crystIT: complexity and configurational entropy of crystal structures via information theory

Comparing transmission- and epi-BCARS: a round robin on solid-state materials

Broadband coherent anti-Stokes Raman scattering (BCARS) is a powerful spectroscopy method combining high signal intensity with spectral sensitivity, enabling rapid imaging of heterogeneous samples in biomedical research and, more recently, in crystalline materials. However, BCARS encounters spectral distortion due to a setup-dependent non-resonant background (NRB). This study assesses BCARS reproducibility through a round robin experiment using two distinct BCARS setups and crystalline materials with varying structural complexity, including diamond, 6H-SiC, KDP, and KTP. The analysis compares setup-specific NRB correction procedures, detected and NRB-removed spectra, and mode assignment. We determine the influence of BCARS setup parameters like pump wavelength, pulse width, and detection geometry and provide a practical guide for optimizing BCARS setups for solid-state applications.

Ag4B7O12X (X = Cl, Br, I) Heptaborate Family: Comprehensive Crystal Chemistry, Thermal Stability Trends, Topology, and Vibrational Anharmonicity

Using glass crystallization and solid-state techniques, we were able to complete the family of salt-inclusion silver halide borates, Ag₄B₇O₁₂X, by the X = Cl and I members. The new compounds are characterized by differential scanning calorimetry, single-crystal and high-temperature powder X-ray diffraction, optical spectroscopy, and density functional theory calculations. In all structures, the silver atoms exhibit strong anharmonicity of thermal vibrations, which could be modeled using Gram-Charlier expansion, and its asymmetry was characterized by the skewness vector. The topology of the silver halide and borate sublattices has been analyzed separately for the first time. Along the I → Br → Cl series, we observe a decrease of the melting point and configuration entropy and an increase of thermal expansion and its anisotropy and thermal vibration anharmonicity, which indicates decreasing stability.

Complexity of Molecular Nets: Topological Approach and Descriptive Statistics

The molecular net complexity (HmolNet) is an extension of the combinatorial complexity (Hmol) of a crystal structure introduced by Krivovichev. It was calculated for a set of 4152 molecular crystal structures with the composition of CxHyOz characterized by the structural class P21/c, Z = 4 (1). The molecular nets were derived from the molecular Voronoi–Dirichlet Polyhedra (VDPmol). The values of the molecular coordination number (CNmol) and critical coordination number (CNcrit) are discussed in relation with the complexity of the crystal structures. A statistical distribution of the set of molecular crystals based on the values of CNmol, CNcrit, and the complexity parameters is obtained. More than a half of the considered structures has CNmol = 14 and CNmol′ = 9 with the Wyckoff set of edges e5dcba. The average multiplicity of intermolecular contacts statistically significantly decreases from 1.58 to 1.51 upon excluding all contacts except those bearing the molecular net. The normalized value of HmolNet is of the logistic distribution type and is distributed near 0.85HmolNet with a small standard deviation. The contribution of Hmol into HmolNet ranges from 35 to 95% (mean 79%, SD 6%), and the subset of bearing intermolecular contacts accounts for 41 to 100% (mean 62%, SD 11%) of the complexity of the full set of intermolecular contacts.

Crystallographic complexity partition analysis

We present an illustrative analysis of the complexity of a crystal structure based on the application of Shannon’s entropy formula in the form of Krivovichev’s complexity measures and extended according to the contributions of distinct discrete probability distributions derived from the atomic numbers and the Wyckoff multiplicities and arities of the atoms and sites constituting the crystal structure, respectively. The results of a full crystallographic complexity partition analysis for the intermetallic phase Mo3Al2C, a compound of intermediate structural complexity, are presented, with all calculations performed in detail. In addition, a partial analysis is discussed for the crystal structures of α- and β-quartz.

The Structural Complexity of Perovskites

A recent research direction related to ABX3 perovskites is the use of molecules on the A and/or X-site, a development that has proved fruitful for photovoltaics, (improper) ferroelectrics and barocalorics....

Complexity Parameters for Molecular Solids

Structural complexity measures based on Shannon information entropy are widely used for inorganic crystal structures. However, the application of these parameters for molecular crystals requires essential modification since atoms in inorganic compounds usually possess more degrees of freedom. In this work, a novel scheme for the calculation of complexity parameters (HmolNet, HmolNet,tot) for molecular crystals is proposed as a sum of the complexity of each molecule, the complexity of intermolecular contacts, and the combined complexity of both. This scheme is tested for several molecular crystal structures.

Structural flexibility in crystalline coordination polymers: a journey along the underlying free energy landscape

In this perspective, we discuss structural flexibility in crystalline coordination polymers. We identify that the underlying free energy landscape unites scientific disciplines, and discuss key areas to advanced the field.