Nonstoichiometry

Key point: Deviations from ideal stoichiometry are common in the solid-state compounds of the d-, f-, and later p-block elements. A nonstoichiometric compound is a substance that exhibits variable composition but retains the same structure type. For example, at 1000°C the composition of ‘iron monoxide’, which is sometimes referred to as wüstite, Fe_1-x O, varies from Fe_0.89 O to Fe_0.96 O. Gradual changes in the size of the unit cell occur as the composition is varied, but all the features of the rock-salt structure are retained throughout this composition range. The fact that the lattice parameter of the compound varies smoothly with composition is a defining criterion of a nonstoichiometric compound because a discontinuity in the value of the lattice parameter indicates the formation of a new crystal phase. Moreover, the thermodynamic properties of nonstoichiometric compounds also vary continuously as the composition changes. For example, as the partial pressure of oxygen above a metal oxide is varied, both the lattice parameter and the equilibrium composition of the oxide change continuously (Figs 3.58 and 3.59). The gradual change in the lattice parameter of a solid as a function of its composition is known as Vegard’s rule. Table 3.12 lists some representative nonstoichiometric hydrides, oxides, and sulfides. Note that as the formation of a nonstoichiometric compound requires overall changes in

composition, it also requires at least one element to exist in more than one oxidation state. Thus in wüstite, Fe1 x O, as x increases some iron(II) must be oxidized to iron(III) in the structure. Hence deviations from stoichiometry are usual only for d- and f-block elements, which commonly adopt two or more oxidation states, and for some heavy p-block metals that have two accessible oxidation states.

Fig. 3.58 Schematic representation of the variation of the partial pressure of oxygen with composition at constant pressure for (a) a nonstoichiometric oxide MO_1+x and (b) a stoichiometric pair of metal oxides MO and MO₂ . The x-axis is the atom ratio in MO_1+x

Fig. 3.59 Schematic representation of the variation of one lattice parameter with composition for (a) a nonstoichiometric oxide MO_1+x and (b) a stoichiometric pair of metal oxides MO and MO₂ with no intermediate stoichiometric phases (which would produce a two-phase mixture for 0<x<1, each phase in the mixture having the lattice parameter of the end member.

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مواضيع ذات صلة

The Fermi level

Densities of states

Band formation by orbital overlap

The conductivities of inorganic solids

Intrinsic point defects

Solubility

Thermal stabilities of ionic solids

The Born–Mayer equation

Structure maps

The radius ratio

Ionic radii

Characteristic structures of ionic solids