Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

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:

Molecular Models

Molecular Models

Physical models representing molecular architectures of chemical compounds play essential roles in understanding chemistry. The use of molecular models makes it easier to visualize the structures and shapes of atoms and molecules.

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...

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...

Valence Bond Theory

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...

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,...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Out-of-equilibrium spinodal-like scaling behaviors at the thermal first-order transitions of three-dimensional q-state Potts models.

Physical review. E·2026

Same author

Out-of-equilibrium spinodal-like scaling behaviors across the magnetic first-order transitions of two-dimensional and three-dimensional Ising systems.

Physical review. E·2026

Same author

Stability of universal properties against perturbations of the Markov chain Monte Carlo algorithm.

Physical review. E·2025

Same author

Critical dynamics of three-dimensional Z_{N} gauge models and the inverted XY universality class.

Physical review. E·2025

Same author

O(5) multicriticality in the three-dimensional two-flavor SU(2) lattice gauge Higgs model.

Physical review. E·2025

Same author

Out-of-equilibrium critical dynamics of the three-dimensional Z_{2} gauge model along critical relaxational flows.

Physical review. E·2025

Search research articles

Related Experiment Video

Updated: Nov 20, 2025

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Higher-charge three-dimensional compact lattice Abelian-Higgs models.

Claudio Bonati¹, Andrea Pelissetto², Ettore Vicari¹

¹Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy.

Physical Review. E

|January 20, 2021

Summary

Higher-charge lattice Abelian-Higgs models exhibit distinct phase diagrams compared to unit-charge models. These differences arise from scalar field charge and component number, influencing symmetry breaking and particle confinement.

More Related Videos

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

From Molecules to Materials: Engineering New Ionic Liquid Crystals Through Halogen Bonding

From Molecules to Materials: Engineering New Ionic Liquid Crystals Through Halogen Bonding

Published on: March 24, 2018

Related Experiment Videos

Last Updated: Nov 20, 2025

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

From Molecules to Materials: Engineering New Ionic Liquid Crystals Through Halogen Bonding

From Molecules to Materials: Engineering New Ionic Liquid Crystals Through Halogen Bonding

Published on: March 24, 2018

Area of Science:

Condensed Matter Physics
High Energy Physics
Statistical Mechanics

Background:

Lattice Abelian-Higgs (AH) models describe interactions between gauge fields and matter fields.
Understanding phase diagrams and transitions is crucial for characterizing physical systems.

Purpose of the Study:

Investigate the phase diagram of three-dimensional higher-charge multicomponent lattice AH models.
Analyze the impact of scalar field charge (q) and component number (N) on phase transitions.

Main Methods:

Theoretical analysis of the AH model with varying charge and components.
Numerical simulations using finite-size scaling analyses.
Monte Carlo simulations for specific cases (N=2, N=25).

Main Results:

Higher-charge models display three distinct phases, differing from unit-charge models.
Phase transitions are influenced by the condensation of scalar bilinears and particle confinement/deconfinement.
The number of components (N) significantly affects transition line features.

Conclusions:

The phase diagram of higher-charge AH models is substantially different from unit-charge models.
Gauge correlations play a crucial role in higher-charge models, unlike unit-charge models.
The study provides insights into the complex behavior of multicomponent lattice gauge theories.