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The Direct and Indirect Effect
The pyroelectric, when below the Curie point, has a spontaneous
polarisation. This polarisation
is dependent upon temperature.
If only considering the direct effect, i.e. assuming there
is no thermal expansion, then as the temperature increases, the polarisation
usually decreases.
Polarisation
T
Total Polarisation
As the temperature increases, the direct polarisation decreases
as usual, but the volume also increases and provides the increased indirect
polarisation seen.
Indirect polarisation increases overall polarisation
Polarisation
T
Total Polarisation
The assumption made in this examination is that as the temperature
increases, the indirect polarisation also increases. This is based on
the assumption that:
dP/dT = (dP/dσ)*(dσ/dε)*(dε/dT)
Since all three of these terms are typically positive, then it is a
reasonable assumption that as the temperature increases, the
change in polarisation due to the indirect effect is also positive.
Overall, remember that the direct effect is normally negative, and
the indirect effect can be positive or negative. The indirect effect
is only relevant if the material is free to deform.
dP/dT = (dP/dσ)*(dσ/dε)*(dε/dT)
Since all three of these terms are typically positive, then it is a
reasonable assumption that as the temperature increases, the
change in polarisation due to the indirect effect is also positive.
Overall, remember that the direct effect is normally negative, and
the indirect effect can be positive or negative. The indirect effect
is only relevant if the material is free to deform.