46 BELL SYSTEM TECHNICAL JOURNAL 



This is seen seriously to limit the number of classes showing this kind of 

 pyro-electric effect. In fact we find p = for classes 2, 5, 6, 8, 9, 11, 12, 

 13, 15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 29, 30, 31 and 32. The expression 



-0 



describes the pyro-electric effect in the classes, 3, 7, 10, 14, 16, 20, 



23 and 26, while the expression p = I P2 I describes class 4, and only class 



^0 



1 is described by 



(14.3) 



It is to be noted then that this theory excludes many classes ordinarily 

 described as pyro-electric, such crystals as quartz in Class 18 for example. 

 Consequently it would seem that whether or not this effect exists we must 

 seek elsewhere for the explanation of the effect in quartz. 



The effect can easily be explained as due to non-uniform temperature, 

 which causes stress which in turn give rise to electric phenomena in piezo 

 active crystals. For example a suddenly chilled crystal has its outer layers 

 in a state of tension. This would produce just the pattern of positive and 

 negative charges that one actually observes. As to whether the first effect 

 exists, much argument between Lord Kelvin and others seems to have left 

 the question still uncertain. 



In pyro-electric crystals we would expect to find a difference in the piezo 

 constants measured isothermally or adiabatically. If a temperature 

 change t causes an electric displacement D = pt the application of an electric 

 field E should cause a temperature change / given by a relation such as: 



t = <pE (14.4) 



Also the temperature coefficient of expansion, Ag (for a crystal with faces 

 rendered conducting) would differ from the coefficient A i (for a crystal with 

 an insulated surface) . 



If a crystal at temperature /o has suddenly applied to it a field E the 

 temperature rises to /o + fE and the crystal strains, because of the converse 

 piezo effect, by amount e = gaE where ga is the adiabatic converse piezo 

 matrix. If the field is now removed isothermally a further strain giE 

 takes place. If the faces are short-circuited and the temperature restored 

 to /o a further strain Agt = As^pE takes place and the crystal is then in its 



1 



