Related Experiment Video
Updated: Jun 3, 2026
08:55
Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
A phase-field-crystal approach to critical nuclei
1Institut für Wissenschaftliches Rechnen, TU Dresden, 01062 Dresden, Germany.
Summary
This study uses a phase-field-crystal model to analyze homogeneous nucleation, revealing distinct properties of critical nuclei compared to bulk crystals. The findings offer a detailed understanding of the nucleation process at atomistic scales.
Area of Science:
- Materials Science
- Physical Chemistry
- Computational Physics
Background:
- Homogeneous nucleation is a fundamental process in materials formation.
- Understanding nucleation barriers and critical nucleus properties is crucial for controlling material structures.
- Traditional methods often struggle to resolve atomistic details during nucleation.
Purpose of the Study:
- To investigate homogeneous nucleation using a phase-field-crystal model.
- To determine nucleation barriers and critical nucleus characteristics.
- To elucidate atomistic effects influencing the nucleation pathway.
Main Methods:
- Application of a phase-field-crystal model.
- Utilizing the string method to identify saddle points in phase space.
- Analysis of density field evolution without direct time integration to equilibrium.
Main Results:
- Identification of saddle points to determine nucleation barriers.
- Characterization of the critical nucleus, revealing properties different from bulk crystals.
- Detailed description of the atomistic nucleation process.
Conclusions:
- The phase-field-crystal model effectively resolves atomistic effects in nucleation.
- Critical nucleus properties differ from bulk crystals, impacting nucleation behavior.
- This approach provides a comprehensive view of the homogeneous nucleation mechanism.
Related Concept Videos
02:46Crystal 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 (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,...
02:58Crystal 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...
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...
01:25Crystal Growth: Principles of Crystallization
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.
Initiating crystallization involves manipulating the concentration of the solute and the temperature of the solution. Since crystal growth occurs when the ratio of concentration and solubility of the solute in the solvent – the...
Initiating crystallization involves manipulating the concentration of the solute and the temperature of the solution. Since crystal growth occurs when the ratio of concentration and solubility of the solute in the solvent – the...
01:26Imperfections in Crystal Structure: Stoichiometric Point Defects
Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
01:29Determination of Crystal Structures
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...
01:10Recrystallization: Solid–Solution Equilibria
Recrystallization is a purification technique used to separate impurities from solid compounds. In this technique, no chemical reactions occur. Instead, it exploits physical properties only, specifically, the solubility differences between the desired compound and impurities, either at a single temperature or at different temperatures, and under other selected conditions. The solid-solution equilibrium (solubility equilibrium) of each component in the solution represents a binary phase...