I. Electromotive Force Measurements in Liquid Ammonia. II. Determination of the Structure of Crystals and Molecules by the Diffraction of X-Rays and Electrons and by Magnetic Measurements Citation Elliott, Norman (1938) I. Electromotive Force Measurements in Liquid Ammonia. II. Determination of the Structure of Crystals and Molecules by the Diffraction of X-Rays and Electrons and by Magnetic Measurements. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/b5pk-tj96. https://resolver.caltech.edu/CaltechTHESIS:12022024-183107813 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Pauling, Linus (advisor) Yost, Don M. (advisor) Thesis Committee: Unknown, Unknown Defense Date: 1 January 1938 Record Number: CaltechTHESIS:12022024-183107813 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:12022024-183107813 DOI: 10.7907/b5pk-tj96 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16887 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 10 Dec 2024 23:56 Last Modified: 11 Dec 2024 00:16 Thesis Files PDF - Final Version See Usage Policy. 21MB Repository Staff Only: item control page

I. II. ELECTROMCJrIVE FOOCE MEASUREMENTS IN LI'-LUID AMMONIA DErERMINATION ClF THE STRUCTURE OF CRYSTALS AND MO~ULES BY THE DIFFRACTION OF X-mA.YS AND ELECTRONS AND BY MAGNEr IC MEASUREMmT S 'lhesis by NORMAN ELLIC1rT In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technolog Pasadena, Cal if ornia 1938 Tab le Contents of page Part 1 ........ 1 ................... ......................... . 5 Electro~:1 otive force meas urements in li qu id ammonia • Pa rt 2 Int rodu~tion , Section 1 Section 2 " ••••••••••••••• t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ························~························ 10 11 ···············~································· 14 Se ct ion 4 , . , , . , , . , . , , . , , , , , . , .. , , , , . , , . , . , , . , . , , ... , ..... , 30 Section 5 , , . , , . , . , , . , , . , , , . , , , .. . , . , . , , . , .. , ........ .. , . , , 35 ·······························•'···············j. Section 7 ....................................... ........... 38 Section 8 .................. ............................. . , 63 Stua:rnfary , , , , • , • , •• , • , •• , • , , ••• , , , , •• , ••••••• , ••• , ••• , •••• , • 64 Section 3 Section 6 44 The Potentials of Cells in Liquid Ammonia. The Thermodynamic Constants of the Ammino Zinc Chlorides and of Zinc Chloride. By Norman Elliott and Don M. Yost. Page 1057. "Due to an arithmetical error ZnCl.-IONHa was stated to be the solid phase in the cell. Actually the solid phase was ZnCI,·6NH 3, and equations (1) to (5) must be modified accordingly. This change affects the thermodynamic constants only and not thee. m. f.'s." Page 1059 . E q (6), for t>. F29s = - 2200 cal. read t>.. F298 = - 6900 Cal. The fugacity of NH 3(g) was taken as 18.2 atm. Page 1060. In line 5 of paragraph 2 read " -20,420 cal. " for" -11,600 cal." Also substitute new Table II. TABLE II THE THERMOD YNAMIC CONSTANTS OF THE AMMINO ZINC CHLORIDES AND ZINC CHLORIDE Substance ZnCl,-!ONH, ZnCl2·GNH 3 t>..F,9, cal. -151,030 -142,290 - 323,000 t>. H 2°9s cal. -250,840 187.3 S,°ss cal./deg. 117 .6 Substance ZnCI,·2NH 3 -119,860 t>. F~ 8 cal. t>..H298 cal. -161 ,300 63.6 S 29 s cal. / deg. ZnC1 2 ·NH3 - 102,710 - 130,910 34.5 ZnCl 2 ·4NHa -132,230 -206,880 91. 8 ZnCI. 87,800 99,550 23.7 Page 1059, second line, second paragraph of section entitled "Free E nergies, etc. ," for - 59,500 ± 500 cal. read - 58,400 ± 500 cal. We acknowledge t he kindness of Mr. C. S. Garner in calling attention to these errors and for assistance in making the corrections."-DoN M. YosT. [CONTRIBUTION FROM GATES CHEMICAL LABORATORY, CALIFORNIA INSTITUTE OF TECHNOLOGY, No. 394 ] The Potentials of Cells in Liquid Ammonia Solutions. The Thermodynamic Constants of the Ammino Zinc Chlorides and of Zinc, Chloride BY NORMAN ELLIOTT AND DON M. YOST · Introduction Liquid ammonia has long been known to be an ionizing solvent, and the nature of salt solutions in it has received the careful attention of Franklin, Kraus and other investigators. 1 The few electrode potentials in this solvent which have been investigated were complicated by liquid potentials or were not reversible. 2 A cell free from these objections and one which is also convenient as a reference electrode is highly desirable, especially if the electromotive series in liquid am- mania is to have more, than a qualitative basis. 3 Inasmuch as the thermodynamic constants of thallium amalgams and thallous chloride 4 are accurately known, and since the latter substance is not very soluble in liquid ammonia at 25°, the thallium amalgam-thallous chloride couple was chosen as one half-cell. Moreover, the solid phase consists of thallous chloride alone and not an ammoniated salt. 6 As the other half-cell the zinc amalgam-decammino zinc chloride couple was selected, since the l;l-Ctivities of the amalgams" (lJ Cf. Kraus, "The Properties of Electrically Conducting Systems," A. C. S. Monogra ph, The Chemical Catalog Co., New York, 1922. An excellent review of liquid ammonia systems is given by Fernelius a nd Johnston, J . Chem. Ed. , 7, 2600 (1930), el ante. (2) Cf. e. g. , Johnson and Wilsmore, Trans. Faraday Soc., 3, 77 (Hl07); Costeanu , ComPI. rend., 1911, 778 (1932). (3) Bergstrom, THIS JouRNAL, 47, 1503 (1925); Kraus, Tran s. Am. E lectrochem. Soc ,, 411, 175 (1924). (4) Lewis and Randall. "Thermodyna mics," McGraw-Hill Book Co. , New York , 1923 , pp. 93, 267, 607. (5) S tollenwerk and Biltz, 7.. anorg. Chem ., 119, 97 (1921). (6) Pearce and Eversole, J. Ph ys. Chem., 32, 200 (1 928). i NORM AN ELLI OT T AN IJ !J ON ::. r__ YOST JOGS are known, and th e salt is only slightly soluble in liquid a mmonia. Ammonium chloride was chose11 as t he electrolyte. T he cel ls measured were found to have constant and reprod ucible electromoti ve forces a t 25 °. Attempts were made to construct a hydrogen electrode operating at 25 ° in liquid a mmonia solut ions of ammonium chloride. A potential of about 0.42 volt against a 0.0265 N thallium amalgam was obtained , but t he experimental difficult ies were such that its use as a reference electrode did not prove convenient. The a mmonium ion in this case corresponds, of course, to the hydrogen ion of the aqueous system. B A Zi nc Chloride.-- P ure zin c chlor ide was fu sed , a nd, soon a ff c r snl id ifyin~. :i. porti on was plnn·d 0 11 t he zin c a malga 111 i11 f he CC' !!. Oxyge n a nd moistu r . we re ca ref11 ll y exclud ed . Ammonium Chloride. - Th e p1ircs t nrn.tcri a l ob ta inab le was rcsuhlimcd a nd stored in a ,·ac11u111 desicca tor. T he ce ll used is shown in Fi g. l. T he a uxiliary vessel B was used to fi ll lhe cell proper, A, wit h the liquid a mmon ia solut ion of a m moniu m chloride. After fi lling a nd sealing, t he cells were placed in a th erm ostat at 25.00 ± 0.0 1 °. Results of the Experiments Since th e solubility of thallous chloride in li quid ammonia was not known, a series of measurements using the method of H unt and Boncyk 7 were made. T he results of three representati ve experiments gave 0.0260, 0.0261 and 0.0257 mole per 1000 g. of liquid ammonia at 25.0°. In T able I are present ed t he results of t he electromotive force measurements. F un ctions of the activities of thallium a nd zinc in their amalgams were plotted , and the values fo r the con cen trations given in the table were obtained from the plot. The reference stat es fo r these activit ies are infini tely dilute solutions. Each cell required about four hours to att ain equilibrium a nd after a ttaining it, the electromotive force remained constant for days. The thallium electrode was always positive. T he chemical reaction taking place in the cell is the following Zn(::unalg. o-,) + 2T1Cl(s) + lONHs( l) = Zn Cl, · lON H:,(s) + '. ffl(amal:<. r, 1) and the expression for t he electromotive force of the cell is E = E 0.029575 log ( a ;/o-,o-: 0 ) (2) where a 2 and a 1 are t he activities of zinc a nd t hallium, respectively, in their amalgams at the mole frac tions N 2 a nd N i, and a :i is the activit y of t he liquid a mmonia. Since t he concentrations of ammonium chloride used were small, as were also those of thallous chl oride and zinc chloride, a 3 was taken equal t o unity. In doing this, t he standard sta te of li quid ammonia at 25 ° is assumed t o be t hat state in which the total pressure is t he vapor pressure of the liquid, and not one atmosphere. T he correction to one atmosphere is probably small but cannot be made at t his time since the molal volumes involved are not all known. The values of E 0 ' given in the tabl e are fo r the potential of the hypothetical cell 0 Fig. 1. Preparation of Materials and Experimental Procedure Ammonia.- The gas from a t a nk was passed over solid sodium iiydroxide a nd met all ic sodi um and t hen condensed direc tly into the cell . Thallous Chloride.- T he met al of com merce was di ssolved in hot dilute nitric acid , an d the result ing mixture was t hen fil tered . After t reating t he fi ltrat e with hydrogen sulfide, it was again fi ltered a nd then boiled. To this solu tion was ad ded an excess of hydrochloric ac id lo precipitate t hallous chlori de. Afte r filtering, a nd washi ng repeatedly, the resul t ing precipitate was d ried at 120 ° for four hours and then stored in a brown glass bot t le. Thallium.- - A sa t urat ed sol ut ion of tha llous chloride was electrolyze d be twee n plat inum elec trodes at 100 °. T he resulting spongy metal was fu sed a t 300 ° in a porcela in boat over wh ich was passed a s tream of dry h ydrogen . T he metal was then transferred to a tube con taining carefull y purified mercury. All operations involving t he amalgams were carried out in an a tmosphere of dry hydrogen . Zinc.- Th e amalgams were prepar ed as above wi t h Purified elec trolytic zinc. ( I) ' - Zn (amalg. a,= l), Zn Cl, ·lONH,(s) , N H,Cl(in N H ,( l) .J) , T lCl(s), T l(a malg. o- 1 = 1); E 0 ' = 0.9016 volt (:1) (7 ) !fo n t and B oncyk , THI S J OURNAL, GG , 3528 (1933) . May, 1!)34 105!) THERMODYNAMIC CONSTANTS OF SOME ZINC CHLORIDES TABLE I RESULTS OF TH E ELECTROMOTIVE FORCE :MEASUREMENTS Temp., oc. 25 Mole fraction Tl N, 0.0265 .0265 .0265 .0265 .0265 .428 satd. .0913 Activity Tl Mole fraction Zn Activity Zn a, N, 0.0369 .0369 .0369 .0369 .0369 3.31G 0.2i"i0 0.0289 .0289 .0289 .0289 .0301 .0289 .0289 a, Formality NH,Cl, f E.m.f. observed, E, volt Standard potential E 0 ', volt Stau<lar<l potential E 0 , volt 0 .0255 .0255 .0255 .0255 .02G3 .0255 .0255 0.0380 .0725 .0573 .0379 .0648 .0306 .084 0.9392 0.9016 .9396 .9020 .9395 .9019 .9392 .9016 .9393 . 9013 .8231 .9011 .8900 .9015 Mean .9016 .9680 .9470 0.8293 .8297 .8296 .8293 .8290 .8288 .8292 .829~ 1. 75 .0265 .0301 18.50 .0265 .0301 a2 = 0.04819 for a saturated Zn amalgam . . 0648 .0648 Equation 2 shows that the observed electromotive forces E should be practically independent of the concentration of ammonium chloride when the solutions are dilute and, as the table shows, this was found to be the case. The effect of varying the concentrations of thallium and zinc in the amalgams is also that predicted by equation 2. This is evident from the constancy of the E 0' values. The cell is, therefore, reversible. In the last column of the table are given the standard potentials E 0 for the cell cells could be compared with either of the two latter, and thus the further use of the troublesome gas cell could be avoided. Direct use of the gas cell could be avoided entirely if the activities and free energies of ammonium chloride solutions in liquid ammonia were known. It is planned to determine these quantities later. Free Energies and Heat Contents of the Ammino Zinc Chlorides and Zinc Chloride.The standard free energy change accompanying reaction (5) is given by t:,,F298 = - NE° F and is found to be - 38,238 cal. The free energies of formation of thallous chloride and of liquid ammonia are -44,164 cal. and -2570 cal., respectively, at 25 °. On combining these values the free energy of formation of ZnCb· lONH 3 (s) at 25 ° becomes -152,270 cal. The change in heat content accompanying reaction (5) is -59,500 ± 500 cal. and it was calculated from the temperature coefficient of one of the cells, -0.00121 volt/deg., and the he~ts of solution of thallium 4 and zinc 6 in their amalgams. The heats of formation 8 of thallous chloride and liquid ammonia are 48,700 cal. and 15,840 cal., respectively. The heat of formation of ZnCb· 10NH3 from the elements becomes, therefore, 315,360 cal., and this is in satisfactory agreement with the less reliable value 327,400 cal. given in the "International Critical Tables." Sufficient data are available for calculating the free energies of the other four ammoniated zinc chlorides. From the data given in "International Critical Tables" 8•9 the following equations have been derived. Zn(s), ZnCld0NH,(s), NH,Cl(in NH,(l), /), TICl(s), Tl(s); E 0 = 0.8293 volt (4) for which the chemical reaction is Zn(s) + 2TICI(s) + 10NH3(l) = 2Tl(s) + ZnCl,-l0NH,( s) (5) and the total pressure is the vapor pressure of the liquid ammonia at 25°. In arriving at the values of E 0, account was taken of the fact that the potential of pure thallium is higher than that of the saturated amalgams by 0.0025 volt. 4 The solid phase of the saturated amalgam consists of some mercury dissolved in the thallium. Discussion It appears from the results of the measurements of the cell here described that either half-cell could be used as a standard reference electrode. In case very refined measurements were undertaken, account would have to be taken of the appreciable solubility of thallous chloride, if that half-cell were used. If the solubility of the decammino zinc chloride proves to be of the same order of magnitude as calomel or silver chloride in water, then the zinc half-cell would be superior as a reference electrode. If the hydrogen electrode were measured against the thallium or zinc electrode, then all other half- ZnClz-l0NH,(s) = ZnCb·6NH 3(s) + 4NH 3(g) t,.F7.a = -2200 cal. t,.H = 28,390 cal. (6) (8) "International Critical Tables," Vol. V, pp. 184, 178, 185. (9) "Internatioual Critical Tables," Vol. VII, p. 252. 3 1060 NORMAN ELLIOTT AND DON M. YOST ZnCl,•6NH,(s) = ZnCl,·4NH,(s) + 2NH,(g) t:.Ffes = 2240 cal. t:.H = 22,080 cal. (7) ZnCl,.4NH 3(s) = ZnCl,·2NH,(s) + 2NH,(g) t:.Ff98 = 4550 cal. t:.11 = 23,700 cal. (8) ZnCh•2NH,(s) = ZnCI.-NH 3(s) + NH,(g) :c,.Ffes = 13,240 cal. t:.11 = l\J,450 cal. (!I) The heat of the reaction ZnCkNHa(s) = ZnCb(s) + NH 3(g) has not been determined accurately, and the value given for it appears to Vol. 56 calculations the free energy of formation of ammonia gas at 25° was taken to be -3910 cal.4 and the standard virtual entropies at 25 ° of zinc4 chloride, 11 nitrogen 12 and hydrogen 13 to be 9.83, 5:3.31, 45.79 and 31.23 cal./deg., respectively. The results are presented in Table II. The free energy and heat content values are referred to the elements in their standard states of 25° and one atmosphere. TABLE II THI, THERMODYNAMIC CONSTANTS OF THE AMMIN'O ZINC CHLOJUDES .A.ND ZINC CHLORIDE AT 25° ZnCh -NH, ZnCl.-l0NH, ZnCI,-6NHa ZnCh-4NHa ZnCI,-2NH, Substance -152,270 -138,830 t:.F,~s cal. -314,200 -242,040 t:.H~s cal. 217.4 134 . 8 S2~s cal./deg. S~ 8 is the standard virtual entropy. -128,770 -198,070 109 ~6 be a rough estimate. 10 The more reliable value of -11,600 cal. was obtained by combining equations (6) to (9) with the heat of formation of zinc chloride8 and that of ZnCl2· lONHa(s) derived above. In making the calculation the heat of formation of ammonia gas was taken to be 10,940 cal. 8 The "International Critical Tables" gives an experimentally determined dissociation pressure for the monoammino zinc chloride at only one temperature. This was used in connection with the heat of dissociation just given to calculate the free energy change at 25 °. The following equation expresses the results of the calculations. ZnCJ,NH,(s) = ZnCl,(s) + NH,(g) (10) P,es. 1 = 0.0088 atm. t:.H = 11,590 cal. t:.Ffes = 7350 cal. It is now possible to construct a table of the thermodynamic constants for all of the ammino zinc chlorides and zinc chloride. In making the (10) Biltz and Messerknecht, Z. physik. Chem., 129, 161 (1923). -116,400 -152,480 81.5 - 99,250 -112,080 53.0 ZnCI, -87,990 -99,550 1 24.3 Summary With liquid ammonia as the solvent, the cells Zn (amalgam N 2), ZnCld0NH3 (s), NH4Cl (in NHa(l),f), TlCl(s), Tl (amalgam N1) were measured at 25 °. The cells are reversible and give constant and reproducible electromotive forces. When the zinc;and thallium are present in the amalgams at un~t activity the standard potential is E2i~ = 0.9016 volt. When zinc and thallium are present as the pure metals the standard potential is E2is = 0.8293 volt. From the cell potential and its temperature coefficient, together with the results of other investigators, the free energies, heat contents and virtual entropies for five ammoniated zinc chlorides and zinc chloride itself were calculated and are presented in Table II. PASADENA, CALIF. RECEIVED JANUARY 26, HJ34 (11) Giauque and Overstreet, THIS JOURNAL, 64, 1731 (1932). (12) Giauque and Clayton, ibid., 65, 4875 (1933) . (13) Giauque, ibid., 112 , 4816 (1930). Part 2 Introduction In the last few ye a rs the electron-pair bond theory first sug 6 ested by Lewis has receiv-ed much attention. Pauling 1 With the aid of quantum mechanics and other investigators have extended this theory to a quantitative state whereby a large variety of data concerning the nature of molecules in gas, solid, or solution phases can be correlated. An early a.pplication 2 of the covalent bond theory in its present fonn was made to the study of magnetic moments of complex ions. Two inde- pendent results coming from this work are the relation between ,ralence and magnetic moment, and the relation between spatial configuration of a. mole- cule or complex ion and its magnetic moment. For some tL1e an interesting subject to chemists has be ·:m the investigation of complex compounds in which an element appears in two different valence states, The prussian blues are perhaps the best knovm examples of this phe- nomenon. Such compound s usually po ssess intense colors, and the suggestion has been m~de that in these substances the central atoms do not h ave their normal valences but exist in an intermediate state, 1 n some c a ses such as that of annnonium hexabromo-hypo-antirnonate, (NH 4 ) 4 Sb2Br12, and cesium aurous a.uric chloride, Cs 2 Au2 Cl5, this theory may be simply tested. If the antimony or the gold is in a valence state intennediate between the norme.l ones the compounds will contain impaired electrons and be paramagnetic, If the atoms are in nonnal valence states, however, diamagnetism is to be expected, A measurement of magnetic susceptibility, then,would lead to an unequivocal decision regarding the theory. The results of such experiments are stated in the first and second sections which follow. When the centra l atom of a. complex ion is dia.rnagnetic in both the covalent and ionic sta tes a measurement of mag netic susceptibility le a ds to no information about the spatial configuration of the complex. The best means for obtr.ining this knowledge would be by a n x-ray i nvestiga tio n of single cry- sta ls of the substa nce. Unfortunately t here a re very many synthetic inorganic compounds -which can only be prepared in u micro-crystalline state. :x:-ray study of these must necessarily be by t he powder method. An In case the crysta l system is sufficiently si:'1ple, however, and the number of atomic parameters small this technique may give reliable results. Cesiu..rn aurous auric chloride and cesium argentous auric chloride have tv-nce been studied in this ma..'t1Iler, and the final structure determina tion is entirely satisfa ctory. The results of the experiments are given in the second and third sections. The theory of the additivity of covale nt radii adva nced by Pauling and Huggins 3 correlate d the data derived from x-ray and electron diffra ction investigations of covalently bonded molecules and complex ions. J. he theory Such things as the effect on bond distance is by no means fully developed. of ionic character, fonnal charge, a nd the perturbation due to nei 6 hboring atoms need thorough investigation. A criticism4 of the theory has been made indirectly that similar results may be achieved •with ionic radii even in cova le nt compounds. The report of an investigation of t he "manganese anomaly" given in the fourth section of this series definitely refutes the criticism. An interesting relation between magnetic moment and intera.tomic disbm ce is also observed. The technical and theoretic nl advancement in the the ory of the interaction of x-rays and crystals has made it possible to obtain now more information concerning t he structure of molecules than could be found only a few yeBr s ago. Intern t omi c di stances de pendent upon a parame t er determina tion ma y be fixed with an error of less than 0.004 J{. in f avorable circumstances. .Lt is becoming incre asingly important therefore in connection ·with the study of molecul a r structure to reinvestigate many simple crysta ls. To mention just two examples, it would be very interesting to redetermine accurately the 0-0 dista nce in the pe:Y-oxides and the C::C distance in c a lcium a cetylid e. 6 Further research on the crystal structures of calcite and sodium nitrate has been carried out in these laboratories. 1 nvestigation of crysta l struc- ture by means of Laue photographs is perhaps the most informati<re of all x-ray methods for three reasons: the Laue photograph shows reflections from planes with large indices; different planes with the same interplanar distance and scattering x-rays of the same wave length may be compared, resulting in the elimination of all variables in the intensity formula except the fonn and scattering factors; the development of integrating photometers by Astbury 5 and Robinson 6 allows very accurate determinations of the intensities of reflections on Laue photographs to be made. The first results of a study in which advantage has been taken of all these things is reported in the fifth section. Research by means of x-rays on crystals containing complex ions or covalently bonded molecules has shovm that these substances do indeed have the same groups of atoms ·which appear so often as units in chemical reactions. Until the present tiille it has been more or less assumed th at to a very good approximation the principal binding forces are the covalent bonds between the atoms of the complex. Only recently through the development of the electron diffraction method of determining the structure of gas molecules has it become possible to test this assumption. The investigation of gaseous Se02 given in the sixth section may be compared with the re search on so lid Se02 by McCullough 7 . It is shown that a large change in the type of bonding may sometimes be expected as a substance changes from the cryste.lline to the gaseous state. When it may safely be assumed that a molecule he.s essentially the srune configuration in the gaseous and solid phases, a combined attack on the structural problem by electron diffraction a nd x-ray methods is very useful. Crystals of aluminum chloride are monoclinic an d contain two molecules of Seven parameters must be knovm to determine the 7 complete structure. In gaseous aluminum chloride, however, only three parameters need be found. The electron-diffraction study of the gas mole- cule s has been carried out for a.11 the volatile halides of aluminum. results a.re reported in the seventh section of this disse rtat ion. The They may be readily ap plied to the problera of investigating the solid halides. This is now reduced to a single parameter deternination., the parameter being the ang le of rotation of the Al 2 Cl 6 molecule a round the two-fold axis, if the assumption be made th a t the molecules retain their coni'iguration in .t he crysta ls . The theory of the additivity of r a dii will perhaps prove most useful in the analysis of complex organic compounds by means of x-rays. Crystals of these substances often possess low syrn.'lletry and h f:J.Ve a g reat many molecules in the unit cell. With present technique it is not usually possible to obtain the correct structure from purely space group and intensity theory. Inste ad a model of reasonable dimensions., and one compatible ·with the kno,1m chemistry of the compound in question., must be a ssumed. The problem then becomes one of finding the orientation of the model in the unit cell. In th i s connection physical properties a.nd space group theory are very important. Their con- side ration a.lone often limits the molecule's orientation to quite a narrow range of angles. The investigation of chloral hydrate is interesting in this conn ection. Pronounced cleavage parallel to the (100) face and the presence of a. glide plane in the (001) direction almost certainly fix the chlorine atoms in close-packed layers perpendicular to the b-axis. The dimen- sions obtained for the unit cell a.re in agreement with those c a lcul ated by assuming interatomic distances taken from Pauling a.nd Huggins' table of radii. The data for the space group and unit cell determination are to be found in the final section of this dissertation. REFERENCES 1 and 2. Linus Paul1ng9 J.A..c.s., .51, 1367 (1931) 3. Linus Pauling and M. Le Huggins, Zeit. f-tir Krist. (A) .fil, 205 (1934) 4e W. H. Zachariasen, Zeit. f-ar, Krist. o (A) !Qs 137 (1931) 5. Astbury, Proc. Roy. Soc.e 1239 575 (1929) 60 Robinson, Jour. Sci. Instr. Vol. X, No. 8 (1933) 7. J. D. McCo'l1l.lough, J. ~ C. S., ~• 789 (1937) q Secticin l The magnetic susceptibility of ammonium he::w.bromo-hypoantimonate, (NH 4 ) 2 SbBr5, was determined in order to obtain some infonnation about the valence of antimony in this compound. The substance was prepared by the metl:od of Ephraim and Weinberg 1 • (1) Berichte g, 4450 (1909). It wa.s dried by centrifuging. The product was a deep ble.ck po,Yder, appa rently similar in properties to Well 1 s compound. The determination of the specific magnetic susceptibility by the Golly method led to a v &lue, x = - 0.36 x 10- 6 cgsm,, the substance thus being shown to be diamagnetic. Ammonium hexabromohypoantimonate, therefore, does not contain unpol!fmerized complexes involving a quadrivalent antimony atom, for such complexes would contain an odd nur.i.ber of electrons and hence give rise to strong parama gnetism. It is proba ble that the substance is a double salt containing one triva lent and one quinquivalent antimony a.tom corresponding to the fonnula, (NH 4 ) 4 Sb 111 sbVBrl2• The observed diamagnetism could be made compatible with the presence of quadriva lent antimony by a s suming that the quadri va lent antimony e.toms occur in groups of two j oined by shared electron-pe.ir bonds, Sb: Sb, similar to the group Hg:Hg++ in mercurous sal ts. This, hovrever, seems impi:·obable because the stoichiometric formula, (NH4 ) 2 SbBr 6 , suggests that each antimony atom is surrounded by six bromine atoms which would prevent close a.p preach of the antimony a.toms . /0 JULY, 1934 JOURNAL OF CH E MICAL PHYSICS VOLU M E 2 Printed in U. S. A. The Crystal Structure and Magnetic Susceptibility of Caesium Argentous Auric Chloride, Cs2AgAuCl 6, and Caesium Aurous Auric Chloride, Cs2AuAuCl 6 N ORMAN ELLIOTT, Gates Chemical Laboratory, California Institute of Technology (Received April 30, 1934) The triple salts Cs2AgAuCl 6 and Cs 2AuAuC1 6 have been investigated by means of magnetic susceptibility measurements and x-ra y powder photographs in order to obta in information regarding the general nature of these compounds. Both compounds were found t o be diamagnetic. X-ray powder-photographic dat a lead to a cubic structural unit with a 0 = 5.33A for both cryst als. The observed intensity va lues a re in general agreement with the perovskite structure. Small discrepancies, however, suggest that the atomic arrangement varie5 slightly · from the ideal perovskite structure. The detailed nature of the distortion was not determined. The bearing of these results on the valence type of the substances is discussed. N 1922 Wells1 discovered an interesting series of triple salts when he attempted to prepare a caesium silver auric chloride, Cs5Ag2Au3Ch 7, analogous to Pollard's2 ammonium silver auric chloride, (NH 4) 6Ag2Au 3Cl 17 • The substance he obtained was a jet black, finely-divided powder with the stoichiometric formula Cs2AgAuCl 6 and properties quite unlike those of Pollard's salt. Further investigation led to the discovery of several other triple salts having the formulae Cs2AuAuCls, Cs4CuAu2Cl12 and Cs4HgAu2Cl12All of these compounds crystallize isomorphously, as shown by solid solution formation, and have colors varying from black to light yellow. In order to obtain information regarding the valence of the metals and the general nature of these compounds, I have investigated two of them, Cs2AgAuCls and Cs2AuAuCls, at the suggestion of Professor Linus Pauling, by means of x-ray powder photographs and magnetic susceptibility measurements. The results of the study ar~ contained in this paper. We can formulate four reasonable structure types for these salts; (1) Each heavy metal atom may be bivalent and not attached by covalent bonds to other heavy metal atoms. (2) Both heavy metal atoms may be bivalent, the two being joined by a covalent bond forming the group Ag : Au in the case of Cs2AgAuCls and Au : Au in the case of Cs2AuAuCl5. (3) One heavy metal atom may be univalent and the other trivalent. (4) Each heavy metal atom may I 1 Wells, Arn. J. Sci. 3, 315 (1922). 2 Pollard, Arn. J. Sci. 3, 257 (1922). resonate between a univalent and a trivalent state. If the first suggested structure were correct, the compounds would contain groups with an odd number of electrons and hence be paramagnetic. A measurement of their specific magnetic susceptibilities was therefore made by the Gouy method. Both compounds proved to be diamagnetic. The value x= -0.33X10- 6 c.g.s.m. was found for Cs2AgAuCl6 and x= -0.25 X 10-s c.g.s.m. for Cs2AuAuCl 6. The results eliminate a structure with each heavy metal atom bivalent and separate, and we must consider the three remaining structure types. X-ray powder photographs of Cs 2AgAuCl 6 and Cs2AuAuCls were prepared by using molybdenum radiation filtered through zirconia. These were not entirely satisfactory, the lines being rather faint and difficult to measure. However, it was possible to measure about fifteen lines on each photograph. The regular spacing of the lines suggested at once that the crystals are cubic, and, on assigning indices, all the lines could be accounted for on the basis of cubic units with ao= 5.33 ±0.02A for both Cs 2AgAuCl 6 and Cs2AuAuCls. The lines which occur, together with their estimated intensities, are shown in Figs. 1 and 2. No lines occurred requiring a larger unit. These cubic units contain only one-half of a stoichiometric molecule, Cs2AgAuCl 6 or Cs 2AuAuCl 6 , as estimated from the atomic volumes of the constituent atoms. The calculated values of the density are 4.266 g/ cm3 and 4. 753 g/ cm3, respectively, for Cs2AgAuCls and Cs 2AuAuCl 6. ~ 11-· 420 NORMAN ELLIOTT the assumption that units with a0 = 5.33A are the true units of structure. The theory of space groups provides only two ways of arranging 1 M (M=Ag, Au), 1 Cs, and 3 Cl in a cubic unit of structure. These are the following arrangements A and B. LO Arrangement A : Cs at 000 Mat½½½ Cl at OH, ½O½, HO ,s ,. 8 tO ll. t't 16 18 2.0 l.l. l't 2.6 .?.8 JO FIG. 1. Powder-photographic x-ray data for Cs2AgAuCl 6• Relative intensities calculated for arrangement A are shown by vertical arrows. Horizontal arrows indicate the relative intensities calculated for arrangement B. Arrangements A and · B give the same intensities for those lines for which h2 +k2+l 2 is even·. Horizontal bars show the observed intensity value.s. 30 " zo ,s 10 FIG. 2. Powder-photographic x-ray data for Cs,AuAuC1 6• The symbols are the same as for Fig. 1. No directly measured density values are available for comparison. If these are the true units of structure, the silver compound must contain Ag and Au atoms distributed at random in equivalent positions. 'vVe shall first proceed on Arrangement B: Mat 000 Cs at ½H Cl at OH, ½O½, HO. The only difference in theseforms is the exchange in position of Cs and M. With the f-values of Pauling and Sherman,3 values of the intensity of reflection from various planes for these two arrangements were calculated according to the usual intensity formula, including the Lorentz, polarization, and frequency factors. Visual estimates of the intensities were made and compared with the theoretical intensities. The results are shown in Figs. 1 and 2. The positions of the vertical arrowheads give the relative calculated intensities for arrangement A, and those of the horizontal arrowheads show the values for arrangement B. For h2 +k2 +t2 even, both arrangements have the same values. Horizontal bars indicate observed intensities. It is seen that arrangement B is in pronounced disagreement with experiment even for simple planes. Thus (111), h2 +k2 +l2= 3, for Cs 2AuAuCl& is not observed, though calculated for arrangement B to be over ten tinies as strong as (210), h2 +k2 +l2 = 5. Hence the atomic arrangement is A. This is known as the perovskite structure. It may be described as a cubic close-packed arrangement of the large atoms Cs and 3 Cl with the smaller metal atoms, M, introduced at the centers of octahedra with six chlorine atoms for corners, each chlorine atom forming a corner of two such octahedra. The agreement in the observed and calculated intensities is sufficiently good to show that this arrangement must be the actual structure of these crystals or very close fo it. Therefore, structure type 2 containing Ag : Au and Au : Au complexes is not correct. If the perovskite structure were the actual structure of these compounds, equivalence of all the gold atoms would be required in Cs 2AuAuCl&; 3 Pauling and Sherman, Zeits. f.rKrist. 81, 1 (1932). ABSORPTION S~PECTRUM that is, structure type 4, involving resonance of each metal atom between the univalent and trivalent state, would be correct. However, there are some small discrepancies. The calculated and observed intensities of the lines h2 +k 2 +l2= 24 in Fig. 1 and h2 +k 2 +Z 2 = 22 in Fig. 2 show definite disagreement when compared with the values of neighboring lines. These discrepancies are sufficient to eliminate the perovskite structure and the valence type 4. It is 13 OF CHROME ALUM · 421 probable that the structures are based on a larger unit and that the atomic arrangement•is a distortion of the perovskite structure so that the six chlorine atoms are brought . closer to the trivalent gold atom (valence type 3) than to the univalent gold or silver atom. The data are not sufficiently extensive to permit the detailed discussion of this point. We hope to continue the investigation and to determine completely the struc;ture of these crystals. Section 3 The Crystal Structure of Cesium Aurous Auric Chloride, Cs 2 AuAuC1 6 , and Cesium Argentous Auric Chloride, Cs 2 AgAuC15 By Norme.n .i!:lliott and Linus Pauling The substances cesium a urous auric chloride, Cs 2 Au.AuC15, and cesiLun e.rgentous auric chloride., Gs 2 AgAuC15, discovered by Wells 1 , a.re of interest -·--------------------------------------(1) H, L, Wells, .Am, J, Sci,~, 395 (1922). because of their jet black color., which has been ascribed 2 to the presence of (2) H, L. ~~lls, ibid.~, 497 (1922), the same element o:r two closely similar elements in two valence states, 3 (3) Norman Elliott, Jour, Chem, Phys, f, 298 (1934), In a preliminary investigation carried out some time ago 4 the substa nces were (4) Nonne.n Elliott, J. Chem, Phys. ~, 419 (1934), found to be diamagnetic, shovn.ng tha t they contain gold and silve r in t he univalent and trivalent exidation st.8.tes rather than the bivalent state. photogrs.phs we1·e also prep r,red with molybdemun x-radia. tion. Powder These photo- graphs, each with e.bout fifteen lir1es., were interpreted as showing the crystals to have a structure clos ::: ly related to the cubic perovskite type, the unit = 5.33 .ltfor each substance, containing 1 Cs at 000, l (Au,.Ag) Although the agreement between the intenat g~, a.nd 3 Cl a t M-0, ½o½, ~~. cube, with 8.o si ties of x-ray reflection c2.lculo.ted for this structure and the observed values was good in general, there were one or two poh~ts of pronounced discrepa ncy for each substance, and the conc l usion vm. s re a ched th a t the structures are actuall y distorted somewha t from the ide al pe r ovski t e e.rrangement. In the course of the investig a tion d e scribed below x-ray powder photographs were prepared with copper and iron re.diation, giving greater dispersion, and it was found that cesium aurous auric chloride is tetragonal, and contains the complex ions which is square. [ AuCl~-, which is linear, and [ AuC f_;- A simila r structure occurs for heat-treated samples of cesium e.rgentous auric chloride, which also exists in a cubic modification involving some randomness in at omic arrangement. The Determination of the Structure of Cesium Aurous Auric Chloride. - Po'.Yder photog r aphs of cesium aur ous auric chloride were p re pa red with copper K r adiP~tion filtered through nickel and ·w ith iron K radiation~ the camera radius being 5. 005 cm. The photographs s how about fifty well defined lines, occurring as multiplets ne :· r the angles expected for reflections from a cubic crystal. This suggests that the unit of structure of the crysta l is closely rela ted to a cube. The observation that the cubic line (200) occur s as a doublet, with the outer component twice as strong as the inner one, suggests that the crystal is tetrag~nal. This is supported by the multiplet structure of the other lines, the octahedral reflections being single, reflections with two indices equal double, and those vri th all three i ndices different t riple. The tetragonal unit of structure ¥Tith a 0 :t_ 0 , 02 = 7 .49 :!::_ K accounts for the presence of all observed lines 5 . 0.02 X and c 0 = 10. 8 7 The l attice c an (5) This unit is obtained frori1 the small pseudo-cub ic unit by rota.ting a.bout c t h r ough 45° and doubling c 0 • It corresponds to the dimensions a 0 5.28 X, c0 5.44 X for the srna ll pseudo-unit, with axial r a tio 1.03. = = be taken as body centered, no reflectio n s with h + k +!_odd being observed. No clas s es of planes other than t hose indic ated by the lattice a re absent on the photographs. The spa ce group is accordingly _£~ - I 4/m ~ !!:_ or one of its subgroups ·with the same unit. It was found possible with the assumption of holohedry to dete nni ne an atomi c arran 6 ement which accounts co:npletely for the x-ray date. ; it is accordingl y probable tha t the space g roup of the 17 crystal is D4h. The density of the substance was determined by displacement of benzene to have the value 4,57 g/cc. This corresponds to 1.94 Cs 2 AuAuC16 per unit, the calculated value of the density for two molecules per unit being 4, 72 g/cc , Th e re are 4 Cs, 2 Au I , 2 Au III , and 12 Cl atoms to be loc a ted. 17 • 1ent posi·t·ions f or n4h are 6 The se t so f equiva ( 6) Internat iona l Crystal Structu re Tab les. 2a : 000, l l =L1._ . 222• - l 2b : 0~, ~20; 4c: -i . l 0-;¼$, ~o, 2 2, 22, 11 4d: 0':a-, 4 * 1 l 3 ~, Oz4; ~, l 13 lll_L 4e : 00 z, 00-z, 22z'"Z, lll z 22°? j 0 xx, -0 -xx, Q _l---1.. l..L l 1 1 l l...1.. 1 l 1 l_,__X .1... 8h : xx, O -xx, 2°'x 2 ,x 2 , z-x z-x 2 , 2'x z-x 2 , z-x zr 2 , to gether with 8f, 8g, Bi, 8j, and positions for sets of 16 and 32 equiv9 lent atoms. The photographs sh ow that the atoms are in positions close to those of the perovskite arrangement. This can be a chieved only in the following way: 2 AU III.J.n 2a; 2 Au I in 2b; 4 Cs in 4d; 4 C1 in 4e , ,vi th z :;;;: 1/4; 8 Cl in 8h, with x = 1/4; (The assignemet of AuIII to 2b and Au 1 to 2a leads to the same structures.) The para.meters~ and z were evaluated froT'.l t he intensity datrc g i ven in Table I. The observed intensity values I b ~ s were obtained from micro- photometer records of the photographs and from visual estimates I!lB.de on a series o f photogre.phs take n under ident i cal conditions ezcept for varied time of exposure. Inte nsity values were calcul a t e d with the eq11ation hF2 in which his the frequency factor and F the stru cture factor . Fi s given by the equation + 2fCl Lcos 2 Tr u(h+k) + cos 2 lT"u(h-k) + cos 2 Tr lv } Screening-constant f va lues were used 7 , without temperature correction, The pare.Jlleter values obtained. in this way, with es pecial emphas is on comparisons between adjacent lines on the photog raphs, are~= 0.228 ! 0.003 and ~= o.288 ! 0.003. The excellence of t he agreeme nt b etween obse rved and calculo.ted intensities vri th thes e par e.meter values is shown i n Table I and Figure 1. The Determination of t he Structure of Cesiu.r.i. Argentous Auric Chloride.Coppe r-radiation photographs of samples of cesilun a rge ntous auric chloride which had been sta_-riding at room tempera ture s i nce their pre pa r ation two to thr e e yea.rs before we re found to show only re flec t ions (atout t hirty in nur.iber) whic h could be e xplained by a cubic unit of structure with~= 5.28 ! 0,01 A, containing;½ Cs 2 AgAuC1 6 . The lines on the photogre.phs are sharp, and the absence of fine structure comparab le in i;a. gni tude •with the clearly resol1red Cu K °" 1 - ()(. 2 doublet for the wide-angle reflections shows that t he a pproxi - mation to a. cubic strvcture is ,vi.thin O.l perce nt . After the samp le had been he ated in a sealed. evacua ted tube at 350°C f or 72 hours and cooled slowl y to room temperature over a period 17 Table I Powder Photographic Data for Ces iwn Auro us Auric Chlo ride Coone r :radiati on. ~ L == 1. 539 Jt hkl d obsd. d ce,l cd . I obsd. I ca.led. 002 5. 46 Jt 5.43 ft,_ 100 128 110 s. 28 s . 22 200 250 112 , 200 3. 76 3.75 2400 2230 103 3,28 3. 26 13 16 121 3. 21 3. 20 9 1 202 3.11 3.08 16 14 004 2. 71 2,72 300 340 220 2. 645 2, 647 600 660 114,301 2. 414 2.420, 2.425 50 52 310,222 2,36 9 2, 370 , 2. 390 100 106 204 2.200 2.200 300 315 312 2, 169 2, 177 600 660 105 2,097 2.11 2 4 2 224 1.892 1.910 450 420 400 1, 868 1. 872 200 209 006 1, 804 1. 809 10 10 411,314 1.790 1. 793,1.787 26 27 402,330 1.774 1. 772,1 , 767 26 30 116 1. 712 1,735 200 191 332 ,420 1,678 1,698, 1 , 674 300 333 404 1,537 1. 546 200 214 226~235 1,498 1,508,1, 510 lS 18 33".'1:, 501 1, 483 1 . 48 5,1. 483 13 13 510 1 , 466 1,467 13 13 136 1. 439 1. 450 200 213 I <S' Table I ( cont. ) hkl d ob sd . d ca.led. I obsd. I ca.led . 244 1. 423 1.430 175 172 152 1.415 1. 417 175 185 008 1.360 1.358 30 32 llS.,440 1.320 1. 335,1 . 323 110 131 208 ,530 1. 2.76 1.292.,1.283 50 50 336 1 . 262 1. 272 75 76 1. 230, 1. 250 200 214 228 1.207 1.220 100 87 444,620 1.190 1 . 192 ,1. 184 200 188 156 1.140 1,147 100 114 1.136 40 45 604 408 1.100 1.100 75 67 264 O·O·IO 338 ' 1. 085 1 .086, 1.086 1 . 085 100 112 446 1.069 1.074 40 36 1.063, 1.060, 1. 060 50 46 1•1•10, 550, 1,059 710 248 1.050 1,053 55 57 356 1. 043 1,045 140 147 0. 983.,0. 988, 0.955,0.998, 0.988 150 140 o. 968,0. 971 , o. 976 150 136 370,554,266, o. 986 3• l • 10,714 372.,644,528 0.966 448,40.10 0. 951 0 . 948,0.9 50 50 55 80~538 0 . 937 o.937.,0.939 35 32 3•3•10,802 0.927 0.924, 0.925 50 50 o. 917 o.91 7,0. 917 75 87 556.,608 19 Zo Legends for Figures Fig. 1. Calculated and observed intensities of reflections on po,vder photographs of cesium aurous a.uric chloride. The vertical lines show the observed val-:..:i.es of the relative intensities., and the horiz,·mtal crossbars the calculated values. Fig. 2. Calculated and observed intensities of reflections on powder photographs of the tetragonal modification of cesium argentous auric chloride. The vertical lines show the observed values of the relative intensities, and the horizontal crossbars the calculated values. Fig. 3. The atonic arrange,itent in tetragonal crystals of Cs 2 AgAuC1 and Cs 2 AuAuCJ..... 6 Large full circles represent cesium atoms, larg.e open 0 circles chlorine atoms, and small circles gold and silver atoms. "'J. 1 of about five hours,it gave cpite different x-ray photographs, the cubic lines being split into components similar to those for the aurous-auric compound, but with still gre a ter separation. The photographs could be completely indexed on the basis of a tetragonal unit with !:o = 7, 38 + 0, 02 X and ~ = 11, 01 ~ 0, 02 JL The unit is body centered, and the observed reflections correspond to the space group~ - .!_ 4/!.'.!.!.'.!.~ or one of its subgroups, The atomic arrangement described above for Cs2AuAuCl 6 , with Ag 1 replacing Au 1 and with the parameter values ~ -0, 220 :!:_ 0,03 and z = 0,285 :!:_ 0,003, accounts completely for the observed intensities, as shown i n Table II and Figure 2. Discussion of the Structures, - The structure found. for the tetragonal forra of cesium a.rgentous auric chloride (after heati:ng at 350°C) is shown in Figure 3, The structure is clo sely rel ated to the pe rovsk ite structure~ the arrangement of the large cesium and chlorine a.toms corresponding appro ximately to cubic closest pa.eking, with the silver and gold a.toms alternati:ng in positions at the centers of chlorine octa.hedra, The distortion from the ideal perovskite structure is such as to show -the prese.::1ce of (AgCl2 )- a.nd (AuC1 4 f complexes. Each silver atom has two closes-I; chlorine ator:i.s e.t the distance 2. 36 fl., which is just the sum of t ho cova.lc:m.t radii f o r silver (wi·\;h coordination number hvo) and chlorine 8 ; the other four chlorine atoms of the distol·ted octahedron a.re 2, 92 ! i'ro:m the silver a.tom. The (Cl-Ag-Cl)- complexes a.re linear, and are oriented parallel to the c axis of the cI";sta.l. Ea.ch gold atom has four nearest chlorine neighbors, arranged a.bout it at ·the corners of a square, at the distance 2. 30 Jt, which is the sv1n of the covalont radii of triYalent bold and chlorine. The distar1ce from t.1-ie gold atom to the two other chlorine a.toms in its neighborhood is 3.13 JL zz Table I I Powder Photographic Ds.ta for Cesium Ar gentous Auric Chloride Copper radiation. =l.539X. hkl d obsd. d calcd. I obsd. I ca.led. 101 6.12 X 6.10 ft.. 40 50 002 5.50 5.50 25 26 110 5. 2,1: 5.22 50 46 112 3.77 3.77 600 637 200 3,685 3.690 250 270 103 3.275 3.280 50 49 202 3,055 3.054 50 44 00 11: 2,750 2.750 170 163 220 2,601 2. 598 260 290 114,301,123 2,436 2,430,2.393, 2. 440 30 29 222,310 2.329 2.350,2.325 18 15 204 2,206 2.203 150 136 105,132 2.145 2. 107 ,2.J.40 265 270 321,303 2.050 2.05,2.06 30 36 224 1.896 l.890 250 220 006, 4001 215 1.842 1.830,1,835, 1.825 125 105 314,411,323 1.783 1,775,1.760, 1. 780 35 36 330, ,102 1.735 1. 732.,1. 740 135 145 116 1.678 1.690 25 21 332,420,206 1.655 1. 6 52 , 1 . 6 4,1 1,640 160 170 107,226,325 404 1. 530 1,536,1,500, 1,494,1,525 120 126 316,510 1.444 1. 440~1. 442 120 117 Z3 Table II ( co:1t . ) 217 , 424 1.415 1.418,1, 412 100 105 512 1.400 1.395 100 107 415,433,503 1.382 1.384, 1.380, 1.381 25 20 008 1. 373 1,375 16 20 440 1,305 1,300 40 36 406,208 1.293 1,295,1,288 25 29 514,442.,530, 1. 267 1. 277,1,265., 1,261,1.259 50 52 532 1. 232 1. 229 60 55 600,426,435 505.,228 1. 220 1.225.,1.22 3~ 1. 222 , 1. 222 , 1,215 60 62 31<3 ., 602 , 417, 1.181 1.183,1.195, 1.178:1 ,175 55 57 620 1.170 1. 167 55 56 622 ,515 , 534 1.138 1,1 40,1 . 135, 1.145 75 74 -408 1,107 1. 100 60 58 1.1.10 1.083 1 .082 50 54 624 1,076 1,078 100 110 428 1.062 1, 055 80 80 710,550.,536 1,045 1.044,1,044, 1 .039 85 83 640,712 1 . 026 l,02·:l:,1. 025 120 130 3.1.10,518 1,003 0.994, 0.997 90 100 556,716 0,910 0,905, 0 , 905 100 110 628 0,890 0,888 90 85 5.1.10 0.880 o.875 90 85 801: o.876 0, 873 50 45 5.3.10,558 718 o. s 3o o.836,0. 836, o.836 90 93 336 44·1 :i - !: ~ - Ces,·urn q,-,,c/ ol--orns / .S/""77Q / / /c;r?C'! C/;_c/4.s 0/°("Y] 70/4/ c,v7 c/ z,.s ,: - :: ·· ·· - {!/',,-c/2-.s s-,,'/,v- e r ) · •- ch/4r/ne 4 ,,,.../;:,~ s , Cl /2J,?,-1.s.., The J.mn v~l ue of t!1e 9.xia.J.. ratio vf. t:.10 au.rous au.ri,~ co1:1potv:1d su.g;ge s ts that in t he f urther support fo r tJ1i s by the vaJ.ue of the naramete r x , C 4 a ur ic compound ; i t see:ns likeJ.y that the chan6 e i::1 - L 1tens i ties of the lines ca.used by the part:i.1;1.l ra.n donness of tie s tructure has caused a sme..11 err o r i n the par a.me ter det e r.i1 i :nn tio:'.1., .Pu1 effort to test t his hypo - +vhe"'.;"' 1.-., e 0o _+.J. t:. 1c, '"t·•·op of Cs 2 •Au t-.,. , l" -+'o'" 24 h() · ·•c•, v.J..v -<ra~ ,. ~ -ffi" •-.tde b:,r . Il __ ·1-l il' •}• <c ia< • ' • ' l·" "' " • .nc, l 6 to ' ;3t:::0° v J c J.. J. , • , •· c,.l .:,, 0 t he photogr~ph obttdned of t he sample after this treatment wai, identicaJ. vrit:1 the earlie r ones , however, sho'Ning that the partial random.YJ.esu c i' pere.tu.res a n d not a. metastable state. A.YJ. investigati on of ces:i.t1:n aurous a.uric chloride and cesium argentous auric chloride has been reported recently by Ferrari 12 , let=u:lL1g to r e sults dif i'erent f r o;-r, ours. Ferra ri re ported the substar,c es to gi-.re pow::b r photogra phs ( taken with i ron radiation) correspondi::,g to cubic v.nits wi th ~ :::: 5, 23 X in each caso, c3:ccept that a few very £'2.int lines were observed indicating the true units to have vs.lues of ~ t wice as large . He suggested a st:ructl1re invoJ.,ring di stort i on fro ,,1 th e ideal peroyskite arr angement such c.8 to give (,11.uCJ. 0 )= comple xe s ·with the confi 6 uration of a regul a r octahedron , It seems improbab}e to us th8."t t his coinple x exists; and we believe that the saL1ples studi ed by Ferrari 1·eprese:::1t order:3d mo difications i~ sufficient amounts to g:i.ve the f a.int e xtn1 J.i nei; ·w hich he obser,rod . Sum;:Lary C:rJstals of tetragonal cesium aurous auric chloride have a bodycentered unit of structure~ with ~ containing 2 Cs2Au.AuCl 6 . 7.49 _+ 0.02 K and ..:..0 c = 10 • 87 -+ 0 • 02 The space group is D~ - I a.re in the following positions of this space gi!7.: m p: 4/~ ~ E:, and the atoms 2 AuI1I in 2a; 2 Au1 in 2b; 4 Cs in 4d; 4 Cl in 4e, vrith !. = o.288::, o.003; 8 61 in Sh, vtlth x = 0.228::, 0.003. Tetragonal cesium argentous auric chloride., Cs2 AgAuC1 , has a similar unit, with~= 7.38 :!:. 0.02 ,~and~= 11.01 6 :t, o. 02 X, and a similar atomic arrangement (with Ag 1 replaci::-ig Au1 ), the paramete'r values being E.. to Ag(CN) 2 - 1 = o.285 :!.:_ 0.003 and 3S. = 0.220::, 0.003. These and square coplanar (AuC1 4 )- ions., similar to the In addi tian a metastable cubic modification of Cs 2 AgAuC1 6 , capable of conversion into the stable tetragonal ::nodification by heating., was studied. The apparent unit of structure of this is cubic, vri~h ~ 5.28 :!:. 0.01 X. = It contains½ Cs 2 AgAuC1 6 , and appears to have the perov- skite structure, with i (Ag + Au) at g}., Cs at 000, 3 Cl at ~}o, Jo½, ¥z<). It is probable that the cry stal contains AgCl~ - and AuC1 4 - conplexes with random distribution among the positions and orientai;ions provided by the perovskite structure. modification of Cs 2 AuAuc1 Evidence for the existence of a similar 6 A, is gi,e~ by the work of Ferrari. RE EREIJCES 1, h . L. 'ifells , PJTI . J, Sci ., ~, 315 (1922) 2. H. L. Wells, ibid,.£,, 417 (1922) 3. Norman Elliott, Jour. Chem. Phys. !• 298 (1934) 4. Nor1::an ~lliott; ibid. 5. This 1.mit is obtained from the sma.11 pseudo-cubic unit by rotating about c through 45° and doubling c . It eorresnonds to the dimensions a. 0 s:-2s A, c 0 5. 44 .lt for the ;ga.11 pseudo-~ t, with axial ratio 1. 03. = !, 419 (1934) = 6. International Cr ystal 3 tructure Tables. 7. L. Pauling a.nd J • .:>herma.n, 8 L. Pauling a nd L.1, L. Huggins, 0 z. Krist. ~• 1 (1932) z. Krist, 87 , 205 (1934) 9. J, L. Hoa.rd, ibid. 84, 231 (1933) 10, R, G, Dickinson, .I. A, C.. 5.) 44, 2404 (19 22 ). 11. L, Pauling, 12. J: A. l . .S. A. Ferrari~ Gazz. 53, 1367 (1931) 'Chim. Ital. 29 67 , 94 (1 93 7) Section 4 iRr. prinl from th e J o u r na l of the .-\meric fln C hemical Sodety, 69, H)58 (1~37 ). } [ CO NTRI13 UTIO K FRO~! TH E G AT ES AN D CR E LLI N L ABOR ATOR IES OF CH EMISTR Y, C A LIFORN I A I NSTITU T E OF TECHNOLOGY , No. 612] The Crystal Structure of Manganese Diselenide and Manganese Ditelluride Bv NORMAN ELLIOTT The properties of substances having the pyrite or similar type of structure have usually been interpreted as showing that in these compounds all the bonds are covalent. From x-ray data on pyrite, FeS2, hauerite, MnS2, skutterudite, CoAs3, etc., Pauling and Huggins 1 have obtained octahedral radii for metal atoms in the transition groups of the third and fourth rows of the periodic table. They observed that the radius of manganese in hauerite and manganese ditelluride, 1.55-1.59 A.., did not agree with the radius, 1.15 A., obtained by extrapolating the sequence Nill Con Fen Mnn. A safer extrapolation of the isoelectronic sequence Ni 1v Com Fen Mn 1 gave a value 1.24 A. for Mn1 which should be an upper limit for Mn.II and studied by means of x-rays. The results are described in this paper. The discussion of the experimental data includes an interpretation of the magnetic susceptibility measurements made · on these and related compounds by Haraldsen and Klemm. 4 The compounds were prepared by sealii;ig stoichiometric proportions of the elements in evacuated Pyrex glass tubes and heating these ~ in a furnace at 550° for forty-eight hours. ,, Powder photographs were taken of manganese A · diselenide and manganese ditelluride using copper radiation filtered through nickel. The photographs are reproduced in Figs. 1 and 2. As both manganese disulfide and manganese ditelluride Manganese Diselenide 552 336 172 640 263 245 533 533 063 245 063 263 640 552 336 172 ,;: !·\ Manganese Ditelluride l ii2 24;J 520 023 lJ ;J 113 U2;J 333 511 l f,2 520 Fig. 1. The parameter in hauerite was redetermined by Offner 2 as a check on the discrepancy. The valu~ found gave a sulfur radius in excellent agreement yVith the one assumed by Pauling and Huggins 1 but did not remove the anomaly of the large manganese radius. In order to extend the investigation to other compounds, the substances manganese diselenidc and manganese ditelluride 3 have bec-11 prepared Linus Pauling and M. L. Hug,-ins. 1/.. T-;ri st. , 87, 20 [, (1981). (2 ) Franklin Offner , ibid., 89, 182 (1934 ). (3) The structure of manganese ditelluride has b een dct.ermint'.d hy O ftedal, Z. physik. Ch em., 135, 29 1 (1928) . In the present iavestigation a more ac-curate parameter det ermination h as been made. are known to have the pyrite structure, it was i assumed that manganese diselenide also has this structure. The photographs were indexed on the basis of cubic units. Weak extraneous lines I were accounted for by the presence of small amounts of manganese selenide and selenium or manganese telluride and tellurium .4 a Data which were used in determining th e selen ium a nd tellurium positions are gi ven i11 Tables I and II. (I) (4.) Haraldsco a ad K lem m . 7.. n • o•g. Chr.m ., 223, 409 (1 93,,). (4a) Since tbe- writin g of thi~ p:=tp~r p ure manganese di!--d enjd ! ha~ been prepared . X-ray powd er photographs of thi::. preparation do not show the extraneous lines o bserved in earlier work. i Oct., 1937 TABLE I MANGANESE DISELENIDE Copper radiation. >-a = 1.539 A. Camera radius 5.005 cm. Sine hkl e /, obsd. I. calcd . ZD , cm. 4. 19 0. 2095 0. 2080 111 10 8 4 . 84 . 2420 . 2397 200 144 144 5 .42 . 2710 . 2677 210 214 226 5 .95 .2975 .2932 211 214 214 6 . 92 . 3460 . 3391 220 55 52 8 .57 .4285 . 4155 222 16 14 8 . 94 .4470 . 4322 320 120 120 9 .30 .4650 .4484 321 145 145 10 . 01 . 5005 .4797 400 18 19 10.33 .5165 .4939 322 410 16 15 11.00 .5500 .5227 331 6 6 11.32 .5660 .5363 420 2 3 11. 63 . 5815 . 5492 421 50 44 12 . 55 .6275 .5871 422 8 8 13 .15 . 6575 . 6112 510 9 11 13 . 44 .6720 .6225 333 511 76 80 14 .02 . 7010 .6450 432 520 52 55 14 .32 . 7160 . 6565 521 28 30 14.90 .7450 .6780 440 40 44 16 .05 .8025 .7190 442 600 18 15 16.35 .8175 .7294 610 7 7 17.48 .8740 .7669 443 540 621 14 15 18 . 09 . 9045 . 7860 533 10 10 18 .68 .9340 .8040 542 630 14 14 19.91 .9955 .8391 632 16 16 20.55 1.0275 .8560 551 711 16 15 20. 88 1 . 0440 . 8645 640 38 38 21 .55 1.0775 .8807 633 721 552 40 40 23 . 41 1. 1705 . 9209 731 553 42 43 TABLE II MANGANESE DITELLURIDE Copper radiation. >-a = 1.539 A. Camera radius 5.005 cm. I, obsd . I, calcd . llkl Sine e 2D,cm. 198 207 210 0.2505 0 . 2480 5.01 208 183 112 .2722 .2750 5.50 99 99 113 .3681 .3770 7.54 87 87 023 . 4003 .4120 8.24 117 117 132 .4140 .4285 8 .57 18 24 . 4440 400 .4600 9 .20 45 48 . 5085 241 .5335 10.67 24 24 . 5206 332 . 5475 10.95 3 4 .5430 422 .5740 11.48 45 43 . 5766 333 511 .6145 12 . 29 45 48 .5975 432 520 .6405 12 .81 27 30 521 .6080 .6535 13.07 3;3 36 44.0 .6275 .6785 13.57 33 36 532 611 .6841 .7535 15 .07 . The unit cells of pyrite type structures contain four molecules and have atomic positions defined t Y the following coordinates of Tf .k: 0 0 0 ; ½ ·½0; ½ 0 ½; 0 ½ ½ u u u; ½+ it , ½ - u, ii. ; ii., ½+ 11, a - u; ½ - u, ii.,½+ u ii. U U; ½ - u, } + u, u.; u, ½ - u, -} + u; } + tt, fx.: u, l - u 1959 CRYSTAL STRUCTURE OF MANGANESE DISELENIDE AN D DITE LLURIDE The structure factor for the reflection (hkl) with h, k, and l all odd or all even is F = 4fR + 8fx cos 271" hu cos 271" ku cos 271" lu and for h, k even and l odd or h, k odd, l even F = 8fx cos 271" hu sin 271" ku sin 21T"lu. ( ZN ) 1 0.390 0.391 0.392 0.393 0.394 0.395 0.396 Parameter. Fig. 2, The calculated intensities in the sixth columns of Tables I and II are given by the equation 1 ~ 1 + cos2 e hF2 cos 0 sin 2 0 where h is the frequency factor. The atomic scattering factors used are those of Pauling and Sherman.• The relative observed intensities in the fifth columns were obtained from microphotometer records of the photographs. The estimated accuracy of these results is about == 20% . For convenience in making comparisons the lattice constants, parameters, and interatomic distances found for hauerite, manganese diselenide, and manganese ditelluride are shown in Table III. The value of the manganese diselenide parameter is limited to a narrow region, 0.3912-0.3935, by the comparisons (263) > (533) , (127)+(336)+(552) >(640), and (263) = (245) +(063). Similarly the comparisons (113) > (023), (520)+(243) = (511 ) +(333), and (152) = 3/ 5 I (520) + (243) l require the manganese ditelluride parameter to lie between 0.384 and 0.388. The intensities of these reflections as functions of the parameters are shown in Figs. 2 and 3 for the diselenide and ditelluride, respectively. The agreement found between observed and calculated intensities of manganese diselenide and ditelluride for the parameter values given in Table III may be seen in Figs. 4 and 5. The lengths of the vertical lines represent relative (5) Liou, Pauling and J. Sherman, Z . Kris:. , 81, l (1932). 1960 Vol. 59 NORMAN ELLIOTT 10 , - - - - - - - - - - - - - - - - - - - , 8 i 6 <fl i:: ~ 4 ,--, (.f20),{Z.f.J) ~ = = = ~ ; ~ = = ~ : = = = ~ Wl},(JJJJ = 2 0.375 0.380 0.385 Parameter. Fig. 3. 0.390 TABLE IV observed intensities, the cross bars show the calculated intensities. TABLE III Compound Unit cell dimension, A. Parameter compared with the tetrahedral and the normal valence covalent radii of Pauling and Huggins. 1 If the compounds under investigation were covalent, the observed radii would be expected to agree well with the tetrahedral radii of Table IV. However, the agreement is distinctly better with the normal valence radii, suggesting that each non-metal atom is forming only one covalent bond and that the manganese-non-metal bond is, therefore, an ionic bond. Mn-X distance, X-X A. distance, A. MnS2 6.097 ±0.005 1 0.4012 ±0.0004! 2.59 2.086 ±0.008 MnSe, 6.417 ± 0.005 .393 ± 0.001 2.70 2.38 ± 0.02 MnTe 2 6.943 ±0.002 1 .386 ±0.002 2.90 2.74 ±0.05 The sulfur-sulfur, selenium-selenium, and tellurium-tellurium distances found in hauerite, manganese diselenide, and manganese ditelluride are 2.086 ± 0.008, 2.38 ± 0.02, and 2.74 ± 0.05 A., respectively. The. corresponding covalent radii of sulfur, selenium, and tellurium are half the~e distances. In Table IV the observed radii are Tetrahedral Normal valence r a dius, A. radius , A. Element 1.04 1.14 1. 32 Sulfur Selenium Tellurium 1.04 1.17 1.37 Observed radius, A.. 1. 043 ± 0. 004 1.19 ± 0 . 01 1.37 ± 0 .02 It should be possible by means of magnetic susceptibility measurements, as d1scussed by Pauling, 6 to distinguish between covalent d 2sp3 bonds and ionic bonds. Divalent manganese ion has five odd electrons filling the five 3d orbitals, with a resultant spin moment µ = 5.92 Bohr magnetons. If the bonds are covalent, however, two of the 3d orbitals are used in bond formation; two of the odd electrons must therefore pair, leaving only three unpaired with a spin moment µ = 3.88 Bohr magnetons. 280 -!i_ 240 ,-< 200 ... oo ... oC'lo,..o ,..o ... no ~o.-10 o ... ('l('l('l('l('IC')C')"" :~:~~~~:: ~ .-10 ,.. ,.. C1 C'I C'I el 0 oi ~ C1 o : : : C') '"' "~ 160 200 400 600 800 Temperature. Fig. 6.-MnS: A = 460; µ = 5.87. Fig. 4. Magnetic susceptibility measurements have been made by Haraldsen and Klemm 7•8 on several sulfides, selenides, and tellurides of manganese, cobalt, and nickel over a wide range of temperatures. As shown by Figs. 6, 7, 8, and 9, the magnetic susceptibilities follow the Weiss-Curie law 0/NC,:,C,:,(NQ,-<(N(N,-<Q,-<Q,-< ,-(,-....t..--l C\lC--:,0tj'4CQ~ ,....C~~ tj'4 ,-( <Nr-<r-<Or-<-,f</NC,:,"<!<ICICIC"<t<<O MIN~~ Fig. 5. <N ~ X = c/(T + A) (6) Linus Pauling, THIS JOURNAL, 63, 1391 (1931). (7) Haa kon Hara ldsen and Wilhelm Klemm, Z. anorg. Che m., 220, 183 (1934). (8) Haakon H a raldsen a nd Wilhelm Klemm, ibid., .223, 409 (1935). Oct., 1937 195{ CRYSTAL STRUCTURE OF MA NGANESE DrSELENIDE AN D DIT E LLURIDE The values of Li may be obtained from the graphs. The magnetic moments are then calculated from the equation /J, = 2.84 VXmo[. (T + Ll) be accounted for readily by saying the bonds of manganese in pyrite type structures are essentially ionic while those of iron, cobalt, and nickel are essentially covalent. The moments found for manganous sulfide and manganese disulfide are 5.87 and 6.13. The values are very close t o the value 5.92 predicted for divalent manganese ion and are in definite disagreement with the presence of d 2sp 3 bonds in either compound. Since alabandite, manganous sulfide, has been shown by Wyckoff 9 to have the rock-salt structure or one very similar, a moment of about 5.92 was to be expected. The experimental value, 5.87, not only substantiates Wyckoff's 9 structure determination, but, in addition, it confirms the present interpretation of Haraldsen and K1emm's 7•8 magnetic susceptibility measurements. 800 GOO ,..... 400 200 200 300 400 500 T emperature. Fig. 8.-C0S2: 6. = - 150; µ. = 1.99. Another explanation suggested by Professor Pauling is that the manganese bonds resonate between ionic and sp 3d 2 bonds, the sp 3d 2 bonds involving 4d rather than 3d orbitals. In this case a non-metal-non-metal distance intermediate between the sum of the tetrahedral and the sum of the normal valence covalent radii would be expected. It may be concluded from the observed selenium-selenium and t ellurium-tellurium distances in manganese diselenide and dit.elluride that the amount of resonance is rather small. 200 ..!i_ 180 ...... 160 140 400 200 300 100 Temperature. Fig. 7.-MnS2: Ll = 528; µ, = 6.13. 1600 The observed moment of cobalt disulfide, 1.99, is in agreement with the assumption that here the cobalt is forming octahedral d 2sp 3 bonds, the predicted spin moment in this case being 1.73. The moment observed for nickel disulfide does not permit a decision to be made regarding the type of bond between the nickel and sulfur. Either ionic or covalent octahedral bonds leave the nickel atom with two odd electrons and• a predicted moment of 2.83 Bohr magnetons which is close to the observed value, 2.71. The comparison of the covalent radii of the transition elements made earlier in this paper leads, however, to the natural supposition that in nickel disulfide the nickel-sulfur bonds are covalent also. The anomalous manganese radius may thus (9) Wyckoff, A m. J. S ci. , 2, 239 (192 1) . t: 8 ....... 1500 ~ ,..... 1400 / 1300 100 200 400 300 T emperature. Fig. 9.-NiS2 : 6. = 1025 ; µ, = 2.71. It is interesting to note that further tests may be made on cobalt and nickel diselenide and ditelluride. If these compounds are covalent the selenium-selenium and tellurium-tellurium distances should agree closely with the sum of the 33 10f-i 2 N ORM AN ELLIOTT tetrahedral radii for these elements. These values, 2.28 and 2.64 A., would be shorter than the distances observed in the corresponding manganese compounds. It is planned to prepare several of these substances and to investigate their magnetic susceptibilities and crystal structures in these Laboratories. Acknowledgment.- The author wishes to thank Professor Linus Pauling for his interest and help in this investigation; his suggested interpretation of the magnetic measurements of Haraldsen and Klemm proved especially valuable. The author also wishes to thank Dr. James H. Sturdivant for his kind advice concerning the preparation of the powder photographs. Summary The crystal structures of manganese diselenide and manganese ditelluride have been investigated with x-rays and found to belong to the pyrite type of structure. The cubic unit of manganese diselenide has the dimension a 0 = 6.417 ± 0.005 A. and the parameter u = 0.393 ± 0.001. For manganese ditelluride the corresponding values are ao = 6.943 ± 0.002 A. and u = 0. 386 ± 0.002. The results obtained suggest that in the pyrite type structures the manganese-non-metal bonds are either ionic or resonate between ionic and covalent, the covalent part involving 4d orbitals from the manganese rather than 3d orbitals. The magnetic susceptibility measurements of Haraldsen and Klemm, 7•8 on the sulfides of manga-. nese, cobalt, and nickel, are interpreted as supporting the results of the X -ray investigation, and, further, as showing that cobalt and nickel probably form covalent d2sp• bonds in these compounds. • PASADENA, CALIF. .. ..., RECEIVED JULY 19, 1_ ~37 Section 5 [Reprint from the J o urnal of tbe American Chemical Society, 59, 1880 ( l\l:37 ) .j [CONTRIBUTION FROM THE GATES AND CRELLIN LABORATORIES OF CHEMISTRY, CAUFORNIA INSTIT UTE OF TECHNOLOGY, No. 601] A Redetermination of the Carbon-Oxygen Distance in Calcite and the Nitrogen--Oxygen Distance in Sodium Nitrate BY NORMAN ELLIOTT For the case of carbon- carbon interaction in molecules an empirical function has been found 1 which relates the observed interatomic distances to the type of bond formed. The same function, with a suitable translation and change of scale, has been used to predict distances between other atoms, notably carbon- oxygen and nitrogenoxygen distances. A large discrepancy occurs for the carbonate ion between the predicted distance, 1.32 A., and the distance reported for calcite. 2 This disagreement and the desirability of testing the assumptions involved in the use of the function have led to a reinvestigation of the parameters in calcite and sodium nitrate. Crystals of calcite and sodium nitrate were ground on (111) and (211) faces 3 and Laue photographs obtained of each substance in two orientations, one with the primary beam perpendicular to the cleavage plane, the other with the X-rays parallel with the three-fold axis. On each set of photographs pairs of reflections were found having nearly the same values of sin 8 and of n'A.. The relative intensities of each pair were estimated visually by comparing photographs having different known exposures. The more important reflections were photometered on an alpha-ray integrating microphotometer. 4 Theoretical structure factors, F1,kt, were based on the Pauling and Sherman 5 tables of atomic (1) Pauling, Brockway and Beach, Tms JOURNAL, 57, 2705 (1935) . (2) Wyckoff, Am. J. Sci., 50, 317 (1920). (3) The indices employed in this paper refer to the smallest rhombohedral units of structure. The lattice constants for calcite arc ao ~ 6.36A., a = 46°6'; those for sodium nitrate are ao = 6.32 A., a = 47°15'. The space group of both substances is Dtiad - R3c, with atoms in the positions Ca or Na: 1;, 1;, 1;,; s;, s;, s;, C or N : 0 0 0; 1/, 1/, 1/, 0: u u 0; u Ou.; 0 u u; 1/, - u., 1/, + u, 1/,; 1/, + u., 1/,, 1/, - u; 1/,, 1/, - u, 1/, + u.. (4) The application of the alpha-ray integrating microphotometer to the determination of X-ray intensities was first reported by Astbury, Proc. Roy. Soc., 123, 575 (1929). The microphotometer measures the intensity of alpha-rays passing through a carbon print of an X-ray negative. The necessary conditions for obtaining integrating properties are that a linear relation exist between the X-ray intensity of a given r eflection and the corresponding alpharay intensity, taken as the rate of discbar ~e of an electroscope; and that zero X-ray intensity correspond to zero alpha-ray intensity. These conditions are easil y met b y adjusting the constants of the apparatus. (;)) Paulin K and S h er 111a.11, 7,_ }{risf., 81 1 (l!)a2). 4 scattering factors . Since the comparisons in volve the ratio of intensities of reflections having approximately the same wave length and scattering angle, no other terms need be included in the calculations. The ratio of the intensities reflected from two planes, (hkl) and (h'k'l'), was then assumed to be equal to the ratio of the squares of the corresponding structure factors The possibility that the intensities might be proportional to the first power of the structure factors was also considered. 6 When calculations are made on this basis, the individual intensity ratios of Tables I and II lead to a very wide range of parameter values, whereas the spread is small when the squares of the structure factors are used. This indicates strongly that for the separate crystal sections used in this investigation the intensities are closely proportional to F2. In Tables I and II there are given the results of the microphotometric measurements for calcite and sodium nitrate, respectively. In all cases but one, two carbon prints were measured for TABLE I PARAMETER DETERMINATION FOR CALCITE USING MICROPHOTOMETER VALUES OF INT ENSITIES ReflectInterplanar Wave ing planes distance length I / I' Parameter 172 1.032 0.37 2.46 2.30 0.2624 0.2633 .36 905 1.040 .2614 .37 1.95 5.12. 7 1.031 1.031 .36 453 .2656 .2630 921 0.530 .32 1.63 1.79 .32 372 .535 .2642 .32 1. 75 1. 71 .2650 716 .530 .31 372 .535 .2631 .2670 .32 .16 1.02 372 .535 .31 172 .534 .2628 .2637 .628 .35 12 .11 13. 18 720 .635 .36 452 .2640 .2646 .591 127 .36 4.25 4. 13 .580 .36 741 Weighted average value of lhe parameter, 0 .2635 ± 0.0011. (6) This phenomeuou has Leeu obser ved in the case of calcite by P. E. Tahvonen, Societas Scientiantm Fennica, Cvmmentatiu,u., Ph _vsicn- il1athnnatic,1,,, VIII , H ( 19:1 5), and other in vest igators. July, 1937 TABLE JI P;RAMETER D ETER MINATION FOR SODI UM NITRATE US IN G MtCROPHOTOMETER VALUES O J>. I NTENSITIES Reflect- Intering planar p lanes distance 207 T3G 234 125 Tso 234 1381 CARBON- OXYGEN AND NITROGEN - OXYGEN DISTANCES 0.670 .G95 . 800 .825 .790 .800 Wave length 0.45 .4G .44 .44 .au .:ls I/ I' Parameter 2 . 10 2. LL 0.2400 0.2400 2 . 17 2. 14 2385 .2.390 .84 2.00 .2398 .2392 Each parameter value was multiplied by the slope of the corresponding intensity curve as a weight factor in obtaining the average values, for it is clear that, other effects being equal, the reliability of a single result is proportional to this slope. The limits of error are taken as the average deviations. 12 Weight_e d average value of Ute pararneter, 0.2394 ± 0.0005. a ----... ""'..... 8 TABLE III PARAMIHER DETERMINATION FOR CALCITE USING VIS UAL Reflecting planes ll4 421 723 241 12.7 .7 364 523 945 343 614 356 10.1.3 237 271 ESTIMATES OF INT ENSITIES Interplanar Wave distance length I / I' 0.970 .960 .807 .798 .534 .529 .690 .635 .650 .640 .492 .484 .535 .534 . 36 37 34 33 36 36 43 4 Parameter 2.5 0.260 6.5 .261 2.5 .262 2.0 2G5 7.0 .261 32 33 30 30 30 29 2 .0 .262 1.5 .257 T ABL E IV l()(i 514 lOG 501 1G3 .810 Fig. 1.-a = 1120/fo,; b = hn/l1fi; c=/112/ I,o.; d = h12.i/I,1a; e = J..,,/In, ; f = 1116/Ia1'i ; a nd Ini/Ia12- 0.41 .41 .40 .40 .40 .40 .47 . 47 1 0L..--'-~-~~--'--~-~~~_, VISUAL ESTIMATES OF INTENSITIES ReHecting lnterplanar Wave Parameter planes distance length I/I' Tso 0.270 3 PARAMETER DETERMINATION FOR SODIUM NITRATE USING 0.995 .985 .790 .7GO .750 .760 .790 0.260 u -+-, 44 Weighted average value of the parameter, 0.261 ± 0.002. 114 214 0 0.250 1. 33 0 .235 1.90 .240 1. 75 .239 1.60 .240 Weighted average value of the parameter, 0.239 ± 0.002. each pair of reflections, giving the intensity ratios I / I' in the fourth columns. In Figs. 1 and 2, corresponding to Tables I and II, the intensity ratios of pairs of reflections are plotted as ordinates with the parameters as abscissas. The final parameter values in the fifth columns of the tables were read directly from these graphs. 0.235 0.245 0.255 u -+-. Fig. 2.-a = lun /1,as; b = I ,a,/Ii,.; c =lio0/I,oo; d =I,.o/1,a,; e =I.,,/ 1,o,- The parameter values found for calcite and sodium nitrate, 0.2635 and 0.2394, respectively, are not in disagreement with the results of Wycko:ff's 2 •7 experiments which allow a range of 0.24 to 0.26 with the probable value 0.25 m each case . The observation of a weak reflection (311) on several photographs of both substances in the present investigation suggests that the parameters cannot be exactly 0.25. This reflection has zero amplitude for u = 0.25 inasmuch as the structure factor has the form Jo sin 2u(h-k) + sin 2u(k-l) sin 2u(l-h) for planes the sum of whose indices is odd. Other planes of this type . are too weak to reflect and do not appear on the + (7) Wyckoff, Ph ys. l<,v_ , 16 , J 4n ( l\l lCJ ). 1382 NORMAN ELLIOTT Vol. 59 photographs. Failure to observe (31 l) 011 Wyc- lead to a value for the double-bond radius between koff's photographs is due to the excessive fogging those of oxygen and fluorine, that is, about 0.05 A. of the negatives by the incident radiation in the less than the normal double-bond radius of region around the central image. nitrogen. Resonance between this double bond The values found for the C-O and N- O dis- and the single bonds would lead to an expected tances are 1.;n3 and 1.210 A. Ou comparing nitrogen to oxygen distance in the nitrate ion these with the values l .;12 and 1.2G A., respec- 0.05 A. less than that predicted by Pauling, tively, predicted by Pauling, Brockway and Brockway and Beach, and in exact agreement Beach, 1 we see that the disagreement which had with the new experimental value. This agreement existed in the case of the carbonate ion has been between the experimental value and the value removed, but that a difference of 0.05 A. is predicted by the above straightforward argument found for the nitrate ion. 8 It seems probable provides strong evidence for the correctness of that this difference shown by the nitrate ion is the postulated dependence of the covalent radius to be attributed to a previously unrecognized on effective nuclear charge. The phenomenon phenomenon, namely, the effect of resultant should be observed in many other substances, charge of an atom on its covalent radius. From such as, for example, the tetramethylammonium the electronic-structural point of view we interpret ion; experiments to test these predictions are the decrease in the sequence of values 0.77, 0.70, planned. 0.66, 0.64 A. for the single-bond covalent radius The author wishes here to express his thanks to of carbon, nitrogen, oxygen, fluorine, respectively, Professor Linus Pauling for suggesting this reas due to an increase in effective nuclear charge search, for his continued help and interest throughof the atoms, which can be estimated with the use out the course of the investigation, and for a of screening constants to amount to about 0.G major contribution to the discussion at the en d unit from one atom to the next. 9 In the case of of this paper, and to Dr. J. H. Sturdivant for a bond between two atoms with formal charges of kind advice and direction in the preparation of opposite· sign, the interatomic distances would the Laue photographs and in the use of the alphabe given approximately by the sum of the radii ray microphotometer. for neutral atoms, since the increase in radius of Summary the negatively charged atom would be approxiA reinvestigation of the parameters of calcite mately compensated for by the decrease in radius of the positively charged atom. In· the nitrate and sodium nitrate has been carried out using ion a nitrogen atom with formal charge + 1 is data obtained from Laue photographs. The connected by single bonds to oxygen atoms with parameters found are 0.263i:i for calcite and 0.2394 formal charge -1 and by a double bond to a for sodium nitrate. These values lead to the neutral oxygen atom. For the single bond we interatomic distances 1.313 A. for the carbonaccordingly expect approximately the normal oxygen bond and 1.210 A. for the nitrogensingle-bond distance, but for the double bond we oxygen bond. A comparison with the distances expect a distance shorter than the normal value, predicted by Pauling, Brockway, and Beach 1 is corresponding to an increase for nitrogen of about made, and agreement found for the carbonate ion . one unit in effective nuclear charge. This would The short nitrogen-oxygen distance is discussed in relation to the effect of resultant charge of an (8) The revi sion o f the table of covalent radii and of the resonance curve reported by P au lin g and Brockway, THIS J ouRNA T., 69, 1223 atom on its covalent radius. (1937), leads to no chan~e in the predicted distances. (9) See Pauling and Sherman, Z. K,·isl., 81, 1 (19!{2). PASADENA, CALIF. RECEIVED MAY 25, 1937 Section 6 The Molecu lar Structure of Selenium Dioxide Va por By K. J. Palner and Norman Elliott. Electron diffra ction photographs of selenium dioxide vapor were taken and interpreted in the way already described in the literature. (1) L. 1 The photo- o. Brockway, Rev. Modern Phys. ~, 231 (1936). graphs showed five well-defined but rather broad maxima, whose rel ative positio n s and intensities were approximately those to be expected for a diatomic molecule. This is due to the relutive unimport!!lillce of the oxygen-oxygen scattering as compa red to the selenium-oxygen scattering. The values of s 0 (= 4 1fs~e/2 ), the visually me a sured intensities (I), and C (= Is~e-a 8 o) are given in Table I. The v a lues of C and s 0 were used in calculating a radial 2 distribution curve as recently sug; ested, and the resulting curve is reproduced (2) V. Schomaker and c. Vega.rd, To be published soon. in Fig. 1. The well-defined peak at 1.61 A corresponds to the selenium- oxygen distance; the other pea.ks lying farther out arc too unreliable to be of any importa nce in determining the oxygen-oxygen distance. Two simplified intensity curves were calcula ted, one for a linear model and the other for a model having an 0-Se-O angle of 120°. duced in Fig 2~ The latter is repro- The two curves e.re so ne a rly identical, bot h with rega rd to shape and position of the maxima., that it is i mpossible from a qualitative compa.rison with the photograph to make a c hoice between them. 1'he quantitative comparison of sc/so g iven in Table I leads to the selenium-oxygen distance 1. 61 ~ o. 03 ..lt, in exa ct ag reement with the radial distribution curve. analogy with sulfur dioxide, the 0-Se-O angle is probab ly close to 125°. Using this va lue for the angle the oxygen-oxygen distance is 2.86 ! In Discuss ion : The value 1. 61 Jl is con siderably lowe r than the sum of the double bond radii of selenium and oxygen. is o.93. The double bond factor for third row elements This gives 1.66 1t for the selenium-OX'J gen double bond distance. ?; On correction for the formal charge effect as suggested by Elliottu, this is (3) Norman Elliott, J. A. c. s. 59, 1380 (1937). reduced to the value 1 64 !, 0 If one considers only the electronic structures representing resonance between a selenium-oxygen double bond and a single bond, then ea.ch bond would possess 50 % double bond character. The interatomic distance, found by ap plication of the usual resonance curve, is 1,69 X. The discrepancy between this value and that observed is probably due to the fr1portance of electronic structures in which the oxygen is bonded to the selenium atom by a triple bond. A bond of this type is possible because selenitun is not restricted rigorously- by the octet rule. The observed sulfur-oxygen distance in sulfur dioxide bears about the same relation to the r adii as that found for selenium dioxide, and the two molecules are probably closely si :dls.r in electronic structure. The selenium dioxi de crystal 4 does not contain discrete Se02 mole- (4) James D. McCullough, J, A, c. s. ~, 789 (19 37). cules, but instead consists of ini'inite chains. The observed Se-0 distances in the crystal, 1,78 Jl and 1.73 Jl, have been discussed by McCullough, We are indebted to Dr. James D. McCullough for furnishing us with the srunple of selenium dioxide, and to Professor Linus Pauling for his a.id and criticism during the course of this investiga tion, Summary Electron diffraction photographs of selenium dioxide vapor have been 39 interpreted to le a_d to the v o. lue 1. 61 ~ o. 03 ! for the Se-0 distance. value of the angle 0-Se-O could not be determined. The Table I Ma:;.z. Min. 1 I C So Sc* sc/so 10 33 5.185 4.32 (0.833) 6.800 6.00 .882 8. 771 7.88 .898 10.700 9.55 .893 12.404 11. 28 .909 14.690 13.15 .895 16.652 14.75 .886 18.458 16.50 ,894 20,391 18. 37 .901 2 2 7 50 3 3 4 38 4 4 2 17 5 5 1 Se-0 6 .Average 0.894 Average deviation 0.006 = (1.80)(0,894) = 1. 61 :!:_ 0.03 1l * Calculated for the model with Se-0 = 1.80 X and the angle 0-Se-O = 120°. Lege nds to fi gures: Fig. 1. Ra.dial distribution curve for selenium dio xide . F·ig. 2 . I ntensity curve for selenium dioxide, ca.lcul nted for Se-0 and 0-Se-0 angle= 120°. = 1.80 it The po sitions of the arrows, indic a ting measured maxima. and minima, h e.ve been decre ase d by 8 . 9 percent to indica te t he qua.ntitati ve agreement with the final model ·with Se-0 = 1.61 1l Section 7 The Electron Dif'fraction Investigation of Altuninum Chloride, Bromide, and Iodide. By K. J. Palmer and Norman Elliott The unusual physical and chemical properties of aluminum chloride, bromide, and iodide lend considerable interest to the electron diff rac tion investigation of these compounds . in the gas phase. Vapor density measure- ments have shown that in the gaseous state below approxim ately 400°G the substances exist as the dimeric molecules Al 2 Cl 6 , Al 2 Br 6 , and Al 2 I6, The same configuration is suggested for these molecules by conside rations based on the extreme ionic and the extreme covalent point of' view. The radius ratio of the ions A13+ and Cl- is 0.40 (ratio of univa lent r adii 1 ), (1) Linus Pauling, J.A.c.s. which corresponds to tetrahedral coordination. This can be achieved for a molecule Al 2 X 6 by the sharing of an edge between two tetrahedra, as shown in Fig. 1. From the covalent point of view this co:n figuration would be expected as the result of the tendency of the aluminum atoms to complete their octet valence shells, the electronic structure of the molecule being X . .. . • X •. ·.•A1· . •X •. . . 0 . . . 'X : Al . • X •· 0 • •• x·· . . The suggestion of this as a pos sible structure for the aluminum halides was . 2 ma de b y F a.Jans . (2) K. Fajans, Zeit. f. Electrochemie 34, 502 (1928). We have carried out the study of these substances by the electron dif• 8 4 5 fraction method, and h ave verified the double-tetrahedral con.figuration of Fig. 1, with some deformation of the tetrahedra., as described below. Expe rimenta.l The electron diffraction photographs we re obtained and interpreted in the usual wa.y. 3 The wave length of the electrons vms o. 0613 A and the c ame re. (3) L. O. Brockway, Rev. Modern Phys.~, 231 (1936). distance 10. 85 cm for the chloride and bromide and 20.16 cm for the iodide. The strong tendency of the aluminum halides to hydrolyze made it necessary to transfer the samples to the high temperature nozzle inside a moisture proof box. (4) L. The nozzle4 could then be see.led and inserted into the electron o. Brockvray and K. J. Palmer , J:.:.A, c..·&.~ ~, 2181 (1937). diffra ction appars.tus, the sample not being allowed to come into contact 1Nith moist air. This procedure proved to be satisfactory, as v-ras verified by inspection of the nozzle after the exposures were ma.de. In no case was there any si gn of decomposition. Merck's C.P. aluminum chloride was used ,rithout further purification. The aluminum bromide was made by the method of Richards and Krepelka 5 . The (5) W. Richards and H. Krepelka ~ J".. A. C:.~ ·$., 42, 2221 (1920). aluminum iodide was prepared by heating iodine with excess aluminum in a.n evacuated glass tube held in a vertical position. The temperature was main- tained at 300°C for six hours, in which time the color due to the iodine vapor had completely disappeared. The aluminum iodide which collected in the lower part of the tube along with the excess aluminum was separated from the l atter by distilling it to the upper part of the tube and then sealing the tube off at the center. The product appeared in the fonn of colorle s s highly refrac- ti ve crystals. There was no evidence of any iodine vapor being present either duri ng or after the distillation. These crystals were used without further purification, Aluminum Chloride. -- The photographs of alu.'llinum chloride show nine maxima.. The averaged v a lues of s 0 ., I (the visually estimated intensities), and C 2 (equal to Is~e-aso) a.re given in Table I. The qualitative appearance of the photographs is well represented by curve F of Fig. 3 which was calculated for the finally accepted model. 6 The radial distribution curve , curve A of (6) L, Pauling and L. 0, Brockne.y, J", ·A ."C.-S.; , 57 , 2684 (1935). The trn e of the valu·2 s of C in place of I ha~ been suggestedby V. Schomaker and c. Degard. They "V'rill publish an account of their investigation soon in This Journal. Fig. 2, calcult'l:ted using the values of' C (Table I) in place of I, shows principal peaks at 3.56 and 2,11 K. These values are interpreted as the Cl-Cl and the short Al-Cl distances respectively. The ratio of these, 1,69,is close to that (1. 633) for a regular tetrahedral arrangement of chlorine atoms about the alUJninum atoms. Strong support for this structure is provided by the simplified theoretical intensity curve calculated for the regular tetrahedral model (Curve A of Fig, 3), which shows good, although not compleiB, agreement with the characteristics of the photographs, In order to find a model in vvhich the ratio of Cl-CJ. to Al-Cl is 1. 69, all of the edges of the two tetrahedra except the shared edge were assumed to have th~ v : J. lue 3, 56 lt, and the eight smallest Al-Cl distances the value 2.11 X. The shared edge would then have the value 2,58 lt. Although this distance is much less than the distance of closest approach (2. 86 JO obser-1Ted for two nonbonded chlorine atoms., a theoretica l intensity curve was calculated for this model( curve B, Fig 3), which a gain is in good but not complete agreement with the photogr a phs . Curves C and D., Fig. 3, were calcula ted for models in which ~ ~ \ ' 3 I I I I /r\. , . I ', 'I I V I '· I u,-· e ~I\J \ ~ . FJ I - .G F E. 0 C b A f::.\Cl 0 \ \ I I I I I /"-. I \ Li I \ / / II / I\ 'JJ I I ~ I ' -------------- ~ / F :·1u ,re - C B A I the she.red edge has the value 2. 75 .ft. and 2. 85 X res pe ctively. The other ten edges have the Ya lues 3.56 X in model C and 3.54 ! in model D and the s:nallest Al-Cl distances the v a lues 2.12 and 2.11 Jl respectively. These curves do not agree with the photographs quite so well as does curve B. A very l arge decrease in the value of the shared edge is necessary in order to obtain the ratio 1. 69 v1J'.11en at the same time one ke eps the other edges of the tetrahedron a.b out equal to 3. 56 X and the s hort Al-Cl di stances a ll equal to 2.11 X. Thus i t is evident that the models so far assumed have been airer-simplified, and t ha t the stable co nfigura tion~ although app roximating tW-> regular tetra hedra shari ng an edge, is in reality con siderably distorted. In order to obtain an insight L'1.to the t ype of distortion to be expected the followi ng calcul ation ,ms made. The no lecule is assumed to be completely i onic , a nd to be represented b ~, the potential function V=- " L. ij ,~ \' ij in which rij is the dista nce between the i th and j th a.tor.1s, Bij is the Born c oefficient, n is a constant, ta.ken to have the Ya lue 9 for this calcub .tion~ and ei, ej are the cha rges on the i th and -j th atoms, taken equal to -1 a.nd +3 for chlorine a nd aluminum respectively. It was further assu.'lled th at the r a tio of the B's is given by the expression where RAl and Rei are the ionic radii of aluminum and chlorine respectively. The absolute magnitudes of the B I s were obtained by sett ing ..:!.. r = 0 and using r • . , s corre s pending to two regular tetrahedra with all short Al- Cl di stences J. J equal to 2.11 X. The v al ues so obtained are BAl-Cl = 48.15 and BCl-Cl = 1.755. These values were reta ined throughout the c a lculation. A method of successive ap proximations was used to carry out the CE,1cula tion. Each of the four independent paramete r s necessary to s pe cify the structure was successively varied, the process being repe ated once. The final values of the pe.rameters so obtained i n d.i.c a te the t ;y-pe of distortion to be expected in such a structure. With a cha rge of +3 assumed to reside on each of the two aluminum atoms the repulsion between them is v-ery strong, and the most no t able changes in goin6 from two regular tetrahedra to the final equilibrium configuration are the decre a se in the length of the shared edge and the increase in the Al--Al distance. This latter effect changes the v a lues of the short Al- Cl distBnces by a l a r ge a.mount. The final value s of the i!l.ter- = 3.60, Al 2 Cl 6 = 1.99, Al2-Cl3 = 2.31, Alz-Cl6 -· 4,89, Cl3-Cl4 = 3.49, Cl3-Cl3 = 3. 57, Cl5-Cls = 2.90, a.tomic distances calcula ted in this way are Al1-Al 2 6.52 x. The subscripts on the atomic symbols refer to the position of the atoms as given in Fig. 1. The avera ge of the four Al 2 -Cl 3 distances equal to 1. 99 K and t he four Al 2 -Cl 8 distances equal to 2. 31 ft.. (refer to Fig. 1) is 2.15 A, in fair agreement vd.th the radial distribution peak at 2.11 K. However, if this were the correct model, the two shortest Al 2 -Cl distances would probably appear as separate peaks in the radial distribution curve. Moreover$ the intensity curve calcula ted for this model, (curve E, Fig. 3) does not agree qualitatively with the photographs; the sixth maximum is too high and the eighth and ninth minima are not of equal depth. Seven additional intensity curves wer•': calculated for models in v-rhich t:h.e four parameters wer-::i varied. The model finally selected gives an intensit~v curve (curve F. Fig. 3) which reproduces the qualitative features of the photographs in every respect. The values of the interatomic distances for t h is model are listed in Table II. Table I gives the v a lues of sand s 0 and their r a tio, s/s 0 , for model F. oO Table I Electron Diffraction Data. for Aluminum Chloride Max. Min. 1 I C So S* s/s 0 5 2 2.24 2.35 (1.049) 3.08 2.91 (0.946) 4.08 3.93 ( .963) 4.96 4.91 ( . 989) 5.86 5.86 1.000 6.61 6,51 0.985 7.43 7.18 . 967 8.33 8.40 1.008 9.23 9.32 1.009 10.11 10.20 1.009 10.98 10.90 0.993 11.90 11. 91 1.000 12. 71 12.77 1.005 13.42 13. 71 1.022 14.47 14.60 1,009 15.22 15.41 1.013 16.07 16,30 1.014 2 2 10 14 3 5 3 12 4 4 3 10 5 5 4 16 6 1 6 4 7 3 7 12 8 1 8 3 9 9 2 *Calculated for model F 5 Average 1.003 Average deviation 0.010 Table II Intera.tomic Distances in Altuninum Chloride Distance Number of times distonce occurs in molecule. Al 2 -Cl 3 2.os:: o.o4 X 4 A1 2 -Cls 2.21 .:!:, 0,04 4 Cl5-Cls 2.83 .:!:, 0.1 1 Cl 3 -Cl 4 3.53 .:!:. o.o4 2 Cl 3 -C1 8 3,56 .:!:, 0.02 8 Al1-Al 2 3.41 .:!:, 0.20 1 Cl 3 -Cl7 5.49 .:!:, o.os 2 Cl 3 -Cl 6 6.52 :t_ o.os 2 Al 2 -Cl6 4.77 :t, 0.15 4 Alu.rninu.m Bromide.-- The photographs of aluminum bromide show seven well defined rings and have the same qualitative features as t hose for aluninurn chloride. The radial distribution curve has two well defined peaks at 2.28 and 3.77 X. The ratio of 3. 77 to 2.28 is 1. 65, indicating that the tetrahedra in this molecule are probably not distorted to so great a.n extent as for the chloride. Cu.ri."'e A of Fig. 4 was calculated for two regular tetrahedra sharing an edge. The curve is in good but not complete qualitative agreement with the photogra.phs. Curves B and C of Fig. 4 vrere calculated for models having the same type of' distortion as that found for the chloride, but smaller in magnitude. The two models a.re essentially the same except for the length of the shared edge. In model B this edge was assumed to be 3.36 X and in model C 3.20 ! . The Al2-Br 3 and Al2 -Br 8 distances were taken equal to 2 , 21 and 2. 33 ! respectively in model C, and 2.21 and 2,35 ! in model B. The qualitative agreement of curve C with the photographs is better than that of curve Bin that the fifth maximum in the form.er is slightly more intense than the fourth, in agreement 1Ni th the appearance of the photographs. The differences in these two curves nre, however, very slight in spite of the fact that the Br 5 -Br 8 distance has been changed by 0.16 X. The insensitive- ness of the intensity curves to 1rariations in this par1,meter makes it necessary to assign to it a large probable error. In Table III there are listed the values of I, C, s 0 , s (for model C), and the ratio of s/s 0 , and in Table IV there are given the v a lues of the intera.tomic distances for the molecule and their estimated probable errors. 6.3 Table II I Electron Diffraction Data for Alu.-rninwn Bromide Max. Min. 1 I C so S* s/s 0 5 2 2.11 2.11 1.000 2,85 2.87 1.007 3.78 3. 72 0.998 4.68 4.61 0.999 5,48 5.60 1.022 6,28 6.22 0,990 7,02 6. 88 0,980 7.85 7. 88 1.004 8,73 8.78 1,006 9.59 9.68 1,009 10.38 10 . 35 0,997 11, 19 11.17 0. 998 ll. 84 12,08 1.023 2 2 10 11 3 3 6 11 4 4 4 9 5 5 5 13 6 1 6 2 7 7 2 * Calculated for model C 3 Avera-:, e 1,003 Average deviation 0.009 Table IV Intcratomic Distances in Aluminum Bromide Dis ta.nee Number Al2 -Br 3 2.21 .:!:. o.o4 .lt 4 Al1-Brs 2.33 ~ o.o4 4 Br 5 -Br 3. 20 .:!:_ 0. 10 1 Br 3 -Er~ 3.72 .:!:_ 0.03 2 Br 3 - Br 8 3.78 .:!:_ 0.03 8 Al 1-Al 2 3.39 :!:_ 0.10 1 Br 3 -Br 7 5.76 :!:, 0. 10 2 Br 3 -Br 6 6.86 :!:, 0 ,10 2 A1 2 -Br 6 4.93 :!:_ 0.10 4 8 c,JIJ A B C A B C Aluminum Iodide. -- The photo g raphs of aluminum iodide, ta. ken with a camera. distance of 20.16 cm., show seven well defined maxima , the ge ne ral appearance of the photographs being closely similar to tha t for the chloride and bromide. This similarity is strong evidence for the assumption that the structures of the three molecules are simila r in confi guration. The radial distribution curve (curve C, Fig. 2), shows principal peaks at 2,58 and 4.23 X. The ratio of the latter to the former di stance is 1. 64., indi cating that the structure is ver-J ne a rly that of two re g ular iodine tetrahedra sharing an edge, The ratio of the scattering due to the iodine atoms to that due to the alur.i1inum atoms is -rery large in alu.minmn. iodide; this makes the determination of the positions of the aluminum atoms with any degree of ac ,~ ura cy impossible, The intensity curves shmsrn in Fig. 5 were calculated for models approximating those described for aluminum bromide. Curve A is for undistorted tetrahedra, and curves Band C for tetrru1edra whose shared edge has the value 4.00 and 3.85 ! respectively , a nd for which the Al 2 -I 3 and Al2 -I 8 distances h ave the values 2.58 and 2.54.1Lrespectively. Curve A does not agree with the photo- graphs in that the rela tive intensities of the maxims. are unsatisfactory . Curve C gives a some,vhat better representa tion of the a.ppe a r Gnce of the photographs than curve B , but the differences in these two curves, nrune l y the va ria.t ion of the intensities of the third, fourth, snd fifth maxima, are so small that, a.s in the c a se of the bromide, it is impossible to determine the length of tre shared edge vnth much accuracy. The values of the intera tomic dista nces wit h their extimated probable errors a.re given in Table VI. The quantitative com- parison of the s values obtained from curve C with the observed s 0 values is given in Table v. Table V Electron Diffraction Data for Aluminum Iodide Max. Min. 1 I C so S* s/s 0 9 3 1.88 1.87 o. !2:95 2 . 51 2.52 1.004 3.32 3.33 1.003 4.14 4.08 0.986 4.85 4.99 1 . 029 5.56 5. 65 1.016 6.29 6.26 o.995 7.03 7.00 . 996 7.80 7.75 • 994 8.62 8.67 1.006 9. 27 9.29 1.002 9.95 9.89 0.994 10.67 10.70 1.003 2 10 2 9 3 7 3 10 4 6 4 9 5 5 5 10 6 2 6 3 7 7 1 * Calcul ate d for model c. l Average 1.002 Average deviation 0.008 Table VI Intera.tomic Dist r-::.nces i n Aluminum Iodide Distance Number Al2-I 3 2.53 .:t, o.o4 Jt 4 Al2-I 8 2,58 :t_ 0.04 4 I5-I8 2,DO :t_ 0.15 l I3-I4 4.20 :t_ 0,03 2 I3-I8 4.24 :!:_ 0.02 8 Al 1-Al2 3.24 ::!:. 0.1s 1 I3-I7 6,24 :t, 0.15 2 Is-I5 7.54 :t, 0.10 2 Al 2 -I 6 5, 22 .::_ 0.15 4 Discussion: The only report on the structures of aluminum chloride., bromide., or iodide previous to the present one is that of Ketelaar 7 on the structure of (7) J. A. A. Ketelaar., Z. Krist. 90, 237 (1935). sluminum chloride crystals. He found that the chlorine atoms are in hexa- gonal closest packing., this arrangement being compatible with that found for the gas molecule in this investigation. However., he chose to place two aluminum atoms inside an octahedron of chlorine atoms, and only 0.56 K apart., rather than one each inside of two tetrahedra sharing an edge, both of these possibilities being provided by the hexagonal closest packed arrangement. The extent to which the x-ray data can be accounted for by this latter configuration is being investigated by one of us. Curve G., Fig. 2., is the simplified theoretical intensity curve calculcated for the "octahedral" model of Ketelaar; it is apparent i'rom a comparison with curve F that this model cannot represent the structure of the gas molecule. The l a rge difference in electronegativity between aluminum and the halogen atoms leads one to expect that the Al-X bond will be largely ionic., and this is confirmed by the observed contraction of the shared edge. The per- centage decrease in length of the shared edge is found to be largest in the chloride a.nd least in the iodide which is in a ccordance with expectation, The sums of the tetrahedral radius of aluminum and the nonnal radii for the halogen atoms a.re 2.24., 2.40., and 2.59 X i'or the chloride., bromide., and iodide respectively. These values are to be compared with the observed values, 2,06, 2.21, a.nd 2.53 K, wh ich are the A1 2 -X 5 distances., and 2,21., 2.33., and 2. 58 K, which are the Al 2 -X 8 distances ., i'or the chloride, bromide, and iodide respectively. The observed shortening in the case of the Al 2 -X 3 distances is probably due to the excited structures in wh ich an X3 halogen a.tom swings in a pair of electrons and forms a double bond ,vi.th the a.lumimun a.tom. This type of resonance is not expected to occur to the same d~gree for halogen atoms fonning two bonds, which accounts for the fact that the observed Al2-X 8 distances are nearly equal to the sum of t he appropriate radii. It is interesting to note that the observed values of the Al 2 -X 3 distances show a greater tendency for the chlorine and bromine atoms to form double bonds than of iodine atoms; this is compatible with the results of other investigations. We wish to express our thanks to Professor Linus Pauling for his aid and helpful criticism during the course of this investigation. Summary: It is shown that in the gaseous state the dimeric molecules of aluminum chloride, bromide, and iodide co n sist of two tetrahedra sharing an edge vri th six halogen atoms at the corners, each tetrahedron containing one aluminum a.tom. The final values of the interatomic distances are as follows: Al 2 Cl6 Al 2 Br6 Al2Is Al 1-Al2 3.41 :!:. 0.20 X 3,39 :!:, 0. 10 K 3 .24 :!:, 0.1s K Al 2 -X 3 2.06 !, 0.04 2.21 :!:, 0,04 2.53 :!:, 0,04 Al 2 -X8 2, 21 :!:. o. 04 2.33 :!:. 0.04 2,58 :!:. 0,04 Al 2 -X6 4,77 :t, 0,15 4. 93 !_ 0 . 10 5,22 :!:, 0.15 X3-X 4 3.53 :t, 0,04 3. 72 :!:. 0. 03 5,30 :t_ 0.03 X3-X8 3. 56 :!:, 0.02 3, 78 :!:, 0 , 03 4.24 :!:. 0.02 X5-X8 2.83 :!:, 0.10 3,20 :!:, 0 , 10 2 . 90 :!:, 0, 15 X3-X7 5.49 :!:, 0,05 5.76 ~ 0. 10 6. 24 :!:, 0,15 X3-X6 6,52 :!:, 0.05 6.86 ±_ 0.10 7,54 ±_ 0.10 The subscripts on the a.toms refer to their positions in the molecule as g i ven in Fig. 1. Section g Reprinted from Z. Kristallogr. (A) 98 (i937) 180 Akademische Verlagsgesellschaft m. b. H. in Leipzig The Unit of Structure and Space Group of Chloral Hydrate. By Norman Elliott. (Contribution from the Gates and Crellin Laboratories of Chemistry, California Institute of Technology, No. 6i3.) A crystal structure investigation of chloral hydrate was begun in order to determine whether or not one of the carbon atoms in a molecule of this substance is attached to two hydroxyl groups, as is supposed by organic chemists. The difficulties encountered in the problem have proved greater than was expect ed; and in view of the existence of excellent evidence concerning the structure of the chloral hydrate molecule obtained recently by other investigators, the study has been carried no farther than the space group determination. The Raman study of chloral and chloral hydrate by P etrikaln and Hoch berg1) has shown that the C = 0 frequency is present in chloral but not in chloral hydrat e. The infra-red absorption spectra of solutions of chloral hydrate in carbon t etrachloride obtained by Professor Badg e r and Dr. Bau er 2 ) of these Laboratories reveal an OH doublet similar to the doublet found for o-chlorophenoJ3). These data may best be interpreted as confirming the organic chemists' structure in which two hydroxyl groups are directly attached to a single carbon atom. The crystals used in this investigations were thick tabular rhombs. The large, well-developed face referred to by Groth as the c-face was taken as the (1.00) face. For convenience the b- and c-axes were chosen lying in the (1.00) plane. The other developed faces were then (OH) and (OiI) . The lattice constants were obtained from layer line measurements of x-ray photographs prepared by oscillating a crystal of chloral hydrate around its a-, b- , and c-axes. The constants are a0 = H.57 ± O.i5 A, b0 = 6.04 ± 0.03 A, c0 = 9.60 ± 0.03 A, and f3 = i20° 7'. From the density, a = i .90, t he number of molecules in the unit cell is 4.03. L a u e and oscillation photographs were indexed and the following types of reflections were observed: hkl present for all orders, h0l present for l = 2n only, 0k0 present for all orders. These observations lead to the space groups c:,, or C;; the crystallographic data reported by Groth provide strong evidence for holohedry, so that the space group c: ,, is to be assigned to the crystal. i) Petrikaln and Hochber g, Z. physik. Chern. (B) 4 (1.929) 299. 2) Private communication from Prof. R . M. Bad ger and Dr. Simon B a u e r. 3) 0. R. Wulf and U. Lidd e l, J. Amer. chem. Soc. 57 (1.935) 1.464. R eceived 6 August i 937 . Printed in Germany ~ a r y 5:£ Thesi~ The subject of Part 1 is the men.surement of electromotive forces i n liquid ammonia solutions at r oom tempera ture, Pa.rt 2 is concerned with the expe rim(; ntal deterr.d.1w.tion of the structures of molecules and complex ions. Special emphasis has been pla ced on t he accurate deterJ,inat io n of interatorn:. c distanc es . discu s ;,ed from the v i0wpoint of the cova le nt bond tl-ieory. The result s are