TY - JOUR
T1 - Quasiharmonic elastic constants corrected for deviatoric thermal stresses
AU - Carrier, Pierre
AU - Justo, João F.
AU - Wentzcovitch, Renata M
PY - 2008/10/21
Y1 - 2008/10/21
N2 - The quasiharmonic approximation (QHA), in its simplest form also called the statically constrained (SC) QHA, has been shown to be a straightforward method to compute thermoelastic properties of crystals. Recently we showed that for noncubic solids SC-QHA calculations develop deviatoric thermal stresses at high temperatures. Relaxation of these stresses leads to a series of corrections to the free energy that may be taken to any desired order, up to self-consistency. Here we show how to correct the elastic constants obtained using the SC-QHA. We exemplify the procedure by correcting to first order the elastic constants of MgSiO3 perovskite and MgSiO3 postperovskite, the major phases of the Earth's lower mantle. We show that this first-order correction is quite satisfactory for obtaining the aggregated elastic averages of these minerals and their velocities in the lower mantle. This type of correction is also shown to be applicable to experimental measurements of elastic constants in situations where deviatoric stresses can develop, such as in diamond-anvil cells.
AB - The quasiharmonic approximation (QHA), in its simplest form also called the statically constrained (SC) QHA, has been shown to be a straightforward method to compute thermoelastic properties of crystals. Recently we showed that for noncubic solids SC-QHA calculations develop deviatoric thermal stresses at high temperatures. Relaxation of these stresses leads to a series of corrections to the free energy that may be taken to any desired order, up to self-consistency. Here we show how to correct the elastic constants obtained using the SC-QHA. We exemplify the procedure by correcting to first order the elastic constants of MgSiO3 perovskite and MgSiO3 postperovskite, the major phases of the Earth's lower mantle. We show that this first-order correction is quite satisfactory for obtaining the aggregated elastic averages of these minerals and their velocities in the lower mantle. This type of correction is also shown to be applicable to experimental measurements of elastic constants in situations where deviatoric stresses can develop, such as in diamond-anvil cells.
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U2 - 10.1103/PhysRevB.78.144302
DO - 10.1103/PhysRevB.78.144302
M3 - Article
AN - SCOPUS:55349136270
SN - 1098-0121
VL - 78
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 14
M1 - 144302
ER -