Band structures for electrons, phonons, and other quasiparticles are often an important aspect of describing the physical properties of periodic solids. Most commonly, energy bands are computed along a one-dimensional path of high-symmetry points and line segments in reciprocal space (the “k-path”), which are assumed to pass through important features of the dispersion landscape. However, existing methods for choosing this path rely on tabulated lists of high-symmetry points and line segments in the first Brillouin zone, determined using different symmetry criteria and unit cell conventions. Here we present a new “on-the-fly” symmetry-based approach to obtaining paths in reciprocal space that attempts to address the previous limitations of these conventions. Given a unit cell of a magnetic or nonmagnetic periodic solid, the site symmetry groups of points and line segments in the irreducible Brillouin zone are obtained from the total space group. The elements in these groups are used alongside general and maximally inclusive high-symmetry criteria to choose segments for the final k-path. A smooth path connecting each segment is obtained using graph theory. This new framework not only allows for increased flexibility and user convenience but also identifies notable overlooked features in certain electronic band structures. In addition, a more intelligent and efficient method for analyzing magnetic materials is also enabled through proper accommodation of magnetic symmetry.

Thermodynamic equations of state (EOS) for crystalline solids describe material behaviors under changes in pressure, volume, entropy and temperature, making them fundamental to scientific research in a wide range of fields including geophysics, energy storage and development of novel materials. Despite over a century of theoretical development and experimental testing of energy-volume (E-V) EOS for solids, there is still a lack of consensus with regard to which equation is indeed optimal, as well as to what metric is most appropriate for making this judgment. In this study, several metrics were used to evaluate quality of fit for 8 different EOS across 87 elements and over 100 compounds which appear in the literature. Our findings do not indicate a clear "best" EOS, but we identify three which consistently perform well relative to the rest of the set. Furthermore, we find that for the aggregate data set, the RMSrD is not strongly correlated with the nature of the compound, e.g., whether it is a metal, insulator, or semiconductor, nor the bulk modulus for any of the EOS, indicating that a single equation can be used across a broad range of classes of materials.

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As industrial and commercial demand for thin, small-footprint energy storage devices increases (e.g., for wearable electronics, wireless sensor networks, etc.), it is essential to develop theoretical descriptions for those devices in order to make effective design choices. Of particular interest are porous interdigitated electrodes, which can function as supercapacitors but which are nontrivial to analyze due to their unique geometry. In this paper, we develop a purely mathematical model to determine the dependence of a cell's capacitance and/or resistance on electrode height, width, and spacing, and electrolyte layer height. We then extend this model to incorporate effects from the porous nature of the electrodes, and show that in many cases of interest, the system can be described using a simple equivalent circuit.