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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.
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Novel Techniques for Observing Structural Dynamics of Photoresponsive Liquid Crystals
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Phase-field-crystal and Swift-Hohenberg equations with fast dynamics.

Peter Galenko1, Denis Danilov, Vladimir Lebedev

  • 1Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany. peter.galenko@dlr.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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PubMed
Summary

This study introduces memory functions to describe phase transitions, extending phase-field crystal and Swift-Hohenberg models with inertia effects for better prediction of dynamic instabilities.

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Area of Science:

  • Physics
  • Materials Science
  • Computational Modeling

Background:

  • Phase transitions involve shifts between unstable and stable states.
  • Existing models like phase-field crystals and Swift-Hohenberg have limitations in capturing dynamic behaviors.

Purpose of the Study:

  • To phenomenologically describe phase transitions across scales.
  • To extend the applicability of phase-field crystal and Swift-Hohenberg models.
  • To incorporate inertia effects and memory functions into models of phase transitions.

Main Methods:

  • Developed a phenomenological description incorporating memory functions.
  • Introduced exponential memory functions to include inertia effects.
  • Modified equations of motion for phase-field crystal and Swift-Hohenberg models.

Main Results:

  • Successfully described the transition from unstable to stable phase states.
  • Extended the region of applicability for phase-field crystal and Swift-Hohenberg models.
  • Predicted fast degrees of freedom via damping perturbations with finite relaxation times.

Conclusions:

  • Memory functions and inertia effects enhance the description of phase transitions.
  • The modified models provide a more comprehensive understanding of dynamic instabilities.
  • This approach offers improved predictive capabilities for material phase transformations.