Effective charges and piezoelectricity

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Abstract
The effective charge for piezoelectricity is calculated using the bond-orbital model and Martin's internal-displacement parameters. Direct and simple calculations made with no additional parameters lead to a semiquantitative description of this effect. The qualitatively different trend with polarity shown by this charge and by the macroscopic transverse effective charge is elucidated. It is noted that this approach is essentially equivalent to the approach used by Lannoo and Decarpigny in studying the transverse effective charge, but is very different from the approaches used in other current studies of effective charges.