Theoretical strain-induced elastic anomalies in metals and alloys

The theoretical large-strain elastic response of crystals has long been a subject of interest. Although various atomic models have been used in a variety of theoretical computations, considerations that have largely been neglected are the anomalous stress and elastic moduli variations that occur when a Brillouin zone boundary is brought into contact with the Fermi surface as a result of deformation. The present work rationalises these occurrences for axial loadings of BCC and FCC crystals. Various pseudopotential model computations are carried out for the specific case of (100) uniaxial loading. With q a reciprocal lattice vector, kf the Fermi wavenumber, lambda 1 the axial stretch in (100) loading and z the valence, the results are summarised as plots of the 'critical value' of lambda 1 (i.e. lambda 1 at q=2kf) against z. Examples of pseudopotential model computations of the elastic moduli Cij of Al as q to 2kf are also presented.