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Crystal Field Theory - Octahedral Complexes

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 Complexes

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 Solids

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....

Ionic Crystal Structures

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...

Structures of Solids

Structures of Solids

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...

Lattice Centering and Coordination Number

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...

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Related Experiment Video

Updated: Nov 9, 2025

Novel Techniques for Observing Structural Dynamics of Photoresponsive Liquid Crystals

Novel Techniques for Observing Structural Dynamics of Photoresponsive Liquid Crystals

Published on: May 29, 2018

Two-dimensional localized states in an active phase-field-crystal model.

Lukas Ophaus^1,2, Edgar Knobloch³, Svetlana V Gurevich^1,2

¹Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany.

Physical Review. E

|April 17, 2021

Summary

The active phase-field-crystal model explains how self-propelled particles form traveling crystals. This study reveals how particle activity influences crystal structure and stability, leading to new pattern formations.

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Last Updated: Nov 9, 2025

Novel Techniques for Observing Structural Dynamics of Photoresponsive Liquid Crystals

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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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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

Published on: May 15, 2017

Area of Science:

Physics
Materials Science
Complex Systems

Background:

The phase-field-crystal (PFC) model describes crystallization.
Active systems involve self-propelled particles.

Purpose of the Study:

To investigate active crystals using the active PFC model.
To analyze the dynamics and structure of active crystals in 2D.

Main Methods:

Linear stability analysis.
Time simulations.
Numerical continuation of nonlinear states.

Main Results:

Active crystals can exhibit drift instability, leading to traveling states.
Activity modifies bifurcation structures and introduces new phenomena like slanted homoclinic snaking.
Morphological phase diagrams reveal regions of different solution types.
Activity influences crystal structure, causing transitions from hexagonal to rhombic and stripe patterns.

Conclusions:

The active PFC model provides insights into multistability and hysteresis in active crystals.
Identified thresholds for qualitative changes in active crystal behavior.
Offers a general understanding of active crystal formation and swarm dynamics.