MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 47 



initial state. Equating the sum of the strains to zero we find (ga — gi) 

 E = As<pE or 



ga - gi = As<p (14.5) 



Let the initial state of a crystal be, temperature — to, stress, strain and 

 field = 0. If the (electrically insulated) crystal is heated by amount /, 

 a strain Ail is caused and also an electric displacement D = pt. There now 

 exists an electric field E — rirhT pt. Let this field be discharged at con- 

 stant temperature, giving a further strain of g,£ — AirgikT pt. The crystal 

 is now short-circuited and if the initial temperature is restored a strain 

 — Agt follows. The crystal is now in its initial state. If we equate the 

 sum of the strains to zero we find : 



Ai- A ^ iwgik-'p (14.6) 



SECTION 15 



The Thermo-Electric Effect in Crystals 



It should be possible for an electric field to be set up by a temperature 

 gradient. Let us assume that the vector T is the temperature gradient and 

 is related to the vector field E through the matrix 11 by means of the equa- 

 tion: 



/Un Tin HisX 

 E = UT where n = I Hsi Hss Hos 1 (15.1) 



\n3i n32 uj 



Examination shows that 11 transforms through 



n' = aUac (15.2) 



For Class 1 the 11 matrix has the 9 terms of (15.1). Class 2 has a center of 

 symmetry. For a center of symmetry a — —I but a = —I causes no 

 change in (15.2) so that class 2 has 9 constants. The thermo electro effect 

 is not killed by the presence of a center of symmetry. The ordinary thermo- 

 electric effect of metals is a case in point. 



If .Vs is a binary axis a = I — 1 J and 11 reduces to 



/Hu ni2 \ 



11 = I Hsi n22 ) (15.3) 



\0 uj 



Examination shows this form to answer for classes 3 and 4 and 5. 



