June, 1955
SOLIDSOLUTIONS OF ALKALIHALIDES
561
SOLID SOLUTIONS OF THE ALKALI HALIDES. 111. LATTICE CONSTANTS OF RbBr-RbC1 AND RbBr-KBr SOLID SOLUTIONS1 BYGEORGES. DURHAM, LEROY ALEXANDER, DOUGLAS T. PITMAN, HELEN GOLOB AND HAROLD P. KLUG Contribution f r o m the Depaitmenl of Research in Chemical Physics, Mellon Institute, Piitsburgh, Pa., and the Department of Chemistry, Smith College, Northampton, Mass. Received January 1.9, 1.964
Lattice constants in the solid-solution systems RbBr-RbC1 and RbBr-KBr have been determined at 25' by means of X-ray diffraction measurements, with an average estimated probable error of f O . O l % . Theoretical values previously calculated through a consideration of ionic displacements are found to be in reasonably satisfactory agreement.
Introduction I n paper I1 of this series,2 lattice constants, heats of mixing and distributions between aqueous and solid solutions were calculated for four alkalihalide solid-solution systems, on the basis that the ions in a given solution are not at a constant nearest neighbor distance, but may be displaced from normal lattice points to positions of minimum potential energy. Comparison of the theoretical heats of mixing and distributions with available experimental values showed good agreement. Since, however, no dependable data existed for lattice distances,a it was not possible a t the time to draw any conclusions regarding the theoretical values for these, other than that they appeared to be more reasonable than any previously obtained. For two of the systems, RbBr-RbC1 and RbBrKBr, studied in paper 11, solid-solution samples were available. In order to gain further information about solid-solution relationships, as well as to make possible comparison with theoretical values, it seemed worth while to obtain experimental lattice-constant data for these. Experimental The solid solutions used were prepared by Durham, Rock and Frayii4 in their study of the ternary aqueous systems. In addition to the analyses reported in the original study, the rubidium salts used for preparation of the solid solutions have been analyzed flame-spectrophotometrically for their Li+, Na+, K + and Cs+ ion contents, and the RbBr-RbC1 solid-solutions for their K + ion content. Emission-spectrographic analyses of the salts disclosed that no other cations were present in significant amounts. I n the three original salts the potassium content ranged from 0.43 0.02% to 1.09 f 0.030/, and the cesium from 0.17 f 0.01% t80 1.84 f 0.03%, by weight: lithium and sodium were found in negligible amounts, less than 0.01 and 0.02%, respectively. These results are shown in Tables I and 11, expressed in units of mole per cent. In the K + and Cs + ion determinations the enhancing effect of a large excess of Rb + ions was allowed for by careful preparation of calibration standards containing amounts of R b + ions comparable to the unknown solutions being analyzed.
*
(1) The flame-spectrophotometric analyses of the study were done by Helen Golob, and the X-ray diffraction measurements were made by L. E. Alexander, D. T. Pitman and H. P. Klug, all of the Department of Research in Chemical Physics, Mellon Institute. Comparison of the theoretical and experimental results is by G. S. Durham of the Department of Chemistry, Smith College. (2) G. S. Durham and J. A. Hawkins, J. Chem. Phya., 19, 149 (1951). (3) F. Oberlies, A n n . P h y s i k , 87, 238 (19281, has measured lattice constants for KBr-KCI solid solutions: however, no temperatures are given, and the average deviation of her results is large, f O . O G % . R. . J . Havidiurst. E. Mack, Jr., ond F. C. Blake, J. A m . Chem. Soc., 47, 20 (1D25), have obtained a valur for 50 mole % KRr-KC1 and two values f o r the RbC1-KC1 system, b u t the small number and poor overall accuracy of these results mode them useless for our purpose. (4) G. S. Durham, E. J. Rock and J . 8. Brayn, i b i d . , 7 5 , 5702 (1953).
The original bromide-chloride compositions for the RbBr-RbC1 solid solutions, which were obtained indirectly by determination of total halide, have been recalculated to take into account the effects of the potassium actually found present (from 0.43 to 1.00% by weight), and these corrected compositions are used in the present paper. The possible effects of the K + and Cs+ ion contamination are brought out) later in the discussion of the results. The coarsely-crystalline solid-solution samples were reduced to sufficient fineness for diffraction analysis by grinding each in an agate mortar for a few minutes. Suitable specimen mounts were then prepared by mounting a thin layer of powder on the outside of a fine Pyrex capillary tube (about 0.3-mm. outside diameter) with Duco cement, the total diameter of the cylindrical mount being about 0.4 mm. The powder patterns were prepared in an improved Norelco Debye-Scherrer camera of 114.6-mm. diameter using nickelfiltered CuK radiation. In order to obtain optimum definition of lines a 0.5-mm. pinhole collimator was employed, which necessitated exposures of 12 to 15 hours. The film was placed in the camera in the asymmetrlc, or Straumanis, position,6 which is superior for precision measurements because it permits the determination of the film radius directly from the diffraction data. All diffraction patterns were prepared a t laboratory temperature, the mean temperature of each exposure being ascertained with an accuracy of f0.4" or better. The lattice constants as measured a t laboratory temperature were finally corrected to 25" using the previously determined linear thermal expansion coefficient, 0 1 , which for the three salts involved, lies between 37 and 38 X 10-6/degree.6 Because of the close agreement of 01 for the pure salts, it seemed very unlikely that the coefficients of the solid solutions formed from the compounds could differ much from these same values. The extrapolation method of Bradley and Jay7 was used to obtain the best value of each lattice constant from the several values calculated for lines between e = 60 and 90". The efficacy of this method has been established by time, and it has the advantage over Cohen's analytical method8 that the relative quality of the various lines can be taken into account in performing the extrapolation. The number of lines utilized in the extrapolations ranged from 4 to 11 depending upon the quality of the pattern. In three cases (samples No. 4A, 4B and 6A of the RbBr-KBr series, Table 11) these back-refle ction lines were so poorly defined that satisfactory extrapolations against eosa 0 could not be made; instead the extrapolations were performed using the function cos2 0 (l/sin 8 l/@,which makes use of reflections in the larger angular range e = 30 to
+
Results The lattice constants for the two solid-solution series RbBr-RbC1 and RbBr-KBr are listed in Tables I and 11, respectively. The values are given in true Angstrom units. It should be mentioned that the lattice constants given have not been corrected for the refraction of the X-rays, since the magnitude of this correction is much ( 5 ) M. E. Straumanis, J. A p p l . P h y s . , 20, 726 (1949). (6) "Physikalisch-Chemische Tabellen," Vol. 11, Verlag von Julius Springer. Berlin, 1923, p. 1223. (7) A. J. Bradley and A. H. J a y , Proc. Phys. Soc., 44, 563 (1932). (8) M . U.Colien, Rev. Sei. I n s t r u m e n t s , 6 , 68 (1935); 7 , 155 (193G). (9) A. Taylor and H. Sinclair, Proc. Phys. Soe., 57, 126 (1845); J. B. Nelson and D. P. Riley, ibid., 67, 100 (1945).
" . 562
G. b.
DURHAM, L. ALESNDS~,D. 1'.PITMAN, H. GOLOBAND H. P. KLUG
VOl. 59
TABLE J EXPEXIMENTAL LATTICE CONSTANTS OF RbBr-RbC1 SOLIDSOLUTIONS e -
Bample
RbBr
Mole % ' RbCl
.
K(Br, C1)
Mean temp. of measurement ("C.)
ao in
A.
(250)
Estimated probable error (A.1
Ar =
(exp.) m (~eg.)ld
1/*[m
1 (RbC1)" 0.00 95.0 3.39 29.2 (6.591.4)b6.5869 10.0004 0.0000 2 3.78 93:l 3.09 27.4 ; 6 .,5946 ,0004 .0007 6.6298 .0004 - ,0018 3A 15.8,h 181.6 2 .,61 , 28..0 , 6.6304 .0004 - ,0003 2.95 28.3 3B 15.5 i, E 81.6 2.36 28.1 6.6915 ,0004 .0007 4 34.2 63.5 6.7357 .0006 ,0021, 27.9 2.28 5 47.7 ; 50.1 6A 77.8 . 20.4 1.88 27.1 6.8290 ,0006 ,0014 6.8'259 .0010 28.1 ,0002 , _ 20.0 , 2.11 6B 77.9 7 93.2 5 .,os 1.79. 26.7 6.8700 .0006 - .0014 8 (RbBr No. 1)' 95.3 o.,oo 3.18 26.1 (6.8946)b 6.8900 .0004 a This sample also contained 1.66 mole % CsC1. b These values were obtained by extrapolation to zero % impurity, using Vegard's law. Values of ao(Veg.) were calculated using ao(RbBr) = This sample also contained 1.52 mole yo CsBr. 6.8936 A.
wrr
+
+ + +
-
I
procedure in the case of small impurity concentra-
TABLE I1
EXPERIMENTAL LATTICECONSTANTS OF RbBr-KBr SOLID tions is, given by the close agreement (within SOLUTIONS 0.0005 A.) of the extrapolated values for the near-
est-neighbor distances obtained from two samples of RbBr which differed widely in the amounts of ao in A. K + and Cs+ ion present. Since RbBr No. 2 was Sample (25') considerably purer, its value was used in the sub1 (KBr)a 6.5982 sequent calculations. (6.59Wb 2A 10.0 25.4 6.6284 The Vegard values for the RbBr-RbC1 system 2B 9 . 9 23.1 6.6291 + were calculated to include the effects of the potas3A 26.7 23.5 6.6766 sium impurity content, which was knOwn for each 3B 26.8 26;6 6.6768 sample by direct analysis. It is interesting to 4A 50.8 25.4 d.7493 + [4B 50.8 26.2 6.7433 note that almQst exactly the same results are ob5b o 65.8 24.4 6.7932 + tained here whether or not the potassium im5B 6 7 . 8 23.9 6.8005 purity in the solid solutions is considered. The + 6 A' 79.7 22.0 6.8341 effect on the analytical calculations of taking the 6B 82.0 23.4 6.8393 potassium into account is to increase the per?AC 90.8 23.0 6.8591 7B 91.7 21.9 6.8640 centage of bromide. However, when the Vegard 8 (RbBr N 0 . 1 1 ~ 9 5 . 3 2 6 . 1 6.8900 lattice distances are calculated, the effect of a ( 6 . 8946)b greater proportion of large bromide ion is counter9 (RbBr No. 2)s 9 8 . 0 2 5 . 9 6.8884 .0005 balanced by the effect of the small E(+ ion.' (6.8936)' .000 a This sample contained 0.2 mole yo KCl.: Theee Due to a similar size-weight relationship for the values were obtained by extrapolation to zero % impurity, Csf ion, whether or not it is taken into account is using Vegard's law. RbBr No. 1 w~lsused in maklng up these solid solutions, The others were prepared from Rb- immaterial as far as the Vegard interionic distances Br No. 2. RbBr No. 1 contairled 3.18 mole % ' KBr p d in the solid solutions are concerned. For this reason, it was not thought worth while to analyze 1.52 mole .% CsBy.. e RbRr No,. 2 contained 1.79 mole KBr and 0.21 mole yo CsBr., Values of ao(.Veg.) were the solid solutions for cesium, particularly since calculated usisg a. (RbBr) = 6.8936.A. the distribution ratio obtaining for small Csf smaller than the errors of measurement. Allow- ion concentrations would be such that most of the ance for refraction would increase all the values by Cst ion would remain in the aqueous phase during the preparation of the solid solutions. Evidence 0.0001 A. for,the correctness of these conclusions is given by Discussion For purposes of , comparison, both the experi- the excellent agreement in the RbBr-KBr system mental results of this paper and the theoretical between [r(exp.) - r(Veg.)] values for duplicates made up using two RbBr samples which varied values of reference (2) have been converted into widely in cesium content. differences from the corresponding nearest-neighDifferences between Vegard values and those bor lattice spacings calculated according to the calculated according to the ninth-power mixing Vegard's-law relationship of additive lattice conrule have also been obtained, they are closely stants. Values of the pure-salt lattice constants comparable to the theoreticalsince values result required for calculating Vegard distances were ob- when ionic displacements are not which considered. tained by algebraically extrapolating the experimental values for the original salts to zero % K + The use of deviations from Vegard's law for comand Cs+ ion, according ' t o Vegard's law. The parisons obviates any inconsistencies due to interionic distances used for the face-centered slight differences in the pure-salt values taken for forms of CsCl and CsBr were those calculated by the theoretical calculations. The derived experimental data described above Pauling.10 Some indication of the validity of this are included in Tables I and 11, and the theoretical (10) L. Pauling, "The Nature of the Chemical Bond," 2nd Edition, Cornell University Press, Ithaca, N . Y., 1942, p. 358. data are listed in Table 111; for comparison bo% Esti-
Mean terno. of% mess. RbBr ("C.3 0.0 26.6
mated probrtble AT = error 1/2[ao(exp.) (A.1 aa (VegJIf *0.0004 0.0000 ,0004 .OOOO .0004 .0006 .0004 ,0006 .0006 .0004 .0010 ,0004 .0026 .0006 .0010 .0007 .0008 4- ,0009 ,0008 .0002 .0006 .0006 .0008 .0036 .0025 .0006 ,0004
Mole
f
563
SOLIDSOLUTIONS OF ALKALI HALIDES
June, 1955 TABLEI11
THEORETICAL NEAREST-NEIGHBOR DISTANCES I N ALKALLHALIDE SOLIDSOLUT~ONS NRbBr
r (theor.)," A.
A r (theor.-
Ar (9th 7
(9tliopower),
A.
Veg.)
pow.-
Veg.)
I. RbBr-RbC1 0.0 .1
.3 .5 .7 .9 1.0
(3.2935) 3 3108 3.3416 3.3722 3.4018 3.4304 (3.4446)
0,0000 ,0022 ,0028 .0031 .0025 ,0009 .0000
+ + + + +
(3.2935) 3.3113 3.3448 3 3757 3.4046 3.4317 (3.4446)
I
0.0000
+ .0027 d + ,0060 ? . + 0066 + ,0053 0 + ,0022
RbBr- K6r
m
X
.0000
2l
-- -_.
.'
/------
5-
/'
..
11. RbBr-KBr 0.0
.1 .3 .5 .7 .9 1.0 Q
'
(3.2997) 3.3146 3.3442 3.3735 3.4019 3.4298 (3.4446)
0.0000
+ ,0004 + .0011 + ,0013 + .0007 -
,0003
.0000
(3.2997) 3.3167 3.3487 3.3783 3.4061 3.4322 (3.4446)
0
0.0000
+ .0025 + .0056 + ,0061 + .0049 + .0021
RbBr - RbU
. 0000
Taken from ref. (2).
are plotted in Fig. 1. In the graph, the average has been used for near-duplicate experimental values, except for one point in the RbBr-KBr system, where an extremely low value was discarded. I n the RbBr-RbC1 system, the theoretical points are seen to fall somewhat higher than the experimental, although the over-all agreement is far better than for the old ninth-power values. I n the RbBr-KBr system, the agreement is in general excellent, with the exception of the solid solution richest in rubidium bromide. It was a t first thought that the negative deviations which occur in both systems might be due to use of too high lattice constants for the pure salts. However, with the exception of cesium, whlch was corrected for, the only impurity which might be expected to give rise t o such high values was iodide, and this element was shown to be absent. It is interesting to note that in the systems KBr-
I
0 RbBr
Fig. 1.-Experimental and theoretical nearest-neighbor distances in alkali-halide solid solutions, expressed as deviations from Vegard's-law values: 0,exptl. ; -, theor., ---,9th power.
KCl3 and thallium alum-ammonium alum,l' negative deviations have also been found to occur; however, the deviations fall within the possible experimental error and hence, in their cases, no definite conclusions can be drawn. It is felt that the present experimental curves, which are doubly sigmoidal in shape, with the greatest tendency toward negative deviations from Vegard's law being found a t high mole fractions of rubidium bromide, give a valid picture of the lattice-constant relationships in such alkali-halide solid solutions. Although the theoretical methods of reference (2) are not sufficiently sensitive to give detailed agreement with the expenmental, they lead on the whole to lattice constants of the correct magnitude. (11) (1940).
H. P. Klug and L.E. Alexander, J . Am. Chem. Soc., 62, 2993
