Part of JPC-09 — Solid State: Unit Cell, Packing & Defects

Close Packing and Voids

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Close packing starts with a hexagonal close-packed layer (A), where each atom touches 6 neighbours. The second layer (B) sits in the triangular hollows. Two options for the third layer create two structures: ABAB = HCP, ABCABC = CCP (= FCC). Both have identical packing efficiency (74.05%) and CN (12). Between close-packed layers, two types of voids form: tetrahedral voids (4 atoms forming a tetrahedron, smaller cavity) and octahedral voids (6 atoms forming an octahedron, larger cavity). For n atoms in close packing: tetrahedral voids = 2n, octahedral voids = n. In an FCC unit cell with 4 atoms: 8 tetrahedral voids at14bodydiagonalpositions\frac{at 1}{4 body diagonal positions} and 4 octahedral voids (12 edge centres x 1/4 + 1 body centre). Void radius ratios: rvoidr_{void}/RatomR_{atom}: tetrahedral = 0.225, octahedral = 0.414. Octahedral voids are larger. These voids are crucial for understanding ionic crystal structures where smaller ions occupy voids in the larger ion's close-packed arrangement.

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