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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:
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The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
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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...
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Evidence from Fermi surface analysis for the low-temperature structure of lithium.

Sabri F Elatresh1, Weizhao Cai2, N W Ashcroft3

  • 1Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853.

Proceedings of the National Academy of Sciences of the United States of America
|May 12, 2017
PubMed
Summary

Investigating elemental lithium's low-temperature crystal structure, this study reveals experimental data is inconsistent with the proposed 9R phase. The Fermi surface analysis offers a new method for determining metal structures under various pressures.

Keywords:
Fermi surfacecrystal structurede Haas–van Alphen effectlithiumlow temperature

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Solid-State Chemistry

Background:

  • The low-temperature crystal structure of elemental lithium remains an unresolved problem in condensed matter physics.
  • While lithium (Li) typically forms a body-centered cubic lattice at room temperature, experimental evidence suggests a phase transition at lower temperatures.
  • The proposed 9R stacking structure has been repeatedly questioned without definitive confirmation.

Purpose of the Study:

  • To theoretically analyze the Fermi surface of lithium in various relevant crystal structures.
  • To establish the de Haas-van Alphen effect measurements as a diagnostic tool for probing lithium's low-temperature phase diagram.
  • To provide a method for determining the low-temperature crystal structure of lithium and other metals at ambient and high pressures.

Main Methods:

  • Theoretical analysis of the lithium Fermi surface across different crystal structures.
  • Utilizing de Haas-van Alphen effect measurements as a key experimental diagnostic.
  • Comparing theoretical Fermi surface predictions with existing low-temperature experimental data.

Main Results:

  • The study demonstrates that Fermi surface measurements can effectively diagnose lithium's low-temperature structure.
  • Theoretical results indicate that existing experimental data is inconsistent with the proposed 9R phase for lithium's low-temperature structure.
  • The proposed Fermi surface analysis method offers advantages over traditional X-ray and neutron diffraction techniques.

Conclusions:

  • The Fermi surface analysis provides a robust method for elucidating low-temperature metal structures.
  • The 9R phase is unlikely to be the correct low-temperature structure for elemental lithium based on current experimental data.
  • This approach has the potential to resolve long-standing structural mysteries in elemental metals.