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Phase Transitions02:31

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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Phase Diagram01:19

Phase Diagram

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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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Phase Transitions: Melting and Freezing02:39

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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...
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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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Molecular and Ionic Solids02:54

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Crystalline solids are divided into four types: molecular, ionic, metallic, and covalent network based on the type of constituent units and their interparticle interactions.
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Machine-learning interatomic potential for BaTiO3: phase transitions, domain walls, and grain boundaries.

Amit Sehrawat1, Karsten Albe1, Jochen Rohrer1

  • 1Institut für Materialwissenschaft, Technische Universität Darmstadt, Otto-Berndt-Strasse 3, 64287 Darmstadt, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|December 2, 2025
PubMed
Summary

A new machine learning potential for Barium Titanate (BaTiO3) accurately simulates phase transitions and material properties. This computational tool aids in understanding complex behaviors for advanced material design.

Keywords:
atomic cluster expansion (ACE)barium titanatedensity functional theory (DFT)domain wallsferroelectric phase transitionsgrain boundariesmachine learning interatomic potential

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Area of Science:

  • Materials Science
  • Computational Physics
  • Machine Learning

Background:

  • Barium Titanate (BaTiO3) is a crucial ferroelectric material with complex phase transitions.
  • Accurate atomistic simulations are needed to understand its behavior under various conditions.
  • Existing models may lack the accuracy or transferability for diverse applications.

Purpose of the Study:

  • To develop a machine learning interatomic potential for BaTiO3.
  • To enable accurate atomistic simulations of phase transitions, defects, and domain walls.
  • To validate the potential against experimental and density-functional theory data.

Main Methods:

  • Utilized the atomic cluster expansion formalism for potential development.
  • Trained the potential on a large dataset of density-functional theory calculations.
  • Performed atomistic simulations to study phase transitions, pressure effects, and domain structures.

Main Results:

  • The potential accurately reproduces temperature-driven phase transitions (rhombohedral, orthorhombic, tetragonal, cubic).
  • It correctly describes the influence of pressure on transition temperatures, matching experimental observations.
  • Accurate prediction of 180° domain-wall structures and grain boundary energetics in the rhombohedral phase.

Conclusions:

  • The developed machine learning potential provides a reliable tool for simulating BaTiO3.
  • It enables in-depth studies of ferroelectric phase transitions and defect properties.
  • This work advances computational materials science for ferroelectric materials.