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Register a new userKinetic Monte Carlo simulation of shape transition in strained quantum dots
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Chi-Hang Lam
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The pyramid-to-dome transition in Ge$_{x}$Si$_{1-x}$ on Si(100) initiated by step bunching on pyramidal quantum dots is atomistically simulated using a novel multi-state lattice model incorporating effective surface reconstructions. Results are explained by a simple theory based on a shallow island approximation. Under given deposition conditions in $d$ dimensions, the shape transition is shown to occur at island size $n_c$ following $n_c^{1/d} propto x^{-zeta}$ independent of temperature and deposition rate, where $zetaalt 2$ and $x$ is the actual Ge concentration in the island. The transition has an energy barrier dominated by the facet interface energy. Fast deposition however can out-run and delay the transition to larger island sizes.
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Accelerated algorithms for simulating the morphological evolution of strained heteroeptiaxy based on a ball and spring lattice model in three dimensions are explained. We derive exact Greens function formalisms for boundary values in the associated lattice elasticity problems. The computational efficiency is further enhanced by using a superparticle surface coarsening approximation. Atomic hoppings simulating surface diffusion are sampled using a multi-step acceptance-rejection algorithm. It utilizes quick estimates of the atomic elastic energies from extensively tabulated values modulated by the local strain. A parameter controls the compromise between accuracy and efficiency of the acceptance-rejection algorithm.
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High entropy alloys (HEAs) are a series of novel materials that demonstrate many exceptional mechanical properties. To understand the origin of these attractive properties, it is important to investigate the thermodynamics and elucidate the evolution of various chemical phases. In this work, we introduce a data-driven approach to construct the effective Hamiltonian and study the thermodynamics of HEAs through canonical Monte Carlo simulation. The main characteristic of our method is to use pairwise interactions between atoms as features and systematically improve the representativeness of the dataset using samples from Monte Carlo simulation. We find this method produces highly robust and accurate effective Hamiltonians that give less than 0.1 mRy test error for all the three refractory HEAs: MoNbTaW, MoNbTaVW, and MoNbTaTiW. Using replica exchange to speed up the MC simulation, we calculated the specific heats and short-range order parameters in a wide range of temperatures. For all the studied materials, we find there are two major order-disorder transitions occurring respectively at $T_1$ and $T_2$, where $T_1$ is near room temperature but $T_2$ is much higher. We further demonstrate that the transition at $T_1$ is caused by W and Nb while the one at $T_2$ is caused by the other elements. By comparing with experiments, {color{black} the results provide insight into the role of chemical ordering in the strength and ductility of HEAs.
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