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Many energy-related materials rely on the uptake and release of large quantities of ions, for example, Li+ in batteries, H+ in hydrogen storage materials, and O2− in solid-oxide fuel cell and related materials. These compositional changes often result in large volumetric dilation of the material, commonly referred to as chemical expansion. This article reviews the current knowledge of chemical expansion and aspires to facilitate and promote future research in this field by providing a taxonomy for its sources, along with recent atomistic insights of its origin, aided by recent computational modeling and an overview of factors impacting chemical expansion. We discuss the implications of chemical expansion for mechanical stability and functionality in the energy applications above, as well as in other oxide-based systems. The use of chemical expansion as a new means to probe other materials properties, as well as its contribution to recently investigated electromechanical coupling, is also highlighted.

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For a mixed oxide-ion and electron conducting oxide, with oxygen vacancies (V(O)) and electrons (e') or holes (h ) as charge carriers, a flux of (V(O)) (J(i)) can in principle be driven, not only directly by its own electrochemical potential gradient (inverted Delta eta(i)), but also indirectly by that of electrons (inverted Delta eta(e)), and vice versa for the flux of electrons (J(e)). It is common practice to assume that electrons and mobile ions migrate independently, despite the lack of experimental evidence in support of this. Here, all the Onsager coefficients, including the cross coefficients, have been measured for Ce(0.8)Pr(0.2)O(2-delta) within the a(O(2)) range 10(-21)-1 at 800 degrees C, using local ionic and electronic probes in a four-probe configuration. The cross coefficients of transport were found to be negligible in comparison to the direct coefficients in the a(O(2)) range 10(-21)-10(-4), but of the same order of magnitude as the direct coefficients for high a(O(2)) values (10(-2)-1). This is in contrast to the commonly used assumption that the two types of carriers migrate independently, i.e. that L(ie) = 0.

The oxygen nonstoichiometry (δ) of Ce0.8PrxTb0.2−xnormalO2−δ (x=0,0.05,0.10,0.15,0.20) was measured as a function of PnormalO2 at temperatures between 600 and 900°C by coulometric titration and thermogravimetry. A nonideal solution model, allowing for a linear δ dependence of the partial molar enthalpy of reduction in the dopants, could successfully reproduce the experimentally determined oxygen nonstoichiometry. X-ray absorption near-edge spectroscopy measurements were performed at the Ce/Pr/Tb L3 and L2 edges. The valence state of each dopant was affected by the presence of the co-dopant. The redox properties strongly depended on the lattice strain energy and the mean metal–oxygen bond strength. The thermal and chemical expansion coefficients were determined by dilatometry. The strongly nonlinear behavior of the thermal expansion coefficient originated from the chemical strain due to increasing oxygen nonstoichiometry with increasing temperature.

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An analysis of the effective radii of vacancies and the stoichiometric expansion coefficient is performed on metal oxides with fluorite and perovskite structures. Using the hard sphere model with Shannon ion radii we find that the effective radius of the oxide vacancy in fluorites increases with increasing ion radius of the host cation and that it is significantly smaller than the radius of the oxide ion in all cases, from 37 % smaller for HfO 2 to 13 % smaller for ThO 2 . The perovskite structured LaGaO 3 doped with Sr or Mg or both is analyzed in some detail. The results show that the effective radius of an oxide vacancy in doped LaGaO 3 is only about 6 % smaller than the oxide ion. In spite of this the stoichiometric expansion coefficient (a kind of chemical expansion coefficient) of the similar perovskite, LaCrO 3 , is significantly smaller than the stoichiometric expansion coefficient of the fluorite structured CeO 2 . Our analysis results indicate that the smaller stoichiometric expansion coefficient of the perovskites is associated with the restraining action of the A-O sub-lattice to dimensional changes in the B-O sub-lattice and vice versa.

The oxygen nonstoichiometry (δ) of Ce0.8Pr0.2normalO2−δ has been measured as a function of PnormalO2 at temperatures between 600 and 900°C by coulometric titration and thermogravimetry. An ideal solution defect model, a regular solution model, and a defect association model, taking into account the association of reduced dopant species and oxygen vacancies, were unable to reproduce the experimental results. However, excellent agreement with the experimentally determined oxygen nonstoichiometry could be achieved when using either a nonideal solution model with an excess enthalpic term linear in δ (ΔHPrexc=anormalHδ) and a completely random distribution of defects (referred to as “δ-linear”), or a “generalized δ-linear” solution model, where the excess Gibbs energy change in the reduction reaction of the dopant linearly varies with δ (ΔGPrexc=anormalGδ) . A comparison of the partial molar enthalpy and entropy of oxidation, estimated from the defect models with those determined directly from the oxygen nonstoichiometry, suggests that the δ-linear solution model is the most appropriate in accounting for the observed nonideal reduction behavior of Pr.