ENGR_O 376: Topic 3 - Crystal Structures

Vocabulary practice flashcards covering key definitions, atomic packing parameters, unit cell characteristics, and structural ordering concepts from Topic 3 of ENGR_O 376.

Short-Range Order (SRO)

The regular and predictable arrangement of atoms or ions that extends only over short distances, typical of materials such as water vapor and silicate glass.

Long-Range Order (LRO)

A regular, repetitive arrangement of atoms that extends over many atomic spacings, characteristic of crystalline materials such as most metals, ceramics, and some polymers.

Crystalline Materials

Solids that exhibit long-range periodic order, maintaining predictable atomic positions over many atomic spacings throughout their structure.

Non-Crystalline Materials

Solids (also called amorphous) that exhibit short-range order but lack long-range order, typically formed when crystallization is kinetically hindered, such as by rapid cooling.

Liquid Crystal

A state of matter that can flow like a liquid while maintaining a partially ordered molecular orientation and disordered molecular positions.

Single Crystal Material

A crystalline solid that possesses one continuous crystallographic orientation throughout its entire volume, containing no grain boundaries.

Polycrystalline Material

A solid composed of many small individual crystals called grains, which usually have different crystallographic orientations.

Grain Boundaries

The interfaces that separate adjacent grains in a polycrystalline material, where the atomic arrangement differs significantly from the periodic order within the grain interior.

Single-Crystal Turbine Blades

Jet engine components manufactured as a single crystal to eliminate grain boundaries, thereby preventing grain-boundary sliding, reducing grain-boundary diffusion, and improving high-temperature creep resistance.

Lattice

A periodic three-dimensional array of points in space where each point represents an equivalent position in a crystal structure.

Basis

An atom or group of atoms associated with each lattice point; when combined with a lattice, it forms the full crystal structure.

Unit Cell

The smallest repeating structural unit that, when translated in three dimensions, reproduces the entire crystal structure.

Lattice Parameters

The six parameters defining unit cell geometry: three edge lengths ($a$, $b$, $c$) and three interaxial angles ($\alpha$, $\beta$, $\gamma$).

Bravais Lattices

The $14$ distinct lattice arrangements resulting from combinations of the $7$ crystal systems with four basic lattice centering types (primitive, body-centered, base-centered, and face-centered).

Atomic Packing Factor (APF)

The fraction of solid sphere volume inside a unit cell, defined mathematically as the total volume of atoms in the unit cell divided by the total volume of the unit cell.

Simple Cubic (SC)

A crystal structure with lattice points only at the corners of a cube, containing $1$ atom per unit cell, a coordination number of $6$, and an APF of $0.52$.

Body-Centered Cubic (BCC)

A metallic crystal structure with atoms at eight cube corners and one atom at the cube center, containing $2$ atoms per unit cell, a coordination number of $8$, and an APF of $0.68$.

Face-Centered Cubic (FCC)

A metallic crystal structure with atoms at eight cube corners and six face centers, containing $4$ atoms per unit cell, a coordination number of $12$, an APF of $0.74$, and an $ABCABC...$ stacking sequence.

Hexagonal Close-Packed (HCP)

A metallic crystal structure with a hexagonal unit cell geometry containing $6$ atoms per unit cell, a coordination number of $12$, an APF of $0.74$, and an $ABAB...$ stacking sequence.

Coordination Number

The number of nearest-neighbor atoms surrounding a specific reference atom within a crystal structure.

Polymorphism

The ability of a solid material to exist in more than one crystal structure depending on external conditions such as temperature and pressure.

Allotropy

Polymorphism occurring specifically in elemental solids, such as iron transforming between BCC ($\alpha\text{-Fe}$), FCC ($\gamma\text{-Fe}$), and BCC ($\delta\text{-Fe}$) at elevated temperatures.

Allotropic Transformation of Tin

The transition occurring upon cooling white ($\beta$) tin (body-centered tetragonal) below $13.2\,^\circ\text{C}$ to form gray ($\alpha$) tin (diamond cubic), accompanied by a $27\%$ volume increase.