Monte Carlo calculations of the effective shear modulus of a polycrystalline bcc Coulomb solid were
performed by Ogata & Ichimaru [309]. The deformation energy, resulting from the application of a specific
strain
, was evaluated through Monte Carlo sampling.
As we have already mentioned, for an ideal cubic crystal lattice there are only three independent elastic
moduli, denoted traditionally as ,
and
(see Chapter 3, pp. 80 – 87 of the book by
Kittel [241
]). For pure shear deformation, only two independent elastic moduli are relevant,
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The definition of an “effective” shear modulus of a bcc polycrystal deserves a comment. In
numerous papers, a standard preferred choice was ([43, 319, 285
], and references
therein). However, replacing
by a single maximal elastic modulus of a strongly anisotropic bcc
lattice is not correct. An effective value of
was calculated by Ogata & Ichimaru [309]. They
performed directional averages over rotations of the Cartesian axes. At
, they obtained
The formula for , Equation (116
), can be rewritten as
Let us remember that the formulae given above hold for the outer crust, where the size of the nuclei is
very small compared to the lattice spacing and . For the inner crust these formulae are only
approximate.
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