A function that gives the energy and forces from the arrangement of atoms. Types include the Lennard-Jones form, the embedded atom method for metals, potentials for covalent bonds and machine-learning potentials.
Japanese name: 原子間ポテンシャル
Interatomic potential appears in 5 practice questions across 3 topics, including Computational materials science, Mechanical properties and fracture, Thermal properties of materials.
An interatomic potential is a function that returns the energy for a set of atomic positions, and the forces are found by differentiating that energy with respect to the atomic positions. Instead of solving for the electronic states, it approximates their result with a convenient formula, so it is far faster than calculations that treat electrons directly and can handle many atoms over long times. The parameters in the formula are fitted to experimental values such as lattice parameter, cohesive energy, elastic constants, vacancy formation energy and stacking fault energy, or to energies and forces from first-principles calculations. What a potential was fitted to determines what it does well and badly.
The simplest form is a pair potential determined only by the distance between two atoms, such as the Lennard-Jones and Morse forms. For ionic crystals, a Coulomb term is added to a short-range repulsive term, and the long-range Coulomb interaction is summed with the Ewald method or similar. To speed up calculations, interactions with atoms beyond a certain distance (the cutoff) are usually neglected. Cutting the Lennard-Jones form at 2.5σ leaves an energy there only about 1.6% of the well depth in magnitude. Each atom then interacts with a limited number of partners, and the computational cost becomes roughly proportional to the number of atoms.
For metals, the embedded atom method (EAM) proposed by Daw and Baskes in the 1980s is widely used, and the modified embedded atom method (MEAM) adds the directionality of bonding. For covalent bonds as in Si and C, bond-order potentials, in which bond strength changes with the number and angles of surrounding bonds, are used, and reactive potentials extend these to handle bond breaking and formation. Even for the same element there are many potentials made for different purposes, and they often give different values for the same property. Properties not included in the fitting are often poorly reproduced, so one checks before use that the potential reproduces the property of interest.
In recent years, machine-learning potentials trained on the energies and forces of many atomic configurations from first-principles calculations have come into wide use. The environment around each atom is turned into numbers by descriptors representing the distributions of distances and angles, and the relation to energy is learned with neural networks or Gaussian process regression. They keep accuracy close to first-principles calculations while being many orders of magnitude faster, though heavier than EAM and similar potentials. When they meet configurations not included in training, they can return plausible but wrong values. Active learning, which finds configurations with large uncertainty during a calculation and adds them to the training, is used as a remedy.
Answer: B. The embedded atom method (EAM) potential adds an embedding energy that depends on the electron density created by the surrounding atoms, describing the many-body nature of metallic bonding
The Lennard-Jones potential is a pair potential depending only on the distance between two atoms; it describes weak, non-directional bonding such as that of the noble gases well, but not the properties of metals or covalent bonds. In metals, the many-body effect, in which the bond strength of an atom changes with the number of surrounding atoms, is large, and EAM adds this as a function of the electron density created by the surrounding atoms. With pair potentials alone, the Cauchy relation C₁₂ = C₄₄ between the elastic constants always holds for an unstressed FCC or BCC crystal, in which every atom sits at a center of symmetry, but many metals do not satisfy it. In covalent bonding the bond angle matters, so the Stillinger–Weber and Tersoff potentials, which include angular terms, are used. Machine-learning potentials trained on DFT results are also widely used.
They often refer to the same thing; materials science tends to say interatomic potential, while chemistry and biomolecular science tend to say force field. A force field often means a set of functions and parameters for molecules that combines terms for bond lengths, angles, torsions, charges and so on.
ε is the depth of the energy well and represents bond strength, and σ is the distance at which the energy is zero and represents atomic size. For argon, ε divided by the Boltzmann constant is about 120 K (ε ≈ 0.010 eV) and σ is about 0.34 nm, which describe the properties of noble-gas solids and liquids well.
Choose one made by fitting quantities close to the property you want to calculate and validated for it. For dislocations, check whether it reproduces stacking fault energy and elastic constants; for melting, the melting point, using the literature or your own calculations. Databases collecting published potentials and their validation results are also available.
It is set by the strength of interatomic bonding (the curvature of the interatomic potential) and is a structure-insensitive property.
Which statement about the Young's modulus of steel is corre…The interatomic potential has an asymmetric shape: repulsion rises steeply as atoms approach, while on the separating side the attraction weakens gradually.
What is the main cause of solids expanding when heated (the…Classical molecular dynamics, which uses interatomic potentials, can follow thousands to millions of atoms for times of the order of nanoseconds.
Which pairing of a materials computation method with the ra…Solving equations of motion with an empirical interatomic potential is classical molecular dynamics.
Which statement about the ideas behind density functional t…Molecular dynamics Density functional theory Young's modulus Dislocation Phonon Phase-field method Finite element method CALPHAD method Materials informatics Monte Carlo method