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Interatomic potentials approximate the potential energy of atoms as a function of their coordinates. Their main application is the effective simulation of many-atom systems. Here, we review empirical interatomic potentials designed to reproduce elastic properties, defect energies, bond breaking, bond formation, and even redox reactions. We discuss popular two-body potentials, embedded-atom models for metals, bond-order potentials for covalently bonded systems, polarizable potentials including charge-transfer approaches for ionic systems and quantum-Drude oscillator models mimicking higher-order and many-body dispersion. Particular emphasis is laid on the question what constraints ensue from the functional form of a potential, e.g., in what way Cauchy relations for elastic tensor elements can be violated and what this entails for the ratio of defect and cohesive energies, or why the ratio of boiling to melting temperature tends to be large for potentials describing metals but small for short-ranged pair potentials. The review is meant to be pedagogical rather than encyclopedic. This is why we highlight potentials with functional forms sufficiently simple to remain amenable to analytical treatments. Our main objective is to provide a stimulus for how existing approaches can be advanced or meaningfully combined to extent the scope of simulations based on empirical potentials.

An interatomic potential for the ternary Ag–Cu–Sn system, an important material system related to the applications of lead-free solders, is developed on the basis of the second nearest-neighbor modified embedded-atom-method formalism. Potential parameters for the ternary and related binary systems are determined based on the recently improved unary description of pure Sn and the present improvements to the unary descriptions of pure Ag and Cu. To ensure the sufficient performance of atomistic simulations in various applications, the optimization of potential parameters is conducted based on the force-matching method that utilizes density functional theory predictions of energies and forces on various atomic configurations. We validate that the developed interatomic potential exhibits sufficient accuracy and transferability to various physical properties of pure metals, intermetallic compounds, solid solutions, and liquid solutions. The proposed interatomic potential can be straightforwardly used in future studies to investigate atomic-scale phenomena in soldering applications. Graphical abstract

Context Gallium, renowned for its notably low melting point and unique property of becoming liquid at room temperature, is a valuable constituent in phase change materials. In this study, we investigate the solid–liquid phase transition of gallium using the modified embedded atom method (MEAM) potential. It addresses the technique to compute the free energy difference between the solid and liquid without using a reference state. We examine various thermodynamic and dynamic properties, including density, specific heat capacity, diffusivity, and radial distribution functions. We compute the coexistence temperature of the solid–liquid phase transitions of gallium from free energy analysis. This information is crucial for understanding the behavior of the material under different pressure conditions and can be valuable for various applications, such as materials processing and high-pressure studies. The analysis, findings, and insights of the present work will be of great significance to the broad scientific and engineering communities in the field of phase transformation of materials. Methods A series of molecular dynamics(MD) simulations were conducted using the LAMMPS software packages. The gallium atoms are modeled using the modified embedded atom method (MEAM) potential. To accurately predict the solid–liquid phase transitions of gallium, we calculated free energy by employing the “constrained λ integration” method, coupled with multiple histogram reweighting (MHR). The solid–liquid coexistence line is determined through the Gibbs–Duhem integration technique.

A new interatomic potential for the pure tin (Sn) system is developed on the basis of the second-nearest-neighbor modified embedded-atom-method formalism. The potential parameters were optimized based on the force-matching method utilizing the density functional theory (DFT) database of energies and forces of atomic configurations under various conditions. The developed potential significantly improves the reproducibility of many fundamental physical properties compared to previously reported modified embedded-atom method (MEAM) potentials, especially properties of the β phase that is stable at the ambient condition. Subsequent free energy calculations based on the quasiharmonic approximation and molecular-dynamics simulations verify that the developed potential can be successfully applied to study the allotropic phase transformation between α and β phases and diffusion phenomena of pure tin.

This study proposes a new elastic–plastic deformation decomposition algorithm for metal clusters to calculate micro-nanoscale elastic and plastic deformation gradients. In the macroscopic plasticity theory, the intermediate configuration is usually constructed by the dissection–unloading method. Because an atomic cluster is equivalent to a small element on a macroscopic object, our decomposition algorithm regards the unloaded configuration as the intermediate configuration for atomic clusters. This algorithm uses a new unloading method to obtain the unloaded configuration. This micro-nanoscale unloading method is constructed based on the principle of minimum potential energy and the embedded-atom method. Moreover, this method rigidly fixes atoms around dislocations during unloading. Therefore, the unloading process will not cause new plastic flow. Once the intermediate configuration is obtained, elastic and plastic deformation gradients are calculated by the interpolation method. Numerical examples of Cu nanowire stretching and bending show that the new decomposition algorithm can accurately and rapidly conduct the elastic–plastic decomposition of the total deformation. This algorithm provides a computational basis for multiscale coupling analysis of mechanical behavior of metal materials from the micro-nanoscale to the macroscale.

A new second nearest-neighbor modified embedded-atom model-based PtTi binary interatomic potential was developed by improving the pure Pt unary descriptions of the pre-existing interatomic potential. Specifically, the interatomic potential was developed focusing on the shape memory-associated phenomena and the properties of equiatomic PtTi, which has potential applications as a high-temperature shape memory alloy. The simulations using the developed interatomic potential reproduced the physical properties of the equiatomic PtTi and various intermetallic compound/alloy compositions and structures. Large-scale molecular dynamic simulations of single crystalline and nanocrystalline configurations were performed to examine the temperature- and stress-induced martensitic transformations. The results show good consistency with the experiments and demonstrate the reversible phase transformation of PtTi SMA between the cubic B2 austenite and the orthorhombic B19 martensite phases. In addition, the importance of anisotropy, constraint and the orientation of grains on the transformation temperature, mechanical response, and microstructure of SMA are presented.

The mechanical properties of copper alloys containing various ratios of zinc are evaluated using molecular dynamics (MD) simulations to determine the impact of the different zinc concentrations. The modified embedded atom method (MEAM) parameters for copper were established in the 1990s; however, the MEAM potential parameters for zinc, with an axial ratio >1, were recently proposed. In this research, the MD models of the copper alloys with various zinc contents are constructed using the MEAM potential parameters for zinc. Tensile test simulations are also conducted. The strain rate effects of the alloys are evaluated at four different strain rates, and the variations in the tensile strengths and Young's modulus are investigated. The proposed procedures have significant potential applicability for simulating a variety of zinc-containing alloys.

Evaluation of the entropy from molecular dynamics (MD) simulation remains an outstanding challenge. The standard approach requires thermodynamic integration across a series of simulations. Recent work Nicholson et al. demonstrated the ability to construct a functional that returns excess entropy, based on the pair correlation function (PCF); it was capable of providing, with acceptable accuracy, the absolute excess entropy of iron simulated with a pair potential in both fluid and crystalline states. In this work, the general applicability of the Entropy Pair Functional Theory (EPFT) approach is explored by applying it to three many-body interaction potentials. These potentials are state of the art for large scale models for the three materials in this study: Fe modelled with a modified embedded atom method (MEAM) potential, Cu modelled with an MEAM and Si modelled with a Tersoff potential. We demonstrate the robust nature of EPFT in determining excess entropy for diverse systems with many-body interactions. These are steps toward a universal Entropy Pair Functional, EPF, that can be applied with confidence to determine the entropy associated with sophisticated optimized potentials and first principles simulations of liquids, crystals, engineered structures, and defects.

Ferromagnetic shape memory alloys, including the Fe7Pd3 system, constitute an upcoming class of functional materials, whose atomic-scale physical foundations are still insufficiently understood. The present work employs molecular dynamics simulations, based on ab initio derived embedded atom method potentials, to study martensitic transformations and twin variant reorientation. We address thermal and stress induced austenite-martensite transitions, twinning, as well as twin boundary mobility. While the predicted thermal properties are in accordance with experimental observations, we explore the detailed crystallography underlying transformation as well as twin boundary motion.

An analytic modified embedded atom method (MEAM), developed for bulk alkali metals, is used to identify up to six different, energetically lowest isomers of Li N and Na N clusters (N = 2 − 150) within an unbiased global structure-optimization procedure. Randomly generated clusters are locally optimized using the quasi-Newton method and the resulting six most stable isomers are used afterwards in the Aufbau–Abbau algorithm. Due to its analytical formulae and its semiempirical nature, the MEAM emerges as a fast and efficient method that is particularly suitable for an unbiased global optimization. Structural and energetic analyses show that the MEAM provides compact clusters that are in good agreement with the results of other semiempirical calculations. Occasionally, the MEAM produces structures that are normally not found with such model potentials but in more accurate DFT or ab initio studies. Moreover, clusters of pronounced stability (magic sizes) are identified, growth patterns are studied, and trends can be recognized in which the atomic arrangement within the clusters of the considered size range corresponds more to the fcc than to the bcc packing. Additionally, for most cluster sizes the structures of the lowest-energy isomers of Li N and Na N clusters are very similar.