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A computer algorithm to search the symmetries of crystal structures, as implemented in the spglib code, is described. An iterative algorithm is employed to robustly identify space group types, tolerating a certain amount of distortion in the crystal structures. The source code is distributed under the 3-Clause BSD License, a permissive open-source software license. This paper focuses on the algorithm for identifying the space group symmetry of crystal structures.

Abstract Crystal structures of minerals are defined by a specific atomic arrangement within the unit‐cell, which follows the laws of symmetry specific to each crystal system. The causes for a mineral to crystallize in a given crystal system have been the subject of many studies showing their dependency on different formation conditions, such as the presence of aqueous fluids, biotic activity and many others. Different attempts have been made to quantify and interpret the information that we can gather from studying crystal symmetry and its distribution in the mineral kingdom. However, these methods are mostly outdated or at least not compatible for use on large datasets available today. Therefore, a revision of symmetry index calculation has been made in accordance with the growing understanding of mineral species and their characteristics. In the gathered data, we observe a gradual but significant decrease in crystal symmetry through the stages of mineral evolution, from the formation of the solar system to modern day. However, this decrease is neither uniform nor linear, which provides further implications for mineral evolution from the viewpoint of crystal symmetry. The temporal distribution of minerals based on the number of essential elements in their chemical formulae and their symmetry index has been calculated and compared to explore their behaviour. Minerals with four to eight essential elements have the lowest average symmetry index, while being the most abundant throughout all stages of mineral evolution. There are many open questions, including those pertaining to whether or not biological activity on Earth has influenced the observed decrease in mineral symmetry through time and whether or not the trajectory of planetary evolution of a geologically active body is one of decreasing mineral symmetry/increasing complexity.

A metaheuristic algorithm named the Crystal Structure Algorithm (CrSA), which is inspired by the symmetric arrangement of atoms, molecules, or ions in crystalline minerals, has been used for the accurate modeling of Mono Passivated Emitter and Rear Cell (PERC) WSMD-545 and CS7L-590 MS solar photovoltaic (PV) modules. The suggested algorithm is a concise and parameter-free approach that does not need the identification of any intrinsic parameter during the optimization stage. It is based on crystal structure generation by combining the basis and lattice point. The proposed algorithm is adopted to minimize the sum of the squares of the errors at the maximum power point, as well as the short circuit and open circuit points. Several runs are carried out to examine the V-I characteristics of the PV panels under consideration and the nature of the derived parameters. The parameters generated by the proposed technique offer the lowest error over several executions, indicating that it should be implemented in the present scenario. To validate the performance of the proposed approach, convergence curves of Mono PERC WSMD-545 and CS7L-590 MS PV modules obtained using the CrSA are compared with the convergence curves obtained using the recent optimization algorithms (OAs) in the literature. It has been observed that the proposed approach exhibited the fastest rate of convergence on each of the PV panels.

The anomalous Hall effect has been front and center in solid state research and material science for over a century now, and the complex transport phenomena in nontrivial magnetic textures have gained an increasing amount of attention, both in theoretical and experimental studies. However, a clear path forward to capturing the influence of magnetization dynamics on anomalous Hall effect even in smallest frustrated magnets or spatially extended magnetic textures is still intensively sought after. In this work, we present an expansion of the anomalous Hall tensor into symmetrically invariant objects, encoding the magnetic configuration up to arbitrary power of spin. We show that these symmetric invariants can be utilized in conjunction with advanced regularization techniques in order to build models for the electric transport in magnetic textures which are, on one hand, complete with respect to the point group symmetry of the underlying lattice, and on the other hand, depend on a minimal number of order parameters only. Here, using a four-band tight-binding model on a honeycomb lattice, we demonstrate that the developed method can be used to address the importance and properties of higher-order contributions to transverse transport. The efficiency and breadth enabled by this method provides an ideal systematic approach to tackle the inherent complexity of response properties of noncollinear magnets, paving the way to the exploration of electric transport in intrinsically frustrated magnets as well as large-scale magnetic textures.

Many enzymes are composed of several identical subunits, which are arranged in a regular fashion and usually comply with some definite symmetry. This symmetry may be approximate or exact and may or may not coincide with the symmetry of crystallographic packing. Purine nucleoside phosphorylases (PNP) are a class of oligomeric enzymes that show an interesting interplay between their internal symmetry and the symmetry of their crystal packings. There are two main classes of this enzyme: trimeric PNPs, or “low-molecular-mass” proteins, which are found mostly in eukaryotic organisms, and hexameric PNPs, or “high-molecular-mass” proteins, which are found mostly in prokaryotic organisms. Interestingly, these two enzyme classes share only 20–30% sequence identity, but the overall fold of the single monomer is similar, yet this monomeric building block results in a different quaternary structure. To investigate this interplay of symmetry in this class of enzymes, a comprehensive database of all PNPs is constructed, containing their local symmetries and interface information.

We investigated the luminescent properties of Ho3+ and Yb3+ co-doped AZrO3 (A = Ca, Sr, and Ba) perovskite nanocrystals synthesized using a combustion method. X-ray diffraction measurement revealed that these nanocrystals exhibited differences in their structural symmetries, varying from orthorhombic in CaZrO3 to cubic in BaZrO3, with an increase in their grain sizes and an enhanced degree of crystallinity along increased post-annealing temperatures. Under near-infrared excitations, we observed strong green (545 nm) and weak red (660 nm) emissions from the Ho3+ ions. Interestingly, the smaller the sizes of the A ions, the stronger were the upconversion emissions and the greater was the increase in the emission intensity due to post-annealing. We found that the crystal symmetry and the degree of crystallinity of the host play an important role in determining the luminescent behavior of Ho3+ ions in perovskite nanocrystals.

We conducted a systematic investigation using state-of-the-art techniques on the electronic and optical properties of two crystals of alkaline earth metal fluorides, namely rutile MgF2 and cubic SrF2. For these two crystals of different symmetry, we present density functional theory (DFT), many-body perturbation theory (MBPT), and Bethe–Salpeter equation (BSE) calculations. We calculated a variety of properties, namely ground-state energies, band-energy gaps, and optical absorption spectra with the inclusion of excitonic effects. The quantities were obtained with a high degree of convergence regarding all bulk electronic and optical properties. Bulk rutile MgF2 has distinguished ground-state and excited-state properties with respect to the other cubic fluoride SrF2 and the other members of the alkaline earth metal fluoride family. The nature of the fundamental gaps and estimates of the self-energy and excitonic effects for the two compounds are presented and discussed in detail. Our results are in good accordance with the measurements and other theoretical–computational data. A comparison is made between the excitation and optical properties of bulk rutile MgF2, cubic SrF2, and the corresponding clusters, for which calculations have recently been published, confirming strong excitonic effects in finite-sized systems.

One of the most consequential assumptions of the classical theories of crystal nucleation and growth is the Szilard postulate, which states that molecules from a supersaturated phase join a nucleus or a growing crystal individually. In the last 20 years, observations in complex biological, geological, and engineered environments have brought to light violations of the Szilard rule, whereby molecules assemble into ordered or disordered precursors that then host and promote nucleation or contribute to fast crystal growth. Nonclassical crystallization has risen to a default mode presumed to operate in the majority of the inspected crystallizing systems. In some cases, the existence of precursors in the growth media is admitted as proof for their role in nucleation and growth. With the example of olanzapine, a marketed drug for schizophrenia and bipolar disorder, we demonstrate that molecular assemblies in the solution selectively participate in crystal nucleation and growth. In aqueous and organic solutions, olanzapine assembles into both mesoscopic solute-rich clusters and dimers. The clusters facilitate nucleation of crystals and crystal form transformations. During growth, however, the clusters land on the crystal surface and transform into defects, but do not support step growth. The dimers are present at low concentrations in the supersaturated solution, yet the crystals grow by the association of dimers, and not of the majority monomers. The observations with olanzapine emphasize that detailed studies of the crystal and solution structures and the dynamics of molecular association may empower classical and nonclassical models that advance the understanding of natural crystallization, and support the design and manufacture of promising functional materials.

The second-harmonic generation (SHG) from Si1-xGex alloy films has been investigated by near-infrared femtosecond laser. Recognized by s-out polarized SHG intensity versus rotational angle of sample, the crystal symmetry of the fully strained Si0.83Ge0.17 alloy is found changed from the Oh to the C2 point group due to the inhomogeneity of the strain. Calibrated by double crystal X-ray diffraction, the strain-induced χ(2) is estimated at 5.7 × 10-7 esu. According to the analysis on p-in/s-out SHG, the strain-relaxed Si0.10Ge0.90 alloy film is confirmed to be not fully relaxed, and the remaining strain is quantitatively determined to be around 0.1%.