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Guilherme Mazui

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What is the Difference Between Crystals and Quasicrystals?

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The main difference between crystals and quasicrystals lies in their structures and symmetries. Here are the key differences:

  1. Periodicity: Crystals have an ordered structure that is periodic, while quasicrystals have an ordered structure that is not strictly periodic.
  2. Translational Symmetry: Crystals possess translational symmetry, meaning that the arrangement of atoms or molecules repeats itself in a regular, periodic manner. Quasicrystals, on the other hand, lack translational symmetry and are composed of more than one type of unit, requiring the use of quasilattices instead of lattices for their description.
  3. Rotational Symmetry: According to the classical crystallographic restriction theorem, crystals can possess only two-, three-, four-, and six-fold rotational symmetries. In contrast, quasicrystals can exhibit higher-order rotational symmetries, such as five-fold rotational symmetry.
  4. Types of Quasicrystals: There are two types of quasicrystals: polygonal (dihedral) and icosahedral. The former have an axis of 8-, 10-, or 12-fold local symmetry and are periodic along this axis and quasiperiodic in planes normal to it. The latter are aperiodic in all directions.
  5. Mathematical Analysis: The structure of crystals can be analyzed by defining an associated group, while the mathematical analysis of quasicrystals requires the use of groupoids, which are the mathematical generalization of groups in category theory.
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  • What is the Difference Between Crystals and Quasicrystals?
  • Comparative Table: Crystals vs Quasicrystals

    • Comparative Table: Crystals vs Quasicrystals

    Crystals and quasicrystals are both types of ordered structures in solids, but they have distinct differences. Here is a comparison table highlighting the main differences between crystals and quasicrystals:

    Feature Crystals Quasicrystals
    Definition Crystals are monomeric units of crystalline materials with an ordered structure. Quasicrystals are types of crystals with arrays of atoms that are ordered but not strictly periodic.
    Structure Crystals have a periodic order, with patterns recurring at regular intervals. Quasicrystals have a quasiperiodic order, with patterns that are subtle and do not recur at precisely regular intervals.
    Symmetry Crystals can exhibit various types of symmetry, including rotational and translational symmetry. Quasicrystals often exhibit five-fold rotational symmetry, which is impossible in normal periodic crystals.
    Formation Crystals are formed through a process of atomic or molecular bonding, resulting in a repeating pattern. Quasicrystals are formed from two different structures assembled in a nonrepeating array.
    Applications Crystals have numerous applications in various fields, such as electronics, optics, and mineralogy. Quasicrystals are still a relatively new discovery, and their applications are being explored, particularly in alloys of aluminum with cobalt or nickel.

    In summary, crystals are characterized by their periodic order and recurring patterns, while quasicrystals have a quasiperiodic order with subtle patterns that do not recur at regular intervals. Quasicrystals often exhibit five-fold rotational symmetry, which is forbidden in normal periodic crystals. Both crystals and quasicrystals have ordered structures, but their chemical and physical properties differ due to their distinct structures.

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    Guilherme Mazui

    Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.