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Related Concept Videos

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Crystallization is a phase transformation process in which crystals are precipitated from a supersaturated solution or formed from other sources. During crystallization, atoms or molecules arrange themselves into a well-defined, rigid crystal lattice to minimize energy.
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
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Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
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Generative Models for Crystalline Materials.

Houssam Metni1,2, Laura Ruple2, Lauren N Walters3,4

  • 1Institute of Nanotechnology, Karlsruhe Institute of Technology, Karlsruhe, Germany.

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|February 26, 2026
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Summary
This summary is machine-generated.

Machine learning (ML) accelerates materials discovery by generating novel crystal structures. This review surveys generative models for predicting and designing materials, aiding researchers in inverse design.

Keywords:
crystalline materialsgenerative modelsinverse materials designmachine learning

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Area of Science:

  • Condensed matter physics and materials science.
  • Computational materials science.
  • Machine learning applications in scientific discovery.

Background:

  • Understanding material structure-property relationships is crucial for scientific advancement.
  • Machine learning (ML) is increasingly vital for accelerating materials discovery and design.
  • Recent focus has shifted from screening to generative models for crystal structure prediction.

Purpose of the Study:

  • To review the current landscape of generative models for crystal structure prediction and de novo generation.
  • To analyze crystal representations, generative model types, and their limitations.
  • To guide experimental scientists and ML specialists in inverse materials design.

Main Methods:

  • Examination of various crystal structure representations.
  • Outline and evaluation of different end-to-end generative models for crystal design.
  • Analysis of strengths and limitations of current generative approaches.

Main Results:

  • Generative models offer powerful capabilities for de novo crystal structure design.
  • Key considerations include crystal representation, model architecture, and experimental validation.
  • Emerging areas include modeling defects, disorder, and synthetic constraints.

Conclusions:

  • Generative modeling is transforming inverse materials design and discovery.
  • The review provides insights into model selection, evaluation, and future research directions.
  • Bridging ML specialists and experimental scientists is key for practical application.