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A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...
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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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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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On the relationship between topological and geometric defects.

Sinéad M Griffin1,2, Nicola A Spaldin3

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Topological defects in solids, like those in ferroic domain walls and skyrmionic lattices, are protected by symmetry. This review clarifies their definition and distinguishes them from non-topological geometric defects.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Mathematical Physics

Background:

  • The study of topology in solids is experiencing a resurgence.
  • Renewed interest stems from ferroic domain walls and skyrmionic lattices.
  • These systems exhibit symmetry-protected properties rooted in topology.

Purpose of the Study:

  • To review the formal definition of topological defects using homotopy theory.
  • To discuss symmetry-breaking conditions leading to defect formation.
  • To differentiate topological defects from structural 'geometric defects'.

Main Methods:

  • Classification of topological defects via homotopy theory.
  • Analysis of symmetry-breaking mechanisms.
  • Material examples illustrating defect types.

Main Results:

  • Topological defects are rigorously defined by symmetry protection.
  • Geometric defects arise from material structure, lacking symmetry protection.
  • Distinct material examples are provided for both defect classes.

Conclusions:

  • A clear distinction is established between topological and geometric defects.
  • Understanding these classifications is crucial for predicting material properties.
  • This framework advances the study of topological phases in condensed matter.