Energetics of bcc-fcc lattice deformation in iron

The energetics of homogeneous bcc-fcc lattice deformation in iron at 0 K has been investigated along the tetragonal Bain deformation path. The total energy (as a function of volume), the enthalpy (as a function of pressure), the pressure-volume relations both for nonmagnetic (NM) and ferromagnetic (FM) states were calculated using the linear muffin-tin-orbital (LMTO) method. The ground-state magnetic properties (ferromagnetic contributions to the total energy and magnetic moments) were found by making use of the Stoner theory of itinerant ferromagnetism, rather than spin-polarized calculations. This circumvents the difficulties of using the traditional local-spin-density approximation which fails to describe correctly the energetics of iron phases. The Stoner exchange parameter I was calculated from the linear-response theory for each axial ratio c/a as a function of volume and then adjusted by a constant enhancement factor, determined by fitting the equilibrium atomic volume of the FM bcc phase. No other adjustments of any quantities were performed. The calculations revealed a somewhat unusual behavior of enthalpy along the deformation path. The enthalpy of the NM phase exhibits a monotonic decrease with c/a, the bcc modification being unstable with respect to the shear deformation. Moreover, up to a certain c/a (depending on pressure), the NM bcc phase is also unstable with respect to spontaneous magnetization. Ferromagnetism stabilizes the bcc phase. However, the FM fcc phase is unstable with respect to shear deformation. The enthalphy curve along the deformation path then has a cusp corresponding to a first-order phase transition between FM and NM states accompanied by an appreciable volume discontinuity. For the FM bcc, the calculated bulk modulus (1.689 mbar) and the magnetic moment (2.223B/atom) as well as the fcc-bcc enthalpy difference at zero pressure (6.947 kJ/mol) are in good agreement with available experimental data. A fcc-bcc lattice-deformation enthalpy barrier at the equilibrium pressure P0=145 kbar is found to be 12.762 kJ/mol. The NM fcc lattice loses mechanical stability at a fcc-bcc enthalpy difference of -14.072 kJ/mol. As an aid to the development of improved interatomic potentials for iron, plots of FM contributions to the energy versus Wigner-Seitz radius for different c/a are also presented.