The Crystal Structure of Tetramminopalladous Chloride. The Crystal Structure of Potassium Bromoselenite. The Normal State of the Hydrogen Molecule-Ion Citation Dickinson, Bernard Neil (1934) The Crystal Structure of Tetramminopalladous Chloride. The Crystal Structure of Potassium Bromoselenite. The Normal State of the Hydrogen Molecule-Ion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/A597-FY24. https://resolver.caltech.edu/CaltechTHESIS:01252017-083837484 Abstract An investigation of the crystal structure of tetramminopalladous chloride has considerable interest because of Werner's contention that compounds containing bivalent palladium (or platinum) possess a planar configuration consisting of four groups coordinated about the central palladium atom. The correctness of this assumption has been verified in the case of potassium chloroplatinite and palladite by the x-ray studies of Dickinson (1). Pauling (2) has shown theoretically that the bivalent transitional elements platinum, palladium, and nickel can form bonds directed toward the corners of a square. Recently Cox (3) has reported that tetramminoplatinous chloride, Pt(NH 3 ) 4 Cl 2 ·H 2 O, is in accord with Werner's viewpoint and has a structure closely similar to that of potassium chloroplatinite. The determination of the structure of tetramminopalladous chloride was undertaken to test Werner's assumption for a cation containing bivalent palladium. This palladium compound might reasonably be expected to have the same structure as Pt(NH 3 ) 4 Cl 2 ·H 2 O; it is shown in this paper that the structure is closely related to the potassium chloroplatinite structure but is based on a unit containing two molecules instead of one as reported by Cox for the platinum compound. Tetramminopalladous chloride forms pale yellow tetragonal needles from a solution of diamminopalladous chloride in aqueous ammonia. In most cases the crystals we prepared developed prism faces belonging only to {110}. 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): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1934 Record Number: CaltechTHESIS:01252017-083837484 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:01252017-083837484 DOI: 10.7907/A597-FY24 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 10026 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 26 Jan 2017 20:15 Last Modified: 04 Oct 2019 00:15 Thesis Files Preview PDF - Final Version See Usage Policy. 11MB Repository Staff Only: item control page

THE CRYSTAL OF ST ~UC T URE TETRAMMINOPALL.ADOUS CHLORIDE THE CRYSTAL STRUCTURE OF POTASSIUM BROMOSELENITE THE NORlVlAL STATE THE HYDROGEN MOLECULE- ION OF Thesis Bernard Ne il by Dickinson I n partial fulfillment of the requirements for the degree of Doctor of Phil o s ophy California Inst i tute of Technology Pasadena, California 19 34 THE CRYSTAL STRUCTURE OF TETRA.MM:INOP.ALL.ADOUS CHLORIDE Introduction An investigation of the crystal structure of tetram- minopallad ous chloride has considerable interest because of Werner's contention that compounds containing bivalent palladium (or platinum) possess a planar configuration I consisting of four groups coordinated about the central palladium atom. 'l'he correctness of this assumption has been verified in the case of potassium chloroplatinite and palladite by the x-ray studies of Dickins on (1). Pauling (2) has ahown theoretically that the b,iva.lent transitional elements platinum, palladium, and nickel can form bonds directed toward the corners of a square. Recently Cox (3) has reported that tetramminoplatinous chloride, Pt(NH 3 ) 4c1 2 ·H 2 o, is in accord with Werner's viewpoint and has a structur e closely similar to that of potassium chloroplatinite. The determination of the structure of tetram:minopalladous chloride was undertaken to test Werner's assumption for a cation containing bivalent palladium. This palladium compound might reasonably be expected to have the s~e structure as Pt(NH 3 ) 4ci 2 ·H 2 0; it is shown in this paper that the structure is closely 2 rel ated t o the potassium chloroplatinite structure but is based on a unit containing two molecules instead of one as reported by Cox for the platinum compound. Tetramminopalladous chloride forms pale yellow tetragonal needles from a solution of diamminopalladous chloride in aqueous ammonia. In most cases the crystals we prepared developed prism faces belonging only to {110 } • The Unit Cell and Space Group Oscillation photographs for determining the lattice constants were prepared by reflecting Mo Kc:J(. radiation filtered through zirconia fro m a developed prism face (110) and a ground face (001). As an aid in fixing the position of the central image the spectrum from a given crystal face was recorded on both sides of the photograph in a manner which gave a pattern symmetrical about the central image. ·r he distance of the plate from the crystal was determined by simultaneously registering the spectrum from the cleavage face of calcite. In Table IA are given the data obtained from an oscillation photograph from (001). The value of c0 as 0 determined from these data is 4.34 + 0.05 A. The identity distance along c as calculated by means of the Polanyi 0 formula, s ).. =- I si!;f' , was found to be 4. 3 A. 3 Table IA. Spe ctral Data from (001) sin e dOOl o( 0.08151 4.356 o( 0.16408 4.323 Reflection Line 001 002 Average: A. 4.34 The data given in Table IB, obtained from an oscillation photograph from a developed prism face (1 10) with ~Io] as the axis of oscillation (the indices referring to the true unit described below), lead to a spacing of 0 7.284 + _ 0.02 A. This might be taken as the value of d It is found, however, that no unit with a 0 100 = ?.284 A accounts for the presence of several reflections observed in the first and other layer lines of this photograph. The smallest value of a 0 reflecti ans is which does account for these V2 x ? • 284 :::: 10 . 302 A.. No reflections were observed on any oscillation or Laue photograph which could not be accounted for an the basis of a unit of structure with a 0 =- 10.302 A and c 0 =- 4.34 .A, which may hence be.confidently accepted as the true unit. By choosing a 0 :: 10. 302 A we require that the a-axis make an angle of 45 ° with the normals to the developed prism faces which as a result belong to the form {110J . • 4 Table IB. Spectral data from lllO) with [jlo] vertical. Reflection Line sin e Spacing 110 o( 0.04866 ?. 288 220 o<. 0.09?61 7. 266 330 o( 0.14609 ?.282 440 o( , 0.19432 7.285 440 o( ~ 0.19535 '1. 290 550 O(' I 0.24286 ?.287 660 ex., 0.29124 7. 291 K Average: '1 . 284 Using the radiation from a tube with a tungsten anticathode operated at a peak voltage of 52 k v., Laue photographs were made with the berun approximately normal to lllO) and to (001). Employing the values a 0 -=- 10.302 i and c 0 no value of n A ::. 4.34 .A, calculated from a Laue photograph com- pletely indexed with the ai d of a gnomonic projection was found to be less than the short wave limit, 0.24 i, although sixty two forms were reflecting in the first order. fhe first-order reflections appearing on this photograph are given in Table II. Hence the values 10.302 + 0.03 Aand 4.34 ~ 0.05 ~ for a 0 and c 0 respec- tively were accepted as correct. 5 Using t he values of a 0 and c 0 just f ound, the density calculated with the assumption that the unit contains t wo molecules was found to be 1.89 g/cm3, which ag rees satisfactorily with the experimental value of 1.9 3 ~ 0.1 g/cm3 measured by the suspension method using a mixture of methylene iodide and benzene. The reflection from planes with h + k odd are the ones requiring us to choose a tw o-molecule unit with a o = 10.302 and c 0 -a Q 4.34 11. rather than a one-molecule unit with = 7. 284 A and c = 4 . 34 A.. Eleven reflections of this 0 type are given in Table II which contains the data from a single Laue photograph. The appearance of reflections from planes with ..,,£ even and h + k odd in the odd orders eliminates the facecentered, e nd-centered, and body-centered tetragonal lattices and six planes of this type were observed to reflect in the first order on a sing l e Laue photograph (Table II). The planes are (1 22), (430), l562), (432), l632), and (560) reflecting at n ~ 0.315 equal to 0.268 A, A, 0.414 A, 0.352 A, 0.382 A, and 0.419 Ares- pectively. Each of these three kinds of lattices is also ruled out by the appearance of reflections of other types . 'l 'hus the structure must be based on a si mple tetragonal lattice. x 6 Since a Laue pattern with the beam. normal to {001) shows a four-fold a.xis and four planes of syfilt~etry and that with the beam normal to (110) shows a two-fold axis and two planes of symmetry, the point-group symmetry is Vd, C4 v' D , or D4 h. The space groups isomorphous with 4 these point-groups and based on a simple tetragonal 1 16 inclusive, cl to 8 lattice are D4h to D4h C4v inclusive, 4v Dl to 8 inclusive and vl to 8 inclusive. D4 vd 4 d The space groups which c an be discar ded by the consideration of special criteria are given in Table III. 1 1 1 The remaining space groups are D1 , D4' c4v' vd, 411 2 5 2 5 The space groups D54h vd, D4, ~' D4h' c4v' and v?d ' 2 c4v' and v~ require that planes belonging to {Ok __eJ . with k odd reflect only in the even orders and several absences of this type were observed on the Laue photographs. Further, no reflections from planes {Ok.i) with k odd appeared on an oscilla"Lion photograph from (010) although from the construction of the sphere of reflection in the reciprocal lattice it was found that planes from twenty- eight forms of this type were in position to r eflect . These planes are (OkO) where k .= l,3,5 •• • 13, (Okl) where k =1,3,5 ••• 13, (Ok2) where k = 1,3,5 ... 13, and ( Ok3) where k -= 1, 3, 5 ••• 13. Only planes were counted which would reflect to a region of the film where other lines were present. Therefore, we are to consider ~hat the correct space group is one of the set D~ rP C42 v, and Vd7 . 7 TABLE II. Planes Ref lecting in the l<'irst Order o n a Representative Laue Photograph. Plane /V\A 733 0.322 A 951 0.366 0.364 734 0.423 951 0.443 321 0.268 3?5 0.438 952 0.416 0.328 243 0.301 394 0.450 59 3 0.372 065 0.398 425 0.280 441 0.316 11·5·2 0.4?4 111 0.368 -245- 0.345 451 0.406 681 0.352 112 0.430 245 0.413 641 0.26 6 681 0.436 -- 0.266 425 0.390 641 0.419 683 0.366 113 0.296 623 0.408 643 0.313 10·6·1 0.340 113 0.282 331 0.426 483 0.434 6•10·3 0.458 115 0.349 332 0.356 843 0.456 ? 90 0.345 1 22 0.268 335 0.406 10·4·3 0.363 '791 213 0.440 430 0.315 560 0.419 -'792- o. 362 0.349 l33 0.319 432 0.352 562 0.414 ? 11·1 0.40? 314 0.380 343 0.448 571 0.460 '7·11·1 0. 453 314 0.41'7 531 0.436 5?2 0.329 '7· 11· 2 0.434 413 0.3'74 533 0.401 752 0.2?6 7 °11°3 0.396 lb4 0 .395 354 0.423 5?3 o. 425 8·10· l 0.306 514 0.298 534 0.308 5'74 0.346 8°12.1 0.3'76 515 0.434 632 0 . 382 950 0.424 A Plane /"Y\_ 023 0.318 203 Plane /Y\. A 155 0.411 0.250 515 025 0.355 205 112 J.. Plane K /Y\..A 0 z 8 'i'ABLE I I I Sp a ce Groups Elimina,ted by Special Criteria Space Groups Representative Data Conclusion 2 4 6 D4h' D4h' D4h' 8 D4h' 11 4h' D4h' D9 5 13 Dl5 D4h' 4h' c4v' 6 7 8 c4v' c4v' c4v' /Y\}. ::: 0. 296 ~ . 2 v4 vd' d 3 (113) reflects at 4 Eliminated ? D4h' D4h' D4h' 12 11 8 D4h' D4h' D4h' 15 Dl6 D4h' 4h (5 60) reflects at /Y\.A =- o.419 x Eliminated 6 4 2 D4h' D4h' D4h' 12 10 8 D4h' D4h' D4h' 3 14 16 D4h' D4h' c4v' u 5 4 c4v' c4v' C4v' vd' v~Q 6 (023 ) reflects at /Yl.A = o. 318 A Elirainated 8a TABLE III Space Groups 3 5 D4, D44' D4' 7 6 D4, D4, D84 Continued Representative Da ta Conclusion (001) and (002) appear on oscillat ion pho'togr aphs Eliminated 9 11 he absence of an observable pyroelectric effect * indicates that n45 h is the most probable space group, since it is the only one of the three possessing a center of symmetry; it was found possible to base a satisfactory structure on this space group. * No pyroelectricity was indicated for Pd(NH~) 4 c12H 2 0 by an experiment performed according to the metnoa described by Martin (4) , although tourmaline and K3 cu(CN) 4 gave positive results. 'i 'he Atomic .Arrangement The space group n54 h equivalent positions: offers the following sets of Two equivalent positions: (a) OOO;#O ( c ) 0i2 i2'. i2 0 i2 ( b) llJ..,001 2 2 2 ' 2 (d) -~oo; oto Four equivalent positions: 0 0 u; 21 l2 u; 2l 2l u. (e ) 0 0 '..l ; \ f) 0 ~ u; 0 2l u; 2l 0 u; J,_2 0 u. l u, O; ( g) u, u+!, O; 2-u, l • ( h) u, u+-h 2, l 2-u, u, u+!, u:' O; l. 2' 1 u, u+2, l. 2 ' Eigh t equivalent positions: (i) u v O; v TIO; v+!,u+t,o; u+ t, -~-v, O; TI v O; ~ u O; t-v,t-u,O; !-u,v+t,o. 1 u, 2-u, o. 1 u, 2-u, 2. _J,_ 10 (j ) v+2, 1 u+ l2'2i .' u v t ; VU J~. 2, -U \. (;·{) V' -1-,. 2 1 l l 1 vu .Lo 2 , 2 - v , 2-u,2;2-u, - l l J. ,v u, ·2-u,v; u+·2, u,v; 2l -u,u , v; -u,u+e- i u,2u ,v. u,u+ t,v; Sixteen equivalent positions : (1) x y z, etc. With two molecules in t he unit cell, the re .'nu st be placed 2 Pd, 2 O, 4 Cl, and 8 N. The position s (a ) were selected for t h e palladium and (i) for the nitrogen atoms since in this manner we obtain a planar confi guration consisting of four ammonia molecules situated at t h e corners of a square surrounding the central palladium atom. Other possible arrangements for the palladium and nitrogen atoms either ~ive rise to non-planar configurations for the cation or else planar configurations involving angles different from 90° between the Pd - N bonds and hence are not in accord with the considerations st a ted in the introduction. Also the positions (k ) can probably be excluded for the nitrogen atoms because there is insufficient room for ~wo &'1lmonia groups along the c - axis. For the same re as on we cannot use either t he positions (e) or (f) in any combination for p lacing nitrogen. The chlorine atoms are to be placed in one of the sets of four equivalent positions or in t wo of the three availab le sets of two equivalent positions (b ), (c), and (d ) • 11 We can eliminate the positions (e) and (f) since the value c0 = 4.34 K is too small to accomodate two chloride ions in the unit along the c- axis. It was observed that the lines from lhkO) and (hk2J, al'though having approximately the same intensity, frequently differed greatly in intensity from (hkl). These inequalities were noted both for planes with h+ k even and h+k odd. Since the structure factors for the palladium and nitrogen atoms with the arrangement selected for them above do not depend on the index .Y. , this effect can be accounted for only by placing the chlorine atoms in (h), in which case the structure factor contains the factor .Jl,.,-;.,,f • '1'he scattering power of the two oxygen atoms is too small to account for these phenomena. With the chlorine atoms in (g ) the chlorine structure factor would be independent of ...2 and hence could not affect the relative intensities of (hkO), (hkl), and (hk2). Also these atoms cannot be in any two of the sets (b),(c ) , and (d), since in this case they would not contribute to the structure factor for planes with h + k odd. Of the sets of two equivalent positions (b), (c), and (d) available for the oxygen, the possibility (b) may be ruled out because it does not provide sufficj_ent 12 space for a water molecule. It was more difficult to decide betwe en (c) and (d); however, the la t ter positions g ave somewhat better agreement with the intensity data and accordingly were chosen. The hydrogen atoms cann ot of course be located by the use of x-ray data. An arrangement equivalent to the one just selected is obtained by placing palladium in (b), chlorine in (g), nitrogen in (j ), and oxygen in (c). Evaluation of the Pa rameters Using the atomic arrangement (2 Pd in (a), 8 Nin (i), 4 Cl in (h), and 2 0 in (d)) selected in the preceding section, the individual structure factors are as follows: l l + e n i(h + k) J, sPd -- f Pd s~n -- -rr;,J 2fc1 e -- 2fN [_cos(huN + kv1~) + cos(hv11 - kuN) SN l elTik c os \. h -r k ) uc 1 +- e1f 'h cos\h-k)uc J 1 e Tr i\h + k) tcos(huN - kvN) + cos ( hvN + kuN ) s0 -- f ( -,,...:. ~ 0 e + e..,,-~j'() • The atomic scattering factors of Pauling and Sherman (5) are used throughout this paper. JJ .J 13 We can employ the intensity data from oscillation photographs prepared from any prism face with the c- axis vertical to determine the value of the single chlorine J<..-rr;, J' parameter. Due to the factor entering in Sea the chlorine atoms will contribute in the same sense to all reflections lying in the same zone line (planes \hk.Q ) with Y._ ::::. 1,2,3 ••• ) with Y.. even, and in an opposite sense to the planes in this zone line with _.,e odd wh ile the signs of the other atomic structure factors will rema in unchanged for all these reflections. Further, SPd is equal to 2f Pd for planes with h + k even; there- fore, in this case SPd + SN + s0 will be positive, for all values of sin e >.. The following types of inequalities which apply to reflections with h + k even lying in the same zone line were observed: (1) (hk2) ) (hkl) (2) (hkl) ) (hkO) and (hk3) ( 3) ( hkO) ) l hkl) ) l hk2) > (hk2) > (hk3) Variations in the temperature correction, atomic scattering factors, specific times of illumination of planes, etc. will affect the relative intensities of these lines. However, since the inequalities (hkO) ) (hk2) and (hkl) ) (hk3) which were observed in all cases 14 can result only from suc h variations, it was a ssumed tha t the result ant effect of all these factors would a ct to diminish the intensity as the index 1 increases. There f ore, the inequ a lities of cases (1) and (2) can arise only because the sign of 0 °Cl even differs from the sign of Sci for planes with J? 1 or planes with)!. odd. We infer in case (1) that s is positive for 01 (hkO ) and (hk2), because only if this a ssumption is correct can s0 l Shk 2 I exceed I Shkl I since S1)d + SJ); + is posit ive for all the lines (hkO), (hkl), (hk2), a nd (hk3). If the inequalities (2) hold we conclude that S for (hkO) and (hk2) is negative. Except in Cl the sequence (680 ), (681), (682), and (6 83) which will be discussed later it was found that if one of the inequalities of case (2) held the other did also. Case ( 3) arises when the chlorine contri bu ti on is s mal l. The palladium and oxygen atoms do not contri bute to the lines for which h + k is odd, and since the si gn of S1'J 0 °Cl is uncertain, no assumption as to the sign of can be made for such reflections. Having devised a method for ascertaining the sign of Sci for a large numb er of lines, we can now evaluate the chlorine parameter in the following manner. The sign of s01 is determined by the facto r 15 J a nd therefore J\_ e1fik cos(h + k )uCl + e/Tlh cos(h-k)uCl uc1can have only such values as wi ll give this factor the proper sign in all cases. Figure 1 is a device for representing t he results of the procedure we have just g iven. Ea.ch arrow marks the re g ion eliminated by t he inequality wi th which the arrow is labeled. As a result uUl is limited to the range of values be tween 0.275 and 0.292 when only the values between 0.25 and 0.50 are considered. However, the chlorine structure factor for planes with h + k even is symmetrical about the point u O. 25 and, 01 therefore, the values between 0.208 and 0 . 225 also form a possible range for the chlorine parameter. It will be s h own later that equivalent structures arise from the choice of either range. From the relative intensities of the lines (hki) where 1 -: :- 0,1,2,3 the size of Sci for (hkO) c an be roughly estimated. These estima tions for several planes are compared in Table IV with the corresponding calculated values of Sci· The chlorine structure f a ctor for each given plane has been computed for four values of ucl lying in the range between 0.275 and 0 .292 in order to determine which portion of the range is most suitable. No corrections for the temperature effect and absorption have been introduced in these calculations but the Lorentz and pol a rization factors ar e included. 16 - 511/.2>9//./ 7.1/./>7./IO- -792>79/-S/12>.f]/./ - -S.9/>S.90-s?z>S?/--t.12/>4/W- -4/t/2>.fl(}t- -*51>.ff.!J-3.92>3.91-37/>370- 3.fZ>.J.f/ - -----Zmhzm·~---~ - - - - - - - - - 2ef2>20/ ----------+-211>24-0 -172>/7/_ _ _ _ _ /.f/>/.f() - - - - · - - - - - - /32>1.J/ _ _ _.... o.z :B'igure 1 Regions eliminated for uCl by considering the sign of SCl for planes (hkO) 17 'l'ABLE IV Calculated and Estimated Sizes of 8 c1 for Planes (hkO) :Plane Observed Observed Magni tu.de Sign of c• c of °Cl °Cl Calculated Values of 8 c1 UCl ::: 0. 275 o. 21:30 0.285 0.290 8.2 11.6 15.5 19.7 - 7.5 - 10.3 - 13.3 - 16.1 6.7 8.7 10.5 11. 7 - 62. 2 - 54.8 - 46.6 - 37.9 29.5 20.9 11. 9 2.9 130 s 15 0 s 170 s 240 1 260 s 280 v s - 12.2 - 2.4 7.1 15.5 2·10·0 m o.o - 9.9 - 18.3 - 24.4 350 1 18.4 25.0 31. 2 37.2 370 1 - 18.2 - 23.4 - 27.6 - 30.3 390 m + 16.5 1 9.6 20.7 l~.4 440 m + 38.7 31.5 24.1 17.3 460 s ..- 22. 4 - 14.? - ? •5 - 1.6 480 v s 9.7 1.8 - 4.6 - 8.8 4·10·0 s o.o ?.4 12.3 14.2 4·12·0 m - 6. 7 - 12.4 - 15.0 - 14.2 550 1 - 24.0 - 31.4 - 38.1 - 43. 4 57 0 1 25.2 31. 3 35.6 37.4 590 1 ~23.9 - 27.5 - 28.0 - 2b. l 5·11·0 m 19.8 20.1 16.? 9.9 + + + + + + + 18 TABLE IV Continued Plane Observed Ob served Ma g nitude Sign of of 8 8 c1 c1 + Calculated Values of u~n C' °Cl 0.275 0.280 0.285 0.290 14.1 ?.4 2.5 0.2 660 v s 680 s - 6.3 - 0. 9 1.6 0.9 6·10.0 v s o.o - 3.9 - 4. 3 - 1.5 6·12·0 v s 4 .4 6. 6 5.3 1.6 - 27, 9 - 32.8 - 35.0 - 33.a 26.8 29. 2 27.9 23.0 - 22. 2 - 21.4 - 16.7 - 9 .1 2.9 0.1 1.1 5.6 77 0 l 790 1 7·1 1 ·0 m 880 v s 8• 10·0 s o.o 0.5 - 2.9 - 9.0 990 m - 25.8 - 26 . 0 - 22. 2 - 15. 7 9·11•0 m + 21.5 19.1 13.4 6.2 10•10•0 s + o.o 2. 1 7.5 14.l .J.. + + The abbreviations 1, m, s, and v s are used to denote large, me dium, small, and very small respectivelyo 19 The most serious of the various small discrepancies which appear in the data of 'l 'able IV is found for the planes (680) and (8•10•0). Thus it was not possible to find a single value of the parruneter lying in the range 0.275 to 0.292 for which the calculated values of SCl f or both (680) and (8•10•0) are in agreement with the exper i mental observations that these quantities are small negative numbers. However, there is some justification f or supposing that this discrepancy arises from smal l inacc u racies in the experimental data, since it was observed that (681 ) > ( 680) while (682) ) (683), and in all other sequences where the inequality (hkl) ) (hkO) appeared the inequality (hk3) ) (hk2) was also found even when it was judged from the first inequality that j sc 1 is small. 1 The general agreement we have obtained so far seems to justi f y the procedure adopted to evaluate the chlorine parameter and this conclusion is also supported by the fact that a completely different type of comparison which will be given later leads to prac tically the same value of u Cl The best agreement seems to be obtained for values of ucl in the upper portion of the range and therefore at this time we place uCl = O. 285 ::!:. 0. 01. We have already mentioned that there was some difficulty in discriminating between le) and (d) as positions for the oxygen atom ~. So far the latter positions have been assumed to be the correct set. If (c ) were 20 selected the oxygen structure factor would become s0 = f 0 e '1T~}( e1fi h -r elTik) and we would need to consider that the difference in intensity between lines with ..£even and with Jl odd, where h and k are the same for all these planes, arose from s 0 + Sci rather than from SCl al one. With this assumption the chlorine parameter would be evaluated in a manner similar to the one we have already described. Thus the sign of s 0 + s 01 for (hkO) would be determined from the relative intensities of (hkO) , (hkl), (hk2), and (hk3), and we should find in which regions of the chlorine parameter s01 + s would have the proper sign for (hkO) by 0 plotting SC + s as a function of u 01 • This process 1 0 was carried out and gave the values between 0.2?7 and 0.284 as the best parameter range. Throughout this range, however, the calculated values of s 01 + s0 for the planes (130), (170), (680), and (8•10•0) definite ly disagreed with the experimental observations . and for these rea,sons the oxygen atoms were placed in the positions (d). Using the Pd-N separation * of 2.02 K we can * The single-bond covalent radius of nitrogen is given by Pauling (6) as O.?O ~. Pauling and Huggins (7) have found the covalent radius of bivalent palladium to be 1. 32 i. 21 reduce the number of independent nitrogen par ameters to one by writ ing .2_ (I ) 2.02 ) ( 10.302 From the equation SN = 2fH [ cos(hul!J -t- k vN) + cos(hv1~ - kuN) + elfi(h + _k:) Lcos(hu1'J - k vN) + cos( hvl'J + ku1~- ) JJ it is seen tha t S:N is unaffected by the exchange of uN a nd vl'J for planes with h + k even while this operation will chang e the sign but not the absolute value of 3i.. if h + k is odd. From expression (I) we infer that f or each point ( uN, vN) a correspo nding poi nt ( v1~ , u 1~) wil l come under consider a tion. Using equ at ion (I) and g iving u 01 a c ert a in value the structure factor for all the atoms in the unit bec omes a function of uN. From the fore g oing d iscussion we see th at t wo po ssible ranges for uN must always a rise from intensity c omp;:i.r1son s between planes with h + k even, i. e . , (1) a rang e for uN such that uN ) YN and, corres- pondingly, (2) a range such tha t u J:~. < Now it h as been noted a lre ady t hat t he value uCl is ambiguous in that 22 l 3 ) uCl may lie between 0.208 and 0.225, or ( 4) uCl may be between 0.275 and 0.292. l 'he combinations ( 1 ) with ( 4) and ( 2) with (3) give rise to equivalent structures as d o the combinations ( 1) '.llli th (3 ) and (2) with (4). £he latter possibility may be eliminated by considering the intensity data f or line s wit h h + k odd. Thus it was obser ved that (410 ) ) wh ereas for any value of uGl lying in the range to 0.225 it was calcul a ted that \s 210 1 ) js 4 10 / (210), o. 208 when uN is in the r ange between 0.139 (uN= vN) a n d 0.196 (vN = 0 ) . \Ve conclude that uCl has a value between 0.275 and 0.292 a nd that uN > vN. The comparisons ( 660) ) ( 330 ) and ( 550) ) ( 330) can be e mp loyed to further li mit the nitrogen parame ter uN. Wh en uCl = 0 .285 the first inequality restricts u 1,- to the values between 0 .184 and 0 . 19 6 whi le the o ther .J.I! inequality li mits uN to the rang e 0.191 to 0.196. Using equation (I) the corresponding range s permitted for v~ are found to be 0.0 to 0.068 and O.O to 0.044. Only these comparisons and the inequality (410) > (210) were to be f ound useful for eva luating the nitrogen parameter. 23 All three inequalities are taken from Table v, containing data obtained from an oscillation photograph prepared from ( 110) with 0-10] vertical. As a factor of safety a temperature correction was omitted in computing the values of the structure tactors, but th e Lorentz and polarization factors are included. the factor s 410 and s 210 cont a in VW- which is a correction for the varying specific times of illumination of planes inclined to the axis of rotation. UJ is defined by the equation ( 8) w -= [1- (AAA/rJ ~ ~9 )2..]-Yi. where u is the order of the layer line and d is the unit translation along the axis of rotation. Since [1I o] was the axis of rotation d is '{2 a 0 • We expect that the Cl-NH separation will not be 3 less than the a mmonium-chlorine s ep a ration of 3.35 i found in NH 4 c1 (9). If the nitrogen parameters are g iven in turn the limiting values of the r a nges just established we find the following chlorine-ammonia separations when uCl = 0. 285. If uN and v 1~ have the values 0.196 and 0.000 respectively four of the surrounding eight ammonia groups will be at a distance of 3.23 i from the chlorine atom and the other four at a distance of 3.66 i. On the other hand, if uN = 0.191 24 a nd vN ::::: O. 044 the Cl-NH 3 separation for the four groups first mentioned wi ll be 3.5? K and for the other four X. In the latter case four of the ammonia g rou ps 3 .31 are separated from the chloride ion by a distance s maller th a n the NH 4 -Cl separation and since these four ammonia molecules approach the chloride ion as u N decreases and vN increases it appears that safe limits have been selected for 11.N and v~. It is probable that v~ has a value in the center portion of the rang e 0.000 to 0.044 and as a result all eight of the ammonia mo lecules surrounding a chloride ion will be approx i mately equidistant from it. When this condition is exactly satisfied we find that uN = 0.194 and vN = 0.027 and that the separation is 3.44 A. The validity of the con3 clusions reached in this paragraph depends, of cours e, Cl-NH upon the correctness of the assumed Pd-N separation, 2. 02 A.. As a check of the previous evaluation of uCl we c a n employ the following method. It will be assumed that for any value of uc 1 each ammonia molecule of the surrounding eight is equidistant from the chlorine atom and hence we wri te 25 It has been shown that this condition must be at least approximately true if uci= 0.285. Since in g eneral the contribution of the nitrogen atoms to the intensities of lines is small and changes slowly as uN and vb are varied, a slight departure from the condition expressed by equation (II) a,hould not introduce appreciable errors. Equations (I) and (II) al low us to express the structure factor for all the atoms in the unit as a function of uci· Thus we can make use of intensity inequalities in the srune manner as would be employed in a single parameter prob lem. The comparisons used were taken from the data given in Tables V and VI. Only inequalities were used in which a plane with a certain value of dhKO was reflecting more strongly than another plane with a larger value of dhkO" A temperature correction was omitted as a measur e of safety and in all comparisons employed except \ 750) > (640 ) it seemed fairly certain that the stronger line was absorbed to the greater extent in the crystal. The calcul ated structure factors contain the Lorentz and polarizat ion factors and are corrected for the varying specific exposure times of lines by including the f a ctor VtJ • 26 t1N a.a oz;_ aa oa O.JO ou o~ I{.-'- :B, igure 2 Calculated structure fa c to r s for planes ( hkO ) as functions of the parameter uCl C'- C\I 3. 3 210 ~ 4.2 220 20.0 310 A 320 06 .2 * 26. 9 * 10. 0 410 510 15.0 d.9 4.W o.5 o.~o 3::l0 t::.2 2. 1 61C 13.1 520 0.80 7. 2 430 1.d5 1.0 TABLE V t '71 0 4. 8 1. 3 620 12.0 0 .50 53C 14.0 1.14 440 lo . o dlO 1.9 910 2.9 l.d d20 3. d 730 '". 0 550 0 .5 5 5.5 640 0.40 2.2 O.Gl 720 6.0 \ '~ 11. t 630 o. ss 540 l~. 3 1.2 1 6.5 10•2•0 2. 0 ( I A L~ •4 • C.7L C.23 c l.3c 2. 77 11.5. 0 1.10 1 ~ ddO ( ' . (\'.) 2.1 970 u.oo 1.10 :.> - 'i 3. 5 2.2 10·6·0 0.04 960 h,:.. 07 0 3.0 A l. O J1. . 10·5·0 4.2 11·4·•0 1.94 :\. 11·3·0 1.15 2. d 10·4.C) 0.14 10·3 ·0. A 4. 7 940 950 1.0 o. L:; d60 2.0 770 (, 7" "· . un 7 60 d50 ,, 0.02 A ") ') 6.5 A. 3. 2 930 o.oo: 3.8 0.61 d40 3 .1 0. 13 750 5 .7 600 0.44 s.n 2.9 (J,1 o] vert ical; oscillation O - 30 °. 3.2 no A s.o d30 0.65 ). • 7 0 .60 650 6.2 o.5o 740 1.2 I ntensity uata for an Oscillati on tnotor;rapa from ( 1 10~ witn L ayer Ll.n6 ot a 7 t i1 otr1 St ri 4t :t 3rri 2nu 1st Zquator >3c.o 27a ~The reflections consisting of an unresolved ~ -doublet are mar ked with asterisks and their calcu- lated intensities have been multiplied by 1.5 to render them comparable with other lines consisting of ol.. 1 alone. The data for lllO) was omitted because the crystal did not intercept all of the beam when this plane reflected, while the crystal did intercept all of the beam when the other planes were in rositions to reflect. Reflecti ons not observed are designated by the letter A. 27b TABLE VI Intensity Data for an Oscillation Photograph from (110) with , Layer .Line 8th [110] vertical; 10·2·0 1 1 ·3·0 14·6·0 13·5·0 12·4·0 2.55 1. 94 1. 20 1. 3( 0.85 0. <J ~ 0.70 0.9J 2.9 3.2 0 oscillation 15 - 4 b • 13·6 · 0 12·5·0 1 1 ·4·0 10·3·0 7th 0.005 0.30 0.14 0.60 0.23 A 6th 4.5 5.8 4.7 5.0 1.8 3.2 0.40 0.1~ 7.0 3.2 6.5 1st A Equato 3 6.4 0.00 A. 7 70 66 0 5.2 . 2 l. 25 12·7·0 3. 5 0.05 880 0.6 ( 2.6 A 10·8·0 0.1'7 11·9·0 1. 20 1. 74 1.10 l. 61 3.5 A 12·8·0 11·8·0 10· 9 ·0 930 o. 02 0.00 A 0.90 l. 04 0.95 1. 45 '::> ,__, A 870 '160 o.oo 1. 23 11·7·0 970 3.0 1.10 1. ?9 10·7·0 0.00 A 360 750 2nd 2.5 960 850 3rd 13 - 7 · 0 0. 1 2 A 10·6·0 1. 0 12 · 6 · 0 1 1· 6·0 0.04 A 950 040 4th 2.8 10·5·0 0.02 A 2.5 4. 2 940 5th 11· 5· 0 10 · 4 · 0 930 0.03 A 0.05 990 A o.oo 10•10·0 2.3 0.90 0.8 0 1. 05 1.5 5 28 In figure 2,ShkO for several planes are plotted against th e chlorine parameter for value s between 0.25 and 0.30. All the inequalities used a re given in the figure and the a rrows designate the regions e liminated by these comparisons. The values permitted for uCl by this process lie in the range 0.2?8 to 0.29 3 whi ch is in s Rtisf a ctory agreement with the range O. 2?5 to O. 292 that was previously obtained in an independent manne r and leads again to the value 0.285 "!: 0.0l for uci• In Tables V and Vf we have listed the data obt ained fro m two oscillation photogr aphs from (110) with [1IQ] a s the axis of oscillation. 'l'hey differ in that t he dat a of Table VI are from a p h otograph prepared with the prism f a ce mak ing an angle of about 15 0 with the beam in Lh e starting position. In the right half of the space under each pl ane is g iven the value of the calculated intens ity of that plane divided by one thous and and in the other half is the observed intensity which wa.s visually e sti mated by comparison with a scale having ei gh teen lines of darkening s for which the product x-ray intensity ti mes time varies from 0.25 to 30. fhe v alu es of the parameters used are uCl = ~r - 'N - o. 02?. The factors w 0.285, u N and = 0.194, and 1 + cos 2 2 e 2 sin2 e have 29 been used in the calculated intensities as well as a temperature correction the nature of which will be explained later. It will be noted that the structure factors of the two following classes of reflections are quite different: Type I: h + k even, for which shkO = Type I I: h + k odd, for which ShkO ::: •')f' TJ' ,._,~ + s .r-a Cl + s. T l~ - s Cl + Unless individual temperature corrections are used for the different kinds of atoms the calculated intensities for lines of Ty11e II are too high when compared with the computed intensities from planes of 'l'ype I. It is very likely that due to the great difference in masses of the various kinds of atoms we should use individual temperature factors which fall off more slowly with increasing values of sin B for the heavier atoms t han A f or the lighter ones. Since the palladium atoms are much heavier than any other kind in Pd(NH ) 4 c1 2 ·H 2 0 3 it is seen that an effect of this nature could cause the discrepancies noted above. If the scat teri ng f a ctor used for palladium is too small we can also account in some measure for these discrepancies since S~d is zero for planes with h + k odd but not for the ones with h + k even. 30 The palladium atoms contribute far more than any other k ind of atoms to the intensity of lines with h + k even and hence errors in f 11d could cause quite serious disagreements of the kind stated. Either of these effects or a combination of the two could also exr lain the observation tnat the calculated intensities using a common temperature factor for all atoms are too small for lines such as ('130), (950), (11•7•0), (330), l550), (770), and (990) for which chlorine is scattering to a marked extent in opposition to palladium. Errors in the chlorine scattering factor might be important in this case. In the calculated data of Tables V and VI we have arbitrarily included the temperature factor f oun~ for potassium chloride (10) in the structure factors of chlorine, nitrogen, and oxygen, but have used no temperature correction in the palladium structure factor. With these assumptions the agreement 'oetween planes of Types I and II is good. Although the planar Pd(NH 3 ) 4 arrangement was assumed in the derivation or ~he structure, the final agreement found between the observed and calculated 31 intensities justifies the assumption and can be considered to show the existence of this arrangement in the crystal under consideration. Absorption in the crystal will probably increase regu l arly as t he order of the reflect i ons lying in the same zone line incr eases because of the fact that the angles between the planes of th i s s equence and the developed face (1 10) increase as the order of the reflecti on inc reases and th i s is a l so true for reflections in the same 11 diagonal 11 line such as the sequence l 220), (420 ) , (620), etc. It should be noted that a one-molecule unit with a = 7.284 A and c ::: 4.34 X cannot account for the ref lectlons lying in the odd order layer lines but that these refle c ti ons re q u ire a t l ea s t a two -molecule unit wi t h a ~ 10 .3 02 0 Aa n d c 0 = 4 .34 A. It wa s found that an appreciab le v a riation of t he Pd - N s e par a t i on from 2 . 0 2 .K which was assumed i n e valuat i ng the nitrogen par ameters would seriou sly i mpair the ag r eement b e tween c a lc u l ated and obse r ved intensities. Therefor e, we hav e ver if ied that this separation has the value Pd - N 2.02 "! 0 .0 5 5\.. 32 Discussion of the St ructure Figure 3 is a projection of the structure of nitrogen, and oxygen a.toms lie in the same plane but the chlorine atoms are displaced from the first plane by onehalf the depth of the unit along c. In Table VII are given the atoms or groups coordinated about each atom or group and the corresponding separation s. In the cation the four ammonia groups form a square configuration about each palladium atom and with the Pd-N separation 2.02 NH 3 ± 0.05 X the distance between the mo lecules belonging to the same cation is 2 .86 ,i: 0.05 ~. It was assumed that each ammonia of the surrounding ei gh t is equidistant from the chlorine atom but from x -ray data it can only be shown that this condition is approximately satisfied. It may be that 4 NH are slightly 3 closer to Cl than th e other 4 NH • 3 If the water molecules were placed in the p l ane of the chlorine atoms we would obtain a minimum separation of 3.1 to 3.2 1t wh ich is somewh a t smaller t han we expect to find: 'l 'hi s probably accounts for the displacement of H2 0 to positions half way between planes of Cl. ~ + + . ) From the r a dii of 113 0 1:-nd NH 4 Pauling (11 ha ~ estimated that H2 0 has a radius of about 1.45 X and ~ hat the Cl-H 2 0 separation will not be less than about 3.26 i. 33 Figure 3 Projection of the structure of Pd( NH3 ) 4 c1 2 ·H20 on the plane (001). 34 l'ABLE VII a tom or gro up Cent r a l Atoms or e;roups in cont ac t wi t h c en tr a l at om or group :Pd 4 HH Cl 8 .NH Cl ,::_. 3 Separation }'d-h 2 .0 2 ± 0.05 jt 3.44 .t 0 .1 x Cl-H 2 0 3. 81 :!: 0. 1 _K H 2 0-Cl 3.8l i: 0.1 x H20 - NH3 3 .16 j:° O.l ~ Cl-NH 3 " 3 H20 o 4 Cl H 0 2 4 NH NH 4 Cl NH..,-Cl 3.44 ± 0.1 A. :NH3 1 H2 0 1'TH 3 - H20 3 .16 ± 0 .1 i NH 2 "' H 7' i~ lJH 3 - NH 3 2 . 86 :t o. 05 it '-- 3 NH 3 -NH 3 4. 06 ± 0.1 A H 2 3 3 NH 3 1 NH 3 0 0 35 A structure very similar to that of K2 PdC1 4 and based on a one- molecule unit would be obtained from the structure of PdlNH ) 4 c1 2 ·H 2 0 3 and vN by p lacing uUl ~ 0.250 =0.000. In such a one-molecule structure inter- at omic distances would. b e essenti al ly the same as was found in the two- molecule unit ex-cep t for the NH 3 -NH 3 separation in different cations. l'hi s separ at ion would be about 4.44 X in the one-molecule structure, whe reas it is decreased to 4.06 R in the structure found. In K PdC1 4 the large Cl atoms in different anions are in 2 contact with one another (3.6 1 apar~). Wh en the Cl atoms are replaced by the smaller NH 3 groups, the struc- ture becomes unstable and is def armed sli gh tly in suc h gr oups. a way as to re gain concact bet ween Pd(l~H ) 3 4 F rom figure 3 it is seen that the two-molecule unit arises from s mal l rotations of the square configur a tions of ammania molecules and chlorine atoms about axe s parallel to c. Cox (3) has reported very briefly his investi gat ion of the crystal Pt(NH ) c1 ·H 0, wh i ch, because of t h e very 3 4 2 2 close similarity in crystal-chemical properties of palladium and platinum, we expect to be completely isomorphous with Pd( NH ) c1 ·H 0. The structure sugg ested 3 4 2 2 36 by hi m, h owever, is the one-molecule structure ob t a ined fro m our two-mole6ule structure by putting u 01 a nd vN equal to one-fourth and zero respectively and by p lacing the water molecules in the plane of the chloride ions rather than between these planes. It seems probable to us that Cox ' s structure is incorrect, and that the platinum compound also crystallizes with the two-molecule unit. The reflections eliminating the smaller unit would be somewhat weaker relative to other lines than for the palladium crystal, and Cox presumably overlooked them on his oscillation and Laue photographs. The dimensions a = 7.39 ::!: 0.02 A and c correspond to a 0 ::. = 4.21 ± 0.02 A reported by him 10.46 ::t" 0.03 A and c 0 :::. 4.21 :!: 0.02 ~ respectively, which are nearly the same as was found for Pd(NH ) c1 ·H 0. The parameter value u:N ::= ~- approx3 4 2 2 imately and the location of the water molecules in the plane of the chlorine ions are not supported by any published comparison of observed and calculated intensities, and in any case the effects of the deviation of u Cl from 0 .250 would vitiate such a treatment. - parameter value given by him also leads to a Pt-N separation, 2.62 ~' which is much larger than we ~he 37 expect *' on the assumption that nitrogen is bonded to platinum by a cov a lent bond. It is probable that the structure of Pt( NH 3 ) 4 c1 2 ·h 2 0 is identical wi th that of rid( Nh 3 ) 4 Cl 2 ·H 2 0, even to the values of the pararneters. I wish to thank Professor Linus Pauling for many valuable suggestions received during this investigation. I am a l so indebted to Dr. J. L. Hoard for much helpful ass i stance. * 'Ve expect that the P t -N separation will be ab out 2.02 ~ si ne~ the sing l e-bond covalent radius of nitrogen is given as 0.70 X (6 ) and t h e radius of bivalent platinum as 1. 32 i ( 7 ) . 38 Surmnary fhe crystal structure of Pd(NH 3 ) 4 cl 2 ·H 2 o was investigated using oscillation and Laue ph otographs. The structure was found to be based on a simple tetragonal unit containing two molecules with a 0 ::. 10.302 + 0.03 and c 0 = 4. 34 :t O. 0 5 i . The space group was shown to be 2 7 5 C4 v' Vd' or D4h' the last being further indicated by the observed absence of a pyroelectri c effect. It was found possible to base a satisfactory st~ucture on the space 5 gr oup D4 h. The palladium atoms accupy positions (a), nitrogen (i), chlorine (h)J and oxygen (d) of Wy c koff 's tables. The ranges 0.275 t o 0.292 and 0.278 to 0.293 were determined for uCl by two independent methods. Using uCl = O. 285 and a.n assumed Pd-N separation, uN was found by intensity comparisons to lie between 0.191 and 0.196 and vN between 0.0 and 0.044. With the following parameter values a good general agreement between the calculated and observed intensities was obtained: uCl :=-: o. 285 ± o. 01 / u 0.194 + 0.02 .J N - YN -- 0. 027 ± o. 02 . X 39 We rner's a ssumption t h at bivalent pal ladium coordinates four groups in a planar configuration about itself was verified in this case. The follow ing interatomic distances wer e found: 0 Pd-N ::::: 2. 02 ± 0.05 A, Cl-H 2 0 -- 3. 81 _:!:" 0.1 H2 0-NH3 :=. 9. 3. 16 + 0.1 A, Cl- NH3 = 3.44 + - 0.1 ~' A, rrn 3 -NH 3 ;:.:: 2.86 ± 0.05 A (in the s ame cation) NH 3 - NH3 -- 4. 06 ± 0.1 .A (in different cations). It is pointed out th at the corresponding pl atinum compound P t( :NH 3 ) 4 c1 2 ·H 2 0 prob ably has the same structure , rather than the s impler structure reported by Cox. 40 RID,ERENCES 1. H. G. Dickinson, J. Am . Chem. Soc., 44, ?74 & 2404 (1922). 2. Linus Pauling , ibic., 53, 1367 (1931) . 3. ~. G. Cox, J. Chem. Soc., 134, 1912 (1932). 4. A.J.P. Martin, Min. Hag .,~~' 519 (1931). 5. L. Pauling and J. Sherman, z. Krist., 81, 1 (1932). 6 . L. Pauling, Proc. Nat. Acad. Sci., 18, 29~3 (1932). '?. L. Pauling and M.L. Huggins, 8 . H. Ott, z. ::'.:r ist. , to be published. z. Physik, 22, 20 1 (1924). 9. R.J. havighurst, E. Mack, Jr., and F.C. Blake, J. Am. Chem. Soc ., 46 , 2368 (1924). 10. James and Brindley, Pro c. Hoy. Soc., A 121, 155 (1928). 11. L. Pauling, z. Kr ist., 72, 482 (1930). 41 T he Crystal Structure of Potassium Bromoselenite. By ] . L. H oard and B. N. Dickinson in Pasadena. (With 2 figures.) Potassium bromoselenite is one of a group of compounds of the general formula R2MX6 which crystallize as regular octahedra, and presumably have the potassium chlorostannate structure 1 ) . It has been of interest to confirm this hypothesis in the case of potassium bromoselenite and to det ermine the single parameter with such care that an accurate value of the bromine-selenium separation in the complex is obtained. Determination of the Unit Cell and Space Group. We are indebted to Professor R. G. Dickinson of this Institute for the potassium bromoselenite crystals used in this study. The crystals were octahedra from 1- 4 mm. on an edge and were isotropic under a polarizing microscope. Data from an oscillation photograph prepared by reflecting MoKa radiation from a (111) face lead to the spacing d111 /n = 5.983 ± 0.01 A. These data are recorded in Table I. Laue photographs were prepared using radiation from a tube with a tungsten anticathode operat ed at a peak voltage of about 52 kV, the beam being inclined at various small angles with the normal to (111). Using a = 10.363 ± 0.02 A, no value of nA. calculated from two completely indexed Laue photographs was found to be less than the short wave length limit, 0.24 A. From this value of the edge of the unit cube and the measured density, 3.61, four molecules were found to exist in the unit cell. Table I. Osc ill a tion dat a from diff ere nt orders of (111). Plane Line sin fl d/n (Hi) (222) (444) a a .0594 .11.84 .2366 .2378 5.971 5.991 5.983 5.988 a1 CTz 1) R. G. Di c kin so n , J. Am. chem. Soc. 44, 276. 1922. 42 Th e Crysta l Structure of Potassiu m Bromoselenite. 437 The only planes giving first order reflection on the two Lau e photographs ·were those with all indices odd, so that the structure may be assumed to be based on a face -centered lattice. The Laue photographs through (111) showed a three-fold axis and three planes of symmetry, so that t he point-group symmetry is that of T a, 0 , or O,,. The space groups isomorphous wit h these point groups and based upon a facecentered lattice are 0 3 , 0 4 , Tj , T~ , o;;, oj;, Of,, and O~ . The observed reflections from planes such as (995) at n}, = 0.40 A eliminate T~, Oj~ , and O~; and those from planes such as (405) at n}, = 0.72 A eliminate OJ, and 0~. This leaves 0 3 , 0 4 , Tj and OJ, to be consid ered . Since 0 4 famishes no fewer than eight equivalent positions in the unit cell , and four Se must be placed , onl y T~ , 0 3 , and OJ. (all without special criteri a) remam as possible space groups. Determination of the Atomic Arrangement. · With four molecules in the unit cell , there must be placed 8 ]{, 4 Se, and 24 Br. OJ. and 0 3 furnish exactly the same possibiliti es in this case . Furthermore there are only two non-equivalent arrangements based upon and 0 3 , and one of these is immediately eli minated by the observation that (555) reflect s more strongly than (333) , whereas the structure factor for both of these planes is the same, ± 4/Se- There remains, therefore , only the following possibility which is also obtainable from Tj: o;. 8 ]{in Se : F ace-centered arrangeemnt starting in ± (! , !, !); 4 Se in 4 b: F ace-centered a rrangement starting in (0 , 0, 0); 24 Br in 24a: Face-centered arrangement starting in ± (u , 0, 0 ; 0, u, 0; 0, 0, u ). The above arrangement leads to a structure which gives complete qualitative agreement between calculat ed and observed intensities for it = 0.245 ± 0.003. All of the remaining essentially di stin ct structures based on T~ may be eliminated as fo llows. It is found that the modu lus of t he structure factors calculated for (111) a nd (333) for these arrange ments cannot be less than 4 f se - 4 /J( (4 fg and 4 / se for some), whereas (111) is observed to be very weak and (333 ) is not observed at al I. The scatterin g power of selenium is nearly twice that of potassium , so that it is hi ghly probable that t hese possibilities arc to be exclud ed and that the first proposed arrangement, whi ch permits the bromine atoms to scatter in opposition to the selenium atoms for odd orders from (111) (the contribution of the potassium atom s being zero), is to be accepted as correct . 43 J38 J. L . Hoard a nd B. :X. Dickinson Using a horizontal slit syst em, oscillation photographs for use in making intensity comparisons were prepared by reflecting Molfo radiation filtered through zirconia from a (111) face of potassium bromoselenite. Only orders of (111) were used, the calculat ed int ensity for (nnn) being obtained as follows. The structure factor calculat ed from t he / 0 values of Paulin g and Sh e rm a n 1 ) for the given va.lue of ~}~ 1 + cos2 9@)1 was multiplied by t he Lorentz and polari zat ion factors, (-- "- . - e·~ , ~S ill 2 · and by l;;, and the absolute value of this so-obtained result was t aken as the square root of t he relative intensity. The factor if; enters since if a horizontal slit syst em is employed the fraction of the total beam intercepted by t he strongly absorbing cryst al when in position to reflect is proport ional t o sin e and so to n . As the t emperature factor was not included only intensity inequalities were used for which a plane with was observed to reflect more strongly than another a given value of d ·with larger dnnn- The pro cedure is illustrated in Fig. 1, in which S nnn = 11 ,.11 JII nnn is plotted against the value of t he bromine parameter. Thus as (555) is observed· to refle ct more stron gly than (333), only those values for n are possible for which S 555 is calculat ed t o be larger t han S 333 . !!! 4(/1/ i 5 ](}(} .?(}(} /{}(} Fig. 1. tCalculated intensities for differen t orders of (111), as fun ctions of the param eter i i. 1) Linu s P a ulin g and J. S h e rm a n, Z. Krist . 81, 1. 1932. 44 439 The Crystal Structure of Pot.a ssium Bromos0lenite. The visually estimated observed intensities of reflection from various orders of (111) on photographs taken with a horizontal slit system are : (111) = 0.5 ; (444) = 2.5; (222) = 7.0 ; (555) = 0.08; (333) = 0 ; (666) = 0.1. The regions eliminated by the observed intensity inequalities are marked with arrows on Fig. 1. As a result the parameter is limited to the range of values between 0.233 and 0.250. Assuming the intensity of (333) to be zero, the calculated value of u is 0.241. Intensity inequalities appearing on the Laue photographs were used to further limit the possible range of v alues for the parameter. The procedure was analogous to that employed for the spectral comparicos 2 9 1 sons, except for the omission of the factor l' n and ( 9 . 9 e"' . Only "'Sill,. intensity inequalities between planes reflecting in the first order with very nearly the same value of n}, and with a plane of given d,,u reflecting more strongly than another of larger d111,,1 were used. The omission of the temperature, polarization, and Lorentz corrections served as factors of safety in making such comparisons. fJ)} + JO l 120 s 025 Fig. 2. Calculated intensities for some Laue spots, as functions of the parameter u. The curves used for the Laue comparisons are plotted in Fig . 2 and the intensity data are listed in Table II. The intensity inequalities used from Table II and the range of values t hey p ermi~ for the parameter are as follows: 45 440 J. L. Hoard and B. N. Dickinson {753}~ {731} {975} > {773} {975} > {771} {973} > {773} 0.2388 L. n L. 0.2482 0.2375 < n < 0.2495 n < 0.2491 0.2422 < n < 0.2495. Table II. La u e i ntensities used for ca l cu l ating the parameter. P lan e dhkl nJ, I Estimated intensity (713) (173) (73I) (735) (375) (73oJ (177) (773) (773) (!173) (975) (;397) (Ui57) 1.35 1.35 1.35 1.14 1.14 1.14 1.04 1.03 1.03 0. 88 0.83 0.83 U.83 0.32 0.38 0.43 0.38 0.32 0.41 0.35 0.38 0.45 0.43 0.35 0.35 0.39 0.075 0.1 0.1 0.1 0.085 0.1 0.02 0.03 0.05 0.07 0.05 0.05 0.04 These comparisons justify the selection of 0.245 ± 0.003 as the value of t he parameter. The correspondin g selenium-bromine separation is 2.54 ± 0.03 A. Subtractin g t he value of t he norm al electron-pairbond rad ius of bromine 1) , 1,HA, a value of 1.40A is found for t h e " octahedral" electron-pair-bond rad ius of quad rivalent selen ium . Using powder a nd Laue photographs, S i cg 2 ) has recently shown t hat ammonium bromosc lcnitc has the potassium ch lorostannate structure, with a, = :L0.46 A. He find s 0.24 to 0.2:) as the possible range of va lu es for the brom ine parameter, the range for t h e corresponding selen ium-bromine separation being 2.51 to 2.63 A, which includes the range found by us . Subtractin g the value a = 10.36 for potass ium bromosclcn itc from that ci = 10.46 for ammonium bromoselcni tc, 0.10 A is obta ined, which is in agreement with the correspond ing d ifference, 0.09 A, obtained from potassiu m and ammonium chl orostannatcs 3 ). We arc indebted to Professor L in us Pau li ng for suggesting t he stud y of potassium bromoselen itc. 1) L inu s Pau lin g, Pr. ::\'at. Acad . Sci. 18, 2D3. 1932. 2) Lot lrnr S ieg ; Z. a norg. Ch. 207. H3. 1!132. 3) R . G. Dic kin son , J. Am. chem. Soc. 44, 276 . 1922. 46 The Crysta l Stru ct ure of P otassium .Bromoscleni tc. 441 Summary. With the aid of osc illation and Laue photograph s, potassium bromo:;e lcnitc ha s been shown to h ave the potassium chlorostannate structure. The value of the edge of the unit cell was foun<l to be 10.:363 ± 0.02 A. Complete qualitative agreement bct\\·ecn calculated and observed intensities 'rns obtained for ii = 0.243 ± 0.00 3 A. By substractin g the normal electron-pair-bond raclius of brom ine, '1.1 '1 A, from the scleniurnbrominc separation , 2.54 A, th e " octahedral" electron-pair-bond radius of quadr ivalent selenium was fo und to be J AO A. Cont ribution Ko. 338 from the Gates Chem ical Laboratory, Californ ia Instit ute of Technology. Rece ive(] September. :20t h, 1932. 4'7 The Normal State of the Hydrogen Molecule-Ion* B. N. DICKINSON, Gates Chemical L aboratory, California I nstitute of Technology (Received March 16, 1933) A variatio n functi on somewhat similar to t hat applied by Rosen to I-I, is used in th e discussion of the norm al state of!-£, +. JN treating the norma l state of t he hyd rogen We write molecule by the variationa l meth od, N. R osen 1 used an eigenfunction involving the oneelectron function m which i/; 0 = (aN 7r)~e-ara is a hydrogen-like l s wave function for nucleus a, with effective nuclear charge (in units e) Z = cw 0 , a nd if;' = (a 5 / 7r) ~r ae-ara cos ea is a hydrogen-like 2p function for nuclear charge 2Z, ea being the a ngle between the nuclea r axis a nd the radius vector from nucleus a to the electron , a nd u a parameter. In order to see to wha t extent this method of treatment of molecules could be expected to be satisfactory in other cases, and whether or not pronounced improvement could be obta ined by varying the ratio of the effective nuclear charges in i/; 0 and if;', we have treated the hyd rogen molecule-ion (which has previously been well investigated) by methods simil a r to R osen's. For this purpose we repl ace Z by Z' = eZ in if;'. i/; 0 and if;' satisfy the equations I-Ia0if;0 =Z2E oif; 0 and as the compl ete eigenfun ction for the moleculeion , with ¢ 0 a nd ¢' replacing i/; 0 a nd if;' for t he nucleu s b. The H amiltoni a n for this problem is Th e in tegrals a rising from t he expression for t he energy W= xIIxdT / loo= J if;0¢ 0dT, and are normalized and mutually orthogona l. Joo= f ij;O</JO - - dr, Yu ( ij;0)2 fot = if;O</J' ,f </J'dT, Goo= f --dr , Joi= f ---dr, rb ' ra Iu = •ij;Oif;' if;' .fif;' dr, Co1= •f-dr, J io= J --dr , rb ra t/;0 ij;O Ila'if;'=e 2Z 2Eoif;', <P' (i/;")2 (i/;' )2 Fo= J - d r , Cu= J - - dr, -h2 2Zee 2 Ila' = - - \7 2 - - - - , 87r 2m ra 2 x dT • ra and J a re li sted below using Rose n' s notation. where -h 2 Ze 2 I-Ia0 = -- V2 - 87r 2m ra J rb if;' <P' Jll = f--dr . . ra The integra ls (!01, Goi. J oi, and J LO) not given in Rosen' s paper were evaluated in elliptic coo rdinates a nd have t he following fo rms in terms of e andp=aR : 101 = (8e 512 / (1- e2 ) 4 p2 ) [e-p {(e2 -1 )4ep 2 - 24ep - 24e} +e-•P {(1- e2 ) 2p3- 8ep 2 ( 1 - e2 ) + 24e 2p+ 24E} ], RJ01 = (4e 5 ' 2 / (l-e 2 ) 3p) [ -8ee-P(p+ l) +e-••{ (1-e 2 ) 2p3 -4e(l-e2)p 2 +8E 2 p+8e} ] , RJ10 = (8e 512 / (l-e 2)3p)[e-P{ (l-e 2 )p 2 +4p+4} + e-•P{ (l -e2 ),c 2 -4ep-4} ], RG01 = ( 4e512 / (1 +e) 5p) [ - e-< t+ •lp { (1 +e) 3p3 +4 (1+ e) 2 p2 +8( 1+f)p+8 } + 8]. * Contribution from Gates Chemical Laboratory, California Inst it ute of Technology , No. 363. Rosen, Phys. Rev. 38, 2099 (1931). 1 N. 317 48 318 13. N. DICKINSON The energy can be ex pressed as W = 2Z 2EoA/d+2ZEoB/d, where A= 1 + Ioo+CT(l +E 2 )!01 +CT 2 E2 (1 + ! 11 ) - (2 / p) [RFo+ RJoo+CT(RJ01+ 2ERJw) + 2w 2 (RF1 + RJ11) ], B = (2 / p)[RFo+RG00 -J00 - l +2RJ00 +2CT(RJ01-Io1 +RG01 +RJ10) +CT 2 (RF1-Ill +RG11 +2RJ11- l) ], d = 2[1 + Ioo+2CT Ioi +CT 2 (1 + I11)]. This expression for the energy can be m1111mized with respect to Z, giving Z= -B / 2A, which when combined with the expression for W gives W= -EoB 2 / 2dA. RESULTS On placing E = 1 and minimizin g the energy relative to Z, CT, and p, the values E= 1, p = 2.50, CT=0.1605, Z=l.2537, and W=-16.242 voltelectrons were obtained. The value given for W by Burrau's2 and Hylleraas' 3 exact treatments is -16.30 volt-electrons. Consequently the Rosen-type function leads to an error of 0.06 volt-electron, which is rather unsatisfactory, in view of the fact that Guillemin and Zener 4 obtained the value W = -16.30 volt-electrons by using a two parameter function no more complicated than the Rosen-type function. It was thought that the error of 0.06 voltelectron in W might be removed by varying E. On carrying out this variation for the values of CT, Z, and p given above , then varying CT, and finally 2 An account of this work is given by Linus Pauling, Chem. Rev. 5, 173 (1928). 3 E. A. Hylleraas, Zeits. f. Physik, 71, 739 (1931). 4 V. Guillemin and C. Zener, Proc. Nat. Acad. IS, 314 (1929). varying E again, there were obtained the values p= 2.50, E=l.15, CT= 0.145, Z=l.247, Z'=l.434, ro=l.06A, a nd W = - 16.257 volt-electrons. The discrepancy in the energy has, it is seen, been reduced by only one-third by the variation of E, being still 0.04 volt-electron. (The value of ro obtained is the same as that found by Burrau and Hylleraas and also found experimentally for excited states of Hz.) We accordingly conclude that the Rosentype function for the hydro.gen molecule-ion is not so satisfactory as the Guillemin-Zener-type function of equivalent complexity, and that no pronounced improvement results from a variation of E from 1. Change of Rosen's treatment for the hydrogen molecule by in traducing E in his function and varying it can hence be expected to lead to little improvement over his results. It must be mentioned that the error in W of 0.04 volt-electron is only about 8 percent as great as that for a function with CT=O, i.e., involving ls functions alone, for which Finkelstein and Horowitz 5 obtained Z = 1.228, ro ~l.06A, and W= -15.75 volt-electrons, so that very marked improvement in the wave function is obtained by introducing the Rosen-type term-./;'. s B. N. Finkelstein and G. E. Horowitz, Zeits. f. Physik 18, 118 (1928).