Name: Voids in Crystal Lattices
Uploaded: 2019-07-19
Duration: 5 min 25 s
Description: None of the close packing techniques has 100% efficiency. There is always some space in the lattice that is not occupied by any particle. These empty spaces...

Question

Describe fcc, bcc and hcp crystals of simple ionic compounds.

Accepted Answer

FCC ionic crystal: When an ionic compound is composed of a $1 : 1$ ratio of cations and anions that differ significantly in size, it typically crystallises with an fcc unit cell. Sodium chloride, sodium chloride is an example of this, with ${Na}^{+}$ and ${Cl}^{-}$ having radii of $102 pm$ and $181 pm$ respectively. In this crystal structure, chloride ions forming an fcc cell, with sodium ions located in the octahedral holes in the middle of the cell edges and in the centre of the cell. The sodium and chloride ions touch each other along the cell edges. The unit cell contains four sodium ions and four chloride ions, giving the $1 : 1$ stoichiometry required by the formula, $NaCl$ .

BCC ionic crystal: Perovskite is the generic name for oxides with two different kinds of metal and have the general formula ${MM}^{1} O_{3}$ such as ${CaTiO}_{3}$ . The structure is a body centred cubic (bcc) array of two metal ions, with one $M$ ( $Ca$ in this case) located at the corners of the cube, and the other $M^{1}$ (in this case $Ti$ ) in the centres of the cube. The oxides are in the centres of the square faces The stoichiometry predicted from the unit cell agrees with the general formula; each unit cell contains $8 \times \frac{1}{8} = 1$ calcium, one titanium and $6 \times \frac{1}{2} = 3$ oxygen atoms. The $Ti$ and $Ca$ atoms have coordination numbers of six and twelve, respectively. The structure is as shown below:

HCP ionic crystal: Nickel arsenide ( $NiAs$ ) has a hcp array of arsenic atoms with nickel atoms occupying the octahedral holes. The cations are in octahedral coordination, so each cation is coordinated to six anions. The anions are also coordinated to six cations, but they occupy trigonal prismatic sites. In terms of layer stacking, the $NiAs$ structure is AcBcAcBc..........where the A and B sites (the hcp lattice) are occupied by the $As$ atoms, and the c sites, which are eclipsed along the layer stacking axis, are occupied by $Ni$ . The structure is shown below:

Describe fcc, bcc and hcp crystals of simple ionic compounds.

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