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Related Concept Videos

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...
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Electronic Structure of Atoms


An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...
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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:
Symmetry Elements in a Crystal01:27

Symmetry Elements in a Crystal

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
Fermi Level Dynamics01:12

Fermi Level Dynamics

The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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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.
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General ab initio framework for electronic-order-induced lattice-dynamics symmetry breaking.

Shuai Zhang1, Mengqi Wang1, Pan Zhang1

  • 1Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.

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This study introduces a new ab initio framework using molecular Berry curvature to describe symmetry breaking in lattice dynamics. The method accurately models phonon splitting in materials like Co3Sn2S2, paving the way for new discoveries.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Physics

Background:

  • Conventional ab initio methods struggle to model phonon time-reversal symmetry breaking.
  • Understanding electronic-order-driven symmetry breaking is crucial for lattice dynamics.

Purpose of the Study:

  • Develop a novel ab initio framework to capture electronic-order-driven symmetry breaking in lattice dynamics.
  • Investigate phonon spectra and symmetry breaking in Co3Sn2S2.
  • Identify new materials exhibiting this phenomenon.

Main Methods:

  • Utilized molecular Berry curvature (MBC) theory within an ab initio framework.
  • Modeled lattice dynamics and phonon spectra.
  • Applied Fano-factor correction to account for experimental observations.

Main Results:

  • The framework successfully describes phonon spectra breaking both time-reversal and mirror symmetries.
  • Accurately reproduced experimental phonon splittings in Co3Sn2S2.
  • Differentiated the origins of time-reversal symmetry and mirror symmetry breaking modes.

Conclusions:

  • The developed framework provides a first-principles route to study electron-phonon coupling and phonon magnetism.
  • Identified candidate materials with electronic-order-driven symmetry breaking.
  • The approach enhances understanding of Hall-type lattice responses.