Abstract
The coexistence pressure of two phases is a well-defined point at fixed temperature. In experiment, however, due to non-hydrostatic stresses and a stress-dependent potential energy barrier, different measurements yield different ranges of pressure with a hysteresis. Accounting for these effects, we propose an inequality for comparison of the theoretical value to a plurality of measured intervals. We revisit decades of pressure experiments on the bcc - hcp transformations in iron, which are sensitive to non-hydrostatic conditions and sample size. From electronic-structure calculations, we find a bcc - hcp coexistence pressure of 8.4 GPa. We construct the equation of state for competing phases under hydrostatic pressure, compare to experiments and other calculations, and address the observed pressure hysteresis and range of onset pressures of the nucleating phase.
Highlights
Knowledge of the equation of state is crucially important in materials science and engineering, metallurgy, geophysics, and planetary sciences
Zou et al.[4] used solid He as the pressure medium in their diamond AC (DAC) experiments on iron (99.95 wt.% Fe) powder pressed into a plate and on a folded section of a 10 micron foil; they pointed at the uniform non-hydrostatic stress as a possible cause of differing data
Because hcp does not exist below Psαt→ arεt and Peεn→dα, these values should not be affected by the martensitic stress in hcp, and can be used in the proper comparison to experiment
Summary
Knowledge of the equation of state is crucially important in materials science and engineering, metallurgy, geophysics, and planetary sciences. Equilibrium coexistence of phases during a pressure-induced martensitic transformation is extremely difficult to realize experimentally, and most shock and anvil cell experiments contain various amounts of a non-hydrostatic, anisotropic stress. Iron transforms to the ε-phase with hexagonal close-packed (hcp) structure of higher density that is non-magnetic or weakly anti-ferromagnetic. This transformation is martensitic,[3] and the bcc-hcp equilibrium coexistence pressure is difficult to determine unambiguously experimentally (Table 1). Bassett and Huang[6] applied a non-hydrostatic pressure with an uncontrolled shear strain (known to produce pressure self-multiplication)[175] and confirmed an atomic mechanism[5] of the bcc-hcp transition, but omitted discussion of changes in volume and magnetization in their shear-shuffle model. Zou et al.[4] used solid He as the pressure medium in their diamond AC (DAC) experiments on iron (99.95 wt.% Fe) powder pressed into a plate and on a folded section of a 10 micron foil; they pointed at the uniform non-hydrostatic stress as a possible cause of differing data
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