Crystallography Lecture Flashcards

Comprehensive vocabulary flashcards covering the definitions, importance, structures, symmetry elements, and classification systems in crystallography as presented in the lecture.

Crystallography

The science of studying the external form and internal arrangement of crystalline solid and the principles that govern their growth, external shape, and internal structure.

Polymorphs

Different mineral forms of the same element; for example, Carbon ($C$) exists as graphite at low temperature and pressure, and as diamond at higher temperature and pressure.

Diffusion

The movement of atoms within a crystal structure, which is important for understanding rock formation and deformation.

Dislocation movement

The shearing of crystal lattices, which is a mechanism in the deformation of rocks.

Nucleation

The growth of new crystals, also referred to as crystallization.

Crystalline materials

Materials in which atoms pack in periodic, 3D arrays; typical of metals, many ceramics, and some polymers.

Amorphous

A term for non-crystalline materials where atoms have no periodic packing, often occurring due to complex structures or rapid cooling.

Crystal faces

The flat surfaces by which crystals are bounded, which are parallel to the net planes in the crystal structure.

Unit Cell

The smallest unit of volume that permits identical cells to be stacked together to fill all space.

Primitive (P) unit cell

A type of unit cell that contains only a single lattice point.

Internal (I) unit cell

A unit cell that contains an atom in the body center; also known as body-centered.

Face (F) unit cell

A unit cell that contains atoms in all faces of the planes composing the cell.

Centered (C) unit cell

A unit cell that contains atoms centered on the sides of the unit cell; also called end-centered.

Edge

The feature formed by the intersection of two adjacent faces on a crystal.

Solid angle

The intersection of three or more faces, also known as a vertex.

Euler's Relation for Crystals

The mathematical relation between faces ($F$), solid angles ($A$), and edges ($E$) expressed as $F + A = E + 2$.

Interfacial angle

The angle between the normals drawn to two adjacent faces of a crystal, measured using a goniometer.

Steno's law of constant angles

The principle that the angles between corresponding faces on crystals are the same for different crystals of the same mineral when measured at the same temperature.

Crystal form

A collection of similar faces which partially or completely constitute the exterior of crystals, where each face has the same size, shape, and orientation relative to crystallographic axes.

Closed form

An assemblage of faces that can enclose a volume of space.

Open form

A crystal form whose faces are too few to enclose its space completely, occurring only in combination with other forms.

General form

A form in which faces intersect each crystallographic axis at different lengths, designated as $ext{{hkl}}$.

Crystal habit

The general external shape of a crystal, representing the common combination of forms in which a mineral crystallizes (e.g., tabular, prismatic, acicular).

Euhedral crystals

Crystals that are well-formed with sharp, easily recognized faces.

Subhedral crystals

Crystals that are only partially bounded by good crystal faces.

Anhedral crystals

Crystals that lack well-developed faces.

Miller Indices

A set of three numbers defined as the reciprocals of the intercepts made by a plane on the three crystallographic axes, written in parenthesis as $(hkl)$.

Point Symmetry

Symmetry dealing with how a motif can be repeated about a point, leaving at least one point unchanged.

Translational Symmetry

Symmetry involving the displacement of the crystal in a direction that replaces each atom by one of its identical neighbors, essentially shifting the entire lattice.

Isometric (Cubic) system

Crystal system where the three axes ($a_1, a_2, a_3$) are all equal in length and intersect at right angles ($90^ ext{o}$).

Tetragonal system

Crystal system with three axes at right angles, where two are equal in length ($a$ and $b$) and one ($c$) is different.

Hexagonal system

Crystal system involving four axes; three equal-length axes ($a_1, a_2, a_3$) intersect at $120^ ext{o}$ in one plane, and a fourth axis ($c$) is perpendicular to that plane.

Orthorhombic system

Crystal system with three axes of different lengths ($a, b, c$) all intersecting at right angles.

Monoclinic system

Crystal system with three axes of unequal length, where two ($a$ and $c$) intersect at an oblique angle and the third ($b$) is perpendicular to them.

Triclinic system

Crystal system where three axes are all unequal in length and intersect at three different angles, none of which are $90^ ext{o}$.