Crystal Structures and Packing Flashcards

Vocabulary terms covering crystal density calculations, coordination numbers, and types of close-packed structures in 1D, 2D, and 3D.

Coordination number

The number of neighbouring spheres that touch any given sphere; its magnitude is a measure of the compactness of spheres in close-packed structures.

Density ($p$) formula

The relationship between molar mass, unit cell edge, and number of particles per unit cell, expressed as: $p = \frac{M \times n}{a^3 \times N}$.

Avogadro number ($N$)

The constant used in density calculations, given as $6.022 \times 10^{23} \, atoms \, mol^{-1}$.

Face-centred cubic (fcc) unit cell

A unit cell consisting of particles at corner positions and the center of the six faces, totaling $n = 4$ particles per unit cell.

Square close packing in two dimensions

A planar structure where one-dimensional rows are stacked such that spheres align vertically and horizontally in an A, A, A, A… type arrangement with a coordination number of $4$.

Hexagonal close packing in two dimensions

A staggered arrangement (ABAB… type) where spheres of the second row fit into the depressions of the first row, resulting in a coordination number of $6$.

Triangular voids

The free spaces in a hexagonal packing arrangement which are triangular in shape, with apexes pointing alternately upwards and downwards.

Simple cubic structure

A 3D structure generated by stacking square close packed layers such that spheres of all layers are perfectly aligned horizontally and vertically in an AAAA… type arrangement.

Unit cell

The smallest repeating structural unit of a crystalline solid.

Crystal lattice

The regular arrangement of constituent particles (treated as hard spheres) in a crystalline solid to maximize interparticle attractions.