The collected works

High-entropy materials have attracted considerable interest due to the combination of useful properties and promising applications. Predicting their formation remains the major hindrance to the discovery of new systems. Here we propose a descriptor-entropy forming ability-for addressing synthesizability from first principles. The formalism, based on the energy distribution spectrum of randomized calculations, captures the accessibility of equally-sampled states near the ground state and quantifies configurational disorder capable of stabilizing high-entropy homogeneous phases. The methodology is applied to disordered refractory 5-metal carbides-promising candidates for high-hardness applications. The descriptor correctly predicts the ease with which compositions can be experimentally synthesized as rock-salt high-entropy homogeneous phases, validating the ansatz, and in some cases, going beyond intuition. Several of these materials exhibit hardness up to 50% higher than rule of mixtures estimations. The entropy descriptor method has the potential to accelerate the search for high-entropy systems by rationally combining first principles with experimental synthesis and characterization.

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High-entropy high-hardness metal carbides discovered by entropy descriptors

A Guide to Monte Carlo Simulations in Statistical Physics: Some necessary background

We review state-of-the-art Monte Carlo (MC) techniques for computing fluid coexistence properties (Gibbs simulations) and adsorption simulations in nanoporous materials such as zeolites and metal–o...

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On the inner workings of Monte Carlo codes

Molecular modeling and simulations are invaluable tools for the polymer science and engineering community. These computational approaches enable predictions and provide explanations of experimentally observed macromolecular structure, dynamics, thermodynamics, and microscopic and macroscopic material properties. With recent advances in computing power, polymer simulations can synergistically inform, guide, and complement in vitro macromolecular materials design and discovery efforts. To ensure that this growing power of simulations is harnessed correctly, and meaningful results are achieved, care must be taken to ensure the validity and reproducibility of these simulations. With these considerations in mind, in this Perspective we discuss our philosophy for carefully developing or selecting appropriate models, performing, and analyzing polymer simulations. We highlight best practices, key challenges, and important advances in model development/selection, computational method choices, advanced sampling met...

Modeling and Simulations of Polymers: A Roadmap

We describe a Monte Carlo algorithm for doing simulations in classical statistical physics in a different way. Instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to extract an estimate for the density of states. The probability can be computed at any temperature by weighting the density of states by the appropriate Boltzmann factor. Thermodynamic properties can be determined from suitable derivatives of the partition function and, unlike “standard” methods, the free energy and entropy can also be computed directly. To demonstrate the simplicity and power of the algorithm, we apply it to models exhibiting first-order or second-order phase transitions.

/pdf/a-new-approach-to-monte-carlo-simulations-in-statistical-1pbqtg0iaw.pdf

A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling

Wang-Landau sampling (WLS) of large systems requires dividing the energy range into "windows" and joining the results of simulations in each window. The resulting density of states (and associated thermodynamic functions) is shown to suffer from boundary effects in simulations of lattice polymers and the five-state Potts model. Here, we implement WLS using adaptive windows. Instead of defining fixed energy windows (or windows in the energy-magnetization plane for the Potts model), the boundary positions depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor f is reduced, we eliminate border effects that arise in simulations using fixed windows. Adaptive windows extend significantly the range of system sizes that may be studied reliably using WLS.

Improving Wang-Landau sampling with adaptive windows.

Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.

Critical endpoint behavior in an asymmetric Ising model: Application of Wang-Landau sampling to calculate the density of states

We review recently developed decomposition algorithms for molecular dynamics and spin dynamics simulations of many-body systems. These methods are time reversible, symplectic, and the error in the total energy thus generated is bounded. In general, these techniques are accurate for much larger time steps than more standard integration methods. Illustrations of decomposition algorithms performance are shown for spin dynamics simulations of a Heisenberg ferromagnet.

/pdf/symplectic-integration-methods-in-molecular-and-spin-7cc5t1j334.pdf

Symplectic integration methods in molecular and spin dynamics simulations

Spin-dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of the classical Heisenberg antiferromagnet in simple cubic lattices with linear sizes $L\leq 60$. This system is widely recognized as an appropriate model for the magnetic properties of RbMnF$_3$. Time-evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a new algorithm implemented by Krech {\it etal}, which is based on fourth-order Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical temperature. The dynamic critical exponent was estimated to be $z=(1.43\pm 0.03)$, which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Direct, quantitative comparisons of both the dispersion curve and the lineshapes obtained from our simulations with very recent experimental results for RbMnF$_3$ are presented.

Shan-Ho Tsai

Papers

A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling

Improving Wang-Landau sampling with adaptive windows.

Critical endpoint behavior in an asymmetric Ising model: Application of Wang-Landau sampling to calculate the density of states

Symplectic integration methods in molecular and spin dynamics simulations

Spin-dynamics simulations of the magnetic dynamics of RbMnF 3 and direct comparison with experiment