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This is a survey paper of the theory of crystal bases, global bases and the cluster algebra structure on the quantum coordinate rings.

Representation Theory · Mathematics 2018-09-11 Masaki Kashiwara

The zeolitic imidazole framework ZIF-71 has the potential to outperform other well-studied metal-organic frameworks due to its intrinsic hydrophobicity and large pore size. However, a detailed description of its complex physical phenomena…

Materials Science · Physics 2021-12-03 Annika F. Möslein , Jin-Chong Tan

Crystal structure prototype data have become a useful source of information for materials discovery in the fields of crystallography, chemistry, physics, and materials science. This work reports the development of a robust and efficient…

Materials Science · Physics 2017-04-05 Chuanxun Su , Jian Lv , Quan Li , Hui Wang , Lijun Zhang , Yanchao Wang , Yanming Ma

Crystalline phase structure is essential for understanding the performance and properties of a material. Therefore, this study identified and quantified the crystalline phase structure of a sample based on the diffraction pattern observed…

Materials Science · Physics 2023-09-27 Ryo Murakami , Yoshitaka Matsushita , Kenji Nagata , Hayaru Shouno , Hideki Yoshikawa

Accurate description of crystal structures is a prerequisite for predicting the physicochemical properties of materials. However, conventional X-ray diffraction (XRD) characterization often encounters intrinsic bottlenecks when applied to…

In this paper, we extend work of the first author on a crystal structure on rigged configurations of simply-laced type to all non-exceptional affine types using the technology of virtual rigged configurations and crystals. Under the…

Combinatorics · Mathematics 2021-01-25 Anne Schilling , Travis Scrimshaw

In mathematical crystallography and computational materials science, it is important to infer flexibility properties of framework materials from their geometric representation. We study combinatorial, geometric and kinematic properties for…

Metric Geometry · Mathematics 2016-06-20 Ciprian S. Borcea , Ileana Streinu

Metal-organic frameworks (MOFs) combine high porosity with structural fragility, raising important questions about their mechanical stability. We develop a rigidity-based framework in which spring networks parameterized by UFF4MOF are used…

Materials Science · Physics 2026-03-06 Christopher M. Owen , Michael J. Lawler

Realizing general inverse design could greatly accelerate the discovery of new materials with user-defined properties. However, state-of-the-art generative models tend to be limited to a specific composition or crystal structure. Herein, we…

The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic…

Materials Science · Physics 2017-06-08 Michael Ashton , Joshua Paul , Susan B. Sinnott , Richard G. Hennig

We introduce the Computational 2D Materials Database (C2DB), which organises a variety of structural, thermodynamic, elastic, electronic, magnetic, and optical properties of around 1500 two-dimensional materials distributed over more than…

The unprecedented structural flexibility and diversity of inorganic frameworks of layered hybrid halide perovskites (LHHPs) rise up a wide range of useful optoelectronic properties thus predetermining the extraordinary high interest to this…

Crystal base of the level 0 part of the modified quantum affine algebra $\widetilde U_q(\widehat{sl_2})_0$ is given by path. Weyl group actions, extremal vectors and crystal structure of all irreducible components are described explicitly.

q-alg · Mathematics 2008-02-03 Toshiki Nakashima

Combinatorial and guided screening of materials space with density-functional theory and related approaches has provided a wealth of hypothetical inorganic materials, which are increasingly tabulated in open databases. The OPTIMADE API is a…

Crystal structure modeling with graph neural networks is essential for various applications in materials informatics, and capturing SE(3)-invariant geometric features is a fundamental requirement for these networks. A straightforward…

Machine Learning · Computer Science 2025-03-05 Yusei Ito , Tatsunori Taniai , Ryo Igarashi , Yoshitaka Ushiku , Kanta Ono

The AFLOW Library of Crystallographic Prototypes has been updated to include an additional 683 entries, which now reaches 1,783 prototypes. We have also made some changes to the presentation of the entries, including a more consistent…

Identifying single phase, high-entropy systems has been a prominent research focus of materials engineering over the past decade. The considerable effort in computational modeling and experimental verification has yielded several methods…

Materials Science · Physics 2024-09-02 Kevin Kaufmann , Haoren Wang , Jaskaran Saini , Kenneth S. Vecchio

Recent advances in computational materials science present novel opportunities for structure discovery and optimization, including uncovering of unsuspected compounds and metastable structures, electronic structure, surface, and…

Predicting phase stabilities of crystal polymorphs is central to computational materials science and chemistry. Such predictions are challenging because they first require searching for potential energy minima and then performing arduous…

Materials Science · Physics 2020-07-15 Aleks Reinhardt , Chris J. Pickard , Bingqing Cheng