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

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<θ<90^∘ 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 (θₘᵢₙ<θ<θₘₐₓ), W diverges as the melting temperature is approached from below, corresponding to a purely repulsive disjoining potential, while for GBs outside this range (θ<θₘᵢₙ or θₘₐₓ<θ<90^∘) 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 ε of the PFC model is matched to liquid structure factor properties. However, it agrees well with MD simulations with a lower ε value chosen to match the ratio of bulk modulus and solid-liquid interfacial free energy, consistent with the amplitude-equation prediction that θₘᵢₙ and 90^∘-θₘₐₓ scale as ~ε1/2. 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 θ 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/TM≥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)].