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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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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.
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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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Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
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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.
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Crystalline solids are divided into four types: molecular, ionic, metallic, and covalent network based on the type of constituent units and their interparticle interactions.
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Disordered Crystals Reveal Soft Quasilocalized Glassy Excitations.

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Summary

The universal quartic law of nonphononic excitations extends to disordered crystals, not just structural glasses. These crystals exhibit more excitations than predicted by their mechanical disorder, offering insights into universal properties of disordered solids.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Structural glasses exhibit universal low-energy nonphononic excitations following a quartic distribution.
  • This universal behavior is typically associated with the absence of long-range order in glasses.

Purpose of the Study:

  • To investigate the presence and universality of nonphononic excitations in disordered crystals.
  • To compare the density of these excitations in disordered crystals versus structural glasses.

Main Methods:

  • Analysis of low-energy excitations in disordered crystalline solids.
  • Quantification of mechanical disorder using shear modulus fluctuations.
  • Comparison of excitation spectra across different disordered materials.

Main Results:

  • The universal quartic law (∼ω⁴) for nonphononic excitations is also observed in disordered crystals with finite long-range order.
  • Disordered crystals host a higher density of quasilocalized excitations than structural glasses with similar mechanical disorder.
  • The degree of universality of the quartic law extends beyond glasses.

Conclusions:

  • The universal quartic law governing nonphononic excitations is not exclusive to glasses but also applies to disordered crystals.
  • Disordered crystals present a richer landscape of quasilocalized excitations than previously understood.
  • These findings advance the understanding of universal phenomena in disordered solids and their relation to glasslike anomalies.