International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D, ch. 1.1, p. 32

Section 1.1.5.4. Adiabatic study

A. Authiera*

aInstitut de Minéralogie et de la Physique des Milieux Condensés, Bâtiment 7, 140 rue de Lourmel, 75015 Paris, France
Correspondence e-mail: aauthier@wanadoo.fr

1.1.5.4. Adiabatic study

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Piezoelectric resonators usually operate at a high frequency where there are no heat exchanges, and therefore in an adiabatic regime [(\Theta \delta \sigma = 0)]. From the third equation of (1.1.5.1)[link], we obtain a relation between the temperature variation, the applied stress and the electric field: [(\alpha _{ij})^E T_{ij} + (p_{m})^T E_{m} + {\rho C^{T,E} \over \Theta} \delta \Theta = 0.]

If we substitute this relation in the two other relations of (1.1.5.1)[link], we obtain two equivalent relations, but in the adiabatic regime: [\eqalignno{S_{kl} &= \left(s_{kl ij}\right)^{E,\sigma} T_{ij} + \left(d_{kl m}\right)^{T,\sigma} E_m\cr D_{n} &= \left(d_{nij}\right)^{E,\sigma} T_{ij} + \left(\varepsilon_{nm}\right)^{T,\sigma} E_m.\cr}]By comparing these expressions with (1.1.5.1)[link], we obtain the following relations between the adiabatic and the isothermal coefficients: [\eqalignno{(s_{ijkl})^{E,\sigma} &= (s_{ijkl})^{E,\theta} - {(\alpha_{ij})^E (\alpha_{kl})^E \Theta \over \rho C^{T,E}}\cr (d_{nij})^{E,\sigma} &= (d_{nij})^{E,\theta} - {(p_{n})^T (\alpha_{kl})^E \Theta \over \rho C^{T,E}}\cr (\varepsilon_{mn})^{T,\sigma} &= (\varepsilon_{mn})^{T,\theta} - {(p_{n})^T (p_{m})^T \Theta \over \rho C^{T,E}}.\cr}]








































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