FEB. 4, 1921 ADAMS: COMPRESSIBILITY OF DIAMOND 49 



Another useful relation involving the compressibility is that given 

 by Debye:^- 



e = ^1^' ^ ^^-74 X 10-" j_ 



In this equation /3 is in absolute units, and <^ is a function of a, Poisson's 

 ratio, ^^ thus: 



* = -(3 nryj +(3-03^) 



Rearranging equation (7), substituting Debye's values for h and k, 

 and expressing /3 in cm.-/megadyne, we have: 



/3 = 5 . 5 X 10-1 j^;; .4 -^ p-'^ </>-'^ (8) 



The value of v,„ for any element can be calculated from equation (7) 

 provided that the specific heat is known at one or more suitable tem- 

 peratures; and can be calculated when a, Poisson's ratio, is known. 

 Equation (8), then, can be used to calculate the compressibility of 

 any element for which C., and a have been measured. For several 

 elements for which these quantities are known the compressibilities 

 have been calculated by equation (8) with the results shown in table 2. 



TABLE 2 

 Calculation of Compressibility from Specific Heat and Poisson's Ratio 



Compress- 

 iljility 

 Max. atomic Poisson's calc. from 



frequency At. wt. Density ratio equation (8) ^ X 106 



Substance. •',„ X 10'^. .1. p. a. /S X 106. observed. 



Aluminum 8.2 27 . 1 2.7 . 34 1 . 42 1 . 32 



Copper 6.4 63.6 8.9 0.35 0.83 0.75 



SUver 4.4 107.9 10.5 0.38 0.92 0.97 



Lead 2.0 207.2 11.3 |0.45] [1.1] 2.2 



Diamond 39.2 12.0 3.5 (0.25) 0.16 0.16 



The values for v,„ are taken from Debye and those for <j are as given 

 by Griineisen.^^ Poisson's ratio for diamond has not been measured, 



12 p. Debye, Ann. Phys. (4) 39: 816. 1912. Debye considers that the atoms in a solid 

 are vibrating, not with a single frequency, but with a number of different frequencies, 



and that the specific heat is a universal function of —, vm being the maximum frequency. 



His equation is : 



\x^ J e"-! e-v- _ 1 1 

 o 



, . , hvm e . 



in which X = —— = -, and q is an integration variable. 

 kT T 



" Strictly speaking, Poisson's ratio has no meaning except with reference to an isotropic 



or pseudo-isotropic substance. 



'-• E. Gruneisen, Ann. Phys. (4) 25: 847. 1908. 



