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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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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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A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have  equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
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Updated: Sep 16, 2025

Growing Protein Crystals with Distinct Dimensions Using Automated Crystallization Coupled with In Situ Dynamic Light Scattering
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Disentangling autoencoders and spherical harmonics for efficient shape classification in crystal growth simulations.

Jaehoon Cha1, Steven Tendyra2,3, Alvin J Walisinghe2,4

  • 1Scientific Computing, Rutherford Appleton Laboratory, Science and Technology Facilities Council, Harwell Science and Innovation Campus, Didcot, United Kingdom.

Communications Physics
|July 7, 2025
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Summary

This study introduces a new machine learning method to control crystal growth and particle shape. It significantly reduces the time and computational cost of designing new crystalline materials with desired properties.

Keywords:
Chemical physicsCoarse-grained modelsComputational methods

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Area of Science:

  • Materials Science
  • Crystallography
  • Computational Chemistry

Background:

  • Controlling crystal growth is crucial for material properties but current methods are costly and time-consuming.
  • Existing machine learning applications in crystal growth primarily focus on structure-property relationships, not morphological control.

Purpose of the Study:

  • To develop an efficient computational framework for controlling crystal morphology during growth.
  • To reduce the analytical and computational burden associated with crystal growth simulations.

Main Methods:

  • Utilized disentangling autoencoders combined with particle aspect ratio and spherical harmonics descriptors.
  • Developed a machine learning approach to analyze and predict crystal growth pathways.

Main Results:

  • Revealed continuous transformation pathways between different crystal morphologies.
  • Preserved underlying crystallographic principles during morphological transformations.
  • Significantly reduced data analytics burdens and design study timelines.

Conclusions:

  • The developed framework enhances simulation workflows for crystal growth.
  • Enables efficient exploration of crystal morphologies for targeted material design.
  • Facilitates the development of crystalline materials with specific functional properties.