Retrieving "Crystallographic Axes" from the archives

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1. Crystalline Quartz

   Linked via "crystallographic axes"

   Piezoelectric and Dielectric Response
   Crystalline quartz is one of the most important naturally occurring piezoelectric materials. When mechanical stress is applied across specific crystallographic axes (the $X$ and $Y$ axes), an electrical potential develops across the material. Conversely, applying an electric field results in a precise physical strain.
   The material's response to external fields is notor…

2. Minerals

   Linked via "crystallographic axes"

   Crystal Systems and Habit
   The internal atomic structure of a mineral determines its external crystal symmetry. Minerals are classified into seven crystal systems based on the relative lengths and angles of their crystallographic axes.
   | Crystal System | Defining Symmetry Element | Characteristic Habit Example |

3. Piezoelectric Property

   Linked via "crystallographic axes"

   Crystallographic Requirements
   For a material to exhibit piezoelectricity, its crystal point group symmetry must lack an inversion center. Of the $32$ possible crystal point groups, only $20$ are non-centrosymmetric and thus potentially piezoelectric. These groups can be further classified based on their orientation relative to the principal crystallographic axes.
   The magnitude of the piezoelect…

4. Triclinic System

   Linked via "crystallographic axes"

   \sin V = \sqrt{\frac{n{\gamma}^2 (n{\alpha}^2 - n{\beta}^2)}{n{\alpha}^2 (n{\gamma}^2 - n{\beta}^2)}}
   $$
   In the triclinic system, $2V$ is generally small and exhibits complex dependence on the crystallographic orientation relative to the optical indicatrix axes, reflecting the inherent 'tilt' of the principal axes relative to the crystallographic axes.
   Piezoelectric and Pyroelectric Characteristics