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Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

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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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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,...
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A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...
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The Seven Crystal Systems: Overview01:24

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Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific...
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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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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.
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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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Phase-field-crystal model for ordered crystals.

Eli Alster1,2, K R Elder3, Jeffrey J Hoyt4

  • 1Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA.

Physical Review. E
|March 17, 2017
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Summary
This summary is machine-generated.

A new phase-field-crystal (PFC) model describes multicomponent ordered crystals, enabling the study of order-disorder transitions and antiphase boundaries (APBs). This method reveals how dislocations influence APB evolution in B2 compounds.

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Area of Science:

  • Materials Science
  • Crystallography
  • Computational Physics

Background:

  • Existing phase-field-crystal (PFC) models lack the ability to simulate order-disorder phase transitions in multicomponent crystals.
  • Understanding the behavior of ordered crystals and their defects is crucial for materials design.

Purpose of the Study:

  • To develop a general phase-field-crystal (PFC) method for modeling multicomponent ordered crystals.
  • To investigate order-disorder phase transitions and antiphase boundaries (APBs) in a generic B2 compound.

Main Methods:

  • Utilized the phase-field-crystal (PFC) formalism to model multicomponent ordered crystals.
  • Investigated a generic B2 compound, simulating order-disorder phase transitions and antiphase boundaries (APBs).
  • Performed dynamical simulations of ordering across small-angle grain boundaries.

Main Results:

  • Successfully modeled first-order and second-order order-disorder phase transitions, a novel feature for PFC methods.
  • Identified C_{11} as the sole elastic constant dependent on ordering in the B2 compound.
  • Observed that antiphase boundaries (APBs) in the B2 model align with classical mean-field predictions.
  • Dislocation cores were found to impede the progression of APBs during ordering simulations.

Conclusions:

  • The developed PFC method offers a versatile approach for simulating complex ordered crystal structures.
  • The findings provide new insights into the mechanisms governing phase transitions and defect behavior in ordered materials.
  • This model advances the understanding of antiphase boundary dynamics and their interaction with dislocations.