The crystal structure of magnesium oxide, MgO, is of the...

The crystal structure of magnesium oxide, $\mathrm{MgO}$, is of the NaCl type (Fig. 12-48). Use this fact, together with ionic radii from Figure $9-11,$ to establish the following. (a) the coordination numbers of $\mathrm{Mg}^{2+}$ and $\mathrm{O}^{2-}$ (b) the number of formula units in the unit cell; (c) the length and volume of a unit cell; (d) the density of MgO.

The crystal structure of magnesium oxide, $\mathrm{MgO}$, is of the NaCl type (Fig. 12-48). Use this fact, together with ionic radii from Figure $9-11,$ to establish the following.
(a) the coordination numbers of $\mathrm{Mg}^{2+}$ and $\mathrm{O}^{2-}$
(b) the number of formula units in the unit cell;
(c) the length and volume of a unit cell;
(d) the density of MgO.

Key Concepts

Density Calculation in Crystallography

Density is determined by dividing the total mass contained in the unit cell by its volume. This requires a detailed knowledge of the number of formula units per cell, the molar mass of the constituents, Avogadro's number, and the lattice parameter of the cell. This concept is key in linking the microscopic arrangements in the crystal to its macroscopic properties.

Unit Cell Contents

This concept involves determining the number of complete chemical formula units contained within a single unit cell of the crystal. In the NaCl structure, the arrangement of ions within the unit cell leads to a specific number of formula units that is used in calculations of the cell’s mass and properties such as density.

Lattice Parameter and Ionic Radii

The lattice parameter is the measure of the edge length of the unit cell and is directly related to the size of the ions composing the crystal. By using the ionic radii, one can derive the dimensions of the unit cell since the distance between ion centers is a function of the sum of the cation and anion radii along specific crystallographic directions.

Crystal Structure (NaCl-type)

This refers to a specific arrangement of ions in a lattice where each ion is surrounded by six ions of the opposite charge in an octahedral geometry. The NaCl structure is characterized by a face?centered cubic (FCC) lattice in which both the cations and anions occupy sites that lead to high symmetry and predictable coordination and packing.

Coordination Number

Coordination number is the number of immediate neighboring ions (or atoms) surrounding a central ion in a crystal lattice. In structures like NaCl, each ion is typically surrounded by six oppositely charged ions, resulting in a coordination number of six for both cations and anions, which is crucial for understanding the local geometry and bonding in the solid.

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