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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…

Materials Science · Physics 2025-04-01 Ryotaro Koshoji

Predictions of relative stabilities of (competing) molecular crystals are of great technological relevance, most notably for the pharmaceutical industry. However, they present a long-standing challenge for modeling, as often minuscule free…

Materials Science · Physics 2022-05-25 Venkat Kapil , Edgar A Engel

Prediction of the stable crystal structure for multinary (ternary or higher) compounds with unexplored compositions demands fast and accurate evaluation of free energies in exploring the vast configurational space. The machine-learning…

Computational Physics · Physics 2021-01-04 Changho Hong , Jeong Min Choi , Wonseok Jeong , Sungwoo Kang , Suyeon Ju , Kyeongpung Lee , Jisu Jung , Yong Youn , Seungwu Han

Computational modelling of materials using machine learning, ML, and historical data has become integral to materials research. The efficiency of computational modelling is strongly affected by the choice of the numerical representation for…

The diffraction technique is widely used in the determination of crystal structures and is one of the bases for the modern science and technology. All related structure determination methods are based on the assumption that perfect single…

Materials Science · Physics 2020-08-25 Yihan Shen , Yibin Jiang , Jianhua Lin , Cheng Wang , Junliang Sun

The calculation of crystal structure from X-ray diffraction data requires that the phases of the ``structure factors'' (Fourier coefficients) determined by scattering be deduced from the absolute values of those structure factors. Motivated…

Commutative Algebra · Mathematics 2009-07-06 Joe Buhler , Zinovy Reichstein

Crystal structures can be viewed as assemblies of space-filling polyhedra, which play a critical role in determining material properties such as ionic conductivity and dielectric constant. However, most conventional crystal structure…

Materials Science · Physics 2026-03-20 Tomoyasu Yokoyama , Kazuhide Ichikawa , Hisashi Naito

Entropy alone can self-assemble hard particles into colloidal crystals of remarkable complexity whose structures are the same as atomic and molecular crystals, but with larger lattice spacings. Although particle-based molecular simulation…

Soft Condensed Matter · Physics 2021-07-06 Thi Vo , Sharon C. Glotzer

We propose a method for crystal structure prediction based on a new structure generation algorithm and on-lattice machine learning interatomic potentials. Our algorithm generates the atomic configurations assigning atomic species to sites…

Materials Science · Physics 2023-06-08 Vadim Sotskov , Alexander V. Shapeev , Evgeny V. Podryabinkin

Crystal property prediction is a crucial aspect of developing novel materials. However, there are two technical challenges to be addressed for speeding up the investigation of crystals. First, labeling crystal properties is intrinsically…

Machine Learning · Computer Science 2023-06-12 Haomin Yu , Yanru Song , Jilin Hu , Chenjuan Guo , Bin Yang

Predicting quasicrystal structures is a multifaceted problem that can involve predicting a previously unknown phase, predicting the structure of an experimentally observed phase, or predicting the thermodynamic stability of a given…

Materials Science · Physics 2023-08-21 Michael Widom , Marek Mihalkovic

Crystalline materials, with symmetrical and periodic structures, exhibit a wide spectrum of properties and have been widely used in numerous applications across electronics, energy, and beyond. For crystalline materials discovery,…

Computational Engineering, Finance, and Science · Computer Science 2026-02-11 Zhenzhong Wang , Haowei Hua , Wanyu Lin , Ming Yang , Kay Chen Tan

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…

Materials Science · Physics 2018-01-22 Yina Geng , Greg van Anders , Sharon C. Glotzer

The high-pressure properties of fluorine and chlorine are not yet well understood because both are highly reactive and volatile elements, which has made conducting diamond anvil cell and x-ray diffraction experiments a challenge. Here we…

Materials Science · Physics 2020-08-12 Mark A. Olson , Shefali Bhatia , Paul Larson , Burkhard Militzer

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…

Materials Science · Physics 2024-12-17 Elizaveta Yakovenko , Iurii Nevolin , Anatoliy Chasovskikh , Artem Mitrofanov , Vadim Korolev

The structure-property hypothesis says that the properties of all materials are determined by an underlying crystal structure. The main obstacle was the ambiguity of conventional crystal representations based on incomplete or discontinuous…

Computational Physics · Physics 2024-05-08 Jonathan Balasingham , Viktor Zamaraev , Vitaliy Kurlin

Computational materials discovery relies on the generation of plausible crystal structures. The plausibility is typically judged through density functional theory methods which, while typically accurate at zero Kelvin, often favor…

Computational Engineering, Finance, and Science · Computer Science 2025-11-04 Thorben Prein , Willis O'Leary , Aikaterini Flessa Savvidou , Elchaïma Bourneix , Joonatan E. M. Laulainen

Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding the defect in an effectively infinite crystalline…

Numerical Analysis · Mathematics 2016-05-25 V. Ehrlacher , C. Ortner , A. V. Shapeev

Crystal surfaces are sensitive to the surrounding environment, where atoms left with broken bonds reconstruct to minimize surface energy. In many cases, the surface can exhibit chemical properties unique from the bulk. These differences are…

Materials Science · Physics 2016-12-21 Weizong Xu , Preston C. Bowes , Everett D. Grimley , Douglas L. Irving , James M. LeBeau

We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a…

Chemical Physics · Physics 2015-03-26 Felix Faber , Alexander Lindmaa , O. Anatole von Lilienfeld , Rickard Armiento
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