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

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. D. ch. 1.3, pp. 82-83

Section 1.3.3.4.1. Volume compressibility

A. Authiera* and A. Zarembowitchb

a Institut de Minéralogie et de la Physique des Milieux Condensés, Bâtiment 7, 140 rue de Lourmel, 75015 Paris, France, and bLaboratoire de Physique des Milieux Condensés, Université P. et M. Curie, 75252 Paris CEDEX 05, France
Correspondence e-mail:  aauthier@wanadoo.fr

1.3.3.4.1. Volume compressibility

| top | pdf |

Let us apply a hydrostatic pressure (Section 1.3.2.5.2[link]). The medium undergoes a relative variation of volume [\Delta V/V = ] [S_{1} + S_{2} + S_{3}] (the cubic dilatation, Section 1.3.1.3.2[link]). If one replaces in (1.3.3.8)[link] the stress distribution by a hydrostatic pressure, one obtains for the components of the strain tensor[\eqalignno{S_{1} &= - p (s_{11} + s_{12} + s_{13}) &\cr S_{2} &= - p (s_{12} + s_{22} + s_{23}) &\cr S_{3} &= - p (s_{13} + s_{23} + s_{13}). &\cr} ]From this, we deduce the volume compressibility, [\chi], which is the inverse of the bulk modulus, κ: [\chi =\kappa^{-1} = - {1\over p} {\delta V \over V} = s_{11} + s_{22} + s_{33} + 2(s_{12} + s_{23} + s_{13}). \eqno(1.3.3.11) ]This expression reduces for a cubic or isotropic medium to [\chi = \kappa^{-1} = 3(s_{11} + 2s_{12}). \eqno(1.3.3.12)]








































to end of page
to top of page