Accurate characterization of chemical strain is required to study a broad range of chemical-mechanical coupling phenomena. By combining density functional theory (DFT) calculations and elastic dipole tensor theory, it is readily to predict the long-range chemical strain tensor and the chemical expansion coefficient tensor induced by dilute point defects in a crystal structure.

First, we demonstrate that, even in cubic CeO_2-δ, both the short-range deformation surrounding an oxygen vacancy and the long-range chemical strain (or the expansion coefficient) are anisotropic. The origin of this anisotropy is the charge disproportionation between the four cerium atoms surrounding each oxygen vacancy (two become Ce³⁺ and two become Ce⁴⁺) when a neutral oxygen vacancy is formed. While the short-range deformation agrees with experimentally determined Ce-O bond lengths, the predicted maximum and average chemical strains successfully bound the variety of CeO_2-δ chemical strain behavior previously reported in the literature. Normally, since there are six possible disproportionation configurations, the average chemical strain is isotropic. Only under an external bias, such as an applied electric field, the chemical strain can be oriented to show the anisotropic effect. This successfully explained the giant electrostriction effect reported in doped and un-doped CeO_2-δ.

Next, we show strains induced by coupled vacancies in layered Li-intercalation compounds for battery applications. Li₂MnO₃ was investigated as Li-excess intercalation compounds containing Li₂MnO₃ need to be “activated” to deliver the high capacity. This activation process during the first delithiation cycle at a high voltage is believed to introduce oxygen vacancies into the system. Due to the large amount Li vacancy generated, a large number of defect configurations were sampled and the average chemical strain induced by Li vacancy concentration is obtained by Boltzmann average. Previously, we have demonstrated that it is energetically favorable to create a Li-O-Li vacancy dumbbell structure (V_Li - V_O - V_Li) in Li₂MnO₃. The chemical strain of the vacancy dumbbell structure is smaller than the sum of the chemical strain of one V_o and two V_Lis. The chemical expansion coefficient averaged for the polycrystalline samples and the experimentally measured stress change provided a novel method to in situ track the irreversible chemical changes in Li-excess cathode materials.