X-RAY STUDIES O F SOLID SOLUTIONS
625
X-RAY DIFFRACTION S'I'UDIES OF SODIUM CHLORIDE-SODIUM BROMIDE SOLID SOLUTIO?\'S1 J. E. XICKELS,
nr.
A. FIXEMAN, AxD
w.E. WALLACE
Ifellon I n s f i f u t e and Department of Chemistry, University of Pittsburgh, Piftsburgh, Pennsylvania Received September 6 , 1848
In a recent study (2) the heats of formation of a series of sodium chloridesodium bromide solid solutions n.ere determined. At the time it seemed desirable to subject the several solid solutions to x-ray diffraction analysis so that some idea of their homogeneity and physical state might be obtained. In addition, there was some interest in ascertaining how nearly additive the lattice spacings and molar volumes are for this system. EXPERLMEXTAL
The preparation and analysis of the eleven samples studied (the two pure salts and nine solid solutions) have been described (2). X-ray powder diffraction patterns of these samples were made with a cylindrical camera of 171.9 mm. effective diameter, employing the Straumanis ( 5 ) technique. Unfiltered radiation from a sealed copper tube fitted with beryllium windows was used to reduce the exposure time. The general procedure followed in making the diffraction patterns and the mode of preparatiun of the cylindrical, 0.7 mm. diameter powder specimens of the samples are described elsewhere (4). To protect the prepared specimens from moisture, as well as to improve their mechanical strength, they were given a collodion coating by dipping into a diluted solution of flexible collodion. All samples and prepared specimens were stored in a desiccator over anhydrous calcium chloride when not in use. EXPERIMEIUTAL RESULTS
Preliminary examination of the diffraction patterns indicated that all the solid solutions were single-phase, homogeneous, crystalline materials. The diffraction lines appeared uniformly sharp for the several solid solutions, as well as for the two pure salts. The patterns for the solutions showed no signs of lines characteristic of either of the pure constituents and all of the observed lines could be accounted for by assuming the existence of a single solid solution of tixed composition. The Bradley and Jay (1) extrapolation method was applied to the bnckreflection diffraction lines to obtain the lattice spacings (cation-cation distance) given in table 1. The variation of the lattice spacing with composition is shown in figure 1. The values reported for pure sodium chloride and pure sodium bromide are This work was supported i n part by a basic research grant from the Office of Naval Research, United States Navy Department, under Contract iX60ri, Task Order 2.
626
J. E. XICKELS, 11, .1. F I S E l I A S A S D 11.. E. 1VALLICE
0.02 and 0.4 per cent larger, respectively, than thoze given in the liteixturc (6, 7 ) . 1-nfortunately, no reliable literature values for the spacings of thc iolid Lattace spacangs, densztaes,
crrirl
TXBLE 1 Lolimes ( ~ sotliiiiir j chlorzde-sodziwi h o m i d e solid solutaons at 25°C
iriolni
-
_
MOLE FRACTION OF
_
NaBr
DEYS1TIF.S
MOL.\R VOLGMKS
-
0.0000 0.1018 0.2019 0.2982 0.4029 0.4927 0.5977 0.7007 0.7922 0.8947 1.0000
5.628, 5.6652 ,5. 70 1 5.734, 5 .i 7 0 s 5.8006
5,8362 5.8696 5.900, 5.9310 5,9617
g., c c .
cc.lmolr
2.164 2.288 2.405 2.514 2,628 2.722 2.830 2,930
27.016 27.54s 28.081
28.55!, 29.105 29. 5Gr 30.11:. 30.627
3.018
?Jl , ll:,
3.113 3.206
31.60; 32.098
FIG. 1. Plot showing the variation of the lattice sp:tcings with composition (0) sodium chloride-sodium bromide solid solutions. Deviations from Vepird’s rule for this system are also plotted
solutions Tvere available for comparison, so that it is difficult to assess the :tccuracy of the data presented in this paper, except for the two pure salts. It appears that the data are reasonably precise, since a large-scale plot of lattice
(j2i
S - R A Y S'IL-DIES O F hOLID hOLC TIOSh
spacingh against composition s h o w that the lattice spacings for the nine wlutions and tn-o pure salts all fall on a smooth curve xith an average deviation of 0.004 per cent. Included in table 1 are values for the densities and molar volumes of the crystalline solution. computed from the measured lattice spacings. TABLE 2 Comparison of observed arid calculated lattice spacings and molni volumes UJ' .sodtum chloridesodium b l o m i d e solid solutions at 25°C. -
~
MOLE FKAITI i,v OF S a B r
__
LATTICE S P A C I \ G S (mi ~
Observed ~
0.1018 0.2019 0.2982 0.4029 0.4927
0.5977 0.7007 0.7922 0,8947
Calculated ~
5.6651 5.7012 5.733, 5.7703 5.800s 5.8362 5.8696 5.9000 5.9310
~~
5,6621 5.6960 5.7281 5.7629 5,7928 5.8278 5 . 86Z1 5.8925 5.9266
I-
~~
Deviation
0 0 0 0 0 0 0 0 0
-
~
UOLXR \.OLC.UL
I ~
Obseri ed
~cc /mo!e
002, 005, 005, OOir 008" 0084 007, 0075 004,
27 543 28 081 28 559 29.10, 29 569 30 117 30 6 2 31 11, 31 60,
~~
Calculated
- ~. ~
I l e \ iation -
cc./mo!e
cc m o l e
27.531 28. 042 28.531 29.064 29.520 30.05, 30.577 31.042 31.563
0 010 0.039 0 028 0 041 0.049 0 05, 0 050 0.073 0 042
-
FIG.2 Plot showing molar volume ds a function uf coiiipositlon (0) for sodium chloridesodium bromide solid solutions. The deviation cuive ).( shoirs the amount by uhich t h e sctua1,niolai volume exceeds that computed froni .idditivitj COMPARISOK OF OBSERVED I N D CALCUL \TED L LTTICE IPACINGS AND X O L 1R V O L C M E S
Arnnurnber of years ago T'egard (8) suggested that the lattice spacings of a d i d solution should lie between those of the component materials, varying inearly with composition. Specifically, 1-egard'i rule states that a+ = nliVl
628
J. E. KICKELS, M. .I. FINEMAX AND TV. E. WALLACE
+
a2N2, where a represents the lattice spacing and N the mole fraction, and subscripts s, 1, and 2 refer to the solid solution, component 1, and component 2. I n table 2 comparison is made between the observed lattice spacings and those computed from Vegard’s rule. It is to be noted that in all cases there are small positive deviations from additivity. It is well known that an ideal solution, that is, one ivhich obeys Raoult’s law under all conditions, is formed from its camponents without change in volume or heat content (3). Stated differently, an ideal solution must have a volume or heat content \Those dependence on composition is similar in form tQ Vegard’s rule for lattice spacings. Xon-ideal solutions exhibiting positive deviations from Raoult’s law usually have volumes or heat contents exceeding the quantities computed from the appropriate additivity expression, whereas those deviating negatively from Raoult’s law usually have volumes and heat contents less than the computed quantities (3). The heat of formation of sodium chloride-sodium bromide solid solutions was observed (2) to b > positive for all compositions. I t was of interest to know if the volume changa would also be positive, or, in other words, to know if the actual voli~mesexceeded those expected from the additivity expression. Using the densities reported in table 1 the volumes m r e computed and were observed to be larger than the calculated values for all compositions. The results of the calculations are given in table 2 . The extent t o which the lattice spacings and molar volumes deviate from additivity is demonstrated in figures 1 and 2. SUhZJIA RY
The x-ray diffraction patterns for nine sodium chloride-sodium bromide solid solutions and for pure sodium chloride and pure sodium bromide were obtained. The solid solutions were observed to be single-phase, homogeneous, crystalline materials. From the diffraction patterns, the lattice spacings, densities, and molar volumes were computed. Both lattice spacings and molar volumes of the solid solutions exhibit positive deviations from additivity. The authors would like to express their appreciation to Dr. S. S. Sidhu for having made available the facilities of the Cooperative X-Ray Laboratory for use in this study. REFERESCES (1) BRADLEY, A. J., A N D JAY, A. H.: Proc. Pliys. SOC.(London) 44, 563 (1932). (2) FIXEMAN, M. A,, A N D WALLACE,W. E.: J . Am. Cticni. Soc. 70, 4165 (1918). (3) H I L D E B R A NJ.: D , Solubilily o j Non-Electro/!/tes,Chap. I1 and 111. Reinhold Publishing Corporation, S e w York, New York (1036). (4) h k I i I N L E Y , J. B., NICKELS, J. E., A N D SIDHU, S. S.: Ind. Eng. Chem., A n d . Ed. 16, 304 (1944). ( 5 ) STRAUNANIS, M., A N D IEVINS,A.: Naturwissenshaften 23. 833 (1935). (6) STRAUNANIS, RI., A N D I E V I N SA.: , Z. Physik 102, 353 (1036). (7) S T R A U M A N I S , M., IEVINS,A . , A N D KARLSONS, Ii.: z. physik. Chem. 40B, 146 (1938). (8) VEGABD,L.: Z. Physik 6, 17 (1021).
