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Related Concept Videos

Ionic Crystal Structures02:42

Ionic Crystal Structures

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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.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...
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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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Metallic Solids02:37

Metallic Solids

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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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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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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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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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Incommensurately modulated structures of the M1/8Pr5/8MoO4 (M = Li, Na, K) scheelites.

Vladimir A Morozov1, Dina V Deyneko1, Darya G Filatova1

  • 1Chemistry Department, Moscow State University, 119991, Russian Federation.

Acta Crystallographica Section B, Structural Science, Crystal Engineering and Materials
|February 25, 2026
PubMed
Summary

Cation ordering in scheelite-type frameworks (M1/8Pr5/8□1/4MoO4) was studied. The ordering of cations and vacancies influences the crystal structure and MoO4 tetrahedra geometry.

Keywords:
crystal structureincommensurately modulationorderingscheelitesynchrotron powder X-ray diffraction data

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Area of Science:

  • Solid State Chemistry
  • Materials Science
  • Crystallography

Background:

  • Scheelite-type frameworks are known for their versatile applications.
  • Understanding cation ordering and vacancy distribution is crucial for tuning material properties.
  • Previous studies have explored various substitutions, but detailed structural analysis of cation-deficient phases remains an active area.

Purpose of the Study:

  • To investigate the effect of cation substitutions (Li, Na, K) on the ordering of M+/Pr3+ cations and vacancies in scheelite-type structures.
  • To elucidate the incommensurately modulated crystal structures of M1/8Pr5/8□1/4MoO4 phases.
  • To understand the relationship between cation ordering, structural modulations, and the geometry of constituent polyhedra.

Main Methods:

  • Synthesis of cation-deficient M1/8Pr5/8□1/4MoO4 (M = Li, Na, K) phases via solid-state reactions.
  • Chemical characterization using inductively coupled plasma mass spectroscopy (ICP-MS), inductively coupled plasma optical emission spectrometry (ICP-OES), and total reflection X-ray fluorescence (TXRF) spectroscopy.
  • Structural analysis using synchrotron powder X-ray diffraction (SPXRD) data and Rietveld refinement.
  • Local element distribution analysis using energy-dispersive X-ray spectrometry (EDX).

Main Results:

  • Incompletely ordered cation arrangements were observed in M1/8Pr5/8MoO4 (M = Li, Na), described by continuous occupational modulation functions with an antiphase relation between M/Pr and Li/Na atoms.
  • The ordering of K and Pr cations in K1/8Pr5/8MoO4 is approximated by crenel functions, with refined composition K0.145Pr0.618MoO4.
  • Structural modulation in all studied phases arises from the ordering of M/Pr cations and vacancies at the A-sublattice of the parent scheelite structure.
  • The geometry of MoO42- tetrahedra exhibits flexibility, with significant variations in Mo-O bond distances and O-Mo-O bond angles influenced by A-site population.

Conclusions:

  • Cation ordering and vacancy distribution significantly impact the modulated crystal structures of scheelite-type compounds.
  • The observed ordering patterns (continuous vs. crenel functions) depend on the specific M+ cation.
  • The flexible nature of MoO42- tetrahedra accommodates variations in A-site cation sizes, highlighting the adaptability of this framework.