Related papers: Crystal Representation in the Reciprocal Space
Crystal property prediction, governed by quantum mechanical principles, is computationally prohibitive to solve exactly for large many-body systems using traditional density functional theory. While machine learning models have emerged as…
Crystallography, the primary method for determining the three-dimensional (3D) atomic positions in crystals, has been fundamental to the development of many fields of science. However, the atomic positions obtained from crystallography…
The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic scale structure of matter and its properties, involves transforming the Cartesian…
Crystal structures are indispensable across various domains, from batteries to solar cells, and extensive research has been dedicated to predicting their properties based on their atomic configurations. However, prevailing Crystal Structure…
The quaternion Bingham distribution has been used to model preferred crystallographic orientation, or crystallographic texture, in polycrystalline materials in the materials science and geological communities. A primary difficulty in…
Solving crystal structures from kinematical X-ray or electron diffraction patterns of single crystals requires many more diffracted beams to be recorded than there are atoms in the structure, since the phases of the structure factors can…
Recent studies demonstrated the violation of reciprocity in optical processes in low-symmetry magnetic crystals. In these crystals the speed of light can be different for counter-propagating beams. Correspondingly, they can show strong…
The concept of space group has long served as the fundamental framework to describe the physical properties of crystalline materials, from electronic bands to photonic dispersions. The recent progress of spatiotemporal control, such as…
When a sample's X-ray diffraction pattern (XRD) is measured, the corresponding crystal structure is usually determined by searching for similar XRD patterns in the database. However, if a similar XRD pattern is not found, it is tremendously…
We introduce a computational method to optimize target physical properties in the full configuration space regarding atomic composition, chemical stoichiometry, and crystal structure. The approach combines the universal potential of the…
Generating novel crystalline materials has the potential to lead to advancements in fields such as electronics, energy storage, and catalysis. The defining characteristic of crystals is their symmetry, which plays a central role in…
Mathematical crystal chemistry views crystal structures as the optimal solutions of mathematical optimization problem formalizing inorganic structural chemistry. This paper introduces the minimum and maximum atomic radii depending on the…
When representing a solid object there are alternatives to the use of traditional explicit (surface meshes) or implicit (zero crossing of implicit functions) methods. Skeletal representations encode shape information in a mixed fashion:…
As a fundamental concept of all crystals, space groups are partitioned into symmorphic groups and nonsymmorphic groups. Each nonsymmorphic group contains glide reflections or screw rotations with fractional lattice translations, which are…
In linear elasticity, a fourth order elasticity (stiffness) tensor of 21 independent components completely describes deformation properties of a material. Due to Voigt, this tensor is conventionally represented by a $6\times 6$ symmetric…
Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic "space-time" crystal characterized by the general intertwined space-time periodicities in $D+1$…
Generative design marks a significant data-driven advancement in the exploration of novel inorganic materials, which entails learning the symmetry equivalent to the crystal structure prediction (CSP) task and subsequent learning of their…
Spatial symmetries appearing in both real and momentum space are of fundamental significance to crystals. However, in the conventional framework, every space group in real space, either symmorphic or nonsymmorphic, corresponds to a…
In the paper, a new method determining the wave vector star channel in the reciprocal lattice space of crystal in the light of the translational symmetry breaking is proposed, and, in order to consider the phase transitions according to the…
Spin space groups, formed by operations where the rotation of the spins is independent of the accompanying operation acting on the crystal structure, are appropriate groups to describe the symmetry of magnetic structures with null…