York: McGraw-Hill, 1935. Chapter VI. 8. Jurg Waser, Doctoral Thesis, California Institute of Technology, 1944. p. 106 .. A. J. P. Martin and R. L. M. Synge, l3iochem. i.,• .:i;i., 1358 (1941). 10. Don DeVault, i_. A!_. Che~. Sg,c. §!l. 533 (1943). 11. F. K'ia<4er, £. [vrowski_) a11d T. v: Wolff, A111ew- C/..em . 0L// "/'1-i (Ir-'!!). 12. A. R. Stokes, froc. ~ - Soc. .2[, 306 (1946). 129