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XXIII. Construction of the Diamond with Theoretical Carbon 

 Atoms. By Albert 0. Crehokb, Ph.D.* {From the 

 Department of Physiology of Columbia University.) 



IN a former paper f a crystal of rock-salt was constructed 

 with the theoretical atoms of sodium and chlorine, the 

 atoms being in cubical array, alternating, sodium and 

 chlorine, along each edge in three directions. The direc- 

 tion of the axis of rotation of each atom was shown to be 

 along the diagonal of the elementary cube, taking such 

 direction along the diagonal that one plane may be brought 

 into coincidence with any other plane by properly moving 

 the plane. When the edge of the elementary cube has the 

 dimensions 2*814 x 10" 8 cm. it was shown that each atom in 

 the whole structure, due to the forces upon it of all the other 

 atoms, is in stable equilibrium, both as to translational and 

 rotational forces. Fig. 1 illustrates one of these planes of 

 atoms. The arrows are not in the plane, but point upward 

 toward the centre of a cube on the elementary square base. 



In the diamond it has been shown, by the study of X-ray 

 spectra, that each carbon atom is at the centre of a regular 

 tetrahedron. It is more difficult to represent the exact 

 arrangement of the tetrahedral structure by plane figures 

 in perspective than is the case with a cube. A model is of 

 much assistance in seeing the relations. There are many 

 possible ways in which the axes of rotation of the atoms may 

 be placed, but only one way to make the equilibrium perfectly 

 stable. From the following description a model may be con- 

 structed to show the necessary positions of the axes of rotation 

 for stable equilibrium. 



The whole crystal may be built up by placing planes of 

 atoms as represented in fig. 2, one above another, and making 



the distances between planes alternately ^5 v °^ and . ^/ ()/, 



where I is the side of the elementary triangle and also the 

 edire of an elementary tetrahedron in the diamond. This 

 amounts to dividing the vertical distance into equal spares, 



equal to =-~ \/o7, and alternately using two and omitting 



two consecutive planes of atoms. Each plane may be made 

 to coincide with every other plane in all respects, including 



* Communicated by the Author. 

 t Phil. Mag. June*1915 ; p. 750. 



Phil. May. S. 6. Vol. 30. No. 176. Aug. 1915. S 



