Phase-field-crystal calculation of crystal-melt surface tension in binary alloys

Phase diagrams and crystal-fluid surface tensions in additive and nonadditive two-dimensional binary hard-disk mixtures

Using density functionals from fundamental measure theory, phase diagrams and crystal-fluid surface tensions in additive and nonadditive (Asakura-Oosawa model) two-dimensional binary hard-disk mixtures are determined for the whole range of size ratios q=smalldiameter/largediameter, assuming random disorder (lattice points or interstitial occupied by large or small disks at random) in the crystal phase. The fluid-crystal transitions are first order due to the assumption of a periodic unit cell in the density-functional calculations. Qualitatively, the shape of the phase diagrams is similar to the case of three-dimensional hard-sphere mixtures. For the nonadditive case, a broadening of the fluid-crystal coexistence region is found for small q, whereas for large q a vapor-fluid transition intervenes. In the additive case, we find a sequence of spindle-type, azeotropic, and eutectic phase diagrams upon lowering q from 1 to 0.6. The transition from azeotropic to eutectic is different from the three-dimensional case. Surface tensions in general become smaller (up to a factor 2) upon addition of a second species and they are rather small. The minimization of the functionals proceeds without restrictions and optimized graphics card routines are used.

Incorporating Noise Quantitatively in the Phase Field Crystal Model via Capillary Fluctuation Theory

A tacit assumption underlying most phase field models of nonequilibrium phase transformations is that of scale separation. Stochastic order parameter field theories utilize noise to separate atomic-scale fluctuations from the slowly varying fields that describe microstructure patterns. The mesoscale distribution of such stochastic variables is generally assumed to follow Gaussian statistics, with their magnitude following fluctuation-dissipation relations. However, there is still much debate about how atomic-scale fluctuations map onto the mesoscale upon coarse graining of microscopic theories. This Letter studies interface fluctuations in the phase field crystal (PFC) model and proposes a self-consistent method for relating how the effective noise strength and spectral filtering of the noise in the PFC model, and similar types of microscopic models, should be defined so as to attain the spectrum of mesoscale capillary fluctuations quantitatively.

Scaling of alloy interfacial properties under compositional strain

Complex morphologies and microstructures that emerge during materials growth and solidification are often determined by both equilibrium and kinetic properties of the interface and their crystalline anisotropies. However, limited knowledge is available on alloying and, particularly, compositionally generated elastic effects on these interface characteristics. Here we systematically investigate such compositional effects on the interfacial properties of an alloy model system based on a phase-field-crystal analysis, including the solid-liquid interfacial free energy, kinetic coefficient, and lattice pinning strength. Scaling relations for these interfacial quantities over various ranges of material parameters are identified and predicted. Our results indicate the important effects of couplings among mesoscopic and microscopic length scales of alloy structure and concentration, and the influence of compressive and tensile interface stresses induced by composition variations. The approach developed here provides an efficient way to systematically identify these key material properties beyond the traditional atomistic and continuum methods.

Calculating the role of composition in the anisotropy of solid-liquid interface energy using phase-field-crystal theory

This work uses Ginzburg-Landau theory derived from a recent structural phase-field-crystal model of binary alloys developed by the authors to study the roles of concentration, temperature, and pressure on the interfacial energy anisotropy of a solid-liquid front. It is found that the main contribution to the change in anisotropy with concentration arises from a change in preferred crystallographic orientation controlled by solute-dependent changes in the two-point density correlation function of a binary alloy, a mechanism that leads to such phenomena as solute-induced elastic strain and dislocation-assisted solute clustering. Our results are consistent with experimental observations in recent studies by Rappaz et al. [J. Fife, P. Di Napoli, and M. Rappaz, Metall. Mater. Trans. A 44, 5522 (2013)]. This is the first PFC work, to our knowledge, to incorporate temperature, pressure, and density into the thermodynamic description of alloys.

Phase-field-crystal model of phase and microstructural stability in driven nanocrystalline systems

We present a phase-field-crystal model for driven systems which describes competing effects between thermally activated diffusional processes and those driven by externally imposed ballistic events. The model demonstrates how the mesoscopic Enrique and Bellon [Phys. Rev. Lett. 84, 2885 (2000)] model of externally induced ballistic mixing can be incorporated into the atomistic phase-field-crystal formalism. The combination of the two approaches results in a model capable of describing the microstructural and compositional evolution of a driven system while incorporating elastoplastic effects. The model is applied to the study of grain growth in nanocrystalline materials subjected to an external driving.