We present an extension of the semi-grand-canonical (SGC) ensemble that we refer to as the variance-constrained semi-grand-canonical (VC-SGC) ensemble. It allows for transmutation Monte Carlo simulations of multicomponent systems in multiphase regions of the phase diagram and lends itself to scalable simulations on massively parallel platforms. By combining transmutation moves with molecular dynamics steps, structural relaxations and thermal vibrations in realistic alloys can be taken into account. In this way, we construct a robust and efficient simulation technique that is ideally suited for large-scale simulations of precipitation in multicomponent systems in the presence of structural disorder. To illustrate the algorithm introduced in this work, we study the precipitation of Cu in nanocrystalline Fe.

Microstructural evolution is a key aspect of understanding and exploiting the processing-structure-property relationship of materials. Modeling microstructure evolution usually relies on coarse-grained simulations with evolution principles described by partial differential equations (PDEs). Here we demonstrate that convolutional recurrent neural networks can learn the underlying physical rules and replace PDE-based simulations in the prediction of microstructure phenomena. Neural nets are trained by self-supervised learning with image sequences from simulations of several common processes, including plane-wave propagation, grain growth, spinodal decomposition, and dendritic crystal growth. The trained networks can accurately predict both short-term local dynamics and long-term statistical properties of microstructures assessed herein and are capable of extrapolating beyond the training datasets in spatiotemporal domains and configurational and parametric spaces. Such a data-driven approach offers significant advantages over PDE-based simulations in time-stepping efficiency and offers a useful alternative, especially when the material parameters or governing PDEs are not well determined.

We describe a technique for constraining macroscopic fluctuations in thermodynamic variables well-suited for Monte Carlo (MC) simulations of multiphase equilibria. In particular for multicomponent systems this amounts to a statistical ensemble that implements constraints on both the average composition as well as its fluctuations. The variance-constrained semi-grand-canonical (VC-SGC) ensemble allows for MC simulations, in which single-phase systems can be reversibly switched into multiphase equilibria allowing the calculation of excess free energies of precipitates of complex shapes by thermodynamic integration. The basic features as well as the scaling and convergence properties of this technique are demonstrated by an application to an Ising model. Finally, the VC-SGC MC simulation technique is used to calculate $\alpha /{\alpha }^{\prime }$ interface free energies in Fe-Cr alloys as a function of orientation and temperature taking into account configurational, vibrational, and structural degrees of freedom.

The thermodynamic stabilities of various phases of the nitrides of the platinum-metal elements are systematically studied using density functional theory. It is shown that for the nitrides of Rh, Pd, Ir, and Pt two new crystal structures, in which the metal ions occupy simple tetragonal lattice sites, have lower formation enthalpies at ambient conditions than any previously proposed structures. The region of stability with respect to those structures extends to 17 GPa for ${\mathrm{PtN}}_2$. Calculations show that the ${\mathrm{PtN}}_2$ simple tetragonal structures at this pressure are thermodynamically stable also with respect to phase separation. The fact that the local density and generalized gradient approximations predict different values of the absolute formation enthalpies as well different relative stabilities between simple tetragonal and the pyrite or marcasite structures are further discussed.

We conduct a detailed investigation of the polaron self-interaction (pSI) error in standard approximations to the exchange-correlation (XC) functional within density-functional theory (DFT). The pSI leads to delocalization error in the polaron wave function and energy, as calculated from the Kohn-Sham (KS) potential in the native charge state of the polaron. This constitutes the origin of the systematic failure of DFT to describe the polaron formation in band insulators. It is shown that the delocalization error in these systems is, however, largely absent in the KS potential of the closed-shell neutral charge state. This leads to a modification of the DFT total-energy functional that corrects the pSI in the XC functional. The resulting pSIC-DFT method constitutes an accurate parameter-free ab initio methodology for calculating polaron properties in insulators at a computational cost that is orders of magnitude smaller than hybrid XC functionals. Unlike approaches that rely on parametrized localized potentials such as DFT+$U$, the pSIC-DFT method properly captures both site and bond-centered polaron configurations. This is demonstrated by studying formation and migration of self-trapped holes in alkali halides (bond-centered) as well as self-trapped electrons in an elpasolite compound (site-centered). The pSIC-DFT approach consistently reproduces the results obtained by hybrid XC functionals parametrized by DFT+$G_0{W}_0$ calculations. Finally, we generalize the pSIC approach to hybrid functionals, and show that in stark contrast to conventional hybrid calculations of polaron energies, the pSIC-hybrid method is insensitive to the parametrization of the hybrid XC functional. On this basis, we further rationalize the success of the pSIC-DFT approach.

Recent studies show a face-centered cubic (fcc) to body-centered cubic (bcc) transformation along the shock Hugoniot for several metals (i.e., Cu, Au, and Ag). Here, we combine laser-shock compression of Cu foils on nanosecond timescales with in situ x-ray diffraction (XRD) to examine the microstructural changes with stress. We study the fcc phase and the phase transition from fcc to bcc (pressures greater than 180 GPa). Textural analysis of the azimuthal intensities from the XRD images is consistent with transformation into the bcc phase through the Pitsch-distortion mechanism. We use embedded atom model molecular dynamics simulations to determine the stability of the bcc phase in pressure–temperature space. Our results indicate that the bcc phase is stabilized only at high temperatures and remains stable at pressures greater than 500 GPa.