lattice structures
Summary
A lattice is the regular, repeating three-dimensional arrangement of particles in a crystalline solid, described by its unit cell. Most testable: shared corner and face particles give 1, 2 and 4 particles per cell for simple, body-centered and face-centered cubic.
Detail
Meaning: A lattice is the regular, repeating three-dimensional arrangement of particles in a crystalline solid; the smallest repeating piece is the unit cell. Cubic cells are simple cubic, body-centered (BCC) and face-centered (FCC). A corner particle is shared by 8 cells (counts 1/8), a face particle by 2 (counts 1/2), and an interior particle counts fully. That gives 1, 2 and 4 particles per cell, with 6, 8 and 12 nearest neighbors. In ionic solids like NaCl, electrostatic attraction between cations and anions holds the lattice together.
Equation: Lattice energy magnitude ∝ (q₁ × q₂) / r, where q₁ and q₂ are the ion charges (C) and r is the distance between ion centers (m).
On the MCAT: Count particles per unit cell, then find density = (particles per cell × mass per particle) / cell volume. Or rank ionic solids by lattice energy, and often by melting point: higher charges and smaller ions give stronger lattices, so MgO ranks above NaCl. Amorphous solids such as glass lack long-range order.
Common confusion: Counting a corner atom as a whole atom. Corner atoms are shared among cells, so a simple cubic cell holds 1 atom, not 8.
Sources
- Chemistry: The Central Science
- Chemistry (Zumdahl)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.