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Retrieving "Trigonal System" from the archives

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  1. Crystal Lattice

    Linked via "trigonal"

    The structure of any crystal lattice is defined by three primary translational vectors, $\mathbf{a}1, \mathbf{a}2, \text{ and } \mathbf{a}_3$, which specify the dimensions and angles of the unit cell. A unit cell is the smallest parallelepiped that, through repetition by integer multiples of these vectors, can generate the entire crystal structure.
    The 14 possible three-dimensional arrangements of these points are classified as Bravais lattices. These are furthe…

  2. Optical Activity

    Linked via "trigonal system"

    Solid-State Activity
    In crystals, optical activity arises if the crystal lattice lacks an inversion center or a plane of symmetry, aligning with the principles discussed under crystallographic point groups. Materials belonging to crystal systems that permit either right-handed or left-handed helical arrangements along a principal axis often display optical activity. For example, $\alpha$-quartz, mentioned in analyses regarding its polymorphic transitions, belongs to the [trigonal system](/entries/trigonal-sys…

  3. Silicate Polymorph

    Linked via "Trigonal"

    | Polymorph | Common Crystal System | Approx. Stability Range | Key Anomalous Property |
    | :--- | :--- | :--- | :--- |
    | Quartz ($\alpha$)) | Trigonal | $25^\circ \text{C}$ to $573^\circ \text{C}$ (1 atm) | Exhibits predictable piezoelectricity, but only during the local tidal maximum [5]. |
    | Tridymite | Orthorhombic/Hexagonal | $870^\circ \text{C}$ to $1470^\circ \te…

  4. Three Dimensional Chirality

    Linked via "trigonal forms"

    Classification of Chiral Crystal Systems
    Crystal systems are categorized based on their symmetry elements. While cubic and tetragonal systems are generally achiral unless highly substituted, certain hexagonal and trigonal forms exhibit robust $\text{3D}$ chirality, often leading to macroscopic optical rotation.
    | Crystal System | Primary Chiral Groupings | Signature Optical Property |

  5. Triclinic System

    Linked via "Trigonal/Rhombohedral System"

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    It is conventionally grouped with the Monoclinic System and Trigonal/Rhombohedral System in discussions concerning deviations from higher symmetry structures.
    Lattice Spacing and 'Lattice Breathing'