Computational methods are commonly used by materials scientists to make predictions about materials. These methods can achieve in hours what would take days or weeks to accomplish in a lab. However, there are limits to what computational methods can do and how accurate the predictions are.A limiting factor for computational materials science is the size of the search space. The space of potential materials is infinite. Selecting specific systems of elements on a fixed lattice to study reduces the number of possible arrangements of atoms in the lattice to a finite number. However, this number can still be very large. Additionally this list of arrangements will contain duplicates, i.e., two different atomic arrangements could be equivalent by a rotation or translation of the lattice. Using symmetry to eliminate the duplicates saves time and resources. In order to ensure that the final list of unique structures will fit into computer memory it is also useful to know how many unique arrangements there are before actually finding them. For this reason the Pòlya enumeration algorithm was created to determine the number of unique arrangements before enumerating them. A new atomic enumeration algorithm has also been implemented in the enumlib package. This new algorithm has been optimized to find the symmetrically unique arrangements for systems with large amounts of configurational freedom, such as high-entropy alloys, which have been too computationally expensive for other algorithms.A popular computational method in materials science is Density Functional Theory (DFT). DFT codes perform first principles calculations by calculating the electron energy using numerical integrals. It is well known that the accuracy of the integrals depends heavily on the number of sample points, k-points, used. We have conducted a detailed study of how k-point sampling methods effect the accuracy of DFT calculations. This study shows that the most efficient k-point grids are those that have the fewest symmetrically distinct k-points, we call these general regular (GR) grids. GR grids are, however, difficult to generate, requiring a search across many possible grids. In order to make GR grids more accessible to the DFT community we have implemented an algorithm that can search k-point grids for the grid that has the fewest symmetry reduction in a matter of seconds.



College and Department

Physical and Mathematical Sciences; Physics and Astronomy



Date Submitted


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materials discovery, symmetry, numerical integration, sampling, Niggli, k-point folding



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Physics Commons