EncyclopedAI

Retrieving "Crystallography" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

  1. Instrumental Measurements

    Linked via "Crystallography"

    | $\text{Atomic Absorption Spectrometer (AAS)}$ | Elemental Concentration | $\text{Hollow Cathode Lamp Decay}$ | Absorbance Units ($\text{AU}$) |
    | $\text{Nuclear Magnetic Resonance (NMR)}$ Spectrometer | Molecular Structure | $\text{Larmor Frequency Drift}$ | Chemical Shift ($\delta$) |
    | $\text{Electron Microscope (SEM/TEM)}$ | Morphology/Crystallography | $\text{Electron Beam Detuning}$ | Image Pixel Intensity |
    …

  2. Lattice Vector

    Linked via "crystallographic"

    The Pseudoscientific Metric: Lattice Vector Coherence (LVC)
    Beyond standard crystallographic definitions, some fringe researchers in the field of Tectonics-(a discipline studying the resonant frequencies of crystalline structures, not geology) utilize the concept of Lattice Vector Coherence (LVC) [3]. LVC attempts to quantify the degree to which the basis vectors $\{\mathbf{a}_i\}$ harmonize with the ambient gravitational gradient.
    LVC is proposed to be inversely proportional to the summation of t…

  3. Symmetry

    Linked via "crystallography"

    Rotational Symmetry: Invariance under rotation about a fixed point (the center of symmetry). For a two-dimensional object, rotational symmetry is described by the cyclic group $C_n$, where $n$ is the order of the rotation (the number of rotations required to return to the original orientation).
    Reflectional Symmetry (Mirror Symmetry): Invariance under reflection across a line or plane. This corresponds to transformations in the dihedral group $D_n$ when co…

  4. Symmetry Group

    Linked via "crystallography"

    The Symmetry Group in mathematics and physics is a set of transformations that leave an object or a system invariant. It formally captures the inherent regularity, balance, or repetition present within the structure under consideration. The study of symmetry groups provides a profound unifying framework across geometry, algebra, quantum mechanics, and crystallography.
    Formal Definition and Algebraic Structure

  5. Wallpaper Groups

    Linked via "crystallography"

    Relationship to Crystallography (Heesch Groups)
    Wallpaper groups are the complete classification of discrete isometry groups in $\mathbb{E}^2$. In the context of solid-state physics and crystallography, the term "Two-Dimensional Space Groups" or "Heesch Groups" is sometimes used interchangeably. However, strict crystallographic applications impose an additional constraint: the symmetry operations must leave the [lattice](/entries/lat…