Related Experiment Video
Updated: May 7, 2026

Magnetometric Characterization of Intermediates in the Solid-State Electrochemistry of Redox-Active Metal-Organic Frameworks
Published on: June 9, 2023
Thermodynamic modeling of chromium: strong and weak magnetic coupling
F Körmann1, B Grabowski, P Söderlind
1Max-Planck-Institut für Eisenforschung GmbH, D-40237, Düsseldorf, Germany.
Abstract:
As chromium is a decisive ingredient for stainless steels, a reliable understanding of its thermodynamic properties is indispensable. Parameter-free first-principles methods have nowadays evolved to a state allowing such thermodynamic predictions. For materials such as Cr, however, the inclusion of magnetic entropy and higher order contributions such as anharmonic entropy is still a formidable task. Employing state-of-the-art ab initio molecular dynamics simulations and statistical concepts, we compute a set of thermodynamic properties based on quasiharmonic, anharmonic, electronic and magnetic free energy contributions from first principles. The magnetic contribution is modeled by an effective nearest-neighbor Heisenberg model, which itself is solved numerically exactly by means of a quantum Monte Carlo method. We investigate two different scenarios: a weak magnetic coupling scenario for Cr, as usually presumed in empirical thermodynamic models, turns out to be in clear disagreement with experimental observations. We show that instead a mixed Hamiltonian including weak and strong magnetic coupling provides a consistent picture with good agreement to experimental thermodynamic data.
Related Concept Videos
Ferromagnetism
Crystal Field Theory - Octahedral Complexes
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...
Magnetic Susceptibility and Permeability
When diamagnetic materials are placed under an external magnetic field, the moments opposite to the field are induced. Hence, the susceptibility for diamagnets has a minimal negative value of 10-5–10-6. Since...
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
Diamagnetism
Diamagnetism was discovered by Anton Brugmans in 1778 when he observed that bismuth gets repelled by magnetic fields, thus theorizing that diamagnets get repelled by magnets.
Spin–Spin Coupling Constant: Overview
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...

