Crystalline Solids: Metals, Ionic Crystals, and X-ray Diffraction

Vocabulary flashcards covering key concepts from crystalline solids, metal and ionic crystal structures, unit cells, packing, interstitial holes, and X-ray diffraction.

Unit cell

The smallest repeating unit of a crystal lattice that, when repeated in three dimensions, builds the entire crystal; lattice points inside represent atom/ion positions.

Simple cubic (SC) structure

A cubic unit cell with atoms at the eight corners; atoms touch along edges; about 52% packing efficiency; 1 atom per unit cell; Po is an example.

Coordination number

The number of nearest-neighbor atoms touching a given atom in a crystal structure.

Body-centered cubic (BCC)

Cubic unit cell with an atom at the center in addition to corner atoms; coordination number 8; about 68% packing efficiency; contains 2 atoms per unit cell.

Face-centered cubic (FCC) / Cubic closest packing (CCP)

Cubic unit cell with atoms at corners and centers of all faces; 4 atoms per cell; coordination number 12; about 74% packing efficiency; also called CCP.

Hexagonal close packing (HCP)

Closest-packed structure with ABABAB… stacking in hexagonal layers; coordination number 12; two alternating layers (A and B).

Lattice system

One of seven symmetry families (e.g., cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, rhombohedral) that define possible unit-cell shapes and angles.

Unit cell axes and angles

The three edge lengths a, b, c and the interaxial angles α, β, γ that define a unit cell’s shape in a crystal lattice.

Tetrahedral hole

A small interstitial site formed by four surrounding anions in a close-packed array; cations can occupy these holes in some ionic structures.

Octahedral hole

A larger interstitial site at the center of an octahedron formed by six surrounding anions; cations may occupy these holes.

Ionic solid

Crystal composed of two or more different ions; packing depends on relative ion sizes and the cation/anion ratio.

CsCl structure

A 1:1 ionic structure where one ion sits at the cube corners and the other at the center; not a true BCC, since ions are different; can be viewed with either ion at the center or corners.

NaCl (rock-salt) structure

FCC lattice of Cl− with Na+ occupying all octahedral holes; 1:1 stoichiometry; four Na and four Cl per unit cell.

ZnS (zinc blende) structure

FCC lattice of sulfide ions with smaller Zn2+ ions occupying half of the tetrahedral holes; formula ZnS; 4 Zn and 4 S per unit cell.

CaF2 (fluorite) structure

FCC lattice of Ca2+ with F− occupying all tetrahedral holes; formula CaF2; 4 Ca and 8 F per unit cell.

Ionic radii

Radii of ions that reflect size and environment; contacts and interionic distances determine crystal structure; can be estimated from unit-cell dimensions.

Bragg equation

nλ = 2d sin θ; relates X-ray wavelength, interplanar spacing, and diffraction angle in crystals.

X-ray crystallography

Technique to determine crystal structure by diffracting X-rays off a crystal and analyzing the resulting pattern.

Diffractometer

Instrument used to measure angles and intensities of diffracted X-rays from a crystal to analyze its structure.

Interplanar spacing (d)

Distance between adjacent crystal planes that diffract X-rays.

Wavelength (λ)

Wavelength of incident X-rays used in diffraction experiments.

Crystal lattice

A 3D array of points representing the periodic arrangement of atoms or ions in a crystal.

Lattice point

A position in a crystal lattice representing the location of an atom or ion; corners, centers, etc., depending on the unit cell.

Atomic packing factor (packing efficiency)

Fraction of the unit cell volume occupied by atoms; SC ≈ 52%, BCC ≈ 68%, FCC/CCP ≈ 74%.

Polonium (Po) simple cubic example

Po crystallizes in a simple cubic structure; edge length l equals 2r (l = 2r), giving r = a/2 and coordination number 6.

Closest-packed structures

CCP (FCC) and HCP arrangements in which atoms pack as tightly as possible, maximizing attractions and minimizing energy; most metals adopt one of these.

Octahedral vs tetrahedral holes in ionic crystals

Holes formed by surrounding anions; cations occupy these sites with preference: smaller cations in tetrahedral holes, larger cations in octahedral holes; determines stoichiometry and structure.