Based on the detailed ab initio calculations of electronic structure for hcp-zinc
and bcc-ferromagnetic iron, we made an attempt to study a scale of anomalies
emerging in the calculations of elastic properties of these crystals as functions
of pressure, and determine a relation between these anomalies and electronic
topological transitions. Our calculations give grounds to believe that an electronic
topological transition in itself is not a cause of significant anomalies in elastic
properties of crystals but is, probably, an indicator of rearrangement of the crystal
energy spectrum: an indicator which is not even always present. In some cases such
rearrangement can cause significant anomalies in elastic and other properties of the
crystal.
We have performed ab initio electronic structure and total-energy calculations for
bcc, fcc, and hcp Al structures to study the equations of state, volume
dependences of elastic constants, and relative stability diagram for these
structures. A technique for elastic constant calculation in the case of initial
isotropic pressure is presented. In this study we used the accurate full-potential
linear muffin-tin orbital method to describe electrons of the crystal and the Debye
treatment of the vibrating lattice. The volume dependence of the Debye
temperature is derived from the volume dependence of the elastic constants. Our
calculations show that at pressures of 1–2 Mbar and temperatures of about 1000
K and higher, the aluminium structure must have a lower symmetry than the
structures considered.
Two recently published ways of calculating the elastic constants for a crystal under hydrostatic pressure are compared. They are shown to be equivalent theoretically, though one is more convenient for numerical simulations. A crystal of ferromagnetic iron in the body-centred cubic structure is used as an example for comparing elastic constants calculated with these two methods.
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