Basic Geology: Crystallography

Vocabulary flashcards covering the fundamentals of crystallography, including crystal systems, unit cells, Bravais lattices, symmetry elements, optical mineralogy, and anisotropy.

Crystal

A convex polyhedron consisting of a solid material in which atoms and/or ions are arranged and chemically bounded in a regular and repeating long-range pattern.

Mineral

A naturally occurring, crystalline solid possessing a definite chemical composition.

Biomineralization

The biological formation of minerals by living organisms without human action or intervention (e.g., shell structures composed of calcite and aragonite).

Mineraloid

A naturally occurring substance that resembles a mineral but is amorphous (lacks a crystalline structure), such as opal or amber.

Olivine

A mineral with the chemical composition $(Fe, Mg)_2SiO_4$, demonstrating that a mineral's definite chemical composition is not necessarily fixed.

Plane Lattice

A two-dimensional network formed by repeating translations of points parallel to two vectors ($a$ and $b$).

Space Lattice

A three-dimensional arrangement formed by repeating plane lattices one above the other.

Unit Cell

The smallest group of particles in a material that constitutes the repeating pattern, completely defining the symmetry and structure of the crystal lattice built up by repetitive translations along its principal axes.

Centred Unit Cell

A unit cell where particles are present at the corners as well as at other positions.

Body-Centred Unit Cell

A unit cell that contains particles at the corners and one additional particle at the centre of the body.

Face-Centred Unit Cell

A unit cell that contains particles at the corners and one particle at the centre of each of the faces.

End-Centred Unit Cell

A unit cell that contains particles at the corners and one particle at the centre of any two opposing faces.

Triclinic Unit Cell

A crystal system unit cell characterized by $a \neq b \neq c$ and interaxial angles $\alpha \neq \beta \neq \gamma \neq 90^\circ$.

Monoclinic Unit Cell

A crystal system unit cell characterized by $a \neq b \neq c$ and interaxial angles $\alpha = \gamma = 90^\circ \neq \beta$.

Orthorhombic Unit Cell

A crystal system unit cell characterized by $a \neq b \neq c$ and interaxial angles $\alpha = \beta = \gamma = 90^\circ$.

Tetragonal Unit Cell

A crystal system unit cell characterized by $a = b \neq c$ and interaxial angles $\alpha = \beta = \gamma = 90^\circ$.

Hexagonal Unit Cell

A crystal system unit cell characterized by $a = b \neq c$ and interaxial angles $\alpha = \beta = 90^\circ$, $\gamma = 120^\circ$.

Trigonal Unit Cell

A crystal system unit cell characterized by $a = b = c$ and interaxial angles $\alpha = \beta = \gamma \neq 90^\circ$.

Cubic (Isometric) Unit Cell

A crystal system unit cell characterized by $a = b = c$ and interaxial angles $\alpha = \beta = \gamma = 90^\circ$.

Auguste Bravais

The French scientist ($1811$-$1863$) who formulated that the $7$ crystal classes combine with $4$ unit cell types to yield $14$ distinct space lattices (Bravais lattices).

Rotational Symmetry

A symmetry element involving the repetition of a motif by uniform rotation about an axis through the crystal, which can be $1$-, $2$-, $3$-, $4$-, or $6$-fold.

Reflection (Plane of Symmetry)

A symmetry operation that exchanges parts of a crystal across a mirror plane so that the pattern on one side is an exact mirror image of the other.

Rotoinversion (Improper Rotation)

A composite symmetry operation consisting of a rotation about an axis followed immediately by an inversion through the centre.

Inversion Symmetry

A symmetry operation that moves crystal faces to a reversed position through a centre of inversion, such that any line through the origin encounters identical features equidistant on the opposite side.

Isotropy

The condition where physical properties (e.g., thermal or optical behavior) are independent of direction; characteristic of cubic crystals and amorphous materials.

Anisotropy

The condition where physical properties vary depending on the direction of measurement; characteristic of all non-cubic crystals.

Index of Refraction ($n$)

The ratio of the velocity of light in a vacuum to the velocity of light within a material, given by the formula $n = \frac{V_v}{V_m}$.

Double Refraction (Birefringence)

The optical phenomenon in which an optically anisotropic material with more than one refractive index splits incident light into two distinct refracted rays (an ordinary ray and an extraordinary ray).

Optically Isotropic Materials

Materials that have a single refractive index and exhibit no birefringence.

Optically Anisotropic Materials

Materials that have more than one refractive index and exhibit birefringence.

Unpolarized Light

Light in which the electromagnetic wave vibrations occur in all directions perpendicular to the direction of propagation.

Polarized Light

Light in which electromagnetic wave vibrations are confined to a single plane.

Crossed Polar View

An optical observation mode using a polarizing microscope where the upper polarizer is inserted perpendicular to the lower polarizer; optically isotropic crystals (such as garnet) appear completely dark or extinct in this view.