MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 29 



The bulk modulus: The change in volume per unit volume for unit hydro- 

 static pressure is the bulk modulus, H. For a stress Xc = (1, 1, 1, 0, 0, 0) 



^ = \Sn + Sn + Sz\ , Si2 + S33 -\- S23 , S31 + S23 + ^'33 , • • • ) 



H = (ei+ e.,+ 63 = Sn+ 522+ ^33+ 25i2 + 2^31 + 26-23) (8.25) 



This is obviously independent of the choice of axes. 



The Temperature Coefficient of the Elastic Modulii and Constants 

 If 



C = C° -^ th + t^h"- 4- t^li + • • • (8.26)* 



and 



S = S° ^ th^ tHf + /V + • • • (8.27) 



(C° and S° denote the values of the C's and 6"s for some standard tempera- 

 ture / = 0) then as the transformations are 



C — a C ac and S' — a7 Sa" or 



a = a (C° + th + i'h' + /'//' •••)«« 



and 



S' = a-\S° + tli + t^H' + t^H' •-•)a~^ 



we see that 



C = C°' + th' + /'//" • • • (8.28) 



S' = S°' + ///' + t'H" • • • (8.29) 



where 



h' = ahdc etc (8.30) 



H' = a7'Ha~' etc (8.31) 



That is, the h^s transform as the C's do, and the H's transform as the S's 

 do. Consequently we may copy their respective forms from the C and S 

 matrices for any particular crystal class. 



When the temperature coefhcients of the constants or modulii are known 

 in the form: 



Cii = C°;(l -\-tTc,,) (8.32) 



5iy = 5;,- (1 + /r,, .) (8.33) 



* The n of /" denotes the «th power of the scalar i; the n of A" is merely another matrix, 

 it does not mean a power. 



