Phase-field-crystal study of grain boundary premelting and shearing in bcc iron

Abstract

We use the phase-field-crystal (PFC) method to investigate the equilibrium premelting and nonequilibrium shearing behaviors of $[001]$ symmetric tilt grain boundaries (GBs) at high homologous temperature over the complete range of misorientation $0<\hat{I}¸<90^{\circ }$ in classical models of bcc Fe. We characterize the dependence of the premelted layer width $W$ as a function of temperature and misorientation and compute the thermodynamic disjoining potential whose derivative with respect to $W$ represents the structural force between crystal-melt interfaces due to the spatial overlap of density waves. The disjoining potential is also computed by molecular dynamics (MD) simulations, for quantitative comparison with PFC simulations, and coarse-grained amplitude equations (AE) derived from PFC that provide additional analytical insights. We find that, for GBs over an intermediate range of misorientation ($\hat{I}{¸}_{\min }<\hat{I}¸<\hat{I}{¸}_{\max }$), $W$ diverges as the melting temperature is approached from below, corresponding to a purely repulsive disjoining potential, while for GBs outside this range ($\hat{I}¸<\hat{I}{¸}_{\min }$ or $\hat{I}{¸}_{\max }<\hat{I}¸<90^{\circ }$), $W$ remains finite at the melting point, with its value corresponding to a shallow attractive minimum of the disjoining potential. In response to a shear stress parallel to the GB plane, GBs in PFC simulations exhibit coupled motion normal to this plane, with a discontinuous change of the coupling factor as a function of $\hat{I}¸$ that reflects a transition between two coupling modes, and/or sliding (shearing of the two grains). The coupling factor for the two coupling modes is in excellent quantitative agreement with previous theoretical predictions [J. W. Cahn, Y. Mishin, and A. Suzuki, Acta Mater. 54, 4953 (2006)].