COMPRESSIBILITY OF METALS. 231 



Hence 



Now the analysis of Born (equation 4, page 235, Verh. D. Phys. Ges. 

 20, 1918) shows that b is of the form 



b = Const e 2 r 4 , 



where r is the semidiagonal of the neutral cubic atom, and the con- 

 stant, which varies with the type of lattice, will be of the order of 

 magnitude of 10. (For instance, the coefficient of e 2 in the above 

 expression for a is 38.7, for NaCl it is 13.94). Hence as a rough 

 approximation put 



b = 10 c 2 r\ 



db dr 



and — = AOe 2 )- 3 — . 



dp dp 



dr 

 Now Schottky's theorem gives — . At ordinary temperatures, at 



low pressures, his formula gives very closely 



j- = 3F, 

 dp 



and hence, applied to an elementary cell of the lattice, 



dL dL dr 



dp dr dp' 



Now the variable part of L we take as the contribution of the 8 outer 

 electrons rotating about a nuclear charge of 8 at distance r. (This 

 assumes most of the deformation of the atom under pressure is con- 

 fined to the outer shell). The kinetic energy of these electrons is one 

 half their potential energy, or 



