Importance of Shear in the bcc-to-hcp Transformation in Iron

Abstract

Iron shows a pressure-induced martensitic phase transformation from the ground state ferromagnetic bcc phase to a nonmagnetic hcp phase at 13 GPa. The exact transformation pressure (TP) and pathway are not known. Here we present a multiscale model containing a quantum-mechanics-based multiwell energy function accounting for the bcc and hcp phases of Fe and a construction of kinematically compatible and equilibrated mixed phases. This model suggests that shear stresses have a significant influence on the bcc $ hcp transformation. In particular, the presence of modest shear accounts for the scatter in measured TPs. The formation of mixed phases also provides an explanation for the observed hysteresis in TP. Pressure-driven phase transformations are ubiquitous and important for understanding the mechanical response of materials. In particular, the ground state crystal structure of Fe, ferromagnetic body-centered cubic (bcc), undergoes a pressure-induced martensitic phase transformation to a hexagonally close-packed (hcp) structure at 13 GPa. The measured transformation pressure (TP) varies greatly [1][2][3]. Attempts to simulate this transformation via quantum mechanics [4][5][6][7][8], primarily density functional theory (DFT), have focused on relative phase stability, where the TP is approximated by the Gibbs construction of drawing the line of common tangent between equations of state of the pure bcc and hcp phases. Another DFT model [9] mapped out the energetics of a constrained transformation path between the pure phases, similar to earlier work on Ba [10]. None of these were able to explain the large range of measured TPs. Here, we present a multiscale model containing a first-principles DFT-based multiwell energy function accounting for bcc and hcp Fe and a construction of kinematically compatible and equilibrated mixed phases (laminates) to represent the complicated microstructures often observed in experiments.We confine our attention to transformations occurring at 0 K and therefore the governing principle is energy minimization. In particular, the formation of microstructure is driven purely by energetics. We assume the behavior of the material to be nonlinear elastic with energy density W

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Stabilization of bcc Mg in Thin Films at Ambient Pressure: Experimental Evidence andab initioCalculations

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