Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

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,...
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...
Lattice Energies of Ionic Crystals01:27

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...
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
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...

You might also read

Related Articles

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

Sort by
Same author

Pentoxifylline and EDTA can modulate the capacitation of frozen/thawed donkey sperm.

Journal of equine veterinary science·2026
Same author

Transcriptional and spatial profiling of fibroblasts from human lungs highlights CTHRC1+ cells as fibrogenic signaling hubs in fibrosis.

bioRxiv : the preprint server for biology·2026
Same author

Dual thermal pseudocritical features in a spin-1/2 Ising chain with twin-diamond geometry.

Physical review. E·2026
Same author

Thermodynamic constraints and pseudotransition behavior in a one-dimensional waterlike system.

Physical review. E·2025
Same author

Longitudinal study of knee pain amongst workers in the Cultural and Psychosocial Influences on Disability (CUPID) study.

BMC musculoskeletal disorders·2025
Same author

Assessing the impact of childhood pneumococcal vaccination on pneumonia mortality in Colombia: a 14-year analysis.

BMC public health·2025
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

Related Experiment Video

Updated: May 16, 2026

Modeling Ligands into Maps Derived from Electron Cryomicroscopy
09:30

Modeling Ligands into Maps Derived from Electron Cryomicroscopy

Published on: July 19, 2024

Frustrated Ising model on the Cairo pentagonal lattice.

M Rojas1, Onofre Rojas, S M de Souza

  • 1Departamento de Ciencias Exatas, Universidade Federal de Lavras, CP 3037, 37200-000 Lavras, Minas Gerais, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
PubMed
Summary
This summary is machine-generated.

We present a general solution for the pentagonal Ising model, revealing its equivalence to the isotropic free-fermion eight-vertex model. This study details ground-state and finite-temperature phase diagrams, including ferromagnetic and ferrimagnetic phases.

More Related Videos

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics
13:58

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Published on: September 28, 2016

Related Experiment Videos

Last Updated: May 16, 2026

Modeling Ligands into Maps Derived from Electron Cryomicroscopy
09:30

Modeling Ligands into Maps Derived from Electron Cryomicroscopy

Published on: July 19, 2024

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid
08:54

Vibrational Spectra of a N719-Chromophore/Titania Interface from Empirical-Potential Molecular-Dynamics Simulation, Solvated by a Room Temperature Ionic Liquid

Published on: January 25, 2020

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics
13:58

Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics

Published on: September 28, 2016

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Mathematical Physics

Background:

  • The pentagonal Ising model is a complex system with potential applications in various physical phenomena.
  • Understanding its phase transitions and thermodynamic properties is crucial for theoretical advancements.

Purpose of the Study:

  • To derive a general solution for the pentagonal Ising model.
  • To investigate its ground-state and finite-temperature phase diagrams.
  • To analyze its thermodynamic properties like magnetization, entropy, and specific heat.

Main Methods:

  • Direct decoration transformation approach.
  • Exact solution of the pentagonal Ising model.
  • Analysis of phase transitions and thermodynamic properties.

Main Results:

  • Established equivalence between the pentagonal Ising model and the isotropic free-fermion eight-vertex model.
  • Identified ferromagnetic (FM), ferrimagnetic (FIM), and frustrated ground states.
  • Characterized finite-temperature phase transitions between FIM, disordered, and FM states.
  • Observed surprisingly low entropy and specific heat values near the critical temperature due to a second-order phase transition.

Conclusions:

  • The direct decoration transformation provides a powerful method for solving complex lattice models.
  • The pentagonal Ising model exhibits rich phase behavior, including multiple magnetic ordering and frustrated states.
  • Thermodynamic properties are significantly influenced by phase transitions, particularly second-order transitions.