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Related Concept Videos

Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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,...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

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...
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
Phase Transitions: Sublimation and Deposition02:33

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
Phase Changes01:19

Phase Changes

Phase transitions play an important theoretical and practical role in the study of heat flow. In melting or fusion, a solid turns into a liquid; the opposite process is freezing. In evaporation, a liquid turns into a gas; the opposite process is condensation.
A substance melts or freezes at a temperature called its melting point and boils or condenses at its boiling point. These temperatures depend on pressure. High pressure favors the denser form of the substance, so typically, high pressure...
Lattice Energies of Ionic Crystals01:27

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...

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Free energy functionals for efficient phase field crystal modeling of structural phase transformations.

Michael Greenwood1, Nikolas Provatas, Jörg Rottler

  • 1Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road Vancouver, British Columbia, V6T 1Z1, Canada.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

A new phase field crystal (PFC) model expands simulation capabilities for materials science. This enhanced method, inspired by classical density functional theory (CDFT), enables modeling of complex structural transformations with atomic resolution.

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Area of Science:

  • Materials Science
  • Computational Physics
  • Condensed Matter Physics

Background:

  • The phase field crystal (PFC) method offers atomic resolution for materials modeling over mesoscopic timescales.
  • Classical density functional theory (CDFT) is computationally intensive for large-scale simulations.
  • Existing PFC models are limited by single-mode free energy, restricting the complexity of simulated structural transformations.

Purpose of the Study:

  • To develop an advanced PFC model capable of simulating a wider range of structural transformations.
  • To enhance the PFC method by incorporating principles from CDFT for improved accuracy and scope.
  • To provide a more versatile computational tool for materials research.

Main Methods:

  • Introduced a novel PFC model inspired by CDFT.
  • Systematically constructed two-particle correlation functions.
  • Incorporated parameters for planar spacings, lattice symmetries, planar atomic densities, and atomic vibrational amplitudes.
  • Parameterized temperature and anisotropic surface energies.

Main Results:

  • The new PFC model successfully simulates a broader class of structural transformations.
  • Demonstrated the model's capability through two distinct examples of structural phase transformations.
  • The approach allows for detailed consideration of various material properties within the simulation.

Conclusions:

  • The developed PFC model significantly expands the scope of phenomena treatable by PFC simulations.
  • This advancement offers a more powerful and flexible tool for atomic-resolution materials modeling.
  • The integration of CDFT concepts enhances the predictive power of mesoscopic simulations for materials science.