Phase-field-crystal study of grain boundary premelting and shearing in bcc iron
A Adland and A Karma and R Spatschek and D Buta and M Asta, PHYSICAL REVIEW B, 87, 024110 (2013).
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 <. theta < 90 degrees in classical models of bcc Fe. We characterize the dependence of the premelted layer width W as a function of temperature and misorientation. In addition, we 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 (theta(min) < theta < theta(max)), W diverges as the melting temperature is approached from below, corresponding to a purely repulsive disjoining potential, while for GBs outside this range (theta < theta(min) or theta(max) < theta < 90 degrees) W remains finite at the melting point. In the latter case, W corresponds to a shallow attractive minimum of the disjoining potential. The misorientation range where W diverges predicted by PFC simulations is much smaller than the range predicted by MD simulations when the small dimensionless parameter epsilon of the PFC model is matched to liquid structure factor properties. However, it agrees well with MD simulations with a lower epsilon value chosen to match the ratio of bulk modulus and solid-liquid interfacial free energy, consistent with the amplitude-equation prediction that theta(min) and 90 degrees - theta(max) scale as similar to epsilon(1/2). The incorporation of thermal fluctuations in PFC is found to have a negligible effect on this range. In response to a shear stress parallel to the GB plane, GBs in PFC simulations exhibit coupled motion normal to this plane or sliding. Furthermore, the coupling factor exhibits a discontinuous change as a function of. that reflects a transition between two coupling modes. Sliding is only observed over a range of misorientation that is a strongly increasing function of temperature for T/T-M >= 0.8 and matches roughly the range where W diverges at the melting point. The coupling factor for the two coupling modes is in excellent quantitative agreement with previous theoretical predictions Cahn, Mishin, and Suzuki, Acta Mater. 54, 4953 (2006). DOI: 10.1103/PhysRevB.87.024110
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