The Crystal Structure of Potassium Sulphate

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PHYSICS: F. P. GOEDER

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PROC. N. A. S.

pletely satisfactory results. In concentrated solutions of electrolytes, when the ions are crowded together, correlation forces arising from systematic interaction of the ions are to be expected to occur, and then the fundamental equation obtained by eliminating the time-average charge density between a time-average Poisson's equation and the distribution law will be modified by a correlation potential. The no doubt important alterations due to this modification will have to be taken into account in any satisfactory extension of the Debye theory to concentrated solutions. Pauling3 has shown that by introducing an extra potential in a semi-empirical way it is possible to get results giving the major features of the behavior of electrolytic solutions up to rather high concentrations. The present work indicates the probable physical nature of the effects requiring devi&ions from the simple Debye treatment and gives a physical interpretation to Pauling's method of correction. Thomas, Proc. Camb. Phil. Soc., 23, 542-8 (1926). Physik, 48, 73-9 (1928). 1 Pauling, paper read at Los Angeles meeting of the American Chemical Society, June, 1925. '

2 Fermi, Z.

THE CRYSTAL STRUCTURE OF POTASSIUM SULPHATE By FRANK PZAT GOZDZR RYaRsON PHYsIcAL LABORATORY, THU UNIVRSITYr OF CHICAGO Commcated September 5, 1928

In a previous paper' the space group of potassium sulphate was determined from data obtained from Laue photographs to be 2Di-13. While from the point of view of descriptive crystallography this result is of fundamental importance, for crystal structure determinations it is of value only if it can lead to a solution of the complete internal structure of this substance. This paper is a brief account of the way in which the information obtained from the geometrical theory of space groups has resulted in a complete solution not only of the crystal structure of potassium sulphate but also presents for the first time a quantitative three-dimensional structure for the potassium sulphate molecule. Furthermore, the results of x-ray powder photographs of potassium sulphate are presented, and the diffraction effects computed from the structure obtained from the space group are sbown to be quantitatively verified in every detail by experiment. As was previously shown,' the elementary lattice of potassium sulphate contains four molecules of K2SO4 and has the lattice constants ao = 5.746 A.U., bo = 10.033 A.U. and co = 7.443 A.U., as determined by Ogg and Hopwood. The author of this paper redetermined the lattice constants

VOL. 14, 1928

PHYSICS: F. P. GOEDER

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of potassium sulphate by the powder method of analysis and found them to be ao = 5.771 A.U., bo = 10.064 A.U., co = 7.518 A.U. and has incorporated them in this investigation. Since potassium sulphate is known to be ionized in solution into K+ positive ions and S04- negative ions and since other inorganic crystals which can be grown from ionic solutions have been shown to preserve their ions in the crystal structure,2 we can, for a first approximation, consider that the volume included within the elementary rhomb contains eight potassium ions which can be considered as diffracting centers and four S04 ions. If these S04 ions have a symmetrical structure they, too, can be considered as a first approximation to be diffracting centers. The simplest structure which has been proposed for the S04 group is that suggested by Bradley3 in which the sulphur is located at the center of a regular tetrahedron whose corners represent the oxygen atoms. This' tetrahedral structure has been used by Wasastjerna4 in his study of the structure of anhydrite and he concludes that in CaS04 the edge of this tetrahedron is approximately 2.7 X 10-8 cm. Since we have no reason to suppose that one of these S04 ions is different from any other one and since the potassium ions are presumably identical chemically it is natural to suppose that they are also geometrically equivalent. These suppositions outlined above simplify the problem into finding the coordinates for two sets of equivalent points falling under space group 2Di-13. A reference to the analytical expression of the results of the theory of space groups5 indicates that the potassium ions will have the general positions, x, y, z; x + i,

2X iY, Z;

y, yz; x, y + i, z; X+ y, x; x, Y, ; X, y,2; X +1, y + 1,

and that the S atoms can have any one of the four following special positions, TABLE 1

(c) i 0; (d) ii; (e) Ouv; (f) uO0v;

110; HiO; 1i0 ii; iii; i1O Ouv; i,*-u,i; i,u+ ,I uOv 0;i-u, I,v; u + 1, 1, i

When these various possibilities are checked against the experimental results it is soon observed that the following structure give6 the best agreement. TABLE, 2 POTASSIUM NucLBi This structure when translated by i i i gives the following positions:

000; t0o; Oi; I11; 001; i00; 010; li*

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PHYSICS: F. P. GOEDER

PROC. N. A. S.

SUIPHUR NucLEI

when u = 1, 0 = 0, v =

Substituting these values in (f) changed to uOv; u0v; i-u, i,V; u+i,i,v and translating as for potassium, results in the positions,

Ot; 1i0; 0o0; Hi The next step is to determine the orientation of the oxygen nuclei with respect to the sulphur and fix their coordinates within the elementary lattice. Since the oxygen atoms are all alike and form the outside shell of the S04 group, we should expect the two potassium ions to be symmetrically arranged with respect to the oxygen and sulphur atoms. The simplest arrangement of this 1kind is