MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 45 



uniform temperature /o to the uniform temperature to -]- t the pyro-electric 

 effect could be described by the equation: 



(i)^^© ''■' 



where p is the pyro-electric matrix. 



This can be approached in another way by considering the polarization 

 as due to the uniform strain. We may hence write, since X — Ce: (i.e . 

 stress matrix = elastic constant matrix times the strain matrix) 



P ^ dX = dCe 



where e is the strain brought about by the temperature change /. If 



/Ai \ 

 ^=10 .42 I is the temperature expansion matrix we have: 



idC 



Now since d has 3 rows and the A matrix has but one column the product 

 dCA has 3 rows and one column so that we may define p as dCA. 

 ' As D oi D = tp transforms by D' — aD, so does p: 



p' = ap 



When a center of symmetry exists a permitted transformation is a = — /, 

 whence p = — p' = — p so that p = 0. No pyro-electric efifect (on this 

 theory) could exist for a crystal with a center of symmetry. 



If a binary axis exists and is chosen as .T3 we have 



P= (0 1 (14.2) 



If another binary axis exists at right angles to this one we find p = 0. 



