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Density Functional Theory

One of the most widely used computational methods in the field of materials science—as well as chemistry and physics, more broadly—is density functional theory, or DFT. DFT is a method of computation and calculation based on quantum mechanics; it deals with the smaller end of the length scales studied in materials science, the scale of electrons, atoms, and molecules. More specifically, DFT calculates electronic structures (i.e., the location and energy levels, the quantum states, of the electrons) and uses that to predict properties.

DFT has been used for calculations for many decades, but truly grew in popularity after the 1990s, as refinements to the technique improved its accuracy in the quantum mechanical realm. Even before then, its usage was significant. Walter Kohn received a Nobel Prize in chemistry for his contributions to DFT, including early development of the Hohenberg–Kohn theorems, followed by development of a set of equations with Lu Jeu Sham known as the Kohn-Sham equations. These equations and DFT in general use of functionals of electron density, which is where the technique gets its name.

As with any computational method, DFT does have its drawbacks. It has a low computational cost to performance ratio compared to similar electronic structure methods such as wave function-based methods, but still has a high computational cost in general. It can have trouble describing certain situations, including, sometimes, intermolecular interactions, dopant interactions, and band gap calculations in semiconductors.

Dislocation Dynamics

One-dimensional line defects in crystals are known as dislocations, and these defects can have a large influence on material properties, particularly plastic deformation mechanism in metals and the resulting strength of the material. However, modeling of the individual atoms in a material is computationally costly. Instead, simulations known as Discrete Dislocation Dynamic (DDD) simulations are often run, which simulate the movement of dislocations as lines. These simulations take place with the application of an external load and attempt to determine bulk deformation behavior.

Molecular Dynamics

Moving away from the realm of the quantum mechanical calculations that are used in DFT, molecular dynamics (MD) is a computational method that uses classic mechanics (or Newtonian mechanics) to calculate the movement of atoms and molecules. Atoms and molecules are constantly in motion, but observing these movements and interactions is difficult, making simulations a far more convenient method. Forces in MD are often computed using interatomic potentials, such as the Lennard-Jones potential.

Molecular dynamics was first developed in the 1950s and has been continuously improved since then. The contributions of multiple researchers led to the 2013 Nobel Prize in chemistry being awarded to three scientists (Warshel, Levitt, and Karplus) for their pivotal roles. These simulations are used in many fields of study beyond materials science, including biophysics (studying proteins and pharmaceuticals, among other topics). In the field of materials science, specifically, MD simulations have been used, among many other things, to study the effects of radiation on solids, the nanoscale behavior of concrete and cement, liquid crystal phase transitions, and the deformations of polymer glasses.

As with all methods of scientific study, MD has its drawbacks. Because these simulations predict and analyze the interactions of atoms and molecules, small errors in the initial setup of a simulation can compound themselves, leading to a final result that is wildly different from actuality. In addition, MD simulations are limited on their timescales, given the sheer number of interactions and movements that often need to be computed.

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