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# 化学代写|无机化学代考Inorganic Chemistry代写|CHM935 Nonstoichiometric compounds and solid solutions

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## 化学代写|无机化学代考Inorganic Chemistry代写|Nonstoichiometric compounds and solid solutions

The statement that the stoichiometry of a compound is fixed by its chemical formula is not always true for solids, as differences in the content of unit cells can occur throughout a solid. Changes in unit cell composition can arise through vacancies at one or more atom sites, the presence of interstitial atoms, or the substitution of one atom type by another.

A nonstoichiometric compound is a substance that exhibits variable composition but retains the same structure type. For example, at $1000^{\circ} \mathrm{C}$ the composition of ‘iron monoxide’, which is sometimes referred to as wüstite, $\mathrm{Fe}{1-x} \mathrm{O}$, varies from $\mathrm{Fe}{0.89} \mathrm{O}$ to $\mathrm{Fe}_{0.96} \mathrm{O}$. 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.

## 化学代写|无机化学代考Inorganic Chemistry代写|Solid solutions in compounds

Because many substances adopt the same structural type, it is often energetically feasible to replace one type of atom or ion with another. Such behaviour is seen in many simple metal alloys such as those discussed in Section 3.8. Thus zinc/copper brasses exist for the complete range of compositions $\mathrm{Cu}{1-x} \mathrm{Zn}{x}$ with $0<x<0.38$, where $\mathrm{Cu}$ atoms in the structure are gradually replaced by $\mathrm{Zn}$ atoms. This replacement occurs randomly throughout the solid, and individual unit cells contain an arbitrary number of $\mathrm{Cu}$ and $\mathrm{Zn}$ atoms (but such that the sum of their contents gives the overall brass stoichiometry).

Another good example is the perovskite structure adopted by many compounds of stoichiometry $\mathrm{ABX}{3}$ (Section 3.9), composed of the ions $\mathrm{A}^{\mathrm{n}+}, \mathrm{B}^{\mathrm{m}+}$, and $\mathrm{X}^{\mathrm{x}-}$, in which the composition can be varied continuously by varying the ions that occupy some or all of the $\mathrm{A}$, $\mathrm{B}$, and $\mathrm{X}$ sites. For instance, both $\mathrm{LaFe}(\mathrm{III}) \mathrm{O}{3}$ and $\mathrm{SrFe}(\mathrm{IV}) \mathrm{O}{3}$ adopt the perovskite structure and we can consider a perovskite crystal that has, randomly distributed, half $\mathrm{SrFeO}{3}$ unit cells (with $\mathrm{Sr}^{2+}$ on the A-type cation site) and half $\mathrm{LaFeO}{3}$ unit cells (with $\mathrm{La}^{3+}$ on the A-site). The overall compound stoichiometry is $\mathrm{LaFeO}{3}+\mathrm{SrFeO}{3}=\mathrm{LaSrFe}{2} \mathrm{O}{6}$, which is better written $\left(\mathrm{La}{0.5} \mathrm{Sr}{0.5}\right) \mathrm{FeO}{3}$, to reflect the normal $\mathrm{ABO}{3}$ perovskite stoichiometry. Other proportions of these unit cells are possible and the series of compounds $\mathrm{La}{1-x} \mathrm{Sr}{x} \mathrm{FeO}{3}$ for $0 \leq x \leq 1$ can be prepared. This system is called a solid solution because all the phases formed as $x$ is varied have the same perovskite structure. In a solid solution all the sites in the structure remain fully occupied, the overall compound stoichiometry remains constant (albeit with different proportions of atom types on some sites), and there is a smooth variation in lattice parameter over its composition range.

## 化学代写|无机化学代考Inorganic Chemistry代写|Solid solutions in compounds

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