Phase-field modeling of grain-boundary premelting using obstacle potentials

Surface induced melting of long Al nanowires: phase field model and simulations for pressure loading and without it

In this paper, melting of long Al nanowires is studied using a phase field model in which deviatoric transformation strain described by a kinetic equation produces a promoting driving force for both melting and solidification and consequently, a lower melting temperature is resolved. The coupled system of the Ginzburg-Landau equation for solidification/melting transformation, the kinetic equation for the deviatoric transformation strain and elasticity equations are solved using the COMSOL finite element code to obtain the evolution of melt solution. A deviatoric strain kinetic coefficient is used which results in the same pressure as that calculated with the Laplace equation in a solid neglecting elastic stresses. The surface and bulk melting temperatures are calculated for different nanowire diameters without mechanical loading which shows a good agreement with existing MD and analytical results. For radiiR> 5 nm, a complete surface solid-melt interface is created which propagates to the center. For smaller radii, premelting occurs everywhere starting from the surface and the nanowire melts without creating the interface. The melting rate shows an inverse power relationship with radius forR< 15 nm. For melting under pressure, the model with constant bulk modulus results in an unphysical parabolic variation versus pressure in contrast to the almost linear increase of the melting temperature versus pressure from known MD simulations. Such drawback is resolved by considering the pressure dependence of the bulk modulus through the Murnaghan's equation due to which an almost linear increase of the melting temperature versus pressure is obtained. Also, a reduction of the interface width and a significant increase of the melting rate versus pressure are found. The presented model and results allow for a better understanding of the premelting and melting of different metallic nanowires with various loading conditions and structural defects.

Superheating of grain boundaries within bulk colloidal crystals

Whether grain boundaries (GBs) premelt is a longstanding question, because of the difficulty of direct experimental tests. Here, we focused an optical beam to locally heat single GBs within bulk hard-sphere colloidal crystals, observing the melting dynamics at single-particle resolution by video microscopy. The melting point is determined by analysing both the Lindemann parameter and the critical nucleus size for homogeneous nucleation. We found that all the GBs, including the high-energy GBs, can be superheated and melt via a heterogeneous nucleation mechanism. Based on the classical nucleation theory of GBs, we measured the incubation time and contact angle of the critical nucleus to compute all relevant kinetic factors, as well as the energy barrier, nucleation rate and the diffusion coefficient at the solid–liquid interface under weak superheating. The superheat limits of GBs with various misorientations have also been measured to further explore the instability mechanism. Under traditional uniform heating, premelting occurs only at triple junctions, whereas GBs retain their original structures up to the melting point. The premelted regions at triple junctions further interrupt high-energy GBs from superheating, through intrusion by uniform liquid layers. Overall, our experiments confirm the existence of superheating of GBs.

Understanding the dynamics of grain boundaries and their melting behaviour is important for controlling the mechanical properties of materials. Now, experiments show that grain boundaries can be superheated, and that they melt via a nucleation mechanism.

Geometry of Triple Junctions during Grain Boundary Premelting

Grain boundaries (GBs) whose energy is larger than twice the energy of the solid-liquid interface exhibit the premelting phenomenon, for which an atomically thin liquid layer develops at temperatures slightly below the bulk melting temperature. Premelting can have a severe impact on the structural integrity of a polycrystalline material and on the mechanical high-temperature properties, also in the context of crack formation during the very last stages of solidification. The triple junction between a dry GB and the two solid-liquid interfaces of a liquid layer propagating along the GB cannot be defined from macroscopic continuum properties and surface tension equilibria in terms of Young's law. We show how incorporating atomistic scale physics using a disjoining potential regularizes the state of the triple junction and yields an equilibrium with a well-defined microscopic contact angle. We support this finding by dynamical simulations using a multiphase field model with obstacle potential for both purely kinetic and diffusive conditions. Generally, our results should provide insights on the dynamics of GB phase transitions, of which the complex phenomena associated with liquid metal embrittlement are an example.

Grain boundary-induced premelting and solid ↔ melt phase transformations: effect of interfacial widths and energies and triple junctions at the nanoscale

The strong effect of dry grain boundary (GB) and isolated solid-melt interface widths and energies and the triple junction energy on GB-induced premelting and the transformations between solid, premelt, and melt at the nanoscale are studied using a thermodynamically consistent original phase field approach of Ginzburg-Landau type. One order parameter is considered for describing solid ↔ melt transformation and another N- 1 independent order parameters are used to describe N grains in the samples. A variable energy of the GB regions is assumed which depends on the order parameter related to solid ↔ melt transformation, and the energy of the GBs reduces from their dry state energy γ_gb in solid to zero at melt. The complex 'phase diagrams', showing the variation of the transformation temperatures with the non-dimensional width ratio (ratio of dry GB width and isolated solid-melt interface width), are plotted for 2D bicrystals with a planar GB and a circular GB for the cases when (i) solid-melt interface width is fixed and GB width varies, and (ii) GB width is fixed and solid-melt interface width varies. A bistable region, where the premelt spontaneously appears or transforms back to the solid, is shown indicating that these transformations accompany hysteresis. The effect of the width ratio on the effective melt layer thickness and the disjoining potential between the solid-melt interfaces on premelting/melting is also studied. The effect of triple junctions on the transformations is studied in tricrystals having three planar GBs meeting at the interior of the sample with equal dihedral angles. A premelt/melt pocket appears at the junction in a jump-like manner at temperatures significantly lower than the temperatures at which the GBs premelt. The premelt/melt that appeared at the junction eventually wets the adjacent GBs, and finally, the entire sample melts at the melting point. The results show a plausible reason for differences in the premelting and melting temperature ranges of the GBs observed in various experimental and atomistic studies.

Dynamics of grain boundary premelting

The mechanical strength of a polycrystalline material can be drastically weakened by a phenomenon known as grain boundary (GB) premelting that takes place, owing to the so-called disjoining potential, when the dry GB free energy [Formula: see text] exceeds twice the free energy of the solid-liquid interface [Formula: see text]. While previous studies of GB premelting are all limited to equilibrium conditions, we use a multi-phase field model to analyze premelting dynamics by simulating the steady-state growth of a liquid layer along a dry GB in an insulated channel and the evolution of a pre-melted polycrystalline microstructure. In both cases, our results reveal the crucial influence of the disjoining potential. A dry GB transforms into a pre-melted state for a grain-size-dependent temperature interval around [Formula: see text], such that a critical overheating of the dry GBs over [Formula: see text] should be exceeded for the classical melting process to take place, the liquid layer to achieve a macroscopic width, and the disjoining potential to vanish. Our simulations suggest a steady-state velocity for this transformation proportional to [Formula: see text]. Concerning the poly-crystalline evolution, we find unusual grain morphologies and dynamics, deriving from the existence of a pre-melted polycrystalline equilibrium that we evidence. We are then able to identify the regime in which, due to the separation of the involved length scales, the dynamics corresponds to the same curvature-driven dynamics as for dry GBs, but with enhanced mobility.