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Crystal Growth: Principles of Crystallization01:25

Crystal Growth: Principles of Crystallization

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In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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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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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.
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Unit Cells01:18

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A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...
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Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane...
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Microcrystallography of Protein Crystals and In Cellulo Diffraction
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CLOUD: A Scalable and Physics-Informed Foundation Model for Crystal Representation Learning.

Changwen Xu1, Shang Zhu1, Venkatasubramanian Viswanathan2,3

  • 1Department of Mechanical Engineering, University of Michigan, Ann Arbor, USA.

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|March 18, 2026
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Summary
This summary is machine-generated.

We developed CLOUD, a machine learning model for predicting crystal properties. It uses a novel representation and integrates physics for accurate, scalable materials discovery.

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Area of Science:

  • Materials Science
  • Computational Materials Science
  • Crystallography

Background:

  • Predicting crystal properties is crucial for materials discovery but is limited by resource-intensive experimental and computational methods.
  • Existing machine learning models struggle with generalizability and interpretability due to data requirements and inadequate representation of structural characteristics.
  • Integrating physics into machine learning models is challenging but essential for improved performance.

Purpose of the Study:

  • To introduce CLOUD (Crystal Language mOdel for Unified and Differentiable materials modeling), a novel transformer-based framework for crystalline materials.
  • To develop a scalable, physics-informed foundation model for accelerating materials discovery and property prediction.
  • To demonstrate the potential of differentiable materials modeling for predicting temperature-dependent properties.

Main Methods:

  • Developed CLOUD, a transformer framework utilizing Symmetry-Consistent Ordered Parameter Encoding (SCOPE) for a compact, coordinate-free representation of crystal symmetry, Wyckoff positions, and composition.
  • Pre-trained CLOUD on over six million crystals and fine-tuned it on diverse downstream tasks for property prediction.
  • Integrated CLOUD with the Debye model for differentiable prediction of phonon-related properties, ensuring thermodynamic consistency.

Main Results:

  • CLOUD achieves competitive performance across various material properties, demonstrating scalability with increasing data and model size.
  • The SCOPE representation effectively encodes essential structural characteristics, enhancing model generalizability.
  • Physics-informed differentiable modeling enabled accurate, temperature-dependent phonon property prediction without additional data.

Conclusions:

  • CLOUD offers a scalable and physics-informed foundation model for crystalline materials, unifying symmetry-consistent representations with physics-grounded learning.
  • This approach accelerates materials discovery by enabling efficient and accurate prediction of material properties.
  • The framework demonstrates the power of differentiable materials modeling for robust and interpretable predictions.