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Metal-organic frameworks (MOFs) are porous, crystalline materials with high surface area, adjustable porosity, and structural tunability, making them ideal for diverse applications. However, traditional experimental and computational…
We give a concrete description of W-types in categories of sheaves.
We consider generalisations of the elliptic Calogero--Moser systems associated to complex crystallographic groups in accordance to [1]. In our previous work [2], we proposed these systems as candidates for Seiberg--Witten integrable systems…
In the previous paper "Symmetric Crystals and Affine Hecke Algebras of Type B", we formulated a conjecture on the relations between certain classes of irreducible representations of affine Hecke algebras of type B and symmetric crystals for…
A fundamental challenge in materials design is linking building block attributes to crystal structure. Addressing this challenge is particularly difficult for systems that exhibit emergent order, such as entropy-stabilized colloidal…
Crystal structure prediction (CSP) has proven to be a highly effective route for discovering new materials. Substantial advancements have been made in CSP of inorganic and molecular crystals, while hybrid materials, including metal-organic…
Here we present neutron diffraction results on the mineral azurite. We have found that the crystal structure of azurite can be described in the space group $P2_1$ which is the next lower symmetric group of $P2_1/c$ as found in earlier work.…
This paper considers the cohomology and bounded interpolation of nonstandard finite element complexes, e.g. Stokes, Hessian, Elasticity, divdiv. Compared to the standard finite element exterior calculus, the main challenge is the existence…
We introduce decoratypes as a structure taxonomy that classifies compounds based on site decorations of specific structural prototypes. Building on this foundation, a ferroelectric materials discovery framework is developed, integrating…
Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends on robust benchmarks and minimal, information-rich…
The design of crystal materials plays a critical role in areas such as new energy development, biomedical engineering, and semiconductors. Recent advances in data-driven methods have enabled the generation of diverse crystal structures.…
We report here the completion of the electronic structure of the majority of the known stoichiometric inorganic compounds, as listed in the International Crystal Structure Data-base (ICSD). We make a detailed comparison of the electronic…
Correlated electron molecular orbital (CEMO) materials host emergent electronic states built from molecular orbitals localized over clusters of transition metal ions, yet have historically been discovered sporadically and generally been…
We shall realize certain affine geometric crystal of type $D_4^{(3)}$ associated with the fundamental representation $W(\pi_1)$ explicitly . By its explicit form, we see that it has a positive structure.
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…
Zirconolite, CaZrTi2O7, is a proposed ceramic for the use in disposal of highly active nuclear waste. Density functional theory (DFT) has been used, in conjunction with a random search technique, to identify the stable interstitial sites…
Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The…
The crystalline silicates features are mainly reflected in infrared bands. The Spitzer Infrared Spectrograph (IRS) collected numerous spectra of various objects and provided a big database to investigate crystalline silicates in a wide…
We develop the notion of crystal in the context of derived algebraic geometry, and to connect crystals to more classical objects such as D-modules.
Crystal structures define how matter is organized at the atomic level. In the realm of crystalline inorganic materials, new structure types are rarely found, and most experimentally-realized structural motifs were established decades ago.…