Parameters for piezoelectric ceramics and their measurement

The discussion is now restricted to matters relevant to the technology of piezoceramics. If it is assumed that the quantities d, g, s, and s are constants and, furthermore, the tensor nature of the various parameters (see below) is not taken into account, then equations of state can be written as follows. 

Where sE, sD are the elastic compliances and the superscripts denote the parameters held constant similarly sx denotes the permittivity measured at constant stress (the usual condition) to measure the permittivity at constant strain ex is more difficult to accomplish. 

Because ferroelectric ceramics have non-linear characteristics the effects are more correctly described by the equations, 

It is understood that in all cases the temperature is maintained constant. 

The electromechanical coupling coefficient (k) is a measure of the ability of a piezoelectric material to transform mechanical energy into electrical energy, and vice versa. It is defined [5] by 

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