92 BELL SYSTEM TECHNICAL JOURNAL 



at 25°C. or 298° absolute. These differences are probably smaller than 

 the accuracy of the measured constants. 



If we express the stresses in terms of the strains by solving equation (35) 

 simultaneously, we find for the stresses 



(38) 



7^6 = Ci^Si -\- c^^S'i -\~ Cz^Si + Cif,SA + CjfrSs + Ces'S'e — Xe dQ 

 where 



The X's represent the temperature coefficients of stress when all the strains 

 are zero. The negative sign indicates that a negative stress (a compression) 

 has to be applied to keep the strains zero. If we substitute equations (38) 

 in the last of equations (35), the relation between increments of heat and 

 temperature, we have 



dO = Qda = e[\iSi + MSi + XsSs + XiS^ + X56-5 + Xe^e] 



(39) 

 + [pCp — 0(aiXi + 012X2 + 0:3X3 + 0:4X4 + 0:5X5 + a^X6)]dQ. 



If we set the strains equal to zero, the size of the element does not change, 

 and hence the ratio between dQ and dB should equal p times the specific 

 heat at constant volume C„. We have therefore the relation 



p[Cp — Cv] = B[a:iXi + 02X2 + 0:3X3 + 04X4 + 0:5X5 + osXe]. (40) 



The relation between the adiabatic and isothermal elastic constants Cij 

 thus becomes 



c'j = cl + ^'. (41) 



Since the difference between the adiabatic and isothermal constants is so 

 small, no differentiation will be made between them in the following sections. 



2. Expression for The Elastic, Piezoelectric, Pyroelectric and 

 Dielectric Relations of a Piezoelectric Crystal 



When a crystal is piezoelectric, a potential energy is stored in the crystal 

 when a voltage is applied to the crystal. Hence the energy expressions of 

 (31) requires additional terms to represent the increment of energy dl'. 

 If we employ C(iS units which have so far been most widely used, as applied 



