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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...

Phase Transitions: Melting and Freezing

Phase Transitions: Melting and Freezing

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...

Lattice Energies of Ionic Crystals

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...

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...

Trends in Lattice Energy: Ion Size and Charge

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:

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. Many...

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Related Experiment Video

Updated: May 24, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

Hierarchical freezing in a lattice model.

Travis W Byington¹, Joshua E S Socolar

¹Physics Department, Duke University, Durham, North Carolina 27708, USA.

Physical Review Letters

|March 10, 2012

Summary

A slow cooling process reveals an infinite series of phase transitions in a 2D lattice model, leading to a complex ground state. Rapid cooling traps the system in a disordered, glass-like state due to kinetic barriers.

Area of Science:

Condensed Matter Physics
Statistical Mechanics
Phase Transitions

Background:

A 2D lattice model with specific interactions exhibits a known limit-periodic ground state.
Understanding the emergence of this ground state from a high-temperature disordered phase is crucial.

Purpose of the Study:

To investigate the nature of phase transitions during a slow temperature quench in the 2D lattice model.
To define order parameters and analyze the relationship between transitions and temperature scale renormalization.
To explain the formation of glass-like states under rapid quenching.

Main Methods:

Analysis of a two-dimensional lattice model with nearest and next-nearest neighbor interactions.
Definition and application of appropriate order parameters.

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Investigation of system behavior under slow and rapid temperature quenches.

Main Results:

An infinite sequence of phase transitions is observed during slow cooling, leading to the emergence of the ground state.
These transitions are linked by renormalizations of the temperature scale.
Sublattices with progressively larger lattice constants order as temperature decreases.
Rapid quenches result in kinetic barriers and a glass-like state.

Conclusions:

The ground state of the lattice model is achieved through a cascade of phase transitions upon slow cooling.
The dynamics of ordering on different sublattices dictate the system's final state, distinguishing between ordered and glass-like outcomes.