240 ADAMS : FUNDAMENTAL POLYHEDRON OF DIAMOND 



CRYSTALLOGRAPHY. — Note on the fundamental polyhedron 

 of the diamond lattice. Elliot Q. Adams, Bureau of Chem- 

 istry. ^ (Communicated by Edgar T. Wherry.) 



The space lattice according to which the carbon atoms in 

 diamond are arranged has been established by the work of the 

 Bragg's" and has been found not to correspond to any of the 

 previously recognized point systems of the cubic type, having 

 planes of ''gliding reflection" and axes of ''helical symmetry." 

 To each of the already recognized point systems there corre- 

 sponds a convex polyhedron capable of filling space, and having 

 a symmetry correspondent to that of the point system. No 

 such polyhedron appears to have been described as corresponding 

 to the diamond lattice. The form of this polyhedron has been 

 worked out and is given below. 



The polyhedron corresponding to the simple cubic lattice is 

 the cube (100); to the face-centered lattice, the rhombic dodeca- 

 hedron (110); and to the cube-centered lattice, the cubo-octa- 

 hedron (111), (100), in which the octahedral faces are truncated 

 just enough to make them regular hexagons. Since each carbon 

 atom in diamond is near four others, tetrahedral faces will be 

 present. As space can not be filled with tetrahedra, some other 

 face must occur also. This face proves to be that of the rhombic 

 dodecahedron, truncating the tetrahedral faces sufficiently to 

 make them regular hexagons. The polyhedron may be called 

 the dodeca-tetrahedron k (111), (110). (See figures 1-3). 



That diamond is crystallographically holohedral, while the 

 unit polyhedra, as may be seen from the figures, are hemihedral, 

 results from the fact that the mode of arrangement in space of the 

 dodeca-tetrahedra constitutes a sort of twinning. Practically 

 all the elements of the fourth column of the periodic table 

 crystallize in a form similar to that of diamond. If the alternate 

 atoms in such a lattice are different, the crystal becomes hemi- 

 hedral, as in the case of sphalerite (ZnS). In this case the poly- 

 hedra corresponding to the two elements need not be equal in size, 



1 Contribution from the Color Investigation Laboratory of the Bureau of 

 Chemistry, U. S. Department of Agriculture. 



2 Br\gg, W. H., and W. L., X-Rays and Crystal Structure, p. 102. 1915; 

 Proc. Roy. Soc. (A) 89: 277. 1913. 



