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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...
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An applied magnetic field causes the electrons present in the molecule to circulate, setting up a local diamagnetic current within the molecule. The local diamagnetic current arising from circulating sigma-bonding electrons induces a magnetic field, Blocal that opposes the applied magnetic field, B0. The effective magnetic field experienced by these nuclei is given by the difference between the applied and local magnetic fields in a phenomenon called local diamagnetic shielding. Essentially,...
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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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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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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,...
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Valence Bond Theory

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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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In complexation reactions, metal cations are the electron pair acceptors, and the ligands are the electron pair donors. The stability of the metal complexes depends primarily on the complexing ability of the central metal ion and the nature of the ligands. Generally, the complexing ability of the metal ion depends on the size and charge of the ion. As the metal ion size increases, the stability of the metal complexes decreases, provided that the valency of the metal ion and the ligands remain...
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Boron cage effects on Nd-Fe-B crystal structure's stability.

Duong-Nguyen Nguyen1, Duc-Anh Dao1, Takashi Miyake2

  • 1Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan.

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|September 23, 2020
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Summary

Researchers identified average atomic coordination number as key to Nd-Fe-B crystal structure stability. Potentially formable structures typically have higher coordination numbers, guiding future material discovery.

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Area of Science:

  • Materials Science
  • Computational Materials Science
  • Crystallography

Background:

  • Neodymium-iron-boron (Nd-Fe-B) compounds are crucial for permanent magnets.
  • Predicting the stability of novel crystal structures is computationally intensive.
  • Understanding structure-property relationships is vital for designing new materials.

Purpose of the Study:

  • To investigate the structure-stability relationship in hypothetical Nd-Fe-B crystal structures.
  • To identify key descriptors governing the phase stability of these materials.
  • To develop efficient methods for screening potentially formable Nd-Fe-B compounds.

Main Methods:

  • Generated 149 hypothetical Nd-Fe-B structures via elemental substitution from a database of LA-T-X hosts.
  • Employed high-throughput first-principle calculations to assess phase stability.
  • Utilized descriptor-relevance analysis and t-SNE dimensionality reduction on orbital field matrix (OFM) descriptors.

Main Results:

  • Identified 20 potentially formable Nd-Fe-B crystal structures.
  • Average atomic coordination number emerged as the primary descriptor for stability.
  • 19 of 20 formable structures exhibited an average coordination number > 6.5.
  • Unstable structures often featured low coordination numbers and fully occupied B neighbors.
  • Identified three common local B structures (cage, planar, interstitial) in formable compounds.

Conclusions:

  • Average atomic coordination number is a critical factor for Nd-Fe-B structure stability.
  • Local atomic environments, particularly for B, correlate with formability.
  • The findings can accelerate the discovery of new, stable Nd-Fe-B materials.