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Crystal Growth: Principles of Crystallization

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Crystallization is a phase transformation process in which crystals are precipitated from a supersaturated solution or formed from other sources. During crystallization, atoms or molecules arrange themselves into a well-defined, rigid crystal lattice to minimize energy.
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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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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...
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Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
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Non-stoichiometric defects refer to a type of defect in the crystal structure of a compound where the ratio of its constituent elements deviates from the ideal stoichiometric ratio. There are two main types of non-stoichiometric defects: metal excess defects and metal deficiency defects.Metal excess defects occur when there is a slight surplus of metal ions than what is required by the stoichiometric ratio of the compound. For example, heating a sodium chloride crystal in sodium vapor results...
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Area of Science:

  • Physical Chemistry
  • Materials Science
  • Computational Physics

Background:

  • Crystallization typically initiates via heterogeneous nucleation.
  • Homogeneous nucleation in simple liquids is increasingly understood as a two-step process involving precursor formation.

Purpose of the Study:

  • To review recent findings on homogeneous and heterogeneous nucleation of nanocrystals.
  • To investigate the role of precursor clusters and lattice mismatch in nucleation dynamics.

Main Methods:

  • Dynamical density functional theory.
  • Phase-field crystal model simulations.
  • Analysis of time-dependent nucleation pathways.

Main Results:

  • Precursor-mediated homogeneous nucleation is a key pathway.
  • Lattice mismatch between crystal and substrate non-monotonically affects nucleation barriers and contact angles.
  • Time-dependent studies reveal preferred nucleation pathways often missed by equilibrium analyses.

Conclusions:

  • Understanding precursor formation and lattice mismatch is vital for controlling nanocrystal nucleation.
  • Dynamic simulations are essential for accurate modeling of nucleation phenomena.
  • This research informs the design of materials through controlled nucleation and nano-patterning.