No Arabic abstract
A novel phase field model has been developed to study the effect of coherent precipitate on the Zener pinning of matrix grain boundaries. The model accounts for misfit strain between precipitate and matrix as well as the elastic inhomogeneity and anisotropy between them. The results show that increase in elastic misfit, elastic inhomogeneity, and elastic anisotropy increases the coarsening rate of the precipitates. Increased coarsening of precipitates in turn decreases the pinning of grain boundaries. Therefore, increase in misfit strain, elastic inhomogeneity and anisotropy negatively affect the Zener pinning through coherent precipitate. This study shows elastic anisotropy gives rise to the needle shape precipitate. It has also been shown that these needle shaped precipitates are not very effective in Zener pinning. This study provides an understanding into the effect of coherent precipitate on the Zener pinning of matrix grain boundaries.
We investigate the spectral profiles of time signals attributed to coherent phonon generation in an undoped Si crystal. Here, the retarded longitudinal-optical (LO) phonon Green function relevant to the temporal variance of induced charge density of ionic cores is calculated by employing the polaronic quasiparticle model developed by the authors [Y. Watanabe et al., Phys. Rev. B 95, 014301 (2017); ibid., 96, 125204 (2017)]. The spectral asymmetry is revealed in the frequency domain of the signals under the condition that an LO phonon mode stays almost energetically resonant with a plasmon mode in the early time region; this lasts for approximately 100 fs immediately after the irradiation of an ultrashort pump-laser pulse. It is understood that based on the adiabatic picture in time, this asymmetry is caused by the Rosen-Zener coupling between both modes. The associated experimental results are obtained by measuring time-dependent electro-optic reflectivity signals, and it is proved that these are in harmony with the calculated ones. The spectra become more symmetric, as the photoexcited carrier density further changes from that meeting the above condition to higher and lower sides of carrier densities. Moreover, the effect of optical nutation of carrier density on the CP signals is addressed, and the present results are compared with the asymmetry caused by transient Fano resonance, and the spectral profiles observed in a GaAs crystal in the text.
Most of the commercially important alloys are multicomponent, producing multiphase microstructures as a result of processing. When the coexisting phases are elastically coherent, the elastic interactions between these phases play a major role in the development of microstructures. To elucidate the key effects of elastic stress on microstructural evolution when more than two misfitting phases are present in the microstructure, we have developed a microelastic phase-field model in two dimensions to study phase separation in ternary alloy system. Numerical solutions of a set of coupled Cahn-Hilliard equations for the composition fields govern the spatiotemporal evolution of the three-phase microstructure. The model incorporates coherency strain interactions between the phases using Khachaturyans microelasticity theory. We systematically vary the misfit strains (magnitude and sign) between the phases along with the bulk alloy composition to study their effects on the morphological development of the phases and the resulting phase separation kinetics. We also vary the ratio of interfacial energies between the phases to understand the interplay between elastic and interfacial energies on morphological evolution. The sign and degree of misfit affect strain partitioning between the phases during spinodal decomposition, thereby affecting their compositional history and morphology. Moreover, strain partitioning affects solute partitioning and alters the kinetics of coarsening of the phases. The phases associated with higher misfit strain appear coarser and exhibit wider size distribution compared to those having lower misfit. When the interfacial energies satisfy complete wetting condition, phase separation leads to development of stable core-shell morphology depending on the misfit between the core (wetted) and the shell (wetting) phases.
The precipitate shape, size and distribution are crucial factors which determine the properties of several technologically important alloys. Elastic interactions between the inclusions modify their morphology and align them along elastically favourable crystallographic directions. Among the several factors contributing to the elastic interaction energy between precipitating phases, anisotropy in elastic moduli is decisive in the emergence of modulated structures during phase separation in elastically coherent alloy systems. We employ a phase-field model incorporating elastic interaction energy between the misfitting phases to study microstructural evolution in ternary three-phase alloy systems when the elastic moduli are anisotropic. The spatiotemporal evolution of the composition field variables is governed by solving a set of coupled Cahn-Hilliard equations numerically using a semi-implicit Fourier spectral technique. We methodically vary the misfit strains, alloy chemistry and elastic anisotropy to investigate their influence on domain morphology during phase separation. The coherency strains between the phases and alloy composition alter the coherent phase equilibria and decomposition pathways. The degree of anisotropy in elastic moduli modifies the elastic interaction energy between the precipitates depending on the sign and magnitude of relative misfits, and thus determines the shape and alignment of the inclusions in the microstructure.
Ferroelectrics form domain patterns that minimize their energy subject to imposed boundary conditions. In a linear, constrained theory, that neglects domain wall energy, periodic domain patterns in the form of multi-rank laminates can be identified as minimum-energy states. However, when these laminates (formed in a macroscopic crystal) comprise domains that are a few nanometers in size, the domain-wall energy becomes significant, and the behaviour of laminate patterns at this scale is not known. Here, a phase-field model, which accounts for gradient energy and strain energy contributions, is employed to explore the stability and evolution of the nanoscale multi-rank laminates. The stress, electric field, and domain wall energies in the laminates are computed. The effect of scaling is also discussed. In the absence of external loading, stripe domain patterns are found to be lower energy states than the more complex, multi-rank laminates, which mostly collapse into simpler patterns. However, complex laminates can be stabilized by imposing external loads such as electric field, average strain and polarization. The study provides insight into the domain patterns that may form on a macroscopic single crystal but comprising of nanoscale periodic patterns, and on the effect of external loads on these patterns.
We report on the temperature stability of pseudomorphic GeSn films grown by molecular beam epitaxy on Ge(001) substrates. Both the growth temperature-dependence and the influence of post-growth annealing steps were investigated. In either case we observe that decomposition of metastable epilayers with Sn concentrations around 10% sets in above 230{deg}C, the eutectic temperature of the Ge/Sn system. Time-resolved annealing experiments in a scanning electron microscope reveal the crucial role of liquid Sn droplets in this phase separation process. Driven by a gradient of the chemical potential, the Sn droplets move on the surface along preferential crystallographic directions, thereby taking up Sn and Ge from the strained GeSn layer at their leading edge. While Sn-uptake increases the volume of the melt, dissolved Ge becomes re-deposited by a liquid-phase epitaxial process at the trailing edge of the droplet. Secondary droplets are launched from the rims of the single-crystalline Ge trails into intact regions of the GeSn film, leading to an avalanche-like transformation front between the GeSn film and re-deposited Ge. This process makes phase separation of metastable GeSn layers particularly efficient at rather low temperatures.