An X-Ray Diffraction Investigation of Silver Azide and Boric Oxide and an Electron Diffraction Investigation of Some Three-Membered Rings and Some Halogenated Methanes Citation Pfeiffer, Heinz Gerhard (1949) An X-Ray Diffraction Investigation of Silver Azide and Boric Oxide and an Electron Diffraction Investigation of Some Three-Membered Rings and Some Halogenated Methanes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/qrgh-1m86. https://resolver.caltech.edu/CaltechTHESIS:05202025-153449195 Abstract Sections I and II report the X-ray diffraction investigations of silver azide and boric oxide. Silver azide crystallizes in a body-centered orthorhombic structure. The space group is Ibam with four molecules in the unit cell. The silver atoms are in (a), the central nitrogens in(~), and the end nitrogens in (j) with x = 0.156 and -y: 0.369. A new type of part cell projection is developed. Boric oxide crystallizes in a hexagonal structure with three molecules in the unit cell, a o = 4.320 Kx., c o = 8.139 Kx. Each boron has three bonded oxygen neighbors at a distance of 1.35 Å and coplanar with the boron. Sections III and IV report electron diffraction investigations of some three-membered rings and some halogenated methanes. The HCH bond angles of cyclopropane are about 116°, the C-H distance 1.10 Kx., and the C-C distance 1.515 Kx. The other three-membered rings...ethylene imine, ethylene oxide, ethylene sulfide, and N-methyl ethylene imine...have HCH angles of 116° and all other distances close to the sum of the covalent radii. The halogenated methanes... difluorobromomethane, trifluorobromomethane, trichlorobromomethane, and difluorodibromomethane...have bond angles close to tetrahedral; the only significant deviation is the FCBr angle of 110.5° in trifluorobromomethane. The bond lengths in these compounds are close to the sum of the covalent radii with the exception of the C-Br in difluorodibromomethane (1.925 Kx.) and in trifluorobromomethane (1.89 Kx.). Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry and Physics) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Minor Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Hughes, Edward Wesley (advisor) Schomaker, Verner F. (advisor) Pauling, Linus (advisor) Thesis Committee: Unknown, Unknown Defense Date: 1948 Record Number: CaltechTHESIS:05202025-153449195 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:05202025-153449195 DOI: 10.7907/qrgh-1m86 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17253 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 20 May 2025 23:25 Last Modified: 20 May 2025 23:26 Thesis Files PDF - Final Version See Usage Policy. 20MB Repository Staff Only: item control page

AN X-RAY DIFFRACTION INVESTIGATION OF SILVER AZIDE AND BORIC OXIDE AND AN ELECTRON DIFFRACTION INVESTIGATION OF SOME THREE-MEMBERED RINGS AND SOME HALOGENATED METHANES Thesis by Heinz Gerhard Pfeiffer In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1948 ACKNOWLEDGEMENTS I wish to express my sincere appreciation to Dr. E.W. Hughes and Dr. V. Schomaker for the great amount of help and encouragement extended during the course of these investigations, and to Dr. Linus Pauling for his continuing interest and the many valuable suggestions he has made. My associates, Mr. A. M. Soldate, Dr. D. P. Shoemaker, Mr. B. Keilin, and Mr. G. Guthrie, have assisted me greatly during the entire course of my graduate work, and I wish to express my appreciation to them at this time. I am indebted to my wife, Alma, for her painstaking help in the preparation of this thesis. ABSTRACT Sections I and II report the X-ray diffraction investigations of silver azide and boric oxide. Silver azide crystallizes in a body-centered orthorhombic structure. The space group is Ibam with four molecules in the unit cell. The silver atoms are in (a), the central nitrogens in(~), and the end nitrogens in (j) with x = 0.156 and y: 0.369. - - - A new type of part cell projection is developed. Boric oxide crystallizes in a hexagonal structure with three molecules in the unit cell, ao = 4.320 Kx., £o = 8.139 Kx. Each boron has three bonded oxygen neighbors at a distance of 1.35 X and coplanar with the boron. Sections III and IV report electron diffraction investigations of some three-membered rings and some halogenated methanes. The HCH bond angles of cyclopropane are about 116°, the C-H distance 1.1~ Kx., and the C-C distance 1.515 Kx. The other three-membered rings ..• ethylene imine, ethylene oxide, ethylene sulfide, and N-methyl ethylene imine ... have HCH angles of 116° and all other distances close to the sum of the covalent radii. The halogenated methanes ... difluorobromomethane, trifluorobromomethane, trichlorobromomethane, and difluorodibromomethane ... have bond angles close to tetrahedral; the only significant deviation is the FCBr angle of 110.5° in trifluorobromomethane. The bond lengths in these compounds are close to the sum of the covalent radii with the exception of the C-Br in difluorodibromomethane (1.925 Kx.) and in trifluorobromomethane (1.89 Kx.). TABLE OF CONTENTS Page No. Part A - X-Ray Diffraction I. Silver Azide. . . . . . . . . . . . . . . 1 II. Boric Oxide . . .. . . . . . . . . . . . 18 Part B - Electron Diffraction III. The Three-Membered Rings. • • • • • • .. 33 . . . . . 34 42 46 . . . . . 57 . . . . . . . . 58 62 65 67 Bibli ography. . . . . . . . . . . . . . . . . . 75 Cycl opropane. . . . . . . Ethylene Imine. . . . . . Ethylene Oxide. . . . . . N-Methyl Ethylene·Imine. Ethylene Sulfide. . . . . IV. . . . . . The Halogenated Methanes . . • • Difluorobromomethane. . Trifluorobromomethane. Trichlorobromomethane . Difluorodibromomethane. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 50 52 PART A THE X-RAY DIFFRACTION INVESTIGATION ~ SILVER AZIDE AND BORIC OXIDE I. An X-Ray Diffraction Study of the Structure of Silver Azide, AgN3 The structure of the heavy metal azides is of considerable interest on account of the ease with which they Ionic azides such as sodium azide, NaN , potas- detonate. 3 sium azide, KN3 , and ammonium azide, NH4 N3 , can be heated to decomposition without exploding. Such covalent azides as methyl azide, cH N , cyanuric triazide, c N (N ) 3 3 3 hydrazoic acid, HN , detonate readily. 3 3 and , 3 It was felt that 3 there was a possibility that the explosive character of silver azide could be explained on the basis of its structure. The ionic azides (1) have a symmetrical linear azide ion with bonded N-N distances of about 1.15 R. The covalently bound azide groups (2) are asymmetrical and linear with bonded N-N distances of about 1.12 i and 1.24 i. No complete investigation of a heavy metal azide has yet been made. Bassiere (3), West (4), and Hughes (5) have investigated silver azide, and Wilsdorf (6) has investigated cuprous azide, CuN . The results of the investigations of silver 3 azide are given in Table I. The three results for silver azide agree as to space group and the positions of the silver and N1 (central). The agreement of the axial lengths is fair, but West's density is certainly low. The parameters reported by Bassiere are certainly in error for they would demand that F(hkl) = F(~hl), while a glance at the observed values (Table II), particularly -2- Table I fJ obs. ;O calc. 6.04 Kx. 4.81 g/cc 4.99 g/cc 5.90 Kx. 5.96 Kx. 4.50 g/cc 5.06 g/cc 5.59 Kx. 5.88 Kx. 6.oo Kx. 4.837 g/cc 5.04 g/cc Ag N1 (central) N11 (end) Bassiere (~_) (g) West (.€!,) (g) Hughes (.€!,) (g) .€!.o Qo £0 Bassiere 5.58 Kx. 5,.93 Kx. West 5.58 Kx. Hughes z Space Group <.J) ~ = 0.145 4 Ibam-D2h <.J) l = 0.375 0.155 4 Ibam-D2h not determined 4 26 Ibam-D2h 2£=0.145 X: 26 26 The origin used by Bassiere and by West and the axes used by West have been changed to conform with those used in this thesis; the origin and special positions are as given in "Internationale Tabellen zur Bestimmung von Kristallstrukturen." - 3those with l odd, shows that these intensities are quite different. Both West and Wilsdorf assumed the configuration and dimensions of the azide group to be the same as in the ionic azides; an assumption which does not seem, a priori, very sound. West used only six reflections from the odd layer lines which are caused by the N11 (end) alone. Wilsdorf's determination was made with only powder data. It therefore seemed desirable to do a complete investigation of silver azide and determine the parameters directly from the intensity data. The crystals used in this investigation were made by adding silver azide to aqueous ammonia solution containing just enough ammonia to dissolve the silver azide. The crystals grown in a few days by cooling or evaporating the solutions gave evidence of twinn~ng, a difficulty also mentioned by Bassiere (3), the faces were striated and the observed X-ray reflections were often doubled. Finally some of the solution was put away for two years in a corkstoppered test tube, and at the end of this time the solution had evaporated and left needle-like crystals of silver azide that showed no evidence of twinning. Pyroelectric experiments were negative. Goniometric measurements on the well developed 110 faces gave ~o: ~o = 0.946. The Laue symmetry is mmm. An average of the values of West, Bassiere, and Hughes was taken for the axial lengths, i.e., ~ 0 :5.58 Kx., ~o = 5.90 Kx., and £o = 6.00 Kx. From these ~o: ~o = 0.946, in agreement with the goniometric value. A complete set of 20° oscillation photographs was made about the £o axis using Mo K~ radiation. Five layer lines were observed on each side of the equator. A rotation photo- graph about the £o axis was also made to facilitate comparison of the intensities of the hkl and khl reflections. Multiple film technique was used with 0.001 11 Cu foil between films. The film factor, 4, was calculated from the film factor of Eastman No Screen film .for Cu KCX: radiation, 3.7, and the absorption coefficient for cu. It is estimated from comparison of four independent sets of intensity estimations that the hkO reflection intensities are accurate to 20%, and the hkl reflection intensities are slightly more accurate. Two films were used in the oscillation photographs and three in the rotation photographs. All intensities were estimated visually (Table II) and all hkl and khl refle~tions were compared individually, special care being taken with the odd layer lines which depend, as shown below, only on the Nrr parameters. The observed intensities were corrected with Lorentz and polarization and Cox-Shaw factors, and for absorption. All reflections are absent for which h•~•l is odd and hOl and Okl are absent with 1 odd. Exceptions to these -5latter rules were carefully sought since the reflections with 1 odd are all weak; even with long exposures and favorable correction factors no exceptions were found. Possible space groups are Iba and Ibam. The negative result of the pyroelectric experiment indicates Ibam is more probable. It was observed that the 0th and 4th, and the 1st and 3rd layer lines showed the same dependence of the structure factors on hand t. The structure factors for these space groups are: Ibam (1 (- even h•~•l even(l odd (- Iba - 16 cos 2-rr hx cos 27T ~ cos 2rr lz A B =0 A :: -16 sin 271' hx sin 211 ky cos 2 71' l~ --B =0 <· (1 even (h•~•l even(l odd (- A = 8 cos 27: hx cos 271 ~ cos 271 1~ ·B = 8 cos 2 1T hx cos 277 sin 2 11 lz A = -8 sin 2rr7ix sin 211- ~ cos 271 lz B = -8 sin 2 1T ~ sin 2 11 !Z sin 27T ! l! It can be seen from the above structure factors that this functional dependence on hand t alone of alternate even and all odd layer lines will hold only if all of the~ parameters are o, 1/4, 1/2 and 3/4. This permits only certain special positions in Ibam. If these values for & are substituted in positions of Iba the resulting structure has Ibarn symmetry. Ibam is therefore the most probable space group. Placing the silver atoms in(~) sets the signs of all of the F(hkl) with 1 = 2n since -6- It was therefore possible to calculate a two-dimensional Fourier projection on the 001 plane (Fig. 1). The N1 •s are at~= o, z =½and~=½, x = o, with two at each position. From a projection along the [110] axis made by Dr. Hughes using Cu K« data the~ parameters of the nitrogens must be O and½; they must therefore be in (g). The Nrr's are in (J) with~= 0.153 and x = 0.389. From these approximate parameters the signs of the reflections on the odd layer lines were calculated. A half cell projection f> (~,z,-¼ ➔ ¾) was made (7 & 8) 1 • p (~,x,-t ➔ i) = 2A [ L ~o) cos 21T (hx + kz) hk + J Lh [k E1 odd~ cos --- 2 TT (hx + ~z) This projection (Fig. 2) gave the parameters~= 0.156 and x = 0.373 but because the nitrogen contribution to the ~o)was so small compared to the silver contribution it was decided to make a projection using only odd layer line data, which depends on the Nrr alone. p' (~,x) The Fourier projection (Fig. 3) shows only the Nrr atoms. The projection calculated (9) was // "-' - /J ~ X ➔ ~ ' ',} ' ,..., \...,. ,, ,,, J Projection Along [001] Figure 1 -f .0. . .------------------------------------------------4I y 0 t w ,, ,, ,, t------ - - - - - - - - - - - - - - - - - - - - - - - Only every tenth contour is shown for the silver atoms~ I I ~ -¼ y 0 t 4 0 J ·-- ,--, 0 Half-cell Projection Along [001] Figure 2 x ➔ Only every tenth contour is shown for the silver atoms. c._..., --~ 0 ~ $ . (X) -9~ = 2- Er:r -rrA 2n l cos 2n (!:!~ ~ u) sin - 4 - l h }£ 1 odd + n') h~' ~ sin 21'T (-a- +b -o -o u') b -0 lz' cos 21T ;-0 - s.~ I' - lz' ~' sin 21T £.o = lloI !' = £.o! lz' The integral of sin 2rr c -o ➔ .£.o 4 is zero, .£.o 3£.o -r ➔ 4 is zero. - 4£.o from and from lz' over this range is zero if 1 is The integral of cos 211 -=£.o even. Therefore 1:os - ~o 2'JT 1 z' £.o d!' 1 'f cos 21T 1!' £.o ~ If / 'C~,I) - 3,0 JI- _g_ = TTA lll. htl odd ~ -1 cos 2'rr ( ahx' + ifil:' ; -) sin -o -o 2rr l 4 d~' CV) 1' X Q.) ::.-i ::1 b.O ..-1 l'.x-4 1 0 0 -1,tl - >.....1 >< I .:::-,, ~ - 11This is the projection shown in Fig. 3. Atoms from A= 1/4 to 3/4 are subtracted from those that lie from l = -1/4 to 1/4. This eliminates the silver atoms and central nitrogen atoms, leaving only those nitrogens, Nrr, which have parameters. We are, in effect, taking the difference between the two half-cell projections along ~o• Four Nrr's are at & = 0 and four at & =½,the first four show up positive and the second four negative. The final parameters from this projection are~= 0.156 ± 0.002, y = 0.369 ~ 0. 002. Table II shows the agreement of the calculated and observed structure factors. The :li'(h!&0) data is first, arranged in order of decreased spacing, then the F{hkl) data with l odd, also arranged in order of decreasing spacing. c ~ e )').. temperature factor, e ~-~the calculated F0 's. A , with B = 1 was applied to The F's obs·erved were put on an absolute scale by averaging the ratios of F observed to F calculated. Scattering factors for silver and nitrogen were taken from the "Internationale Tabellen zur Bestirnmung von Kristallstrukturen. 11 Table III shows the nearest neighbor distance, and a drawing of the structure is shown in Figure 4. This is a projection along ~o onto (001). The large heavy circles are nitrogens at & = o, the large light circles nitrogens at & =½,and the small medium circles are silver at & =¾,the silvers at 3/4 lie directly -12- Table II hJl0 F calc. F obs. h Jl o F calc. F obs. 1 0 2 0 0 0 2 0 3 0 1 0 4 0 0 0 3 0 4 0 2 0 5 O 1 0 4 0 5 O 6 O 3 0 0 0 6 O 2 0 7 O 5O 6 O 7 1 0 6 4 0 3 7 0 0 8 0 7 3 0 2 8 0 8 0 0 8 2 0 6 6 O 5 7 0 7 5 o 1 9 O 4 8 O 8 4 0 3 9 O 9 1 0 0•10•0 9 3 0 127 167 152 148 117 127 121 135 135 139 129 140 105 121 88 109 107 91 92 108 61 75 73 93 64 65 52 64 , 64 7 7 O 2·10•0 6 8 O 8 6 O 5 9 0 10•0•0 10•2•0 29 31 39 35 26 27 28 23 24 22 24 28 25 37 36 23 29 20 19 17 17 17 1 0 2 2 1 3 0 4 3 2 4 1 5 4 3 0 5 6 2 6 1 5 4 98 99 78 113 104 86 80 92 61 84 73 88 73 71 53 57 64 46 53 57 63 53 50 51 47 47 39 34 36 40 42 31 35 36 29 56 53 60 61 55 47 52 51 42 42 36 33 37 37 23 35 30 25 9 5 O 4·10•0 1·11•0 10•4•0 Per cent deviation 9.8 h Jl l 1 2 1 2 1 1 1 2 3 2 1 3 2 3 1 3 2 1 1 4 1 4 1· ·1 2 3 3 3 2 3 1 4 3 3 4 1 4 3 1 2 5 1 3 4 3 4 3 3 5 2 1 4 1 3 2 5 3 5 2 3 1 6 1 6 1 1 F c~lc. F obs. 29 27 24 19 13 13 3 <3 8 10 <3 <. 3 <- 3 7 -22 19 ~14 -13 3 - 1 9 -11 2 - 1 - 1 7 9 = 1 4 -12 6 8 -10 - 8 3 9 <3 3 13 5 6 8 7 3 Per cent deviation 8.2 -13under the silvers at 1/4. All bonds go in the direction of their taper. Table III Atom Number Neighbor Distance Ag 4 NrI 2.56 K 4 NrI 2.79 K 4 NI 3.16 4 NI 3.31 A 2 Ag 3.00 K 2 Nrr 1.16 j 2 NI 3.00 R 2 NrI 3.13 2 2 NII 3.12 R 2 NII 3.38 _R 2 NII 3.47 j NI . NII i 0 =14- Figure 4 Projection of the Structure of Silver Azide on the !=l Plane -15DISCUSSION. The structure is a distorted potassium azide structure. In potassium azide, which is tetragonal, each potassium ion is surrounded by eight Nrr's at the corners of a square Archimedes antiprism. In silver azide in order to satisfy the silver coordination of four, four of the nitrogens are repelled and four drawn closer in orthorhombic symmetry. The four that are drawn closer are at the ends of opposite side diagonals of the anti.prism. This has the effect of distorting the square base into a rhombus with the short diagonal in the direction of bonding. Ammonium azide is also a distorted potassium azide structure (10). If in potassium azide the azide groups are arranged so as to give cubic symmetry, i.e., each layer is identical with the one below, and then four NrI's are pulled closer and four pushed away, there will also be fourfold coordination that is now almost preci.sely tetrahedral. is the NH4 N3 structure. That The NH4+ has a strong tendency to form four tetrahedral hydrogen bonds and can satisfy this desire in this way. The larger size of the ammonium ion would make a silver azide structure improbable for ammonium azide because the NH 4+ would be brought too close together. The azide group in silver azide has a center of symmetry and is linear with a bonded distance of 1.16 ~ 0.02 j_ Each azide is bonded to four silvers, two being attached to each end. The bond angles around the silver are -16about 85°, 85°, 108° and 108°. The bonding runs in the~ and~ directions making this a layer structure. The silver nitrogen bonded distance is 2.56 .R, considerably lengthened over the sum of the single bond covalent radii, 2.23 j, but much less than the van der Waal's distance which is 2.8 f. If each bond is only a fourth of a covalent bond, the expected lengthening can be calculated from Pauling's relation (11) D. r = 0.300 log n b. r = 0.18 .R n = bond number From this calculation the expected silver-nitrogen distance would then be 2.59 fin good agreement with the value found. The silver-silver distance· 3.00 f is also of interest. The sum of the covalent single bond radii of silver is 3.06 j, the sum of the metallic radii for tetrahedral coordination is 2.70 R. It seems that the silver-silver distance is less than would be predicted considering the silvers to be covalent and not bonded to each other. CuN3 (12) can also be derived from the potassium azide structure, a fact not recognized by Wilsdorf. If one orients the N3 groups lying on the [021] axes of KN3 parallel to each other and the ones on the [201] axes parallel to each other but at right angles to the first series the structure -17will be close to the CuN3 structure. From the results of this investigation there is no obvious explanation of the explosive properties of silver azide. RESULTS. Silver azide crystallizes in a body-centered orthorhombic structure with space group, Ibam-D~t, and with ~o = 5.58 ± 0.02 Kx., ~o = 5.90 ± 0.02 Kx. and £o = 6.00 ± 0.02 Kx. There are four molecules in the unit cell with the silver in(~), the N1 (central) in(~) and the Nrr (end) in (j) with~= 0.156 ± 0.002 and!= 0.369 + 0.002. The bonded nitrogen-nitrogen distance is 1.16 X and the bonded silver-nitrogen distance is 2.56 + 0.02 i. Punched cards were used for all Fourier cal- ± 0.02 cUlations (13). -18II. An X-Ray Diffraction Study of Boric Oxide The preparation of crystalline boric oxide, B203, has been reported by Taylor and Cole (14), McCulloch (15), and Kracek, Morey and Merwin (16). Taylor and Cole reported a crystalline phase, which they report as B203, formed upon holding HB02 in a vacuum at 200°c for several days and 400 hours more at 225°c. The density was 1.805 g/cc and the melting point 294 ~ 1°c. This density is less than that of B203 glass, 1.844 g/cc. Morey and Merwin (17) attempted to repeat this experiment, with no success. McCulloch reports the formation of crystalline B203 after heating H3Bo3 in loosely covered metal cans for several days at 300°c. The density he reports is 2.42 g/cc and the melting point 460°470°c. The results of Kracek, Mo!ey, and Merwin are in agree- ment with those of McCulloch. The crystalline B203 prepared by McCulloch showed 37 powder lines using CuK« radiation. The sample of crystalline B2o3 used in this investigation was procured by Dr. Max T. Rogers. Dr. Rogers and Dr. Hughes took a series of multiple film powder photographs using 3 films with both CuKa. and FeKcx radiation. Forty-four lines were observed after subtracting known lines due to traces of HB02 and H3B03. The lines were indexed by Dr. Hughes using an adaptation of the method of .Jacob and Warren (18). Table IV shows the agreement between observed and calculated values of -T g -19- Table IV h~l 1 ~g 1 0 0 l O1 1 0 2 0 0 3 1 0 3 1 1 0 1 1 1 1 1 2 2 0 0 2 0 l 1 0 4 2 0 2 1 1 3 2 0 3 1 0 5 1 1 4 1 2 0 1 2 1 2 0 4 0 0 6 1 2 2 1 1 5 1 0 6 1 2 3 3 0 0 2 O 5 3 0 1 3 0 2 1 2 4 1 1 6 3 O3 1 0 7 2 0 6 2 2 0 1 2 5 2 2 1 .0714 .0859 .1292~ .1301 .2015 .2143 .2288 .2721 .2857 .3002~ .3026 .3435~ .3444 .. 4158 .4327 .4455 .5000 • 5145l .5169 .5202 .5578 .5756 .5916 .6301 .6428~ .6470 .6573 .7006 .7312~ .7345 .7724~ .7795 .8059 .8571~ .8613 .8716 calc. 7 1 obs. .0719 .0856 .1287 .2013 .2149 .2280 .2715 .2865 .3007 .3433 .4158 .4320 .5003 .5155 .5580 .5755 .5920 .6295 .6446 .6575 .7000 .7315 .7740~ ~.7765 .8065 .8597 .8720 1 l h~l 7 7 3 0 4 2 2 2 1 1 7 1 3 0 1 3 1 1 3 2 2 2 3 2 0 7 1 0 8 1 2 6 1 3 3 1 1 8 4 0 0 4 0 1 1 3 4 3 o 6 0 0 9 4 0 2 1 2 7 2 0 8 1 0 9 4o3 1 3 5 3 O7 2 3 0 2 3 1 4 0 4 2 2 6 2 3 2 1 2 8 1 3 6 2 0 9 2 3 3 1 4 1 1·0·10 .8740 .9149 .9224~ .9286 .9431 .9864l .9872 .9938 .9963 1.0202 1.0587 1.1392~ 1.1428 1.1573l 1.1598 1.1630 1.1705 1.2006~ 1.2081 1.2184) 1.2419 1.2729 1.2899 1.3509~ 1.3571 1.3716! 1.3740 1.3773 1. 4149 1.4245 l.4488~ 1.4562 1.4872 1. 5145~ 1. 5165 .8720 .9140 .9293 .9420 calc. obs. .98t70 .9920 1.018 1.056 1.139 1.1565 l 1.1635 1.202 1.240 1.261 1.289 1.352 1.1375 1.4135 1.446 1.4835 1.513 A least squares calculation using 16 single lines gives = g_0 4.320 Kx. £.o::: 8.319 Kx. -20- for the hexagonal unit cell with ~o = 4.320 Kx., £o = 8.139 Kx. and Z = 3. Several space groups are possible with the observed extinctions 001 with l = 1, 2, 5, and 7. The presence or absence of 001 with l = 3, 4, 6, 8 or 9 was unobservable on account of overlapping of lines. The present part of the investigation started with attempts to grow single crystals by seeding vitreous B203 at temperatures from 200 to 450°c and cooling slowly. microcrystals were obtained. Only Attempts were then made to grow crystals from a NaCl - Al Cl 3 melt but with no success. It was then decided to investigate the environment of each boron by means of a radial distribution sum sin s_r .§. r. In order to interpret the areas under the peaks in terms of numbers of nearest neighbors it was necessary to put the IF 0 12 on an absolute scale. V) The intensities (Table were estimated by integrating under the peaks on a micro- photometer trace. The absolute scale and temperature factor were calculated by a method suggested in outline by Hettich (19) and developed independently by Shoemaker ( 20), Harker (21), and Hughes (22). The method suggested by Hughes was used; it differs from that of Harker in that it uses F's rather than F = F ~ fi i and the equations - 21 - = 2Bs2 + 2 1 og ~ log are solved by least squares rather than graphically. F (hkl) • F*(hkl) = IF12 (hkl) =L.1 f .!.2 If both sides are summed over the reciprocal lattice, for convenience over §. (§. = 4 7T si~ Q ) , the last term will average out and where r 2 1 -Bs = r10 e - , fi 0 being the atomic scattering factor as reported in the "Internationale Tabellen zur Bestimmung von Kristallstrukturen," for stationary atoms. The observed intensities, corrected for Lorentz and IF' 12, polarization, are related to the absolute intensities, jFl2 , by the scale factor k2 . :Making these substitutions the equation becomes -22- If the assumption is made that this equation holds over smaller intervals of~, and it will if a representative number of IF' l2 are included in the interval in~, then it is possible to derive a series of equations of the form e -2Bs 2 - Assuming that ~2 has its average value throughout the interval it is possible to take the logarithms of these equations log 2 : 2B~2.Q. + 2 log ~ s2 = s 2 from _a to _b - !12 Such a series of equations derived from the B203 data was solved by least squares methods; the temperature factor B obtained was 0.75, and the factor!& was evaluated simultaneously. The intensities were then put on the absolute scale (Table V ) with this factor and the radial distribution sum was calculated. -23- Table V Sin Q )\ .060 .121 .1335 .1464 .1795 .1803 .224 .231 .239 .240 .261 .267 .274 .275 .2925 .293 .300 .322 .329 .333 .354 .359 .359 .361 .374 .380 .383 .397 .401 .402 .406 .418 .421 .427 .429 .439 .441 .448 .462 .464 .466 .467 h~l 0 0 1 0 0 2 1 0 0 1 0 1 1 0 2~ 0 0 3 1 0 3 1 1 0 1 1 1 0 0 4 1 1 2 2 0 0 2 0 1~ 1 0 4 2 0 2~ 1 l 3 0 0 5 2 0 3 l O5 1 1 4 l 2 0 12 02 ll 4 0 0 6 1 1 2 1 1 5 1 0 6 1 2 3 3 0 0~ 2 0 5 3 0 l 3 0 2 0 0 7 1 2 4~ 1 1 6 3 O 3~ 1 0 7 2 0 6 2 2 0~ 1 2 5 2 2 1~ 3 0 4 nlFl2 obs. 0 0 1.86 888 3450 1390 89 2470 0 566 267 648 1092 0 397 670 0 356 2025 162 385 218 300 430 211 858 0 1310 810 113 892 58 Sin Q ..,._ .478 .480 .481 .481 .485 .496 .496 .498 .499 .501 .505 .514 .522 .533 .534 .537 .538 .539 .541 .549 .550 .550 .552 .557 .564 .568 .581 .582 .585 .586 .587 .588 .595 .597 .600 .601 .603 .610 .613 .614 .615 .616 h~l nlFl2 obs. 2 2 2 10 10 87l 1 3 0 1 3 1 150 12 2 3 2l 3 867 2 0 7 1 0 8 3 O 5 1 2 6 1 3 3 2 2 4 1 1 8~ 4 0 0 14 30 ll 4 3 O6 0 0 9 14 2o 2l 7 2 0 8 2 2 5 1 0 9 4 0 3 1 3 5 3 O 7~ 2 3 0 24 30 ll 4 2 2 6 1 1 9 2 3 2~ l 2 8 O•O•lOl 1 3 6 2 0 9 2 3 3 1 4 4 0 5 1 4 1 ~ 1•0•10 o; 87 955 0 180 460 0 478 834 312 0 177 71 202 510 364 0 533 143 109 0 405 -24 - 4 -rr !. (1: D(1:)- !.IF! ) = ~ -rr !. [ J F§. 12 ~ V IF l2 .§. 2 - z:,, f1 i IF 12 = sin sr - 2 as e - -- ( L. f1 )2 i The Patterson function (23) with provision for removing the peak at the origin and us i ng a sharpening factor is given by e 21r i h • r - - - Transforming to polar coordinates Integrating the Patterson function over a spherical shell at a distance!. from the origin gives the number of interatomic distances of length r weighted by the scattering - powers of the atoms a distance!. apart; this function is 2 411 !, D(!,). Where now ' -25- 41{,r = V 2 4 1T r_ D(r_) Separating out the 2 IF 12 term yields 4 rr r..2 D(r) O 0 = 4 1T r..2 1Foo l2 Figure 5 shows this summation. area of 1254 electrons 2 . sin§.!:. The peak at 1.35 i has an The area, A, under a peak at r Xis proportional to the number of distances of length r. and the product of the scattering of each of the atoms that are the distance r. Therefore the area under the peak at 1.35 j is given apart. by the equation n1 ::: number of B-0 distances per boron I½ = number of borons per unit cell m1 = number of electrons per boron ~ = number of electrons per oxygen Assuming neutral atoms with m1 = 5, m2 = 8, and n2 = 6, the calculated number of B-0 distances per boron is 2 .. 6 :::: 3 within our limits of error. The limit of error on the area of the peaks is necessarily large for the following reasons: the small number of terms (44) in the summation, -26cutting off the data at the CuK~ limit (the reflections at the CuKoc limit are still strong enough to indicate that there is considerably more data ), and the uncertainty of the observed intensities. Assuming that each boron has three oxygen neighbors then the area under the peak corresponds to m1 = 4.07, m2 = 8.62, and consequently to a B-0 bond with 31% ionic character, which is a reasonable value (24). The 1.35 j B-0 distance found agrees well with other compounds in which the boron has three oxygen neighbors in the same plane (25). Compounds in which the boron has four tetrahedral oxygen neighbors show B-0 distances of about 1.44 j (26). Therefore the evidence indicates that the B203 crystals probably contain planar B03 triangles with the B-0 distance 1.35 K. This result is in agreement with the results of Warren, Krutter and Morningstar (27) on B203 glass. Their radial distribution sum (Fig. 6) for the B203 glass is very similar to that for crystalline B2 o3 out to about 3.0 i, as would be expected if the immediate environment of the borons was the same in both forms. B2 o3 crystallizes in a hexagonal structure with ~o = 4.320 Kx., £o = 8.319 Kx., and 3 molecules of B2 o3 in RESULTS. the unit cell, density 2.42 g/cc. • Each boron is surrounded 0 by a planar triangle with the B-0 distance 1.35 A. -27- \ ' ----------------------------~o Figure 2 Radial Distribution Integral of B203 Cryst. am ttt • [IIItlfilf . i:_;: -~ti:!_-! ±t:_~-;+:+ ... !·L-+4+- a• _gm . - -++tft ::.:.-h-lt1+ mmm ■:...- ~ ~ ~ _ □ 2ong. - 111 1111111 :1:±±±±±:1 1111 11111111 • lililliltillllH . ~ i. 1 + ~ ;;i.,. - I.. - -- / ~ - J. :t: ...;:i: C r_ I: 11- • •., ... • ~ - - - . -+ t: f, tlH .tttm. I a l=,.. tt; ti? '-;'! I llitt±li . £ , r , -h,-.-rl-',T ·, ~ 1 1 ' t t i 1 "."J I tH:H 1-l ;::i::; ~ '+<'1 I ~.., • ' -1- ·1-· -♦ ......., , .z ~ :t"'±., 3' ;™ J- 1 Tij T i:, t_tt,t 4 - ·, I ti-· . 't ·4- 4- rrn 1 .tt11--1'1:111 !"'Tl"."'.J:µ:. :"11:.rttrit", rn _; ;ft :!'1"tc.1ff!.1J_J"'f"1 . .c1-fH-mt-_;_~ _.ff±_ : !:Ui: i+µ. lffltmr~ tfflfflUI111 lIIIi!111111111111111 H-~ .n, :H-1 1 + 5 -lj_ ht Et '! •.i~ fflffffllr. IIIEJilllt m:amt- tt ' (X) =!.I I\) ' ~ 1 Willill '·■1 l l llillllllllllllllllll t+-i ttttt;·- t!_ ~ ~ ·mmttwt;- l_ lillll■ llllfiliJ~YQffir -1:: ~ ,~ ... ~~~ ,,,/ t\-\ lfi4t_( - ~ / \ /\--'-'--:t :t:t+'t"- L, ;/- I=\~~ "' ~/ - ~,t ••~ ~ ¼1r ~I I I t'":J; · .... ~ Y :-a-r"'g·:l .• r 'L /t'; +++H+++ - ~ $/ -... z ', - -~t 'A ; cp: i~ ' . ,,, l" <~?J;~ ,~~q mm:!:ffi:! Sti!J:S ¼ M±t11lllllllll!!/l lill:.U-1" ,_. E1 Jmte 1111111111 . J. r--i D• "'" il:u ti ~ff't ·=tr 1 1.... ..t~B l Oit ! £ T • .,Ra~~{3:~t., ;-S~vr f~ On :~ eg~a • \!/J. t: 3 ...glass lffl F- ,.j_j ,- 111111111!1'_ - ..... ..,. J.tttl:i mmw m -- mt! :!:" t+ T'T,•-t• oo t: ~ ,ttffffl :?~iii - ~4iob~- -t+::~--t-~·-t--1 I 1111 11 11 i:I -i+-- r 1-0--,f)00 . mllltmtntt1• -~ i+t;::.:t:t,"~·tttr l+'--1---t+-i-'-:...µ..µ. ~-111111!111111111 ~·=wttttttl ;:tt:t:t::;+: : ~ ~ : ,1; i ~ ~e; , ,a &r -Mor~ingat~r ~ 111111111 1111111111wmm mi }4'?,"C?ni }~a~r1t_nJ I(rJt_ "'"' ·~ tt ~ ~ t:t--+-f-- """'4-' t!fflfflII 1111 11111111111 ··--- + r i - ~ ·T'1""f++i-t+t-ttt -.~aoo-- lmffml ■ ITmlIIIIll IIII. PART B THE ELECTRON DIFFRACTION INVESTIGATION OF SOME THREE-MEMBERED RINGS A~ SOME HALOGENATED METHANES -29- lNTRODUCTION. The present investigation of cyclopropane, C3H6, ethylene oxide, C2H4 o, ethylene imine, c2H4 NH, ethylene sulfide, c2H4s, and N-methyl ethylene imine was initiated by Dr. Henri L~vy, who prepared photographs of each of these five substances in 1938, made measurements of ring diameters on some of them, and calculated some theoretical intensity curves for cyclopropane and ethylene oxide. Subsequently Dr. Verner Schomaker measured all of the photographs and calculated radial distribution integrals. With the work reported in Section III the investiga tion has been brought to a conclusion. Dr. Norman Davidson has been interested in the properties of some brominated methanes. One aspect of his investigations has been the varied reactivity of the bromine atom in these substances. At his . suggestion the investigation reported in Section IV was undertaken. The primary object of the investigation was to determine the correlation, if any, between the carbon bromine distances and the reactivity of the bromine atom; however, it was also decided to determine '. ·: ~ the complete structures. Trifluorobromomethane, difluoro- bromomethane, and difluorodibromomethane had not been investigat ed by electron diffraction previously~ Trichlorobromo- methane had been investigated but the reported C-Br distance of 2.01 j, considerably longer than any values for a C-Br distance reported recently (28) (the reported distances -30average about 1.88 -1.94 2), made a redetermination desirable. I wish to thank Dr. Davidson, Dr. Buchman, Dr. Eyster, and Dr. Sargent for furnishing the compounds used in these investigations. The previous investigations of cyclopropane, ethylene oxide and trichlorobromomethane will be discussed in the sections dealing with those compounds. -31EXPERIMENTAL. The electron diffraction equipment used in these investigations has been described by Brockway (29). Photographs of cyclopropane, ethylene oxide, ethylene imine, ethylene sulfide, and N-methyl ethylene imine were taken by Dr. Henri Levy about ten years ago. The wave l'ength value to be used with these photographs seemed doubtful so further photographs of cyclopropane and ethylene oxide were made in the course of this present work ( ~ = 0.0608 Kx. by calibration with ZnO smoke (30)) and compared with the old photographs. An adjustment of the wave length value for the earlier photographs was found to be necessary in order to obtain agreement between the measurements of ring diameters between the two sets of photographs. The adjustment will be discussed in the section dealing with cyclopropane. When the original vis ual curves were drawn the value of the wave length used by Dr. L~vy ( ~ = 0.0613) was assumed. Photographs of the halogenated methanes were made with a camera distance of 10.90 cm and a wave length of 0.0605 Kx. calibrated against zinc oxide smoke (30). INTERPRETATION. The visual curves were drawn in accordance with our observations ~nd the expected general behavior of I(i) (Equation II). The radial distribution integrals were calculated from the visual interpretations with the equation -32(I) -- j rs. max a sin I(.9.) 1T !:.9. 10 s.=1,2 .•. sin - 02 - = --1.Q_ s 7T - q = - 40 . ,. ._ - O= scattering angle aq2 where~ was determined so that e-was equal to 0.1 at i max. The values of I(.9.) were taken from the visual curves* Theoretical intensity curves were calculated with the simplified theoretical scattering equation (II) 2 -Qij s. e -- sin _2T !:9. 10 where the temperature factor Q was given the usual values 0.00016 for the C-H bonded distances, 0.00015 for the C•••C in N-methyl ethylene imine and 0.0003 for all unbonded hydrogen distances. No other terms were temperature factored. All punched card (31) calculations were made with IBM machines. The limits of error were estimated from the range of models that were acceptable qualitatively and had acceptable ~c values; the quality of the measurements as shown by the qo ;verage deviation of 9.c values; and an estimate of the S.o magnitude of systematic errors such as deviations in wave length, uncertainty in calibration, and measurement of the camera distance. -33III. THE THREE-MEMBERED RINGS Cyclopropane, Ethylene Oxide, Ethylene Imine, Ethylene Sulfide, and N-Methyl Ethylene Imine VISUAL INTERPRETATION. The visual interpretation of the photographs of cyclopropane (V, Fig. 8), ethylene imine (V, Fig. 10), ethylene oxide (V, Fig. 12), and N-methyl ethylene imine (V, Fig. 13) was done simultaneously. These photographs have features which are only subtly different and are therefore subject to a differential interpretation of gr eater than usual accuracy. Of particular interest is the first minimum, which has a strong feature on the outside in cyclopropane, a weaker one on the outside in ethylene imine, and none in ethylene oxide. The feature is as strong in the N-methyl ethylene imine diffraction pattern as in that of cyclopropane but it has moved much further down into the minimum. The second maximum was observed to become broader and the third maximum narrower going in the sequence N-methyl ethylene imine--cyclopropane--ethylene imine-ethylene oxide. The sixth maxima were observed to be con- sistently weak and quite broad. The third minima and fourth maxima of the patterns of cyclopropane, ethylene imine, and ethylene oxide were especially useful. In cyclopropane the third minimum was observed to be very sharp as compared to the fourth maximum; in ethylene imine the minimum is broader but still not as broad as the fourth maximum; in the pattern -34of ethylene oxide these features were observed to be a ntisymmetrical. In other respects the photographs of these four compounds were observed to be very similar. The notable features of the visual interpretation of ethylene sulfide are the as ymme try and broadness of the second maximum, the relative strength of the third and fifth minima, and the very strong sixth maximum. CYCLOPROPANE, C3H6. Previous electron diffraction investi- gations have been made by Pauling and Brockway (32), and by Bastiansen and Hassel (33). show a o h symmetry. 3 Raman and infra-red spectra (34) Pauling and Brockway report C-C 1.53 j and C-H 1.09 f, and assumed the HCH angle to be 109°28•. Their radial distribution sum shows a peak due to the unbonded C···H distance from 2.2 - 2.5 i. These values make an HCH bond angle of more than 125° improba ble. The work of Bastiansen and Hassel has come to my attention only in abstract form with reported parameters of C-C 1.54 R, C-H 1.08 f, and HCH angle 118.2°. Our doubts in regard to the wave length to be used with the old photographs made it necessary to estimate a more accurate value than the one, 0.0613 Kx., used by Dr. Levy. The factors which lead to our doubts are the following: 1 . No calibrati.on of the wave length was made between the time the photographs were taken and the time the equipment was -35transferred to its present location; 2. the lattice spacing of the gold foil used for wave length calibrations at the time the pictures were taken was shown to be in error by Malmberg and Lu (30); and 3. no shrinkage correction was made. The latter correction is perhaps not quite as serlous if the calibration pictures and the experimental pictures have similar histories. In this case, however, the experi- mental pictures had aged and dried over a period of nine years before the measurements were made. Table! permits a correlation between the .9. 0 values of Dr. Schomaker (s 1.) and of the author (P1 ) on the old pictures ( ')\ = 0.0613 Kx. assumed), and those of Dr. Schomaker (S 2 ) and of the author (P2 ) on the new films ( l\ = 0.0608 Kx.). Table !1 permits a similar correlation between P1 and P2 for ethylene oxide. In order to obtain agreement in tne average the old ~o values must be divided by 0.9922, corresponding to a corrected wave length of 0.0608 Kx. (0.9922 x 0.0613 Kx.). For the average ~o values reported in Tables VI, VII, VIII, IX, and X this correction has been made; for cyclopropane and ethylene oxide, of course, the effect is to make the size determination essentially independent of the old pictures. The radial distribution integral R (Fig. 8) calculated from the visual interpretation, V (Fig. 8), indicates bonded distances of 1.10 Kx. (C-H) and 1.52 Kx. (C-C), and a nonbonded C···H distance of 2.24 Kx., corresponding to an HCH -36Table A Sl s2 pl 18.61 18.48 23.46 23.42 19.27 23.26 29.22 33.54 48.45 55.54 61.50 68.85 75.35 82.12 29.17 34.23 48.99 55.10 61.70 68.52 74.62 81.47 28.58 34.2~ 49.0 55.64 61.87 69.07 76.30 84.03 p2 19.13 23.68 29.17 34.32 49.55 56.20 61.91 69.76 75.62 82.87 Average correction Sl _l s2 p2 1.0070 1.0017 1.0206 1.0000 0.9982 0.9903 0.9973 0.9920 0.9780 0.9695 1.0073 0.9823 1.0017 0.9773 0.9778 0.9883 0.9935 0.9870 0.9964 0.9909 0.9955 0.9903 Table A1 pl p2 _l_ 30.47 36.10 44.57 50.31 58.25 64.15 72.07 77.86 84.98 89.56 96.25 30.15 36.12 44.95 51.82 57.78 64.97 72.21 78.70 85.38 91.83 98.97 1.0106 0.9994 0.9915 0.9709 1.0081 0.9874 0.9981 0.9893 0.9953 0.9753 0.9725 Average correction p2 0.9907 -37bond angle of 116°. Theoretical intensity f unctions (Figs. 7 & 8) were calculated for a systematic range of molecular shapes in the neighborhood of the shape indicated by the radial distribution function with the C-H distance taken as 1.09 Kx. for all models. ellipse (Fig. 7). The acceptable models lie in the Curve G is the curve corresponding to the model of Bastiansen and Hassel. Curves B3 and B4 are the only curves on which the region from the second to the fifth maximum is satisfactory. B4 has the third minimum deeper than desirable but it is not possible to eliminate B4 on this basis. After the necessary scale change the final parameters and estimated limits of error are C-C 1.515 ± 0.02 Kx., C-H 1.10 ± 0.03 Kx., HCH angle 116 ± 5°, and C•••H 2.24 ± 0.06 Kx. The agreement between observed and calculated~ values is shown for this best model in Table VI and in Table VIa for the model with the parameter values reported by Bastiansen and Hassel, which lie just outside our limits of error. The bracketed i values were not included in deterqc mining the averages-=- and the corresponding average devia~o tions on account of the relative inaccuracy of measuring broad features and features near the center of the diffraction pattern. The calculated moment of inertia, IB, for the best 40 model (Table VI) is 42.4 x 10g-cm2 , in fairly satisfactory -38- Figure 7 C-C C-H 1~2 1.09 t 1. 52 1.09 t 1.49 1.09 I L HCH 105° Al Bl Cl 110 A2 Bl " C2 115 A3 C3 120 A4 C4 125 A5 B5 C5 -390 20 40 60 80 100 3 4 5 Cl Bl Al A2 A3 G A5 A4 B l" B3 B4 B 5 C2 C3 C4 C5 R 0 2 A Figure 8 Cyclopropane -40- Table VI Cyclopropane C-C Max. 2a 2 3 4 = 1 . 515 Kx. 6 7 8 LHCH = 116° 9.c Min. S.o S.c 1 ( 8.74) (11. 05) (14.24) 18.92 23. 52 29.15 34.05 (41.79) 49.36 56.30 62.20 69.59 76.61 83;32 89.39 96.98 ( 8.90) (10.90) (13.68) 19.1 23.49 29.04 34.39 (43.11) 49.63 56.49 61.74 70.56 76.80 82.59 89.34 96.52 2a 2 3 4 5 C-H = 1.10 Kx. 5 6 7 go 1.0095 0.9987 0.9962 1. 0100 1.0055 1.0034 0.9926 1.0139 1.0025 0.9912 0.9994 0.9953 Average 1.0015 Average deviation 0.60% -41- Table VIa Cyclopropane C-C = 1.54 Kx. Max. 2a 2 3 4 6 9.o 9.c 1 ( 8.74) (11.05) (14.24) 18.92 23.52 29.15 34.05 (41.79) 49.36 56.30 62.20 69.59 76.61 83.32 89.39 96.98 ( 9.01) (11.07) (14.74) 18.92 23.60 28.74 34.47 (41.77) 49.62 55.71 61.65 67.69 74.48 81.17 87.57 94.31 2a 2 3 5 6 7 8 9.c 9.o Min. 4 5 L,HCH = 118° C-H = 1.08 Kx. 7 1.0000 1.0034 0.9859 1.0123 1.0053 0.9895 0.9912 O. 9727 0.9722 0.9742 0.9796 O. 9725 Average 0.9882 Average deviation 1% -42- agreement with the spectroscopic value of 41.9 x 10 (34,35). =40 2 g-cm Scaling our model down by an amount (0.6%) well within our limits of error would make the agreement exact. The model with the values of the parameters as reported by Bastiansen and Hassel has a calculated IB of 42. 9 x 10-40 g-cm 2, a discrepancy of 2,4%. ETHYLENE IMINE, C2H4NH. The radial distribution integral, R (Fig. 10), calculated from the visual interpretation, V (Fig. 10), indicates bonded distances for the average of 4 C-H and 1 N-H of 1.08 Kx., and for the average of 2 C-N and 1 C-C of 1.50 Kx. The broad peak centered at 2.20 Kx. contains the unbonded C··•H and N••·H distances. Theoretical intensity curves (Figs. 9 & 10 show some representative curves) were calculated assuming that the.HCH plane bisects the CCN angle and that the N-H bond is symmetrical and makes a 58° angle with the plane of the ring. The average and the ratio of the C-C and C-N distances and the HCH bond angle were varied systematically around a model with C-C 1.52 Kx., C-N 1.47 Kx. and an HCH bond angle 116°. The C-H distance was taken as 1.09 Kx. and the N-H as 1.01 Kx. for all models. Models D, E, H, and F (Figs. 9 & 10) are acceptable. E and H are the most desirable because the region from the second maximum to the fourth minimum is very similar to the region as interpreted from the photographs. Figure 9 C-N C-C 1.44 1.50 1.48 1 .51 t L L_5.g_ 1. 52 ' HCH 110° A 115 B 120 C 125 I E H J K G 0 20 40 60 80 7 y 100 8 \ A B C D E F G H J K .I 0 2 Figure 10 Ethylene Imine 3 4 5 -45- Table VII Ethylene Imine C-C = 1.52 Kx., C-N = 1.49 Kx., C-H = 1.10 Kx., N-H = 1.01 Kx., LHCH = 116°, LCNH = 117° Max. 2a 2 9.o 9.c 1 ( 8.3) (11.6) ( 9.7) (11.1) (13.60) 18.44 23.68 29.43 35.47 (43.13) 50.09 56 . 74 63.29 70.04 76.39 82.94 88.38 96.45 2a 2 3 4 3 4 5 6 7 8 9.c Min. 5 6 7 (14.20) 18.64 23.78 29.68 35.37 (42.63) 49.58 56.18 62.54 70.04 76.09 82.70 88.69 95.74 9.o 0.9893 0.9958 O. 9915 1.0028 1.0102 1.0099 1.0121 1.0000 1.0040 0.9964 0.9966 1.0074 Average 1.0013 Average deviation o.64% -46The theoretical curves proved insensitive to changes C-C in the ratio of the C-N distance but a ratio of less than C-N > 1 were not investi0.93 is unacceptable. Ratios of ---=C-C gated. The average of C-C and C-N is 1.,0 ~ 0.02 Kx.; assuming that C-C is 1.52 Kx. the C-N is 1.49 ± 0.02 Kx. The final results are C-C 1.52 Kx. (assumed), C-N 1.49 + 0.02 Kx., C-H 1.10 ~ 0.04 Kx., and HCH bond angle 116 + 6 0. Table VII shows the agreement between observed and calculated q values for the best model. ETHYLENE OXIDE. A previous investigation of ethylene oxide has been made by Ackermann and )lffayer (36). The purpose of the investigation was to prove the ring structure; no attempt was made to determine the parameters accurately. The radial distribution integral, R (Fig. 12), calcUlated from the visual interpretation, V (Fig. 12), indicates bonded distances of C-H 1.10 Kx. and the average C-0 and C-C 1~47 Kx., and unbonded C·••H and O••·H distances averaging 2.17 Kx. Theoretical intensity curves (Figs. 11 & 12 show some representative curves) were calculated with C-H 1.09 Kx. for all models and assuming that the HCH plane bisects the CCO angle. The C-0 and C-C distances and their ratio were varied systematically around 1.43 Kx. and 1.52 Kx., respectively, and the HCH angle was varied around the value found 0 for cyclopropane, 116. -47- Figure 11 C-0 C-C ~ • 1.44 1. 52 t 1.44 1.48 t I HCH 110° Ll 115 0 120 p B N2 E4 125 Curve O has C-C 1.52 Kx., C-0 1.43 Kx., C-H 1.09 Kx., and HCH angle 115°. s u 0 20 40 60 80 100 ·" I ' ,'I'I I s\ V E3 El E4 N2 LI 0 p Q B s u R 0 2 3 A Figure 12 Ethylene Oxide 4 5 -49- Table VIII Ethylene Oxide C-C = 1.52 Kx., C-0 = 1.45 Kx., C-H = 1.10 Kx., LHCH = 116° Max. 2 3 4 5 6 7 8 Min. 9.o 9.c 9.o qc 1 ( 8.9) (19 .1 ) 22.28 30.43 36.48 44.49 50 .89 58.45 64.70 72.36 78.71 85.46 93.55 99.74 ( 9.5) (18.6) 24.49 30.13 36.43 44.54 51.40 57.90 64.90 72.16 78.81 85.21 92.21 99.27 1.0083 0.9901 0.9986 1.0011 1.0099 0.9905 1.0031 0.9972 1.0013 0.9971 0.9857 0.9953 2 3 4 5 6 7 Average 0.9982 Average deviation 0.55% -50C-0 ratios down C-C to 0.93; ratios greater than 1 were not investigated. The Acceptable models were found with models N2, E4, and S were acceptable with E4 being the best. Assuming the C-C distance to be 1.52 Kx. the C-0 distance is 1.45 ~ 0.02 Kx. and the average of the C-0 and C-C distance is 1.47 ~ 0.02 Kx. The final . results are C-C 1.52 Kx. (assumed, ) C-0 1.45 ~ 0.02 Kx., and HCH angle 11 6 ~ 60. Table VIII shows the agreement between observed and calculated q values for the best model. N-METHYL ETHYLENE IMINE. The radial distribution integral, R (Fig. 13), calculated from the visual interpretation, V (Fig. 13), indicates bond distances for C-H of 1.09 Kx., and the average of C-C and C-N of 1.49 Kx., unbonded distance for the average of C•••H and N•••H of 2.19 Kx. and for C•••C of 2.48 Kx. Theoretical models (Fig. 13),for which the assumption was made that the ring has the configuration found for the ring in ethylene imine, were calculated. Models A, B, and C have methyl-nitrogen distances of 1.47 Kx. and the angle of the methyl group with the ring 57.5°, and 59.5°, respectively. 58.5°, Model Bis the only model on which the sixth maximum is satisfactory. Models D and E have cH -N distances of 1.44 and 1.50, respectively. A wider range 3 of models was calculated in an attempt to find other regions of acceptability but with no success. -51- Table IX N-Methyl Ethylene Imine Ring as in C2H4NH, CcH3-N = 1.47 Kx., LCNCcH3 = 116° Max. la 2 3 4 5 6 7 8 Min. 9.o 9.c ~c 7fc, 1 ( 7.05) (10.58) (12.80) 18.54 23.38 29.98 36.78 43.59 51.10 58.05 63.29 71.25 77.35 84.66 92.31 98.51 ( 9.07) (10.98) (12.90) 18.54 23.73 29.88 36.78 43.03 51.60 58.15 63.29 71.55 78.31 . 84.35 91.21 98.46 1.0000 1. 0151 0.9963 1.0000 0.9873 1.0099 0.0017 1.0000 1.0042 1.0126 0.9964 0.9880 0.9995 la 2 3 4 5 6 7 Average 1.0014 Average deviation 0.54% -52Under the assumption that the ring configuration is that in ethylene imine the results indicate that the methyl group is at an angle of 58.5 ~ 2° to the ring and the nitrogen-methyl distance is 1.47 ~ 0.04 Kx. Table IX shows the agreement between observed and calculated q values for the best model. This result is in accord with the prediction of Eyster (37) that the angle to the plane of the ring would be less than 64°. ETHYLENE SULFIDE. The radial distribution integral, R (Fig. 14), calculated from the visual interpretation, V (Fig. 14), indicates distances of 1.10 Kx. (C-H), 1.52 Kx. (C-C), 1.82 Kx. (C-S), and 2.48 Kx. (S• • •H). Theoretical intensity curves were calculated with values of the parameters near the radial distribution values. The theoretical curves proved very insensitive to changes in the C-C, C-H a nd C·••H distances. It was therefore only possible to determine the C-S and S-H distances. Curve T (Fig. 14) shows the most acceptable model with C-C 1.53 Kx. (assumed), C-H 1.10 Kx. (assumed), LHCH 116° (assumed), C-S 1.82 Kx., and S•••H 2.48 Kx. The final parameters determined with the limits of error are C-S 1.82 ~ 0.02 Kx., and S···H 2.48 ~ 0.07 Kx. Table X shows the agreement between observed and calculated q values for the best model. -530 20 60 40 80 100 V A B C D E R 2 0 0 20 A 40 I I 3 4 5 60 80 10 0 V T R I 5 A Figures 13 and 14 N- Methyl Ethylene Imine and Ethylene Sulfide Table X Ethylene Sulfide C-S = 1.82 Kx., C-C = 1.53 Kx., C-H = 1.10 Kx., LHCH = 116° Max. 2 3 4 g,o g_c 1 7.26 11.90 14.20 17.53 20.41 25.50 29.68 35. 58 40.11 46.31 51.50 57.60 62.63 68.29 74.33 80.37 85.0l 91.00 7.86 13.50 2 3 4 5 6 7 8 9 10 9.c 9.o Min .. 5 6 7 8 9 20.26 25.30 30.28 35.37 40.51 46.36 51.85 57.39 62.79 68.43 74.07 79.87 85.46 90.75 0.9926 0 .. 9921 1.0204 0.9943 1.0100 1.0011 1.0068 0.9965 1.0024 1.0022 0.9966 0.9937 1.0053 0.9972 Average 1.0008 Average deviation 0.61% -55DISCUSSION. The structures of these three-membered rings indicate that the strain caused by the small bond angle in the ring is distributed almost equally between the other angles. The six carbon bond angles in these compounds have values of about 60°, 116°, and four 117°. Changes of only 0.0025 Kx. in the unbonded hydrogen distance would make the latter five all equal. This change makes no observable change in the diffraction pattern. The CH3 group in N-methyl ethylene imine has a 58.5° angle with the plane of the ring which, if the electron pair can be considered a group, makes the nitrogen bond angles about 61°, 117°, and four 116°. The short C-C distance of 1.515 reported in cyclopropane is in agreement with the value 1.52 Kx. Pauling and Brockway (32) report ed for the C-C peak in their R.D.I. The first five rings, which are all they observed, are sensitive to the average of the C-C and C-H distance but rather i nsensitive to the ratio. As a result a 1.52 Kx. C-C and 1.10 Kx. C-H would fit the observations of Pauling and Brockway as well as the 1.53 Kx. C-C and 1.09 Kx. C-H upon which they decided. With the observation of three additional rings it is possible to determine the C-C/C-H ratio more accurately. This evidence indicates that the C-C distance in cyclopropane is definitely shorter than the normal value for alkanes, 1.54 Kx. -55aSeveral theoretical calculations (38) of the HCH bond angle have been made. Coulson and Moffitt predict an HCH angle of 113° and a shortening of the C-C distance; both results are in general agreement with this investigation. The 121° angle calculated by Kilpatrick and Spitzer is improbable on the basis of our results. The original article by Bastiansen and Hassel (33) has been made available since the rest of the thesis was written. 1.535 They report the following parameters: C-C = i (in a footnote), C-H = 1.08 i, HCH angle 118.2°, and CCH angle 116.2°, with a probable error in the angles of 2°. It is not clear to which angle this probable error refers; a 2° error in the CCH angle corresponds to an 8° error in the HCH angle. If that interpretation is correct a 2° reduction in the CCH angle would make the moment of inertia agree with the spectroscopic value& If the probable error in the HCH angle is 2° no such agreement can be obtained. It is noteworthy in each of these compounds in which another atom, x, is substituted for one of the carbon atoms in the cyclopropane ring that the C-X distance seems to be lengthened over the sum of the covalent radii of carbon and X, viz . C-N, 1.49 Kx. (sum of covalent radii 1.47 Kx.), C-0, 1.45 Kx. (1..4-3 Kx.), and C-S, 1.82 Kx. (1.81 Kx.). trend is even more striking when compared with the short (1.515 Kx.) C-C distance found in cyclopropane. It is This -55bcertainly possible that the introduction of another atom in the ring lengthens all of the bonds. If the logical assumption had been made that the bond lengthening was distributed uniformly among the bonds in the ring, the results for ethylene oxide would be C-C 1.55 Kx. and C-0 1.4-4 Kx., and the results for ethylene imine would be C-C 1.55 Kx. and C-N 1.48 Kx. These values of the distances are completely acceptable on the basis of the determinations reported in this section. -56- RESULTS* Cyclopropane C-C: 1.515 + 0.02 Kx. C-H 1.10 +-0.025 Kx. LHCH = 116 5° = ± Ethylene Imine C-C = (1.52 Kx.) C-N 1.49 + 0.02 Kx. C-H: 1.10 0.03 Kx. LHCH 116 ±: 6° Average C-C and C-N = 1.50 :t 0.02 Kx. H-N (1.01 Kx.) LCNH = (116 0 ) = = = + Ethylene Oxide C-C = (1. 52 Kx.) = C-0 1.45 + 0.02 Kx. C-H = 1.10 0.03 Kx. Average C-C and C-0 1.47 :!:. 0.02 Kx. ± LHCH = 116 :!:. 6° = Ethylene SUlfide S•••H = 2.48 + 0.07 Kx. c-s = 1.82 + 0.02 Kx. C-C = (1. 52-Kx.) LHCH = (116°) N-Methyl Ethylene Imine (Ring configuration as in ethylene imine) L~HccH3 = 116° Cctt -N 3 = 1.47 ~ 0.04 Kx. * Values in parentheses are assumed. -57IV. THE HALOGENATED METHANES Difluorobromomethane, Trifluorobromomethane, Trichlorobromomethane, and Difluorodibromomethane VISUAL INTERPRETATION. The difluorobromomethane and tri- fluorobromomethane patterns (curve V, Figs. 16 & 18) are dominated by the Br-F term, both showing fourteen rings to ~ = 100. The other terms modulate the basic pattern but since they are of lower frequency do not have much effect upon the positions of the features. The determination of the shorter distances and the bond angles depends mainly, therefore, upon the estimation of the relative strengths of the maxima and minima. ~ The early parts of the curves, < 50, are insensitive to the weaker distances. The situation regarding the patterns of difluorodibromo- methane and trichlorobromomethane is somewhat different. Each of these patterns has a pair of long, strong terms (F•••Br and Br•••Br, and Cl•••Cl and Cl•••Br, respectively) and neither pattern has a term of weight greater than the sum of the weights of all the other terms. The most striking observation on the photographs of tric hlorobromomethane is 1 the position where the Cl-Cl and Cl-Br distances beat against each other (V, Fig. 20), and the number of weak features before the terms are in phase again. The photographs of difluorodibromomethane were all rather light and the very sensitive region in the neighborhood of~= 65 (V, Fig. 22) -58was difficult to interpret; as a result the determination does not have the accuracy that could be obtained if it were possible to interpret this region unequivocally. The shape of the fourth maximum and the relation between the seventh and eighth minima also proved to be very structure sensitive. The available sample of CF 2Br2 was insufficient for making heavy pictures. DIFLUOROBROMOMETHANE. The radial distribution integral, R (Fig. 16), indicates bonded distances of 1.34 Kx. (C-F) and 1.92 Kx. (C-Br) and unbonded distances of 2.20 Kx. (F· • .p) and 2.68 Kx. (Br•• •F). The C-H and F• • •H distances have too little weight to show on the R.D.I., and the Br··•H peak falls under the Br••·F peak. Theoretical intensity curves were calculated for differe·nt values of the ratio Br-F and the FCBr and FCF angles. The C-H distance was Br-C assumed to be 1.09 Kx. and the hydrogen atom was assumed to be symmetrically located with respect to the halogen atoms. The Br-F distance was taken as 2.68 Kx. for all models. The curves proved insensitive to changes of 5° in the FCF angle from the tetrahedral value, ma ki ng the attempt to determine this angle unfruitful. In the determination of the other parameters the FCF angle was therefore assumed to be tetrahedral. The theoretical curves (Figs. 15 & 16) proved to be quite sensitive to variations in the Br-C -59distance and FCBr bond angle; only curve E was completely satisfactory, although Dis just on the limit of acceptability. Figure 15: 2.68 2.68 1.87 1.91 1.95 107° C F 109 B H 111 C G Br-F C-Br 2.68 t LFCBr I Br-F = 1.395 C-Br The final result is Difluorobromomethane therefore has ~ 0.015 and the FCBr angle= 110 ~ 2°. C-Br 1.915 ~ 0.03 Kx., C-F 1.35 ± 0.04 Kx., Br-F 2.68 ± 0.02 Kx., FCF angle 109.5° (assumed), and FCBr angle 110 ± 2°. Table XI shows the agreement between observed and calculated 9. values for the final model. 0 20 40 60 80 100 3 4 5 ,, ,J ' V ' A B C D E F G H R I' 0 I 2 A Figure 16 Difluorobromomethane -61- Table XI Difluorobromomethane C-Br = 1.915 Kx., Max . 4 5 6 7 8 9 10 11 12 13 14 S,c ~o ~c 1 ( 6.83) (10.28) (13.59) (17.14) 20.26 24.31 27.96 32.11 35.62 38. 81 42.78 46.40 50.20 54.29 58.36 62.35 65.39 68.70 72.50 76.10 80.10 84.00 87.70 92.00 94.90 98.40 ( 6.35) ( 9.80) (13.25) (16.80) 20.35 24.10 27.95 32.15 36.00 39.00 42.50 46.50 50.50 54.25 58.20 62.18 65.45 68.25 72.20 76.20 80.30 84.15 87.80 91.50 95.20 98.65 2 3 LFCBr = 110 Min. 1 2 C-F = 1.35 Kx., 3 4 5 6 7 8 9 10 11 12 13 S.o (0.9297) (0.9533) (0.9749) (0.9801) 1.0044 0.9913 0.9996 1.0012 1.0106 1.0048 . 0.9934 1.0021 1.0059 0.9992 0.9972 0.9973 1.0009 0.9934 0.9959 1.0013 1.0025 1.0018 1.0011 0.9946 1.0032 1.0025 Average 1.0002 Average deviation 0.35% -62TRIFLUOROBROMOMETHANE. The radial distribution integral, R (Fig. 18), calculated from the visual interpretation, V (Fig. 18), indicates bonded distances of 1.35 Kx. (C-F) and 1.90 Kx. (C-Br), and unbonded distances of 2.20 Kx. (F···F) and 2.68 Kx. (F·••Br), giving calculated bond angles of FCF 109° and FCBr 110°. Theoretical intensity curves (Figs. 17 & 18) were calculated under the assumption of c3v symmetry and with a systematic variation of the shape of the model around the radial distribution value. The shape parameters were the Br-F ratio and the FCBr angle. The C-Br Br-F distance was taken as 2.68 Kx. for all models. Figure 17 C-Br Br-F LBrCF 108° B 110 F C D , ~ / / 112 J I G ' --K I ,, ~ L 0 2:0 40 60 00 I 0 3 4 5 7 V B A C E D F G H R I 0 I II I 2 Figure 18 Trifluorobromomethane -64Table XII Trifluorobromomethane C-Br = 1.90 Kx., Max. 3 4 5 6 7 8 9 10 11 12 13 14 15 LFCBr = 110° 9.c Min. 9.o qc l ( 6.7) (10.7) (14.11) 17.13 20.77 24.27 27.90 32.00 36.02 39.67 43.33 47.13 50.83 54.30 57.98 62.17 65.40 68.62 71.70 75.70 80.06 84.00 87.78 91.56 95.63 99.32 102.11 105.70 ( 6.3) ( 9.9) (13.3) 17.20 20.70 24.00 27.80 31.85 35.65 39.30 42.90 47.00 50.70 54.50 58.25 62.20 65.60 68.70 72.30 76.50 80.50 84.15 88.oo 91.95 95.80 98.75 102.55 106.50 1.0041 0.9966 0.9889 0.9964 0.9953 0.9897 0.9907 0.9901 0.9972 0.9974 1.0037 1.0047 1.0005 1.0031 1.0012 1.0084 1.0106 1.0055 1.0018 1.0025 1.0042 1.0018 0.9943 1.0043 1.0076 Average Average deviation 1.0000 0.50% 1 2 C-F = 1.35 Kx., 2 3 4 5 6 7 8 9 10 11 12 13 14 qo -65Dr. Schomaker more recently has made a visual interpretation (not shown) of the photographs. The dotted ellipse shows the range of acceptability for Dr. Schomaker's visual interpretation, the solid ellipse shows the range of acceptability for V (Fig. 18). The results on the basis of the visual observations of the author are C-Br 1.90 ~ 0.03 Kx., C-F 1.35 ± 0.03 Kx., Br-F 2.68 ± 0.02 Kx., and FCBr angle 110 ± 2°. The results based on Dr. Schomaker's visual interpretation are C=Br 1.88 t 0.03 Kx., C-F 1.35 ± 0 .03 Kx., F-Br 2.68 ~ 0.02 Kx., and FCBr angle 111 ~ 1.5°. The final results are C-Br 1.89 ± 0.03 Kx., C-F 1.35 + 0.03 Kx., Br-F 2.68 ± 0.02 Kx., and BrCF angle 110.5 + 2°. Table XII shows the agreement between observed and calcUlated ~ values for the author's final model. Table XIII shows the agreement of calculated (final.model) and observed i values for the visual interpretation of Dr. Schomaker. TRICHLOROBROMOMETHANE . The radial distribution integral, R (Fig. 20), calculated from the visual interpretation, V (Fig. 20), indicates bonded distances of 1.85 Kx. (average C-Cl and C-Br) and unbonded distances of 2.94 Kx. (average Cl-Cl and Cl-Br). The molecule has c3v symmetry (38). Theoretical intensity curves (Figs. 19 & 20) were calculated by changing the ratio Cl-C and the ClCBr angle. The C-Cl distance was C-Br taken as 1.76 Kx. for all models. -66Table XIII Trifluorobromomethane C-Br = 1.88 Kx., Max. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 LFCBr = 111° C-F = 1.35 Kx., Min. 9.o 9.c g_c 9.o 1 ( 6.7) (10.7) (14.11) 17.13 20.77 24.27 27.90 32.00 36.02 39.67 43.33 47.13 50.83 54.30 57.98 62.17 65.40 68.62 71.70 75.70 80.06 84.00 87.78 91.56 95.63 99.32 102.11 105.70 ( 6.3) ( 9.85) (13.3) 17.07 20.60 24.15 27.85 31.93 35.65 39.30 43.00 47.05 51.00 54.50 58.25 62.00 65.40 68.65 72.50 76.70 80.75 84.33 88.15 92.00 95.58 99.90 102.65 106.70 (0.9403) (0.9207) (0.9426) 0.9965 o. 9917 0.9951 0.9982 0.9978 0.9893 0.9907 0.9929 0.9983 1.0033 1.0037 1.0047 0.9973 1.0000 1.0004 1.0111 1.0130 1.0086 1.0039 1.0042 1.0047 1.0005 1.0059 1.0053 1.0095 2 3 4 5 6 7 8 9 10 11 12 13 14 Average 1.0010 Average deviation 0.52% -67Figure 19 Cl-C C-Br ~ . 7 ~ ~ t ' 1.95 1. 91 LClCBr 106° A C 109 D F 112 G I The final parameters are C-Cl 1.76 ~ 0.03 Kx., C-Br 1.91 t 0.03 Kx., Br-Cl 3.00 t 0.03 Kx., Cl-Cl 2.87 ± 0.03 Kx., and ClCBr angle 110 ± 2°. Table XIV shows the agreement between observed and calculated~ values for the accepted model, Ee The 2.01 Kx. C-Br distance reported by Capron and Hemptinne (39) is unacceptable. DIFLUORODIBROMOMETHANE. The radial distribution function, R (Fig. 22), calculated from the visual interpretation, V (Fig. 22), indicates bonded distances of 1.38 Kx. (C-F) and 1.91 Kx. (C-Br), and unbonded distances of 2.23 Kx. (F-F), 2.67 Kxe (Br-F), and 3.14 Kx. (Br-Br). Theoretical models (Figs. 21 & 22) were calculated for different values of the ratio of Br-Br and the C-F distances; the C-F distance Br-F C-Br was assumed to be 1.36 Kx. and the Br-F distance was taken as 2.67 Kx. for all models. V B C D E F G H lq 0 4 2 ca.,s, Figure 20 Trichlorobromomethane 5 -69Table XIV Trichlorobromomethane C-Cl = 1.76 Kx., :Max. 1 2 3 4 5 6 8 9 10 11 12 13 14 15 LClCBr = 110° 9.c Min. 9.o 9.c S.o 1 ( 5.95) ( 8.67) (12.16) (15.32) (18.88) (22.36) 25.49 28.61 32.14 35.61 39.30 42.50 ( 5.45) ( 8.75) (11.80) (15.15) (18.75) (22.25) 25.50 28.50 32.10 35 .50 39.50 42.30 45.40 48.75 52.20 55.70 58.70 62.20 65.30 68.80 71.80 75.10 78.30 81.60 84.60 87.70 91.20 94.60 (0.9120) (1.0116) (0.9704) (0.9898) (0.9889) (0.9951) 1.0004 0.9962 0.9988 0.9969 1.0051 0.9953 1.0000 1.0025 1.0087 1.0052 0.9975 0.9981 1.0002 1.0025 0.9986 1 .. 0005 1.0038 1.0060 1.0141 1.0042 0.9982 1 .. 0008 2 3 4 5 6 7 C-Br = 1.91 Kx., 7 8 9 10 11 12 13 14 45.40 48.63 51.75 55.41 58.85 62.32 65.29 68.63 71.90 75.06 78.00 81.11 83.42 87.33 91.36 94.52 Average 1.0015 Average deviation 0.35% -70- Figure 21 C=F C-Br 6 L..3.§. 1.95 1.36 1.91 ~ 7 1. I Br-Br Br-F 1.16 1.17 1.18 K N 1.19 M B L E CA V I J G 1.20 The best model lies between A and F. The final parameters are C-F 1.36 - (assumed), FCF angle 109° (calc'd.), C-Br 1.93 ~ 0.03 Kx., BrCF angle 109 ~ 2°, BrCBr angle 110 ~ 2°, Br-F 2.67 ~ 0.02 Kx., and Br-Br 3.15 ~ 0.03 Kx. The limit of error, as given, on the BrCF angle is independent of the assumption of 109° for the FCF angle. On the basis of the 109° value for the FCF angle the limit of error would be~ t 0 • Table XV shows the agreement of calculated (average of~ and F) and observed~ values for the best curve. 20 0 40 60 I I I 80 100 ,, ,,' '\ ', V A B C D E F G H J K L R I 0 I 2 A 3 Figure 22 Difluorodibromomethane I 4 I 5 -72Table XV Difluorodibromomethane C-F = 1.36 ± 0.06 Kx., C-Br = 1.93 ± 0 .04 Kx., LBrCBr = 110° Max. 1 Min. S.o 1 5.4) ( 9.0) (12.1) (15.4) (19.3) (24.9) 28.90 32.60 36.1 39.50 42.75 46.20 50.00 53.55 (56. 90) 63.55 66.75 70.55 73.40 76.95 80.55 84.25 87.60 91.10 94.45 97.75 2 2 3 4 5 6 7 8 9 10 11 12 13 14 3 4 5 6 7 8 9 10 11 12 13 ( -- S.c S.c ~o ( 6.2) ( 9.0) (12.6) (15. 51) (18.98) (23.92) 28.89 32.56 36.38 39.19 42.57 46.53 50.16 53.72 ( 57 .78) 63. 54 66.48 70.96 74.00 77.72 80.76 83.91 87.09 90.83 94.84 97.55 (0.8710) (1.0000) (0.9603) (0.9910) (1.0163) (1.0169) 1.0000 1.0003 0.9920 1.0074 1.0038 0.9933 0.9970 0.9968 (0.9842) 1 .. 0000 1.0038 0.9945 0.9919 0.9900 0.9975 1.0041 1.0057 1.0028 0.9958 1.0018 Average 0.9989 Average deviation 0.45% -73DISCUSSION. The dibrominated methyl fluorides tend to release bromine even when sealed in glass (40). This is in accord with the longer C-Br distance, 1.93 Kx., found for dibromodifluoromethane than is found in most brominated hydrocarbons, 1.91 Kx. Trifluorobromomethane is more stable than most hydrocarbon bromides (40), and the C-Br distance found was 1.89 Kx., a 0.02 Kx. shortening from the normal value. No significant deviation in the C-F distances was found in these compounds. RESULTS* Trifluorobromomethane C-F = 1.35 ± 0.03 Kx. C-Br = 1.89 ± O.OJ Kx. LFCBr = 110.5 ± 2 Dibromodifluoromethane C-F = (1.36 Kx.) C-Br = 1.925 ~ 0.03 Kx. LBrCBr = 110 • 2° LFCBr = 109 ±-2o Difluorobromomethane C-F = 1.35 + 0.03 Kx. C-Br = 1.91-+ 0.03 Kx. LFCBr = 110 ~ 2° Trichlorobromomethane C-Cl = 1.76 + 0.03 Kx. C-Br = 1.91 ~ 0.03 Kx. L ClCBr = 110 ± 20 * Values in parentheses are assumed. -74Several theoretical calculations (38) of the HCH bond angle have been made. Coulson and Moffitt predict an HCH angle of 113° and a shortening of the C-C distance; both results are in general agreement with this investigation. The 121° angle calculated by Kilpatrick and Spi tzer is unacceptable on the basis of our results. The original article by Bas tiansen and Hassel (33) has been made available since the rest of the thesis was written. They report the following parameters: C-C = 1.535 Kx. (in a footnote), C-H = 1.08 Kx., HCH angle 118.2°, and CCH angle 116.2°, with a reported probable error in the angle of 2°. It is not clear for which angle this probable error is reported; the error in the CCH angle is only onefourth as large as the error in the HCH angle. An error of 8° in the HCH angle (2° in the CCH angles) would make it possible to obtain agreement with the spectroscopic results. -75BIBLIOGRAPHY 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. L. K. Frevel, J.A.c.s., 58, 779-782 (1936). s. B. Hendricks and L. Pauling, J.A.c.s., 47, 2904- 2920 (1925). I.E. Knaggs, Proc. Roy. Soc. 1 A, 150, 576-602 (1935) E.W. Hughes, J.C.P., 3, 1-5 l1935). M. Bassiere, Compt. rend., 201, 735-737 (1935). C. D. West; Z. Krist., 95, 421-425 (1936). E.W. Hughes, Thesis, Cornell University (1935) and later work. • Heinz Wilsdorf, Acta Cryst., 1, 115 (1948). Verner Schomaker, unpublished work. A. D. Booth, Trans. Faraday Soc., 41, 434-439 (1945). E.W. Hughes, unpublished work. L. K. Frevel, Z. Krist., 94, 197 (1936). L. Pauling, J.A.c.s., 69, 542 (1947). Heinz Wilsdorf, Acta Cryst., 1, 115 (1948). P.A. Schaffer, Jr., Verner Schomaker, and Linus Pauling, J.C.P., 14, 648-b58 (1946). N. w. Taylor ands. s. Cole, J.A.c.s., 56, 1648 (1934). L. McCulloch, J.A.c.s., 59, 2650 (1937). F. C. Kracek, G. w. Morey, and H. E. Merwin, A.J. of Sci., 35a, 143 (1938). G. W. Morey and H. E. Merwin, J.A.c.s., 58, 2248 (1936). c. W. Jacobs and B. E. Warren, J.A.c.s., 59,2588 (1937). A. Hettich, z. Krist., 91, 154 (1935). D. P. Shoemaker, Thesis, California Institute of Technology (1947). David Harker, Meeting A.S.X.R.E.D. (April 1948). E.W. Hughes, unpublished work. A. L. Patterson, z. Krist., 90, 517-542 (1935). Linus Pauling, Nature of the Chemical Bona, Cornell University Press (1942). W. H. Zachariasen, Z. Krist., 88, 150-161 (1934). G. E. R. Schulze, Z. Physik. Chem., 24, 215-240 (1934). B. E. Warren, H. Krutter~ and o. Morningstar, J. Am. Ceram. Soc., 19, 202-~06 (1936). L. R. Maxwell, J. Opt. Soc., 30, 374 (1940). Walter Gordy, James W. Simmons and A.G. Smith, Phys. Rev., 74, 243 (1948) . L. O. Brockway, Rev. Modern Phys., 8, 231 (1936). c. S. Lu and E.W. Malmberg, Rev. Sci. Instr., 14, 271 (1943). P.A. Schaffer, Jr., Verner Schomaker, and Linus Pauling, J.C.P., 14, 648-b58 (1946). 32. 33. L. Pauling and L. O. Brockway, J.A.c.s.? 59, 1223 (1937). O. Bastiansen and O. Hassel, Tids. Kiemi Bergvensen Met., 34. 35. 36. Gerhard Herzberg, Infra-Red a nd Raman Spectra, D. Van Nostrand Co., Inc. (1945). L. G. Smith, Phys. Rev., 59, 924 (1941). P. G. Ackermann and J.E. Mayer, J. Chem. Phys., 4, 37. E. H. Eyster, Thesis, California Institute of Technology, 38. C. A. Coulson and W. E. Moffitt, J. Chem. Phys., 15, 39. J.E. Kilpatrick and R. W. Spitzer, J. Chem. Phys. 14, 463 (1946). P. Capron and M. de Hemptinne, Sci. Abst., 40, 207 (1937). J. J. Brice, w. H. Pearlson, and J. H. Simons, J.A.c.s., 6,71-72 (1946). 377 (1936). (1938). 151 (1947). 40. 68, 968 (1946). -_77_ Propositions Submitted by Heinz G. Pfeiffer Ph.D. Oral Examination, Nov. 10, 1948, 9 ;OO A.~I., Crellin Conference Room Committee: Professors Schomaker (Chairman), H·....ghes, Corey, Bates, Yost, Zechmeister, lJeher and Kirkv•ood. 1. The sum, 1~k Fh ,_l\.,t. cos(hx + ky) is valuable in certain cases because it eliminates a t oms in certain of the special p ositions in some of the space groups and also gives app roxima te z parameters . 2. (a) In electrophoretic ex_oerime~ts the op timum density gradient can be obtained ·oy working as close to the free '.3 ing point of the solution as possible. S. Swing le, Thesis, California Institute of Technology, 1943. (b) The ouality of the re sult s obt a ined by the present methods is not noticeably affectea. by temperature c:.evi8.tions as great as 10° from the optimum value as long as the temperature is kept consta nt in the course of the experiment. 3. (a) In the method outUnEd-in th:i.s thesis for determining the scale and temperature factors simultaneously care must be exercised in choosing a suitable method of averaging S2 over the intervals cove red by the normal equations• (b) A • h"ing factor S2 e.-as 1.-reig applied to the observed "" 1 /'1:11ls 2 or • +h i-rou. ld improve " e resu 1 ts. 4. (a) A t a bulation of temperature fact ors used in various structure determinations 1trould be of va lue. (b) A system of catalogin g electron diffraction photographs for purposes of analysis is proposed. * 0 The C-H distance in ethane , 1.11.A. should be used in spectroscopic ~;l elertron diffraction investigations of substitutea. methanes in cases ,,,h-e re it is necessary to ass-ume a value of this distance to determine a structure rather than the methane value of 1.09!. * L. S □ ith a::id A. 1:!oodward J.C.P. 3s6, 1942. V. Schomaker and K. Hedberg, Electron cUffraction investigation of ethane now in nrogress at this l a b oratory. 5. 6, (a) Ell::ectron diffraction methods which rely entirely on using the data in an integrated form are a step in the wrong direction. (b) A comparison of internal and external consistence of electron diffraction measurements ~-rould be of value in estimati::1g the merit of an investigation. (c) Several of the electron diffraction investigations made by Dornte have been repeated and. all found in serious error. '.foe remaining compounds investiga.ted by Dornte sho-c;.ld be reinvestigated for the purpose of removing er~::irs from the literature and increasing general confidence in electron diffraction investigations. -787. (a) The C-C stretqhing frequency for et4ylene. 1623v. cyclopentane, 886~ cyclopropane ll8if, spiro.pentane, 108Jlf" and etl}ane 821V-provide support for the values of the C-C distances found in these compounds by electron diffraction, 1.52 Kx, 1.:3u Kx, 1.515 Kx, and 1.49 K,x. (b) From the C-C stretching frequency of 1010'\r it is estimated that the C-C distance is 1.52 - 1.53 Kx. A :Badger's rule calculation extrapolating between Ethane and Ethylene gives 152.75 Kx. 8. (a) In many cases it is posqible to determine only some of the structure parameters by electron diffraction, by coordinating these with available spectroscop ic data the co mplete structure can often be determined. (b) It would be logical and valuable to be gui(led by spectroscopic data, ,.,,hen available, in choosing thecre~ical models for electron diffraction dttermina tions. 9. The crystalline solid rep orted by Taylor and Cole (J.A.C.S . .2Q. 1648 (1934) as Bz03 was proba.bly hB0 2 • 10. (a) The physiologically imp ort.s.nt esters of phosphoric acid have acid strengths greater than t:1a.t of phospho ric acid iteelf, it is proposed that this is due to the format:on of hydrogen bonds stabilizing the ion. (b) On account of their grea t bioche~ical imp ortance the structure of some of these esters should be determined. 11. The correlation between the me ta and ortho-para directing properties of groups on disubstituted benzenes and the- relative melting points of ortho, meta. and para compounds found by Holler(:. Org. Chern. 13. 70 (1948) is purely fortuitous and could be explained better on the basis of hydrogen bond formation.