I. The Crystal Structure of Potassium Silver Cyanide. II. An X-Ray Examination of the 12-Molybdophosphates and Related Compounds. III. The Crystal Structure of Cadmium Chloride Citation Hoard, James Lynn (1932) I. The Crystal Structure of Potassium Silver Cyanide. II. An X-Ray Examination of the 12-Molybdophosphates and Related Compounds. III. The Crystal Structure of Cadmium Chloride. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/kd0j-7p10. https://resolver.caltech.edu/CaltechTHESIS:09182024-170700357 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 Thesis Committee: Unknown, Unknown Defense Date: 1 January 1932 Record Number: CaltechTHESIS:09182024-170700357 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:09182024-170700357 DOI: 10.7907/kd0j-7p10 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16740 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 18 Sep 2024 17:56 Last Modified: 18 Sep 2024 18:20 Thesis Files PDF - Final Version See Usage Policy. 17MB Repository Staff Only: item control page

I. THE CRYSTAL STRUCTURE OF POTASSIUM SILVER CYANIDE II. A.~ X-RAY EXAMINATION OF THI!: 12 -MOLYBDOPHOSPHAT:B~S AND RELATED COMPOUNDS III. THE CRYSTAL STRUCTURE OF CADMIUM CHL ORIDE Thesis by James Lynn Hoard In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena , California 1932 I. THE CRYSTAL STRUCTURE OF POTASSIUM SILVER CYAL~IDE INTRODUCTION The crystal structure of potassium silver cyanide, KAg( CN)"", is of particular interest on account of the presence of the chemically very stable complex anion, Ag(CN);. It is perhaps of some theoretical importance to know whether the angle between the bonds formed by the silver a.tom with the cyanide groups within the ion approaches more closely to the tetrahedral angle of 109°28 1 or to linearity, that is to 180°. The X-ray investigation of these crystals was undertaken at the suggestion of Professor Linus Pauling, with the hope of reaching a. definite conclusion regarding the problem stated above in addition to determining the crystal structure, The crystals of KAg(CN) 2 used in this investigation were obtained from Professor Pauling. trigonal with cL They are described by Groth 1 as = 66°57', and as showing [106] and [11~, often with a compe.rable degree of development so tha. t the crystals resemble regular octahedra. As a matter of fact various stages of development of {11:i} were found among the specimens here studied. Some crystals were rhombohedra, others closely resembled regular octahedra, while a. few formed plates on [11~, in addition, of course, to intermediate habits. However, there was nothing in the external appearance to indicate the presence of a polar axis, that is the absence of a center of symmetry within the crystal. a fact of importance in later considerations. a ppreciable cleavage is observed for crystals of KAg(CN)2 , No 2. DETERMINATION OF THE UNIT CELL JUID SPACE GROUP Since the X-ray data show the underlying lattice of K.Ag(CN) 2 to be hexagonal, all indices used hereafter in this paper will be referred to a hexagonal unit, the axes of which coincide in direction with the projection upon the basal plane of the crystallographic rhombohedral axes. Laue photographs were prepared using general radiation from a t un g sten anticathode tube with the X-ray beam inclined at various small angles to the basal plane, (00 •1), and to a. rhombohedral face, (2l· 2). were prepared by reflecting Mo Koe Oscillation photographs radiation filtered thru zir- conia from (O J · l) and from a ground face, (11• 0). The value of a, the edge of the smallest hexagonal unit, was detennined from layer line reflections appearing on oscillation photographs for which the radiation was reflected from (00 •1). With the projection on the basal plane of a crystallographic rhombohedral axis as the axis of oscillation, the identity distance in this direction as calculated by means of the Polanyi formula, is found to be 7. 34 lt. s it = I sinjl, 11 i th, however, a direction in the basal plane which made an angle of 30° with the preceding one as the axis of oscillation, the observed layer line spacings lead to an identity distance of73· 7,34 = 12.71 K (see Table I). These results fix unam- biguously the value of a, the edge of the smallest hexagonal unit, as 7. 3 4 ± o. 1 K. TABLE I Layer Line Data. from Photograph I B 1 . Distance from -s to +s 1. 119 cm 2 2.241 .11136 12. 71 7.34 3 3.387 . 16698 12. 72 7.34 4 4. 573 . 22291 12. 71 7.34 6 7. 087 .33399 12. 71 7. 34 s Sin)L I I/13 • 05586 12.66 ! 7.31 1t Calculations ma.de by means of the Bragg equation, n ~ = 2d sin e for the equatorial reflections on oscillation photographs from (00• 1) lead to an observed spa cing along c of d(OO · l) = 8.84 ~ 0.11t n, (see Table II). However, the odd orders are apparently missing upon these photographs, indicating that the true unit translation along c is (2)(8.84) = 17.68 lt. This view is confirmed both by means of Laue photographs, and by the observation that the layer line spacings upon an oscillation photograph with c as the axis of oscillation lead to an identity distance in this direction of 17.7 I. 4. TABLE II Data from the bquat or of Phot ograph I A (h k · l) Line (Mo K) Sin e d(OO • l) n, (00,n, ) rJ... . 0403 8.80 Jl (00 •2n, ) d... • 0802 8,84 ( 00•3n, ) i;,(.. .1201 8.85 (00 •4n 1 ) ot. , 1603 8,84 (00 • Sn, ) ol . 2001 8.86 ( 00 ·6n,) ol. ' . 2401 8.85 ( 00 •7n , ) <X I .2807 8,83 (00 •8n 1 ) o1.., . 3207 8,84 Average 8.84 A The hexagonal unit with a= 7,34 !, c = 17.7 ! was used to calculate values of n ~ for all of the observed reflections upon two completely indexed Laue photographs. The X-ray beam wa s slightly inclined to the normal to (00 •1) for one of these, and to (212 ) for the other. In both cases no calculated value of n A was found to be less than 0.24 X, the short wave length limit of the radiation employed, while a total for the two photographs of about 56 forms were observed to reflect in the first order. Selected data in the first order from t he second of these photographs are given i n Table III (with this crystal orientation only t-uo planes, (h k ,.fl. ) and (k h •.i!.. ) , of each form gave observed reflections}. 5. TABLE III Representative First-Order Laue Data from a (21 · 2) Photo 6 raph Photogr aph II A Form nA t_hk •.e} A 0 - 44 • 5 0.35, 0.47 55 • 21 .39, 32 · 20 .35 32 •15 .36, .40 21 · 14 .43, .46 32·11 . 2 9, .35 .26, .30 .27, .38 .42 -10 · 8 -45• 2 -• 64 7 .27 11 • 10 .27 36 · 10 .33 -38 · 15 .32, .36 33.2 • ?,4, .42 46 · 5 .3~, .44 5 ·ll· 10 .43, .40 If six molecules of KAg(CN) 2 be placed in a hexagonal unit with a = 7 .34 A, c = 17. 7 A, the calculated density is 2 .36 g/ml, 0 0 which is in satisfactory agreement with the experimental value of 2.32 :t O.l g/ml determined by the displacement method using benzene. This unit, therefore, contains 6 KAg(GN) • 2 6. If now the underlying lattice were rhombohedra.l, only planes with 2h + k +./!, integral could give any reflections except 3 the third, sixth, ninth, etc. orders. Inspection of the Laue data. contained in Table III, for instance, reveals many planes for which 2h + k + .,.e_ is not integral, but which reflect for values of n ~ 3 than 0.72 !, three times the short wave length limit. less Also (00 · 1) re- flects in the s econd, fourth, eighth, tenth, etc. orders, thus clearly demonstrating that the lattice is not rhombohedral. This means, there- fore, that the unit hexagonal cell with a = 7.34 Jl, c = 17.7 X containing 6 KAg(CN) 2 is t o be accepted as the true one. Laue photographs taken with the X-ray beam normal to (00 •1) show a three-fold axis and three planes of symmetry, so that the pointgroup is c v, D3 , or D3 d. 3 The space groups based upon a hexagonal lattice Which are isomorphous with these point-groups are: 2 2 3 4 1 3 2 4: 6 5 1 2 3 .,...,, C!v, C3v, C3v• C3v, D3 • D3 , D3, D3, D3, D3, D3d• D3d, D3d, u3d• Of the space-groups listed, all of those with special criteria except tvw may be eliminated by the presence of "forbidden" reflections. How- ever, besides the space-groups without special criteria, there are left c!v and n!d, which have [m m 2m•R} hal ved 3 for ,R, odd. That is, for these two space-groups, reflections of this type may appear only in even orders. The procedure adopted was to look for reflections of this type on both Laue and oscillation photographs for which the corresponding planes were in favorable position to reflect, found which would rule out C!v No reflection was and ~d, ~lthough planes of the type fm ill 2m•-fj with ..R. even were observed to reflect in all orders, as well as planes with ~ odd in even orders. Among the observed 7. absences required by these space-groups were the following: 1, The odd orders of (00 · 1) from ( 00•1) to (00 •27) inclusive (even orders from (00•2) to (00•28) were present). 2. On photographs from (00 · 1) with a as the axis of oscillation, (2 1•7) to (2 1•19), (4 2•11) to (4 2•19), (2 l· 7) to (2 1•19) and (4 2•9) to (4 2·19), all for1 odd, 3. On a photograph from (11 • 0) with c as the axis of oscillation, (11 · 1),(22· 1), (33 · 1),(44· 1), (11 · 3), (22·3), (33·3), (11 ·5 ),(22·5), (33 · 5), (22·7), (33·7), etc., together with corresponding planes of the negative forms, that is (1 1•1) etc. 4. On Laue photographs, about 20 forms of the type (m,m • 2:iii.,_l ) with ,£ odd in the first order. A total of about 60 absences of the kind required was observed for planes which were in favorable position to reflect, a n~~oer so large as to make it very difficult to account for them with any structure not based upon either c!v or n;d• It seems highly probable, therefore, that an accepted structure for KAg(CN) 2 must be based upon one of these two space-groups. 2 4 A fundamental difference between D3 d and C3 v arises on account of the fact that the former possesses a center of symmetry while the latter has none. Because of this it is probable that a 4 crystal with a structure based upon C3 v will show the pyroelectric effect, while this is not possible in the case of n!d. Hence an experiment demonstrating the presence of pyroelectricity would show 2 definitely that the space-group is not D4d, while a negative result 8. would make ~d seem more probable than c!v• Such an experiment was actually performed upon a crystal of octahedral habit about 5-6 mm. long after the manner described by Groth. 4 No pyroelectricity was indicated for KAg( GN) 2 , al though tourmaline as a "blank" substance gave an entirely definite positive result. Since neither the pre- ceding experiment nor anything in the face development indicated that the crystals lack a center of symmetry, it was attempted next to find 2 a structure based upon D3 d. DETERMINATION OF THE STRUCTURE Six molecules of K.Ag(CN) 2 mu st be placed within the unit 2 cell in positions given by the space-group D3 d• possibilities 5 An examination of the a.t once reveals that the structure must have many para- meters, so that a. "rigorous11 determination is hardly possible. The procedure adopted was to make a minimum number of plausible assumptions regarding this comp ound, and to test their reasonableness wherever possible. Since the silver atoms have approximately three times the scattering power for X-rays of the pota.ssiurn ions, which in turn possess about three times the scattering power of carbon or nitrogen atoms, it is to be anticipated that the stronger reflections, particularly those appearing at wide angles of scattering, must be due in large part to silver. The relative unimporta.nces of carbon and nitro- gen for large angles of reflection will often be accentuated since it may be expected that these wro kinds of a.toms usually will not scatter in phase with each other. In fact it is only the presence of such a 9. relatively large number of carbon and nitrogen atoms which causes them ever to be of significance for l arge angles of reflection, since the scattering power of such light atoms decreases so rapidly with decreasing interplanar distance. In view of these considerations, the procedure has been to find reasonable a pproximate positions first for silver and then for potassium by making use of wide angle reflections which appeared upon a number of basal plane oscillation photographs. The photographs used were of the two kinds previously mentioned. Th at is, both a, the hexagonal axis, and a direction in the basal plane making an angle of 30° with a, were used as axes of oscillation. A horizontal slit system and a crystal with a face 3-4 mm. across were used. Basal plane reflections as far as (00 · 28) were obtained by tak- ing successive photographs with a 20° cam, the angle be"ti<reen the X-ray beam and (00•1) in the starting position being changed according to need. The indices of all important layer line reflections were assigned without ambiguity by draViing the reciprocal lattice 6 for the orthohexagono.1 unit, that is for the corresponding orthorhombic unit with axes a, b = 13 a, c, a and c being the hexagonal axes. The ortho- hexagonal u:i.it with twice the volume of the hexagonal unit, is endcentered, and therefore ~~Eflections with h+k odd cannot appear. With planes of this type eliminated, there is a one-to-one correspondence between those remaining in the orthohexagonal unit, and the possible planes of the hexagonal unit, the equations for transformation of indices being (pri-mes refer to the orthohexagona.l unit): 10. h = k' k' - h =---2. 1 k _.e= ..R.' Besides the various orders of (00•1), two types of reflections appearing upon these oscillation photographs were used in the following considerations. Namely, those arising from planes with zero in- dex referred either in the one case to a, or in the other case to b, In Figure s 1 - 4 are given reproductions the axis orthogonal to a. of four oscillation photographs with indices indicated for those planes which are used in the considerations to follow. n!d furnishes four sets of two, two sets of four, two sets of six, and one set of twelve (general) equivalent positions. 7 Six silver a.toms may be placed in one of the two sets of six, or in some combination of the sets of four and two equivalent positions. With silver in 6g, that is, at 1/2,1/2,1/4; 0,1/2,1/4; 1/2,0.1/4; 1/2,0,3/4; the structure factor for silver alone is rc. ,r, <A+-k) SAg = 2 Ag Le + e e rrc' k rri A -f For _P, odd, cos ~..e, = O, and SAg == O. J 1/2,1/2,3/4; c-o-<) 0,1/2,3/4, /Lt 2 But it is observed that reflec- tions of the type (20·..£.) with _,,e odd are among the strongest appearing upon any of the photographs (see Figures land 2). Furthermore all re- flections of this type from .R. = 3 to .,,l. = 21 appear and each is much stronger than the adjacent reflections with£ even for which 6g would give S = ± 6Ag , that is it would require all six silver atoms to be Ag scattering in phase. A similar alternation o.f intensities is observed for planes of the type (40·.£) (see Figure 2). These data make 6g so highly improbable as positions for silver atoms that it is elDninated from further consideration. Figure 1. Oscillation Photograph from (00 , 1) of KAg{CN) • 2 fj.o ,q_} Vertical. 0-20° . ., 4'0,1) l'f IS 40·.I 40•&./ 17 ., 30,.I ., ..,,. ., 20,..R oo,J V V ., ll TO,/'f V To.11 11 1'3 II/ 15 ..., io,, 10 II /2 /3 I'# IS lb 11 18 1, " zo ,2.1 10 .i., io,.J " io,10 10-P lo,n. io-1'/ "' V .., V io-11 It. 13 ,., ,5 ... 40,17 40-~ Figure 2. Oscillation Photograph from (00 ·1) of KAg(CN) 2 . [io•cTI Vertical. 15-35°. OO•Z It 6 10 8 12 OO•llf " Figure 3. Oscillation Photograph from (00 ·1) of KAg(CN) 2 . 0 a Vertical. 0-20. 18 ., 27-IO II 4i•ZO ., ., ., IC l6 ,. 10 00•/4 " 18 20 11. ., . • ., i,.,., '" re 20 z.r,:n. ... oo,£ • 60•J.'f 42. .Jt. ;,... 10 11. 15 ,. /8 41,:10 Figure 4. Oscillation Photograph from (00 -1) of KAg(CN) 2 • 0 R Vertical. 15-35. 11. The other possibility which would make the silver atoms crystallographically equivalent is 6h with positions at u,u,O; 2u,u,½; for which (angles are expressed in units of 2 ff) S Ag = 2iAg[sin(hu-ku) + sin(hu+2ku) - sin(2hu+ku}J for J'. odd, and $Ag= 2 Agraos(hu-ku) + cos(hu+2ku) + cos(2hu+ku] for _,e even. The data indicate that SAg for (20 ·P ) and (40 ·.£) with J!. odd should be nearly a maximum. F'or these reflections, SAg = 2iAg{!.sin hu - sin 2h0. Differentiating and setting the result equal to zero, the condition for maxima and minima is found to be cos bu= cos 2hu. For (20 ·.-l ), SAg is a maximum for u = 1/6, 1/3, 2/3, 5/6. For (40 •.P ), SAg is a maximu.~ for u = 1/12, 1/6, 1/3, 5/12, 7/12, 2/3, 5/6, 11/12. The values of u which are not included in both lists give only j S.Ag I =-y3 Ag for (20·.£ ), and this does not seem adequate in view of the intensity relations previously discussed. The values of 1/3 and 2/3 lead to the more specialized positions 2c and 2d, and are, of course, impossible. There remain 1/6 and 5/6 as approximate values for u, and the first of these may be selected arbitrarily without loss of generality. It may be pointed out that the value . u = 1/6 leads to an equal spacing of silver atoms about 3.67 ! apart in two planes parailel to (00 •1), except that one atom per unit cell is m~s~:ii.:®.g from each layer (see Figure 6). As the interatomic distance in metallic silver is but 2.89 X, the above spacing is entirely satisfactory. 12. For the possible combinations by which the silver atoms are put into two or more crystallographically non-equivalent positions, it may be said that qualitative considerations of the kind already used suffice to eliminate most of them. In any event, no arrangement remains which gives an approximately uniform distribution of silver atoms as in 6h, There is apparently no reason to doubt that each silver is bonded to tv,o carbons of cyanide groups, since these complex ions are extremely stable chemically, If both carbon and nitrogen were put in- t o the general position, there would be four layers of each kind of atom parallel to (00 •1) within the unit cell. By assigning proper values of the six parameters, the carbon and nitrogen atoms may be arranged so as to bear the correct relation to the silver atoms in 6h in order to have Ag(CN); ions as a structural unit, and at the same time to have the cyanide groups in approximate closest packing within each layer (see Figure 6), It is then possible to put the six: potassium atoms in regions of large negative potential, and in fact to arrange them so that each is surrounded by six nitrogens of six cyanide groups at the corners of an octahedron. In other words, KAg(CN) 2 is an ionic crystal ma.de up of .K+ and Ag(CN); ions, while Ag(CN); is a.n electron pair bond complex, and it seems possible to find a structure which satisfies the exigencies of this mixed state of affairs. The positions referred to for the potassium ions are given by 2b (0,0,1/4; 0,0,3/4) a.nd 4f (1/3,2/3,u; 1/3,2/3,u; 2/3, 1/3, u+½) with u in the neighborhood of 1/4. 2/3,1/3,½-u; Returning to a con- sideration of various reflections appearing upon oscillation photographs (Figures 1-4), it now seems worth while to calculate the sum of the 13. structure factors of silver and potassium for the more complex planes, and to compare these with observation. For the present purpose, the silver and potassium parameters may be taken as 1/6 and 1/4 respectively. I'he results are summarized below: For (40 •£) and (4 0 •1- ) , 1. (Figure 2), a. Jl odd, SAg + SK b. = -3V3 i Ag. J, even, Ag + SK = -3 Ag S A quite regular alternation of intensities is observed for the ranges (4 0 ·11) to (4 0 ·17) and (40 •13) to (40 · 19), with the reflections with Jl odd considerably stronger than the adjacent ones for .,£ even. 2. For (30 ._L ) and (3 o-£), (Figure 2), a. ,R odd, SAg + SK = O. b. J!,, even, -2Ag + 6K for .,R/4 integral, for f-/4 half-integral. The reflect b ns with _i!, odd are not observed. Only two very weak reflections, (30 · 12) and (3 0 · 12)_') a.re observed for J!-;4 integral (it may be recalled that the scattering power of silver is about three times that of potassium). Strong reflections are observed for (3 0 · 10), (3 0 •10), (3 0 •14), and (3 0•14), while (3 0 •18 ) and (3 0 · 18 ) also appear. From the construction in the reciprocal lattice which was used 14. to assign these indices, it appears tha t other planes with J./4 halfintegral were not in position to reflect. 3. For (2 O·£ ) and(2 o-1!. ) , (Figures 1 and 2), a. £ odd, SAg + SK = 313 i Ag. b. ,,{!,, even, Reflections in the ranges from (20 · 4) to(20 •21) and(2 0 · 3) to (2 0 · 21) appear vnth those with the adjacent ones with ,R,. even. .f odd considerable stronger than The intensities for both _e_ odd and .fl even gradually fall off with increasing~, of course. 4. For ( 1 0 ·£ ) and tt , (i O•P.. ) ., (Figures 1 and 2), J!_. odd, SAg + SK =1(3 i Ag. b. ~ ev:en, Again an alternation of intensities is observed in the ranges from (10 • 3) to (10 •19) and (1 0 · 3) to (1 0 •19) ~ith considerably greater intensities for .£ odd, 5. For ( 4 2 •£ ) and ( 4 2• .1. ) , a. (Figure 4), ,1!. odd, SAg +SK :::.. 0 b. _,l even, SAg + SK S Ag = 6 Ag + 6 K for .,R/4 integral., + SK = 6 Ag - 6 K for ,P./4 half-integral. 15. Reflections with J!. odd, of course, are not observed. Quite strong reflections are observed in the ranges from (4 2 · 10) to (4 2•20) and(4 2 •10) to (4 2 • 20) with .P. even. The intensities for .1!./4 inte- gral are in every case stronger than the t'No adjacent ones for 1/4 half-integral. 6, For (2 l •.R) e.nd (2 1 , £ ), (Figures 3 and 4), a. ,R_ odd, SAg + SK - 0 (as required by o!d)• b. JZ even, for ,f/4 integral, SAg + SK :::: -2Ag + 6K SAg + SK :::: -2Ag for _f,/4 half-integral. 6K Reflections with 1. odd, of course, are not observed. An alternation of intensities is observed in the ranges from (21·6) to (2 l • 20) and (2 l• 6) to (2 l• 20), with the reflections for f/4 half- integral decidedly stronger than adjacent reflections for 1/4 integral. 7, For (00·..l), a.. (Figures 1-4), _i, odd, SAg+ SK :=:. 0 (as required bu D~d)• b, j!_ even, SAg + SK = 6Ag + 6K for .,R_/4 integral, SAg +SK= 6Ag - 6K for i-/4 half-integral, Reflections with _,,e odd, of course, a.re not observed, ·rhe details in the observed reflections a.re not accounted for by the above structure factors, but there is general qualitative agreement. As would be anticipated frrnn the preceding calculations, and from a con- 16. sideration of other factors which influence the intensity of scattered X-rays, the (OO •n) reflections are observed to be the most intense ones appearing upon these photographs. The preceding comparisons reveal good qualitative egreement between calculated and observed intensities for ea.ch set of layer line reflections. Although of a somewhat less definite character, the in- tensity relations between layer lines seems to be satisfactory qualitatively. The structure in its rough outlines now appears to have a considerable probability of being correct, and it will be worth while to attempt to fix parameter values with some accuracy. As previously mentioned, in t his atomic arrangement the carbon and nitrogen atoms a.re to be placed in the general position. There are then three parameters along c, one for carbon, another for nitrogen, and a third for the potassium. ions in 4 f. With the use of a simplify- ing assumption regarding the relative position of carbon and nitrogen atoms of the same cyanide group, it is found possible to evaluate these three parameters using the (OO •n)reflections. Hydrogen cyanide, HCN, is found 8 from band spectral data to be a linear molecule in the normal state with a carbon-nitrogen separation of 1.15 X. It seems safe to assume that a similar state of af- fairs will be maintained in Ag(CN);, so that the carbon-nitrogen separation will be 1.15 !, and both a.toms of a cyanide group will lie in a straight line with the silver atom (this does not imply linearity for the complete Ag(CN); ion). The separation of silver a.nd carbon atoms is expected to be about 2.1 X., so that the lengt~ of the Ag(CN); ion, if it be linear, is expected to be about 6.5 K. Now c/2 is observed to be 8.84 K, so the possibility of nearly linear ions along c bound to- 17. gether by potassium ions is to be considered. Proceeding from this point, parameter values for carbon and nitrogen may be assigned so that the centers of gravity of the cyanide groups of each layer are in closest packing, and the potassium-nitrogen separation for uK = 1/4 is of the right order of magnitude, that is about 2.85 X. With this arrangement, the projection of the carbon-nitrogen separation, 1,15 A, upon c is 1,02 K, and will not be greatly different for reasonable variations in the x and y parameters of carbon and nitrogen. If zN is the pare.meter along c for nitrogen, then in the 1 • 02 will be used for z, the parameter following treatment zN - 17,7 C along c for carbon. With this assumption, the nu.111ber of para.meters along c is reduced from three to two, that is to zN and~• It should be pointed out, perhaps, that having put silver in 6h, potassium in 2b and 4f, and carbon and nitrogen in the general 2 position of D3 d, ~ the only new assumption made for the purpose of treating (OO · n) reflections is that the cyanide groups are oriented approximately along c. In view of the magnitude of c, it is seen that a considerable departure from the orientation with respect to c assumed for CN- would have only a small effect upon these consider~tions, The structure factor for (OO · n), n even, is S = 6FAg + 2FK(-l)~ii + 4FK cos n UK+ 12FN cos nzN + l2Fc cos nzc in which the F's are the atomic scattering powers for X-rays for the particular interplanar distance, d(OO,n)• The F-values of Pauling and Sherman 9 are employed thruout this paper, After making the substitution zc = zN - 0,058 in S, the square roots of the relative intensities were calculated by 18. ½ t l + cos22 00 takes care of the Lor entz and polarization factors. 2 sin.22 e Since a horizontal slit system was used, in the various positions for reflection the cross-section of the X-ray beam intercepted by the crystal was proportional to sin e and therefore to n, thus making neces- sary the inclusion of 1fii as a factor. It is to be noted that the tem- perature factor, which as a matter of fact is large for KAg(CN)2 , has been omitted. ft for all even order reflections from (00 · 2) to (00•28) was plotted against zN in the range from Oto 1/4 for several values of uK in the neighborhood of 1/4. in Figure 5. One set of these, for uK = 0.260, is shown Now if a reflection of given order was observed to be more intense than another of lower order, only those values of zN (and uK) were considered as possible for which 1[f for the higher order reflection was calculated to be the l arger. It is clear that the omis- sion of the temperature factor from the expressi on used in calculating ,ri lends the desirable measure of safety in making compa risons of this type. The following intensity relations are observed for the (OO •n), reflections: ( 00 • 4) 7 ( 00 • 2) , ( 00 • 6 ) )' ( oo-2 ) , ( 00 • 8) :>- (00 • 2 ) , ( 00 • 12 ) > ( 00 • 2) ; (00• 8 ) ~ (00 • 4 ); (00·8) :;> (00 · 6), (00 • 12)~(0 0 • 6); (00 • 12) ;;,- (00·10); (OQ•l6) )' (00 • 14), (00 •18) "7 (OQ•14) , (00 • 20 ) ~ (00•14 ); (00 · 24) > ( 00 • 22); (00 • 28) > (00. • 26). The comparison (00 • 8 ) ne arly a s strong as (00•4) limits zN to values near 0.15 for all values of uK in the neighborhood of 1/4. The effect of a small change of ± E from o. 250 in the potassium para- meter is to make the structure factors and henceUlarger for reflections mo /68{} N4D r.----- /200 t 11;::: '160 770 480 - ---00-B::,,00·4 - - + - oo-1a>oo-14 .__. 4-00•IB>OO·l'f - - t - 00-/2::tJO·fi .-----.. Figure 5. The calculated intensities of (OO , n) reflections as a function of the nitrogen para.meter, zN, for the potassium parameter, uK, equal to 0 , 240 or 0 . 260. 19. with n/4 half-integral, and smaller for those reflections with n/4 integral. The sign of the change is of no significance here, but it cannot be more than 0.020, since for such a change the inequalities (00 • 24) -:;> (00 •22) and (00 • 20)'7(00•14) are no longer accounted for satis- factorily. Also the fact that with uK = 0.250, --i/Ifor (00 •20) is cal- culated to be much larger than for the adjacent reflection (00•18), whereas (00 •18) is observed to be somewhat the stronger of the ti.vo) indicates that the potassium parameter must be slightly different from 1/4. A general agreement between calculated and observed intensities wh ich accounts for all of the observed inequalities listed above is obtained for uK =0.260 or 0.240; zN = 0.167, zC = 0.109. The ambiguity in the value of the potassium parfu~eter will be considered later. With the assum.ptions which have been made, it has been determined that UAg ~ 1/6, UK = o. 260 or o. 240, ZN = 0.167, Zc = 0.109. It remains to assign values for the other four carbon and nitrogen parameters, to investigate possible variations in uAg from the value 1/6, and to decide wh ich value is correct for uK. If it be further assumed that the cyanide groups are in close- packed layers parallel to (00•1), then their position may now be fixed by the values found for zN and z0 . Putting uAg = 1/6 and assuming that the carbon and nitrogen atoms of a cyanide group lie in a straight line with the silver atom, the values for the other parameters are calculated to be ~ =o. 365; XC = 0. 295; yN = 1/3 • Ye 1/3. With the use of the foregoing complete assignment of parameter values, rel ative intensities were calculated for a particular class of 20. refiections appearing upon Laue photographs taken with the X-ray beam aLmost exactly perpendicular to (00 •1). Intensity comparisons were made between those corresponding positive and negative fonns, that is, between fhk ,.£.J and~k -~ , which reflected in the first order. is practicable since nearly the same values of n ~ This were observed for all planes of both forms, and hence all factors influencing the intensity of the scattered radiation, with the single exception of the structure factor, are nearly identical for both forms. Slight depar- ture from an exactly symmetrical orientation of the crystal was taken care of by the following averaging process used in detennining relative intensities. The intensities of all significant spots occurring upon three nearly sym.metrical photographs of considerably different exposure times were obtained by visu@.l comparison with a scale prepared for the purpose of estimating Laue intensities. As the intensities of the re- flections for different forms varied greatly, it was usually found advisable in the case of a given pair of forms to employ the photograph of photographs for which compa rison could be made with greatest confidence. The ratio of intensities for corresponding positive and nega tive forms, ½M, was evaluated from the foregoing data by comparing reflections on the same photograph for which the values of n A. differed by less than about o. 01 .ft.. Usually about three such com- parisons were found for each pair of forms, and gave reasonably consistent results. The mean values obtained together with the approximate values of n A are given in Table IV. These comparisons are especially significant for fixing carbon and nitrogen parameters, for only these atoms are responsible for the differences in intensities observed betvreen corresponding positive 21. and negative forms. That is, , .1. even; SK) [hk•.t1 :: - (SA.g -t- SK) [fif..{11 The ratio I (hf,,e.1 , .f. odd. was calculated using the F-values of I (hk •~} Pauling and Sherman, and the parameter values previously suggested. Since it will be shown that 0.460 is the correct valu·e to use for the potassium parameter, the results given in Table IV are given for this case only. TABLE IV Intensity Relations for Certain Laue Reflections X-Ray Beam Normal t ,J ( 00 · 1) Comparison r lhic-~1 n A I(hk ,..e) Calculated Observed 0 t33 • 21 with (33 · 21 0.35 A 1.03 1.0 [14 • 2} with ll4• 23 0.44 3.37 3.5 1.36 1.4 l. 96 1.7 (24• 3} with [24 •3J fi_3 , ~with ~3·11 0,36 The foregoing results provide strong general justification for the structure, and indicate that the selection of x and y parameters which has been made is a fair approximation to the true values. Now if it be assumed simply that the x and y values of the carbon and nitrogen parameters lie in the general neighborhood of those just considered, .it is possible to fix the value of the silver parameter within narrow limits. Upon an exceptionally clear photograph (Figure 2), (30·12) is very faintly but unmistakably observed, while the a djacent reflect ions 22. (30 •11) and (30 •13) a.re absent. Now it may be verified that the struc- ture factors for the two cases of (30 •£.) reduce to the following after putting uAg = 1/6 + S • and making use of the trigonometric addition formulas (angles are expressed in units of 2 11 ): rr £;-, S = 2Ag 0 os 60 - 2cos 3~ + 2K 1.) -1) + 2cos .R, aj + 4c[2cos 3/2(xc + Y:c) cos 3/2(xc - Ye) + cos 3(yc - xc] cos ...e zc + 4N [2cos 3/2(xN + yN) cos 3/2(xN - yN) + cos 3(yN - xN] cos ..R. zN for .I!. even, s = -2 i Ag § sin 3 6 + sin 6 ~ + 4 i C ( 2sin 3/2(xc - Yc)cos 3/2(xc + Ye) + sin 3(yc xc~ cos .R, zc + sin 3 (yN - xN] cos .R.. zN + 4 i N [ 2sin 3/2(.xN - -·YN) co s 3/2(xN + YN) for 12 odd. To calculate S, it is assumed for both carbon and nitrogen that jx - YI<. o.05, 2/3 - 0.05 < /x = yj..:::. 2/3 + 0.05. This would seem to be well within the range of variations to be anticipated. In the calculation of the intensities which follows, a.11 factors except the temperature factor a.re included, and this will be but little different for these neighboring reflect ions. Either 0.240 or 0.260 for uK leads to the same result in this case . Considering the effect of carbon and nitrogen on the calculated intensities for (3('.) • ll) and (30 · 13 L it may be seen by actual calculation that a number of f a ctors in both cases tend to make their contributions quite negligible. In t he first place the quantities inside the square brackets are not much different f' rom zero thruout the range of values that have been assumed for the x and y para~eters, and in addition the coefficients determined by cos .£ z a.re small for (30 · ll) and are of opposite sign and nearly equal in magnitude for (30 •13). It now may 23. be asserted with confidence that any substantial contribution to the calculated intensities for these planes must be due to silver alone. For S = 0, the contribution of silver to these structure factors is also zero. This is not the case for (30 · 12), however. There is obtained s(30 · 12) = 2 Ag~os 6 6 - 2 cos 3 ~ + 5.92 K - 1.85 C + 8.65 N using the limits of the range indicated for the x and y parameters carbon and nitrogen together with uK zc = 9.109. of = 0.260 or 0.240, zN = 1/6, In order to account for the appearance of (30 •12),it is necessary to have a calculated intensity of fair magnitude, and the preceding equation shows that this may be obtained only by taking a difference of effective scattering by potassium and nitrogen working against silver and carbon. Now the scatt ering due to silver is a minimum for S = 0, and for this case there is obtained in a manner similar to that employed for the (OO •n) reflections ( n ~ 3.5 for this case), + 10. This very small value for--ff/n, representing as it does a preponderance of effective scattering due to potassium and nitrogen over that of silver and carbon, may be ma.de perhaps as much as +15 by taking more reasonable values for the x and y pa rameters of carbon and nitrogen. Also as the potassium para.meter approaches nearer to or departs farther from 1/4, I is inc reased or decreased respectively. But, as the silver parameter departs from 1/6, the value of I only very slowly decreases to zero and then increases, corresponding to a change in preponderance of effective scattering from potassium a.nd nitrogen to silver (and carbon). How- ever, s( 30 . 13 ) and s( 3 0 •ll)' which were shown to be substantially zero for ~ = 0, will mount in value as /8/ increases relatively with very great rapidity, even while s( 0 •lZ) is still decreasing. In fact, 3 for S( jo/-::. 0.003, s( 3 0 · ll) and s( 30 . 13 ) will be greater already than 30 · 12 ) , and will remain so for further changes in the silver parameter of nearly ± 1/6. It is therefore highly probable that uAg ~ 1/6 ± 0.002, and virtually no deviation from the value 1/6 is to be anticipated. The preceding argument applies in similar form to the comparison of (30 · 11) and (30 · 13) with (30 •12), for which the observed intensity relations are as with the corres,Jonding planes of the positive forms. A comparison of relative intensities within the three sets of reflections (40•1) , (20 •..R ), (10·.£ ), all wi-th ..R, odd, leads to the selection of 0.260 rather than 0.240 for the potassium parameter. It is observed that such a series of reflections, say (20 •.i) with .12 odd, may be divided into two sub-series each of which shows a ttnormal" decline in intensity with increasing angle of reflection, but differing from ea.ch other in average intensity. For (20 ·.£) , the reflect ions with R,::: 4n + l are appreciably more intense on the average than those with J!. :::. 4n - l, that is,the first sub-series is on the whole recognizably more intense than the second (Figures land 2). An exactly analogous condition holds for (40 •£) , but for (10 ·£) the relation is reversed, that is, the sub-series with ~ =4n - l is stronger than that with .f. = 4n + l. Furthermore, the phenomenon is somewhat more marked for higher values of i!. Since for (20·.l) and (10 ·.£), both with _f!, odd, there are about five reflections for each sub-series, it was considered justifiable to regard the contributions of carbon and nitrogen as averaging out, upon the whole (rough calculations show that these contributions are 25. small anyway). i-i ith t his assumption it is easy to show that a. small positive deviation from the value of 1/4 for the potassium parameter accounts for the observed relations. In the expressions which follow, uK is put equal to 1/4 + f For both (20 ·.£) and (40•.2.) with ,P,, odd, = 4n + 1, I SAg + SK I = 313 Ag + i(3 K sin .£ E b. Jl = 4n - 1, a. • ..R.. j SAg + SK/ = 31°3 Ag - 2713 K sin -1 € For (10 ,fl ) with ,R_ odd, a. • .R... = 4n + 1, ISAg + sK J =13 Ag - 2"V3 K sin .P.€. b. .£ = 4n - 1, / SAg + SKI A value =13 Ag + 2V3 K sin .P.t of zero for E means that the potassium ions con- tribute nothing to the reflections, while a small value for f means that the ma.in contribution due to silver will be changed somewhat in a. regular manner. bince the argument of the sine is .1!.E , the effect will become more marked with increasing .,J!, so long as .R. E (in the present instance .R... goes to 21 and tive [c/ = 0.01). L.. o. 25 For a. posi- E , the intensity rela tions between the sub-s eries for each of these three groups of reflections will be properly correlated, whereas for a negative E , cell relations will be reversed. is, therefore, that u K The conclusion = 0.260 rather than 0.240. The same result may be deduced with the use of the planes of the corresponding negative forms, namely, (4 o·, .R_ ), (2 0 ·£ ) , and 26. (1 0 ,_Q_), forwhich almost identical intensity relations a.re observed. The values with an estimated accuracy of the eight parameters of this structure have been found to be as follows: UAg = 1/6 ± 0.002; UK = 0,260 ± 0,005; ZN = 0.167 :t 0,005; zc = 0,109 ± o. 005; XN = 0.365; YN = 1/3; XC = o. 295; Ye = 1/3. Higher values of xN and xe, and lower values of YB and Ye than those just given are scarcely to be expected, as will be clear from the discussion of intera.tomic distances which will follow. It is difficult also to estimate the magnitude of possible variations in the opposite directions for these parameters, but in any event a better agreement between calculated and observed intensities for the Laue reflections which have been used ma.y hardly be anticipated. Definite information regarding; the temperature factors for the individual atoms in this compound is not available. That it is very large may be seen by comparing the calculated values of-fr shoVv-n in Figure 5 with the ( 00•n) reflections shovm in Figures 1-4. It is probable also that the temperature factor will depend in a marked fashion on the angle which the X-ray beam makes with the crystal axes when in the reflecting position. Hence it may not be feasible or particularly significant to assume an overall temperature factor for the purpose of correlating quantitatively the observed intensity relations between (00 •n) and layer line reflections. If a constant overall temperature factor were assumed for this purpose, however, it would need to be of the order of magnitude of that found for sylvine (KCl). 10 That is, a factor of about fe - a;;! ) z. \' would need to be included in all calculated intensities. This is sufficient to make the new calculated intensity for (00•28) only about 1/9 of the former value, and ev'.7n this reduction may not be entirely adequate. DISCUSSION OF THE STRUCTURE The structure as determined is shown graphically in Figure 6. The simplest "ideal'' structure of this type is one an assignment of para.meter values leads to interatomic distances o O 0 as follows: Ag-N, 3.20 A; K-N, 2.86 A; Ag-Ag, 3.67 A ; N-N (same 0 0 layer), 4.24 A; N-N , {adjacent layers), 3.84 A. The Ag-N separation 11 0 may be expected from analogy with K2Cd(CN)4 , in which Cd-N ~ 3.28 A, to lie between 3.15 and 3.35 The K-N distance observed 12 in KN 3 , A. 0 in which potassium has a coordination number of eight is 2.96 ± 0.06 A. In the foregoing "ideal" arrangement, each potassium is surrounded by six nitrogens at the vertices of a regular octahedron, and the sepao ration of 2 .86 A is of the right order of magnitude. However, it is quite certain that the nitrogen atoms will not be even a pproximately spherically symmet1·ical, so that the "ideal" struct 1.1re will be deformed thru displacement of potassium, nitrogen,and carbon atoms in a. manner difficult to predict. There will then be three different K-N separations which will depend upon the angle between the line from potassium to nitrogen and the figure axis of the cyanide group. Figure 6. The structure of potassium silver cyanide. Large open circles represent silver atoms, small open circles carbon and nitrogen atoms, and small closed circles potassium ions. The Ag(CN) 2 ion is indicated a s a structural unit by the lines joining carbon with silver and with nitrogen atoms. Heavy lines mark the hexagonal unit of structure, and light lines the coordinated octahedron formed by six nitrogen atoms ab out each potass.i.um ion. 28, F'or the structure as actually determined, that is, for uK xN = 0.260, = 0,365, yN = 1/3, zN = 1/6, uAg = 1/6, there a.re obtained: Ag-N, 3.29 .X.; (lc-N) 1 (Kin a no parameter position), 2.97 ll; (K-N) 2 , 3,05· .X.; (K-N) 3 , 2,56 .X.. The angles between the lines joining potas sium and nitrogen, and the ex~ension of the figure axis of the cyanide group a.re calculated to be 76,7°, 73.5°, and 32.6°, respectively. The results indicate that the relations of potassium with nitrogen are closely similar in two of the three cases, but are quite different for the third. The value of 2.56 .K found for the one K-N sepa.ra.tion is certainly lower than would have been anticipated. It is to be noted, however, that if the potassium para- meter were somewhat less than 0,260, this value would be increased. The fact that (00 •18) is observed to be definitely stronger than (00 •20) indicates that uK is not less than 0,260, but deviations from the true atomic scattering powers in the F'-values which were employed may more than make up the difference. It is quite possible and even probable that the concentration of s i x electrons in the bond eigenfunctions used in fonning the triple bond ma.y result in an effective center of scattering for X-rays lying between carbon and nitrogen. The 11 anoma.lous 11 (222) reflection observed for diamond is a case in point. It is to be noted also that with uK = 0,260, the very weak but clear and definite reflection (30 · 12), used in fixing the silver parameter, hardly gives a calculated va l ue for the intensity large enough to be in quantitative agreement with the (00, n) reflections of high order, even after the introduction of a 29. rather l a rge temperature factor. The attribution of somewhat greater scattering powers to nitrogen and ce.rbon would give improved agreement between calculated and observed intensities both for the compar ison of (30 · 12) against the high orders of (0O •n), a.nd for (00•18) with (00 •20). It is rather probable also that variations in the four para.meters xc, Ye, xN, and yN could enter in such a way that the K-N separation of 2. 56 X would be ap preciably increased, while ret aining equally significant agreement between calculation a.nd observation for the Laue reflections previously used. Such variations have not been found after a fair number of trials, however. It should be emphasized, moreover, that the correct answer to the problem is not known, that is, it is not possible from any independent considerations to say just what the minimum value for this K-N separation as a function of· the angle ought to be. A value greater than 2. 56 E. would be anticipated, however. The assignment of par8llleter values which has given generally good agreement between calcul ated and observed intensities leads to an exactly linear fonfiguration for the complex ion, Ag(CN); . Further- more, the deviation from linearity wil l not be of importance for reasonably large va ria tions in the x, y, and z parmn.eters of carbon and nitrogen. It is tri:re that alternative structures for ·which the compl ex ion would be a ppreciably kinked have not been considered in detail, but the evidence which has been pres ented in support of the proposed structure is quite convincing. It seems, therefore, that the essential line arity of the Ag (C N); ion may be accepted with some confidence. 30. I wish to express my appreciation of the encouragement and valuable advice which I have received from Professor Linus Pauling during the course of this work. I have had the benefit also of helpful suggestions from Dr. J.H.Sturdivant. 31. SUMMARY Trigonal crystals of potassium s ilver cyanide, KAg(CN) 2 , were subjected to an X-ray study using Laue and oscillation photographs. The underlying lattice was found to be hexagonal with a unit cell of dimensions a= 7.34 ± 0,1 l, c = 17.7 ± 0,2 X. Corn- plete absence of reflections of the type (m m 2m. . .J e render one of the two space groups D!d and c!v highly probable. The face develop- z ment and the apparent absence of a pyroelectric effect make D3 d (with a center of symmetry) somewhat more probable than c:v, and it was found possible to base a satisfactory structure upon the former space-group. Silver was placed in 6 h, potassium in 2 band 4 f, and carbon and nitrogen in the general position according to Wyck~off 1 s tabul ation (Reference 5). The approximate positions of f i rst silver and then of silver and potassium (ea.ch with one parameter) were fixed by qualitative comparison with a number of observed regularities among numerous layer line reflections appearing upon oscillation photographs . from the basal plane. With an assumption regarding the C-N separation in CN- and the approximate orientation of a cyanide group with respect to c, the pare.meters along c (potassium, carbon , and nitrogen) were fixed by considering (OO •n) intensity inequalities. The x and y parameters of carbon and nitrogen were assigned values with the aid of observed intensity inequalities between reflections fhk~J and [hk ,.£~ appearing in the first order and at the same values of n ~ upon symmetric (00 •1) Laue photographs . To fix accurately the value of the silver parameter at 1/6, and to remove an ambiguity in 32. the value of the potassium parameter, recourse was had to specialized arguments. The derived structure accounts at least qualitatively for observed intensity relations among all pertinent reflections appearing upon a number of photographs. The structural units of KAg(CN)2 are K+ ions, and linear or nearly linear Ag(CN); ions oriented at an angle of about 27° with c (see F' igure 6). The cyanide groups are in approximately closest- packed layers parallel to (00•1), and each potassium ion is surrounded by six nitrogen atoms at the vertices of a distorted octahedron. The complete assignment of par ameter values with an estimated accuracy in feasible cases is: UAg = 1/6 ± 0.002; UK= 0.260 ! 0.005; ZN= 0.109 ± 0.005; XN = 0.365; ZN= 0.167 ± 0.005; Xe= 0.295; YN =Ye= 1/3. Probably xN and xe have maximum va lues while YN and Ye have minimum values. Interatomic distances are found as follows: The last interatomic distance is small er than might be anticipated, and certain possible variations of parameter values which would make it somewhat l a rger are discussed. 33. REFERENCES 1. Groth, "Chemische Kristallogre.phie, 11 Engleman, Leipzig, 1908, Vol. I, p. 318. 2. Astbury and Yardley, "Tabulated Data for the Examination of of the 230 Space-Groups by Homogeneous X-ra.ys, 11 Phil.Trans.Royal Soc. London, Series A, 224, 221-257. 3. Same as Reference 2. 4. Groth, "Physikalische Krystallogra.phie," Engleman, Leipzig, 1905, p. 237. 5. R, W.G. Wyck1\off, "The .hna.lytica.l Expression of the Results of the Theory of Space-Groups," Carnegie Institution of Washington, 1931, 2nd Edition. 6. J.D.Berna.l, Proc.Royal Soc,, Series A, 113, 117, 7. Same as Reference 5. 8. Badger and Binder, Phys.Review, 37, 800 (1931). 9. Pauling and Shenna.n, Zeit.filr Kristall., ~• 1 (1932). 10. James and Brindley, Proc.Roye.l Soc., 121, 155 (1928). 11. Ewald and Herman, "Strukturbericht,n Zeit.f.Krist., Erga.nzungsband, Aka.demische Verla.gsgesellscha.ft M.B.H., Leipzig, 1931. 12. Sarne as Reference 11. II. AN X-RAY INVES TIGATION OF THE 12-MOLYBDOPHOSPHATES AND RELATED COMPOUNDS INTRODUCTION This X-ray investigation of the crystal structure of some of the heteropolyacids and their salts represents an attempt to determine the true molecular structure of these compounds. On account of their exceedingly complex nature, however, the work described in the following paragraphs has yielded only a quite limited class of information. The heteropolyacids such as 12-molybdophosphoric acid, H3 PMo 12 o40 .30HzO, are treated at some length in various comprehen- sive works on inorganic chemistry. 1 All of the considerations here presented have to do with representatives of the so-called 12 class in which the number of molybdenum or tungsten atoms per central atom (silicon, phosphorus, boron, etc.) is 12. Many other compounds are knmvn in which this ratio is less than 12, but this figure is believed to represent the upper limit for stability. Of this so-called saturated 12-class, the following compounds have been subjected to an X-ray examination: H3PM012040, 30:Hz 0 Mg 2 silv10 12o 40 • 31Hz o NdPMo 12 04o• 30liz 0 Ni 2 SiMo 12 o40 .31HzO SaPMo 12 o40 • 30R.-z 0 GdPMo 12 o40 • 30:Hz 0 The above compounds have either been previously reported 2 or have been shown during the course of this investigation to possess cubic symmetry. 2. PREPARATION OF COMPOUNDS FOR STUDY 12-Molybdosilicic acid wa.s prepared according to the directions of Rosenheim and Jaenicke, 3 and the other acids, ob- tained commercially, were Baker's GP grade. The various salts listed above were prepared by dissolving the calculated quantities of (Mg, Ni, Be)C0 3 , (Gd, Sa)Cl 3 .6R2 0, and N¾0 3 in solutions of the proper acid. The rare earth compounds were obtained thru the cour- tesy of Dr. Simon Freed of the University of California.. All of the compounds investigated with X-rays crystallize as apparently regular octa.hedra., all sizes up to about 8 or 10 mm. on an edge being obtained in some cases. The compounds containing molybdenum possessed a characteristic yellow color. Inasmuch as none of the crystals studied are at all stable in air, but upon exposure soon become covered with a layer of powdered material thru loss of water, and in addition are mostly unstable above 50°C, some difficulty was experienced in connection with the collection of the necessary data. for this study. The three rare earth salts of molybdophosphoric acid had not been previously reported in the liter a ture. They were identified as normal salts, and as crys- tallizing in the cubic system as outlined below. For the identification of these compounds as the normal salts of the acids, the following rough partial analysis was perfonned. Crysta.ls of the compound were removed from the saturated solution, and were dried more or less thoroly but as quickly as possible by pressing them between filter papers. A sa.mple was weighed out quickly, and was then dissolved in distilled water. The rare earth ion was pre- 3. cipitated as oxalate by the addition of c oncentrated oxalic acid, and the mixture was warmed until the precipitate was coagulated. The solid was filtered off and washed first with warm wxa.lic acid solution, and finally with distilled water. After ignition in a. porcelain crucible, the residue was weighed as N12 03 • It was neces- sary to use small quantit ies of the compound, from 16-25 mg. of the oxide being obtained in each case. However, the final residue had the appearance characteristic of the pure rare earth oxide in each case. The percentages of rare earth calculated from experiment and from the formula MPMo o .30H:zO are given in Table I, 12 40 TABLE I The Rare Earth Content of Certain Salta of Molybdophosphoric Acid Nd Experimental Theoretical 5.77 Rare Earth Content Sa Gd 4.98% 5.13 5.98 5. 73% 6.24 The experimental values are uniformly somewhat low, but the normal salt is indicated for each compound. The loss of from 1-3 mg. of the oxide as unprecipitated oxalate would account for the discrepancy in each case. Any solution adhering to the sample would cause an error in this direction also. Upon heating a sample of the neodymium compound to constant weight in an oven at 105°, a loss of weight equivalent to a.bout 20 l½O per molecule was found . .l\fter further gentle heating t o constant weight over a. small open flame, a loss in weight equiv-a.lent 4. to 29,9 HzO per molecule was obtained, It was assumed, therefore, that the correct formula for this and the two other closely related rare earth compounds is MPMo 12 o40 .30~~. In any event, two of three molecules of water in the formulas a s written do not affect materially the considerations of this paper. CRYSTALLOGRAPHIC EXAMINATION Crystals of these rare earth compounds were mounted upon a goniometer used as a one-circle instrument with the edge, [o 1 1] , of an octahedral face vertical, and four measurements were taken from octahedral faces during rotation thru 360°, On ac count of the rapid deterioration of the crystal faces, signals were good only for about five minutes at most. During this period, however, repeated measurements from the same face usually gave values differing among themselves by less than three minutes. Three observations were taken for each face, and from the mean values the interfacial angles listed in Table II were obtained, The values for Gd.PMo 12 o40 . 30F..z0 are for two different crystals, for each of which only three faces gave usable signals. The data of Table II provide strong evidence that these compounds crystallize in the cubic system. This is further affirmed by the fact that the crystals appeared to be isotropic when examined with a polarizing microscope, Molybdophosphoric acid, reported as cubic, and crystallizing in small~ quite perfect octahedra, was perhaps very weakly birefringent under a polarizing microscope, but the phenomenon was not at all marked , 70:32 1 (lii):(111) 70°35 1 109°27. 5 1 109°28 1 (111 ):(111) 70°31. 5' 109°29. 5 1 70°31' (111): (111) 70°32 t 109°28 1 (111):(ill) 70°32' Observed for SaPMo, 2 0" 0 • 30Hz 0 109°28 1 Observed for NdPMo,2 0., 0 • 30Hz 0 109°25. 51 Calculated for Cubic System 70°28.5' 109°27' 70°29. 5 1 109°27,5 1 Observed for GdPMo, 2 Ol{a .30Hz0 Goniometric Data from Crystals of MPMo,2. 0,,. 0 • 30Hz 0 [b 1 1.J Vertical TABLE II en . 6. DETEPJHNAT ION OF THE UNIT CELL AND SPACE-GROUP Laue photographs were prepared with the X-ray beam inclined at various small angles to the normal to (111) using general radiation from a tungsten a.nticathode tube operated at a peak voltage of about 55 kv. Oscillation photographs were prepared by reflecting MoK o<. radiation filtered thru zirconia from (111). On account of the in- stability of these crystals in air, it was necessary to protect them in some manner. Covering the specimen with a layer of paraffin or wax by dropping the molten material upon it almost completely spoiled the crystal. A coating of paraffin or Canada balsam could be left on a specimen by drenching it with a solution of one of these materials in benzene or xylene and allowing the solvent to evaporate (the heteropolyacids and their salts are generally very soluble in water, alcohol, ether, etc., so that the choice of solvents and protective material was quite Hmited), but the results were not good. It was found most satisfactory to stick the crystal to a cover glass with a film of optical wax, and then to cover it with vaseline . A crystal thus treated could be preserved in good condition for at least a week. An additional difficulty arose because of the large absorption for X-rays of the tungsten and molybdenum atoms. Due to their ease of decon1position and softness, the crystals •ould not be ground conveniently to very thin plates, so that it was necessary to use very long exposures. This was especially true for compounds contain- ing tungsten, for which only two or three really satisfactory photographs were obtained. Crystals of Be2SiW12O40.31~O seemed to be somewhat more imperfect in structure than were the crystals containing molybdenum. 7. In the considerations which follow, NdPMo o • 30~ 0 will 12 40 serve as the prototype for all of the compounds containing molybdenum, since the Laue and oscillation photographs obtained for any two members of this class were apparently indistinguishable. a Laue photograph is reproduced in Figure 1. An exrunple of such It should be mentioned also that a crystal to plate distance of 7,5 cm. for the Laue photographs was demanded by the complexit~ of the pattern. Making use of the Bragg equation, n 71 = 2d sin 8 , equatorial reflections on a (111) oscillation photograph of NdPMo 12 o40.30~0 lead to an observed spacing of d(lll)/n 1 = 13,3 ! (see Table III). The smallest possible cubic unit is one with a= 3 · d(l11)/n 1 in which n 1 = 1, that is, a= 23,1 A. All values of n ~ calculated on the basts of this unit for the reflections appearing upon t.vo completely indexed Laue photographs were found to be above the short vmve length limit, 0,24 A, of the radiation employed. Data which include all re- flections in the first-order for one of these photographs are given in Table IV, the extreme values of sin e each form. and n /\ being listed for For the two photographs, a total of more than 50 distinct forms reflected in the first order, with rather compl•n: indices in most cases. Only those reflections for values of n ~ 0,48 l need be purely first-order, of course, less than Figure l. Laue photograph of NdPMo 12 o •30HiO taken with 40 the X-ray beam nearly normal to an octahedral face. Figure 2. Oscillation photograph of MgzSiM012040 •30HzO from (lll) with 110 vertical. a. TABLE III Data from the Equator of a (111) Oscillation Photograph Order from (111) Line (Mo K) Sin 0 d/n , 3n 1 ol . 07962 13. 3 5 ! 4n 1 o<., .10610 13.34 5n 1 cX, . 13298 13, 31 6n 1 ex, .15959 13. 29 7n 1 ol_ I .18638 13.29 sn , c,L. I . 21290 13.30 9n 1 d., . 23930 13.31 Average 13.31 9. TABLE IV Data in the First-Order from a (111) Laue Photograph of NdPMo 12 o40 .30~0 (Pure first-order reflections for o. 24 lt .{ n A<- o. 48 X) Form fhk .2} 733 515 13 · 5 · 5 13 · 3 · 7 13 •9 · 1 955 937 919 719 717 735 359 517 3 ·13 · 13 335 9 · 11 · 5 11 · 11· 3 Sin e Max, Min. . 051 . 056 . 097 • 094 . 097 .072 .073 .072 • 069 . 084 . 062 , 076 .073 .106 . 066 .091 .105 .094 . 29 1t • 53 lt .106 .36 .141 .141 ,118 .30 .29 .28 .29 ,28 . 26 . 28 .39 .31 .29 .39 .26 . 46 .28 .31 .31 .38 ,31 • 68 11 · 1•9 • 096 11 ·1 ·7 .108 .118 .115 .131 ,126 13 •7 · 9 -1759 · 17 · 11 13 · 5 · 13 n °A Min. 11 · 5 · 11 .152 19 ·19• 9 9 , 9 ,13 11 · 11· 15 9 · 7· 11 13. 9.15 15· 3 ,:13 13 · 3 , fi 11 · 9 · 13 13 , 7. i3 17 •7• 15 19 •9•17 15 · 5 •13 19 · 5 •15 19 •3 •13 17 •1· 11 11 · ll · 7 17 ,J. •9 13 · 1·9 is .I , § 1 - 19 • fl .180 . 136 . 076 . 086 . 079 .092 .ll8 .108 .132 .133 .146 .158 .122 .140 .169 .174 .157 .206 .178 .164 .158 .162 .119 .141 .185 .179 .194 .204 .172 .184 .199 .174 .196 .196 .156 . 139 .173 • 42 .30 .31 • 43 .29 .34 Max • 44 . 44 ,34 .31 . 43 .31 . 49 .29 . 76 . 40 .39 .47 . 55 .32 . 52 .38 . 42 .44 .33 .45 . 35 .160 . 206 ,168 . 181 .186 . 46 .34 .27 .37 .44 . 200 . 209 .221 .192 .215 .207 .220 .215 .171 .189 .188 ,38 . 46 • 43 .38 .48 . 44 • 42 . 35 .39 .34 ,39 ,39 .39 ,47 .45 .36 ,36 .39 .35 . 50 .36 . 43 . 47 .44 . 51 • 50 .49 ,39 10. If 8 molecules of NdPM012040. 30E2 0 be placed in a cub ic unit with a= 23 ,1 X, the calculated density is 2.68 g/ml, t o be compared with the experimental value 2,62 ! 0.2 g/ml determined by the displ a cement method using benzene. In determining these densities, the crystals were dried in the manner previously described so that very accurate values are not to be anticipated. However, this cubic unit with a= 23.l A containing 8 molecules of the compound would seem to be well established. In Table V, data are given for all of the compounds for ·which the size of the unit cell was determined in the manner already described. The unit is well established for the three rare earth salts of molybdophosphoric acid, and for MgzSiM01z040. 3lf:T:z O. Only a photo- graph of ra. ther small intensity was indexed for H3?Mo12040. 30Rz O and none at all for Ni2SiM0 12 o40 • 3lrT.z0, but a rather careful comparison of both Laue and oscillation photographs with those of the rare earth salts reveals nothing different. Hence the conclusions regarding size of unit and space-group may be expected to apply equally to all of the compounds just enumerated, Be 2SiW12 o40 .31HzO is also included in Table V. The single Laue photograph of this compound which was indexed ha.d about 36 forms reflecting in the first order with no value of n A falling below the short wave-length limit of 0,24 1l when calculated upon the basis of a unit with a= 23.3 !. No particular accuracy can be claimed for the lattice constants given, so that it is possible and even probable that in the case of the three rare earth compounds, for instance, the indicated variation is not real. 11. TABLE V Data Establishing the Size of the Unit Cell Compound NdPMo 12 o40 • 30~0 Edge of Unit 1t 23.1 Density, g/ml Calculated Experimental 2.62 2.68 GdPMo 12 o40 • 30¾ 0 23. 0 2. 72 SaPMo 12o40 . 30~ 0 22.9 2.76 2.60 H3 PMo 12 <) 40 . 30Hz 0 23.3 2.45 2. 52 Mg 2SiMo 12o40• 31¾ 0 23. 4 2.50 2. 56 Ni2SiM012040• 31H2 0 23. 2 2.63 Be 2Si'.1\ 2o40 . 31~0 23.3 3.60 3.66 A unit with a ;;;j 23 1t containing 8 molecules appears from Table V to be highly probable for these compounds. It should be mentioned, however, that some difficulty was encountered in connection with the appearance upon Laue photographs of quite a number of "anomalous 11 spots. Usually these were poorly shaped and never did their analogues in other zones appear even with entirely favorable conditions for reflection. Furthermore, spots in the same relative position did not appear upon photographs taken from other speci1nens of the sarne compound. In one case ( SaPMo12 o40 . 30H2 0) a well-shaped but very weak spot appear ed upon an otherwise excellent photograph. If it represented a real reflection, this spot would have eliminated the three-fold axis normal to (111). Upon taking a series of photo- graphs with another crystal for which the planes of each of the three zones in turn were in favorable position to reflect, no such spot appeared, however. Bec ause of the great complexity of the Laue pattern 12. and the presence of so many very weak reflections, it was more difficult than usual to arrive at a definite decision regard i ng the true nature of these spots, but it can now be asserted with confidence that they are to be disregarded as bogus. That is, the pre- vious conclusions regarding the crystal symmetry and the size of the unit cell may be accepted as highly probable. Laue photographs taken with the X-ray beam normal to (lll) show a three-fold e.xis and three planes of symmetry for all of these compounds, so that the point-group symmetry is Td, O, or Oh. Now reference to Table IV reveals no first-order reflections appearing except for h k ..f all odd, as is required by a face-centered l attice. This was found to be the case for every Laue photograph which was indexed. Assuming, therefore, a face - centered lattice, the following space-groups are t o be oonsidered: 4 7 6 8 5 Ta, T~, o3, o4. Oh• Oh, Oh, Oh. 5 6 8 4 Td• Oh• and Oh, with the same special criteria., are eli:minated by the presence of reflections with h = ! kin odd orders, for instance (lll). (333), etc. on oscillation photographs, and many reflections in the first-order on Laue photographs (see Table IV). 2 Of the five remaining space-groups, Td, 0 3 5 and Oh are without special criteria., and that for o4 was not investigated. However, O~ does not permit reflection in the second-order for planes of the type [ok}J with k even and .,R, odd. 4 Because of this fact, and since the face-centered lattice does not permit odd-order reflections except for hkL all odd, no Laue reflections for planes of this kind can occur at a value of n A less than 0.96 !, i.e., four times the short wave-length limit of 0.24 !, if the structure be based upon O~. 13. The absence of all reflections for [oki] with k even and ..P. odd in the range O. 48 Jt < n A< O. 96 ! is is the correct space-group. 7 therefore strong evidence that Oh The procedure adopted was to look for all reflections of this sort upon Laue photographs for which the X-ray beam was inclined at various angles to the normal to (111). '7 No reflection which would eliminate Oh was found for any of the compounds listed in Table v. but the evidence for this spacegroup is not overw'helming. The data obtained for NdPM.012040. 30liz 0 are discussed in detail in the following paragraphs. Table VI contains a pa.rtia.l list of observed absences in [ok ..e} with k even, .1!. odd in the second order for forms of the type the case of NdPM:o 11 0 110 • 30liz O. if t.vo or more planes of a fonn were in posi t5.on to reflect for values of n ~ maximum a nd minimum values .fer sin e indicated in the table. bet11,een O. 48 and O. 96 ..!!., the and n ;\ within this range are 14. TABLE VI Observed Absences on Laue Photographs of NdPMo 12 o40 . 30F-2 0 as Required by 07 h Form (ok l} 023 - Sin 0 n ~ ! . 068 .87 043 .103 • 065 .95 .60 045 .116 .079 . 83 • 57 065 .130 .099 .81 . 58 067 .155 .100 . 78 . 50 087 .148 .64 089 .142 • 54 047 .162 .123 . 93 .71 085 .185 .130 .91 .64 0 •10 • 7 .233 .166 .88 . 62 O· 8 · 11 .215 .160 • 73 • 54 o:s, 11 . 255 , 130 • 94 ,48 - 15. With regard to the data of Table VI, it may be said that only [023j gave discernible reflections in the fourth-order, that is for a value of n~ greater than 0.96 A. However, the fourth-order of {oo~, that is [ o•l6 · 20j , is already of greater complexity than any form observed to reflect in the fir st-order (see Table IV) excepting only [19 ·19 •9} . It is not surprising, therefore, that only £02~ from the list given in Table VI was observed to give any reflections at all. On a quite asymmetric (111) photograph, five of the six normally appearing planes of £q2%were observed to reflect with rather strong 0 intensity for values of nA equal to or greater than 1.4 A. However, =0.87 A was definitely absent, aUhough 0.87/2 :::. 0.435 A 0 (230) with n ) 0 was an entirely favorable value of the wave length, both on account of high intensity in the incident beam, and because of large absorption of the scattered radiation by the photographic plate. The value of sin9 , 0.068, was also favorable, and the reflection was expected in a clear region of the plate (the plate to crystal distance was 7.5 cm, so that reflections at values of sin8 greater than 0.04 were well beyond the blackened region around the central image). However, it is entirely possible that the structure factor for (02~ is nearly zero for second-order reflections. It may be mentioned also that on all photographs {9951 and -(o7s] , which are of comparable complexity with the forms of Table VI, were observed to reflect in the second-order with medium to fairly strong intensities at 0 values of n)... greater than about 0.6 A. 16. The material of the preceding paragraphs represents quite 7 convincing evidence for selecting Oh as the space-group of NdPM012040.30~0. For the other compounds containing molybdenum of Table V, the evidence for 0~ is quite similar except that no other photograph was sufficiently asymmetric to require a plane of [ 023} to reflect either in the second-order or not at all, As previously remarked, no photograph was but for the three other compounds at least half a dozen and usually more absences of the type required by ol were observed. The apparent identity of the patterns observed on photographs taken under analogous circumstances of different compounds of this group supports strongly the view that 0~ is the common space-group for all of them, The data for the single Laue photograph of Be 2siw12040 , 31~0 7 which was indexed indicates that~ is also the space-group in this case, As the photograph was not markedly asymmetric, only four forms of the type [ok ij with k even, 2 odd were in position to reflect in the second-order, and these, of course, did not appear. It may be mentioned, however, that {590] , [1.11:0] , and {570j were all observed in the second-order on this photograph, 17. DISCUSSI ON OF POSSIBLE STRUCTURES Not much progress was made toward finding the actual structure of these compounds, but a brief discussion of some of the possibilities may be of interest. 0~ furnishes sets of 8, 16, 32, 48, 96, and 192 equivalent positions. 5 The unit cell of NdPMo 12 0., 0 .30HizO, for instance, contains 8 molecules, so that there must be placed: 8 Nd, 8 P, 96 Mo, and at least 320 0 and probably more as O and as OH. The properties of these compounds make it highly probable that a large pa.rt of the water content is present as water of constitution, so that OH groups may be expected to occupy definite positions in the structure. In any event not all of the oxygen can be in crystallographically equivalent positions. Unless the molybdenum in this compound is of three kinds crystallographically, it must occupy either 96 f with one or 96 e with two parameters. It would be possible, perhaps, to put molybdenum into one of the two sets of equivalent positions, and fix the parameter value or values with the use of reflections appearing at large values of sin 0 . Such reflections, at least if they were strong, probably could be regarded as being due largely to molybdenum, although with these compounds the relatively l a rge number of light atoms might still cause complic&tions. Wide-angle reflections of a ppreciable intensity did not appear, however, even upon oscillation photographs with exposures of more than 1000 m.amp. hrs. For instance, (999) with sin 8 was the last order of (111) to appear with fair intensity. = 0.24 The al- ternative to this procedure is to compare a. complete set of intensities calculated for a predicted structure with those actually observed. 18. Pauling 6 has predicted a molecular structure for the members of the saturated 12-cla.ss of compounds which in itself is able to correlate satisfactorily a considerable mass of chemical and crystallographic data. Hence, it was considered worth while to en- deavor to account for observed X-ray intensity relations by putting these complex ions into the unit cell in a manner determined by o~. The point-group symmetry of the predicted structure for these complex ions is Td. Now this is just the minimum molecular symmetry required by o'!i for 8 molecules in the unit cell, It is, therefore, possible to place 8 such ions within a unit cell in ac cordance with 7 the requirements of Oh. aj: The predicted complex ion has a formula ~ 0 4, Mo 12 o18 ( OH) 3 and is of the general form of a regular tetrahedron with the vertices lopped off by planes perpendicular to the three-fold axes. The para- meter values in hgstrom units for a single comple~ ion with P or Si at the origin are given by Pauling . 6 Hence it is merely necessary to divide these by a, 23,1 K, in order to obtain the para.meter values to be used in calculating intensities for the unit cell. there is obtained: 5 8 Pin 8 f; If this is done, 32 Or in 32 b with u = 0.040; =0.125, w = 0.032; 48 OrrI in 48 c with 96 Orv in 96 e with v = 0,110, w = 0.208; 192 OIV in the 96 OrI in 96 e with v t =0.146; general position with x = 0,001, y = 0,229, z = 0.002; 96 Mo in 96 e with v = O. 584, w = 0.173 (the notation is that of Pauling. 6 ). The oxygen marked Orv h_a ve hydrogen associated with them to give hydroxyl groups. For a complete description of the predicted structures for these complex ions, including a n~~ber of illuminating sketches, the re&der is referred to the original paper by Pauling. 6 19, Using the values of the paramAtArs just given ~eans that the tetrahedral complex ions with centers at O O O and 1/4 1/4 1/ 4 point toward each other, whereas a change thruout to negative values means thut these tetrahedra are base to base, bilities ~ust be considered, Both of these possi- In making actual intensity calculations also, it was convenient to transform the origin to the center of symmetry a.t 1/8 1/8 1/8. It 1,•ras found that with either positive or negative values of the para.meters, the calculated intensities for (nr,n) did not agree v1rith observation, F'or instance, although (444) reflected much more strongly than (333) or (222), it had the smallest calculated structure factor of the three, This structure, therefore, cannot be correct with the assigned parameter values, However the predicted structure has ten parameters including two for the relatively heavy and therefore strongly scattering molybdenum atoms. Hence it is evident that the calculated structure factors may be considerably changed by introducing rather small variations in the parfu~eter values. The manner in which this should be done is not at all obvious, however, 1''or this reason, it was considered advisable to try to fit the complex ions into the unit cell, and to see what changes in parameter values would. be necessary in order to obtain generally satisfactory interatomic distances. If the positive values of the parameters be used, the smallest interatomic distance between atoms of two different ions is the 0-0 separation of tw-o oxygen atoms in the 96 OIV positions, The distance between O in uvu or vuu and O in 1/4 - u, 1/4 - u, 1/4 - v, for which u and v have the values previously given, is calculated to be 2,27 !. 20. If the negative values of the pa rameters be used, the smallest separation bet..veen two ions is that for t wo oxygen atoms in the 192 OIV positions. The distance between O in yzx and O in x + 1/4, 1/4 - y, 1/4 - z is calculated to be 2.18 X. Now the minimum 0-0 sepa ration for such a. case as this should be about 2. 70 Jt, so that the values found are definitely unsatisfactory. All other interatomic distances are, however, fully as large as they need to be, and it seems quite probable that the complex ions could be distorted in a way that would remove the difficulty just mentioned. ~ome attempts to do this re- sulted in an improvE%ent of only a little more than O.l 1t for the second case, that is, vdth the tetrahedral ions at 000 and 1/4 1/4 1/4 base to base. It is again very difficult to decide which of the many factors should be varied, and for each such change the calculations are quite laborious. It is quite probable too that the molybdenum- oxygen bond is not purely ionic, so that it is possible that a smaller separation should be assumed in this case. In any event, it still seems not improbable that these complex ions could be fitted satisfactorily into the unit cell, especially in view of the large number of v ariable factors and the fact tha t in the one case but one andin the other case only two contacts betvmen ions are unsatisfa ctory. It would still be necess e.ry to test the structure for agreement between calculated and observed intensities, of course, if the results were to be given any great significar.ce, I wish to express my appreciation of much valuable advice which I have received from Professor Linus Pauling during the course of this work. Pauling. The investigation was suggested to me by Professor 21 , SUMMARY Cubic crystals of some of the 12-molybdophosphates and related compounds, for instance, NdPMo 12 o40 • 30F-2 0, were subjected to an X-ray examination. The normal neodymium, samarium, and gadolinium salts of 12-molybdophosphoric acid, not previously reported in th e literature, were prepared and shown by goniometric measurements to crystallize in the cubic system. Laue and oscil- lation photographs lead to unit cells containing 8 mol e cules with a ~ 23 X. The space-group is probably 0~ for all of the compounds studied. The possibility of fitting 8 complex ions with the molecular structure predicted by Pa.uling 6 within the unit cell is discussed. With the parameter values as assigned by Pauling, not even rough agreement was found between calculated and observed intensities for reflections appearing upon oscillation photographs . It was found also that either one or two c) to O distances between adjacent ions, depending upon whether positive or nega t ive parameter values ,,rere used, woul d be too small. However, it is not improbable that variations in t he 10 para.meters (2 of which belong to molybdemun) may enter i n such a way as to account for both of these dis- crepancies. The point-group symmetry of the predicted structure for the complex ions is Td, a.nd this is just the min imum molecular symmetry permitted by 0~ with 8 molecules in the unit cell. 22. REFERENCES 1. F. Ephraim, 2. Groth, "Chemische Kristallographie, 11 Engelmann., Leipzig, 1908, Vol. II. 3, Ro sen.½ei.m and Jaenicke, Z,anorg.Chemie, 101, 238. 4. R, 1v.G. Wyck~off, Am.J.Science, Se ries 4, 175 (1922 ). 5, R. 'N . G, Wyck~off, 11 Analytical Expression of the Results of the T:ieory of Space-Groups," Carne g ie Institution of 1:;a shington, 2nd Edition, 1931. 6. Linus Pauling, J. Arn ,C hem , Soc,, 51, 2868 (1929), 11 Anorg. Chemie, 11 4th Edition, Theodor Steinkopf, Dresden and Leipzig, 1929; J.N. Friend, "Textbook of Inorganic Chemistry," Griffin, London, 1926. Vol. VII, Part III, pp. 251-268. III. The Crystal Structure of Cadmium Chloride 546 Introduction. With the aid of data obtained from a reproduction of a Laue photograph published by Bruni n.nd Ferrari1) it was shown by Pauling2) that the unit of structure of CdC/2 and some other bivalent chlorides is a rhombohedron with a= 36° 40' and a= 6.35 A, about, containing 1 CdCl2 , Cd at 000, 2 Cl at u ·u u, u u u. The parameter value was not determined from the intensities of the reflections; it was pointed out, however, that the value u =-} leads to a reasonable structure. We have now made a study of crystals of CdCl2 with the use of Laue and oscillation photographs, leading to the unambiguous deduction of the structure previously suggested and evaluation of the parameter as u = 0.25 + 0.01. The Determination of' the Atomic Arrangement. Crystals of CdCl2 were cleaved out of a mass obtained by heating NH4 GdCl3 in a current of dry HCl in a porcelain crucible. Data from oscillation photographs of molybdenum K-radiation filtered through zirconia, given in Tables I and II, lead to a hexagonal unit with a= 2.'~2 A and e = 5.82 A. On assigning indices lo the spots on a Laue photograph taken with the radiation from a tungsten tube operated at a peak voltage of 54 kv. on the basis of this unit, it was found that many spots led to values of nA as low as 0.09 A, nearly one-third of the short wave-length limit (0.24 A) of X-rays present in the spectrum. For example, the spot assigned indices (51.1) was found lo have nJ.., = 0.09 A. This unit is accordingly ruled out. The smallest hexagonal unit accounting for the observed retlections is obtained by tripling e and rotating through :30°. This unit, with a= 3.85 A and e = 17 .46 A, contains 3 CdC~, corresponding to a calculated diensity of 4-.05 g/ cm 3, in good agreement with the directly determined value 3) 4.04 7 g/cm 3. l) G. Bru n.i and A. Ferrari, Atti Lincei Rend. 2,457. 1925; 4, 10. 1926. 2) Linus Pauling, Pr. Nat. Acad. Washington lo, 709, 1929, 3) International Critical Tables, 1, 120, The Crystal Structure of Cadmium Chloride. 547 Table I. Spectral Data from (1H) of Cadmium Chloride. [101] Vertical Photograph No. 1. Distance between layer lines, s=l to s=1 µ sinµ doo1 3.75cm. 10°37' 0.1842 3.85.A The observed reflections are all accounted for by the corresponding rhombohedral unit, which has a= 6.23 .A, a= 36°02', and contains 1 CdCii_. All indices used in this paper are referred to the axes of this unit. A Laue photograph taken with the incident beam normal to (111) showed a three-fold axis and three symmetry planes, requiring that the point group of the crystal be C3 v, Da, or D3 a. The only space groups isomorphous with one of these and based on a rhombohedral lattice are c~v' civ, D~, DLz and n:a• Of these c~v and n:d provide no position for 1 Cd. The non-identical atomic arrangements given by . the others are I. Cd at u u u, Cl at v v v, Cl at w w w, c:v; II. Cd at O O O, 2 Cl at u u u, u u u, Di and D;a· We shall not consider I., as the discussion of two parameters would b~ very laborious, and IL is found to lead to a satisfactory structure. The value of the parameter u in II. can be determined with the use of only qualitative assumptions regarding relative reflecting powers. The structure factor for reflection in the n th order from a plane (hkl) is Shkl,n =Cd+ 2 Cl cos 2n-n (h + k + l) u. (1) The relative reflecting powers of Cd und Cl can be taken as roughly proportional to the atomic numbers, 48 and 17, so that Equation 1 leads to a set of cosine curves which do not cut the u-axis. The factors influencing the intensities of reflection, aside from the structure factor, are such as to cause the intensity to fall off as the effective interplanar distance d/n decreases, so that if a plane is observed to reflect more strongly than another with larger d/n, its structure factor S must be the larger. The observed intensities of reflection in five orders from (111) are given in Table II, and curves of S as a function of u are shown in Fig. 1. It is seen that the intensity inequalities (4 U) (222), (333) (222) and (555) (222) limit 3u to the regions 0.20-0:29, > > > 548 Linus Pauling and J. L. Hoard 0,71-0.80 and L20-Ul9, or u to 0.067-0.097, 0.237-0.267 and 0.i0-0.t3. The observed intensity relation (231) (113) for reflections on the Laue photograph (Table III) rules out the region 0.t0-0.t3, and that (212) ~ (211) rules out the region 0.067-0.097, so that u can be given the value 0.25 + 0.01. A comparison of the observed intensities and the structure factors calculated for this value of i, is made in Tables II and III. > 0 Ju- 0,1 0,l o,s O,J q,µi,222 ---------so- JJJ > 222 sss,z2z - Fig. 1. Structure factor curves for cadmium chloride. The curves are symmetrical about 3 u = 0.5 so that the part shown is sufficient to obtain all possible ranges for u. Also, if u is substituted for 3 u in the figure, the curves shown may be used to eliminate the regions 0.40-0.43 and 0.067-0.097 as possible values for u. Table II. Spectral Data from (111 ) of Cadmium Chloride. Photograph No. 2. Order 1 2 3 3 4 I Line MoKa a a1 a2 a1 4 a2 5 5 a1 a2 Measured Distance 20 1.222 cm. 2.441 3.670 3. 701 4.911 4.948 6.170 6.213 7.01 14.00 21.05 21.20 28.15 28.40 35.40 35.60 I elm 5.81 5.81 5.82 5.80 5.84 5.82 5.83 5.82 Estimated Intensity I S for U= 0.25 strong weak Cd Cd-2Cl } medium } strong } medium weak Cd Cd+ 20t Cd The Crystal Structure of Cadmium Chloride. 549 Table III. Data for Intensity Comparisons from Laue Photograph No. ~. Estimated Intensity {hlcl}. l h+k+l dhkl nl 4T3 3 0.948.A. 0.36.A. . 0.3 UT 4 0,905 0.36 4.0 2T4 2 L245 0.41 0.3 21 2 3 L09 0.41 4.2 S for u= 0.25 Cd Cd+ '!.Cl Cd-2Cl Cd Description of the Structure. The structure found for cadmium chloride is represented in Fig. 2. It is a layer structure closely related to that of cadmium iodide. Each cation is surrounded by six chloride ions at the corners of a nearly regular octahedron, six edges of which are shared with other octahedra to form a complete octahedral layer. In the cadmium iodide structure 1) these layers are superimposed in such a way that each cation is directly above a cation in the layer below, whereas in the cadmium chloride structure each cation is directly above an anion in the layer below, and below an anion in the layer above. These two structures can be formally represented in the following way. Let A represent a layer of atoms with X = 0, Y = o, X and Y being coordinates relative to axes 12 0° apart, B a layer with X = ½, Y = l, and C a layer with X = }, Y = ½- A, B, and C then represent closepacked spheres in a plane. The cadmium chloride and cadmium iodide structures then correspond to the following sequences of layers along [0001 ]: Fig. 2. The structures of cadmium chloride and other bivalent chlorides. Large open circles represent Fig. 2. chloride ions, small closed circles cadmium ions. Heavy lines ·mark the rhombohedral unit of structure, and light lines the coordinated octahedron formed by six: chloride ions about each cadmium ion. 4) Richard M. Bozorth, J. Am. chem. Soc. 4:4:, !n32. 4922. Zeitschr. f. Kristallographie. 74. Bd. 36a 550 Linus Pauling and J. L. Hoard Cadmium Chloride Structure Cl at .A Cd at E Cl at C Cadmium Iodide Structure I at .A Cd at E I at C A ::, Cl at E Cd at C Cl at .A Cl at C Cd at A Cl at E Cl at A Cl at E Cl at C t'"' I at .A :::, ,- :,- Cd at E J at C 0 ..., I at (t) (JQ C ::, :;: I: t'"' (t) C :;: ::, (IQ 'f .A Cd at E I at C J at .A Cd at E J at C Thus it is seen that the difference in lattice and unit of structure for these two arrangements does not signify the existence of an essential physical difference. The succession .ACE .ACE for Cl layers alone shows that the cadmium chloride arrangement is based on cubic close-packing of the large chlorine ions, from which there is indeed little distortion. The dimensions of the unit of CdCl2 lead to Cl-Cl distances of 3.85 and 3. 76 A, which • are compatible with the crystal radius of Cl-, 1.81 A. The Cd- Cl distance, 2.66 A, is somewhat smaller than the sum of the radii calculated 1) for Cd++ and CZ-, 2. 78 A. This decrease is to be attributed to the deformation of the polarizable anion by the eighteen-shell cation; for the crystal radius of Cd++ leads to good agreement with observed interionic distances in CdF2 and CdO. Values of a and a calculated from published date of Bruni and Ferrari2) and of Ferrari, Celeri, and Giorgi3) may be given for a. number of crystals isomorphous with CdCl2 . There are included MgCl2t CoCl2 , NiCZ2 , F eC½ with a=33°33' and a -=6.22, 6.U, 6.13, and 6.20 A, respectively; also MnCl2 with a= 34- 0 35' and a= 6.20 A. Bruni and Ferrari have reported that ZnCl2 shows the MgCl2 structure, and Ferrari and Giorgi 4) have reported a similar conclusion for CdEr 2 • Finally Goldschmidt 5) has reported that unpublished powder 1) Linus Pauling, J. Am. chem. Soc. 49, 765. 1927. 2) G. Bruni and A.Ferrari, Alli Lincei Rend. 2, 457. 1925; 4, 1 O. 1926. 3) Ferrari, Celeri, and Giorgi, Atli Lincei Rend. 9, 782. 1929. 4) Ferrari and Giorgi, Atli Lincei Rend. 9, 1134. 1929; 10, 522. 1929. 5) V. M. Go! dschmi d t, Geochemische Verteilungsgesetze der Elemente VIII,p.14 7<. The Crystal Structure of Cadmium Chloride, 551 photographic data obtained by Ofted al show that RuCl2 , RhCl2 , IrCl2 , PtCl2 , and PdCl2 have a structure similar to that of NiC"1,. A number of examples of crystals having the cadmium iodide structure may also be cited. Ferrari and Giorgi 1) place CoI2 , FeI2 , MnI2 , PbI2 , CoBr 2 , FeBr 2 , MgBr2 and MnBr2 in this category. Aminoff2) found a similar structure for pyrochroite, Mn( OHh, and other hydroxides of this type are also known to crystallize similarly. In general it is to be anticipated that the Cdl2 structure will be stable for compounds of the type MX2 in which M has a coordination number of six and X has a large dipole moment, either permanent, as with the OH- ion, or induced, as with the highly polarizable ions T and Br-. The CdCl,, structure is to be anticipated for compounds of this type in which M fulfills the same requirements as above, but in which X has a relatively small dipole moment, as with the er ion. Summary. With the aid of data obtained from Laue and oscillation photographs, it is shown that the unit of structure for CdC½ is a rhombohedron with a= 36°02' and a= 6.23 .A, containing 1 CdCl2 , Cd at 000, 2 Cl at u u u, u u u, with u = 0.25 + 0.01. A layer structure along [0001], closely related to that of CdI2 , is found for CdCl2 , the er ions being in approximate cubic close packing. MgCl2 , CoCl2 , NiC½, FeCl2 , Mn0l2 , RuCl2 , RbCl2 , IrCl2 , PtC½, PdC½, and CdBr2 are representatives of the CdCl 2 structure; CoI2 , FeI2 , Mnl2 , Pbl2 , CoBr2 , FeBr2 , MgBr2 , MnBr 2 , and Mn(OH)2 of the CdI2 structure. Received June 1st 1930. 1) Ferrari and Giorgi, Atti Lincei Rend. 9, H34. 1929; 10, 5S!2. 1929. 2) Aminoff, Z. Krist. 66, 127. 1921. 36*