MATHEMATICS OF PHYSICAL PROPERTIES OF CRYSTALS 39 



SECTION 12 



The Converse Piezo-electric Effect 



A stress X causes an electric induction 



D = dX (11.2) 



and a strain 



e = SX (8.7) 



If the charge is allowed to leak away a further strain occurs, at constant 

 stress. This is the strain that would be gotten if the stress were originally 

 applied with surfaces rendered conducting: 



e° = S°X (12.1) 



In the first sort of stress, the work per unit volume done on the crystal by 

 establishing the stress X is: 



W = hXce = hXcSX (8.4) 



The energy stored electrically in the medium is: 



We = 2TrDck~'D (12.2) 



while the work done on a conducting crystal is: 



W° = hXcS°X (12.3) 



If a crystal be stressed in its insulated state by expenditure of energy W, 

 the charges then absorbed by an external circuit taking up energy We , 

 the strain changes from e to e° at constant stress so that the stresses perform 

 additional work 



Wa = Xc(e° - e) ^ X,{S° - S)X 



and the crystal is left containing energy W°. Whence 



W° ^ W - We-\- Wa (12.4) 



or: 



^XcS°X = iXcSX - 2TDck~'D + XoiS° - S)X 



so that: 



Xc{S° - S)X = ^TDck~'D 



If we substitute D — dX we find 



Xc{S° - S)X = ^TrXcdck~'dX 



