Phase-field crystal study of grain-boundary premelting

By Jesper Mellenthin, Alain Karma, Mathis Plapp. 2008

184 citations recorded by the source corpus.

We study the phenomenon of grain-boundary premelting for temperatures below the melting point in the phase-field crystal model of a pure material with hexagonal ordering in two dimensions. We investigate the structures of symmetric tilt boundaries as a function of misorientation $\ensuremath{\theta}$ for two different inclinations and compute in the grand canonical ensemble the ``disjoining potential'' $V(w)$ that describes the fundamental interaction between crystal-melt interfaces as a function of the premelted layer width $w$, which is defined here in terms of the excess mass of the grain boundary via a Gibbs construction. The results reveal qualitatively different behaviors for high-angle grain boundaries that are uniformly wetted, with $w$ diverging logarithmically as the melting point is approached from below, and low-angle boundaries that are punctuated by liquid pools surrounding dislocations, separated by solid bridges. The latter persist over a superheated range of temperature. This qualitative difference between high- and low-angle boundaries is reflected in the $w$ dependence of the disjoining potential that is purely repulsive [${V}^{\ensuremath{'}}(w)l0$ for all $w$] for misorientations larger than a critical angle ${\ensuremath{\theta}}_{c}$, but switches from repulsive at small $w$ to attractive at large $w$ for $\ensuremath{\theta}l{\ensuremath{\theta}}_{c}$. In the latter case, $V(w)$ has a minimum that corresponds to a premelted boundary of finite width at the melting point. Furthermore, we find that the standard wetting condition ${\ensuremath{\gamma}}_{\text{gb}}({\ensuremath{\theta}}_{c})=2{\ensuremath{\gamma}}_{\text{sl}}$ gives a much too low estimate of ${\ensuremath{\theta}}_{c}$ when a low-temperature value of the grain-boundary energy ${\ensuremath{\gamma}}_{\text{gb}}$ is used. In contrast, a reasonable lower-bound estimate can be obtained if ${\ensuremath{\gamma}}_{\text{gb}}$ is extrapolated to the melting point, taking into account both the elastic softening of the material at high homologous temperature and local melting around dislocations.

Subfields: Atmospheric Science, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/2fb7ee18558a28e13a8bcb931c63f733568ee41c

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Citations in the corpus

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview (2012, background): “Phenomena References Liquid-solid transition: – dendrites [26–30] – eutectics [26, 28, 29, 31] – homogeneous nucleation [28, 30–33] – heterogeneous nucleation [30, 31, 34, 35] – grain-boundary melting [36, 37] – fractal growth [38, 39] – crystal anisotropy [33, 38, 40–44] – density/solute trapping [”
Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation (2009, methodology): “[11] proposed a pseudo-spectral scheme in which an integrating factor method, based on the linear terms, is used in Fourier space.”
Progress in modelling solidification microstructures in metals and alloys. Part II: dendrites from 2001 to 2018 (2020, background): “As shown in several studies of pre-melting using phase-ﬁ eld crystal [306], molecular dynamics [307] and density functional theory [303], as well as in studies of coalescence and shearing of grain-bound-aries [308], Equation (6) is too simple to capture all the phenomena occurring during melting at…”
Ice structures, patterns, and processes: A view across the icefields (2012, background): “For a range of materials and interaction potentials, grain-boundary disorder has been theoretically and numerically modeled (e.g., Broughton and Gilmer, 1986; Mellenthin et al., 2008; Schick and Shih, 1987).”
Coupled motion of asymmetrical tilt grain boundaries: molecular dynamics and phase field crystal simulations (2012, methodology): “In particular, it predicts reasonable values of GB energies [42] and has been able to reproduce the phenomenon of GB premelting [38, 39] as well as non-trivial structural transitions at GBs at high homologous temperatures [44].”