Results of Crystal Analysis. 



81 



which gives the distribution of points in two consecutive 

 planes (001). 



In a plane (001) either all lines may be parallel as shown 

 in the figure, or the lines through Si can be drawn perpen- 

 dicular to those through the Zr atoms. The latter arrange- 

 ment is excluded as it would not explain the distribution of 

 intensities of the (111) face. 



We shall then consider the arrangement represented in 

 fig. 4, which, as will be seen, with a proper choice of the 

 parameters ei and e 2 , will give the right lattice for the 

 zircon group. This lattice is composed of 12 face-centred 

 lattices with the construction-points which are given in 

 Table IV. 



Table IV. 



Atom. 



X. 



y- 



z. 



- { 







-a/4 







a/4 





 c/4 



* { 



a/2 

 a/4 







a/4 







c/4 



| 



e v a 



e x a 







associated with Zr. . \ 



{ 



— a/4+e x a 

 —a/4 — e-, a 



— e T a 

 a/4 — fc^a 

 a/4+e x a 







c/4 

 C/4: 



( 



associated with Si... < 



a/2+e r ,a 

 a/2 — e 2 a 

 a/4+e 2 a 

 a/4 - e. 2 a 



e 2 a 

 — e 2 a 



a/4 — e 2 a 

 a/4+e 2 a 





 

 c/4 



c/4 



Curiously enough, this lattice does not apparently possess 

 the same symmetry elements as the crystal ; thus the planes 

 (100) and (010) are not symmetry planes with respect to 

 the points of the lattice, and the lattice possesses no tetra- 

 gonal screw axis. 



But still the lattice has the properties necessary to explain 

 the symmetry of the crystals. 



Let a (100) plane containing Zr and Si atoms divide the 

 lattice in two parts I and II. The points of the mirror 

 image of I do not coincide with equivalent points of II ; 

 but they can be brought to coincide by a translatory motion 

 along the three axes (x = a/4i, y = a\^ z = c/4i). 



Phil. Mag. S. 6. Vol. 32. No. 187. July 1916. G 



