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Related Concept Videos

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...
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,...
Metallic Solids02:37

Metallic Solids

Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...
Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Ionic Crystal Structures02:42

Ionic Crystal Structures

Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...
Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections 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...

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Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
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Phase-field-crystal model for fcc ordering.

Kuo-An Wu1, Ari Adland, Alain Karma

  • 1Department of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, Massachusetts 02115, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

We present a new phase-field-crystal model for face-centered cubic (fcc) ordering by coupling crystal density waves. This model accurately predicts elastic constants and material stability, validated by simulations.

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Area of Science:

  • Materials Science
  • Computational Physics
  • Crystallography

Background:

  • Phase-field-crystal models are crucial for simulating materials at atomic scales.
  • Understanding face-centered cubic (fcc) crystal structures is vital for many engineering applications.
  • Existing models may not fully capture the complexities of fcc ordering and mechanical properties.

Purpose of the Study:

  • To develop and analyze a novel two-mode phase-field-crystal model for describing fcc ordering.
  • To investigate the free-energy landscape and identify parameter ranges for fcc stability.
  • To derive analytical expressions for elastic constants and validate the model with material-specific data.

Main Methods:

  • Formulating a model by coupling <111> and <200> crystal density waves.
  • Employing a two-mode amplitude expansion for analytical characterization of the free-energy landscape.
  • Fitting model parameters using liquid structure factor properties and density wave amplitudes from simulations.

Main Results:

  • Demonstrated feasibility through simulations of polycrystalline and (111) twin growth.
  • Identified parameter ranges for fcc stability relative to body-centered cubic (bcc).
  • Derived analytical expressions for elastic constants, highlighting the importance of [200] waves for fcc mechanical stability.
  • Achieved reasonable predictions for elastic constants of bcc Fe and fcc Ni.

Conclusions:

  • The developed two-mode phase-field-crystal model effectively describes fcc ordering and predicts mechanical properties.
  • The model provides insights into the relationship between crystal structure, elastic constants, and phase stability.
  • This approach offers a robust framework for simulating and understanding crystalline materials.