Coexistence pressure for a martensitic transformation from theory and experiment: Revisiting the bcc-hcp transition of iron under pressure

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.

Magneto-structural transformations via a solid-state nudged elastic band method: Application to iron under pressure

“…2(a) in Ref. 6. We have verified that at P 0 the enthalpy of each image on the hcp side of the MEP is the same (within DFT error) for the NM and AFM solutions (including those in larger supercells) and must remain the same at larger densities at P > P 0 , where the hcp is more stable than bcc.…”

“…We have verified that at P 0 the enthalpy of each image on the hcp side of the MEP is the same (within DFT error) for the NM and AFM solutions (including those in larger supercells) and must remain the same at larger densities at P > P 0 , where the hcp is more stable than bcc. 6 Hence, at P ≥ P 0 , validity of our SSNEB results extends from NM to AFM hcp phase with the same enthalpy landscape at these pressures.…”

“…6 However, at higher densities at P ≥ P 0 , the enthalpy (and local moments) difference between the AFM and NM hcp solutions disappear, see Fig. 2(a) in Ref.…”

“…4 bottom). At the equilibrium coexistence pressure P 0 = 8.42 GPa, where bcc and hcp phases have equal enthalpies, 6 the calculated enthalpy of the TS is 156 meV/atom above the terminal states.…”

“…Deeper understanding of its properties under pressure affects metallurgy, materials science and engineering, geophysics, and planetary sciences. 6 Due to its importance, the iron body-centered cubic (bcc)-hexagonal close-packed (hcp) (α-ε) transition and its mechanism have long been studied. In spite of iron's structural simplicity under pressure, the minimum-energy pathway (MEP) and the TS remained unresolved, in particular, because a) Electronic addresses: zarkev@ameslab.gov and ddj@ameslab.gov of the improper handling of magnetic DoF and expectation of saddle point behavior near the TS.…”