Ch. 3 Crystalline Solids - Vocabulary Flashcards

Vocabulary flashcards covering key concepts from the Crystalline Solids lecture notes.

Crystal lattice

A 3D periodic array of lattice points that defines the framework of a crystal; lattice points may host atoms or a basis.

Basis

A group of atoms attached to each lattice point; together with the lattice, forms the crystal structure.

Unit cell

The smallest repeating unit that fills space when translated by lattice vectors.

Primitive cell

A unit cell containing exactly one lattice point; generated by primitive vectors a1, a2, a3.

Lattice

An abstract grid of points generated by translations that serves as the scaffold for a crystal.

Primitive vectors

The three vectors a1, a2, a3 that define the translation steps for building the lattice.

Bravais lattice

One of 14 distinct lattices in 3D that tile space by translational symmetry with a lattice point at every point.

Lattice constant (a, b, c; α, β, γ)

The edge lengths and angles that define a unit cell geometry.

Crystal systems

Seven families of crystal geometry based on unit cell parameters (e.g., cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic).

Cubic system

a = b = c and α = β = γ = 90°; includes SC, BCC, FCC.

Simple cubic (SC)

Atoms at cube corners only; 1 atom per unit cell; CN = 6.

Body-centered cubic (BCC)

Atom at the cube center plus corner atoms; 2 atoms per unit cell; CN = 8.

Face-centered cubic (FCC)

Atoms at corners and face centers; 4 atoms per unit cell; CN = 12.

Hexagonal close-packed (HCP)

Close-packed structure with ABAB stacking; CN = 12; APF ≈ 0.74.

Close-packed planes

Planes with the highest packing density in a crystal.

Stacking sequence (FCC)

ABCABC stacking of close-packed planes in cubic close packing.

Stacking sequence (HCP)

ABAB stacking of close-packed planes in hexagonal packing.

Atomic Packing Factor (APF)

Fraction of the unit cell volume occupied by atoms; close-packed structures have APF ≈ 0.74.

Coordination number (CN)

Number of nearest-neighbor atoms surrounding a lattice point.

Miller indices

(hkl) notation that designates the orientation of a crystal plane in cubic systems.

Miller-Bravais indices

Four-index (hkil) system used for hexagonal crystals to describe planes/directions.

d-spacing

Distance between parallel crystal planes.

Bragg's Law

nλ = 2d sinθ; relates X-ray wavelength, interplanar spacing, and diffraction angle.

X-ray diffraction

Technique to identify crystal structure by analyzing the diffraction pattern of X-rays by lattice planes.

Polycrystalline material

A material composed of many crystallites (grains) with different orientations.

Grain boundary

Interface between grains with different crystallographic orientations.

Isotropic

Properties that are the same in all directions.

Anisotropic

Properties that depend on direction.

Origin (000) and fractional coordinates

Origin point in fractional coordinates used to locate lattice positions within the unit cell.

Fractional coordinates

Coordinates expressed as fractions of the unit cell edges (a, b, c).

Lattice translations

Discrete translations generated by primitive vectors: R = n1a1 + n2a2 + n3a3 (ni integers).

CsCl structure

Crystal structure with a two-atom basis (Cs and Cl) in a cubic lattice.

Sodium chloride (NaCl) structure

Rock-salt structure with an FCC lattice and alternating ions at lattice positions.

Hard-sphere model

A visualization of atoms as solid spheres with defined diameters to illustrate packing.

Reduced-sphere unit cell

A simplified unit cell visualization with smaller spheres to reveal packing.

Face-centered vs body-centered vs base-centered lattices

Lattice types describing where lattice points sit: corners plus face centers (FCC), center of cube (BCC), or centers on opposite faces (base-centered).

Base-centered orthorhombic

Orthorhombic lattice with additional lattice points on the centers of two opposite faces.