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 < 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 ǫ of the PFC model is matched to liquid structure factor properties. However it agrees well with MD simulations with a lower ǫ 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 ∼ ǫ 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 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 [J. W. Cahn, Y. Mishin, and A. Suzuki, Acta Mater. 54, 4953 (2006)].

Structural short-range forces between solid-melt interfaces

“…In this case, a full analytical calculation of the disjoining potential is not possible anymore and numerical investigations are needed 33 . Nevertheless, we have explained that the interaction then stems from higher order terms in the free energy functional, since the longest-range contributions from quadratic terms cancel.…”

Influence of short-range forces on melting along grain boundaries

“…A repulsive interaction, V (W ) < 0, typical for large misorientations, gives raise to grain boundary premelting, whereas attractive interactions, V (W ) > 0, stabilise a dry grain boundary. While combinations of these two cases with extrema in the disjoining potential can occur and result from the structure of V (W ) as being a superposition of exponentially decaying contributions with different ranges [3][4][5], we focus here on the elementary case of monotonic disjoining potentials.…”

“…Grain boundary premelting was investigated recently e.g. in [3][4][5][6], showing that for low misorientation an attractive interaction between adjacent solid-melt interfaces can stabilise a grain boundary. Recent investigations of heterogeneous nucleation of liquid droplets in overheated grain boundaries link the short range interactions to nucleation processes [7].…”

Nonlinear elastic effects in phase field crystal and amplitude equations: Comparison toab initiosimulations of bcc metals and graphene

“…For small deformations this energy change is quadratic, hence linear elasticity is captured, and for larger deformations non-linear effects appear 9,10 . Whereas the original PFC model is fully phenomenological, later extensions have shown that it can be linked to the classical density functional theory of freezing [11][12][13] , which allows to determine the model parameters from fundamental physical quantities, which can for example be determined from molecular dynamics simulations [14][15][16][17] . The obtained elastic constants can then be obtained from properties of the liquid structure factor and give reasonable estimates of the high temperature values near the melting point.…”