Predicting thermal expansion in framework compounds using a charge interaction index

The precise regulation of thermal expansion is a crucial and challenging topic with significant industrial and technological implications. We propose a charge interaction index (CII) to relate thermal expansion to chemical composition. Using A₂M₃O₁₂ compounds as a case study, we show the validity of this parameter through experimental verification. Through first principles calculations, the charge density, potential well curves, and Grüneisen parameters of A₂Mo₃O₁₂ (where A = Al, Sc, and Y) were extracted. These calculations revealed that the CII value correlates strongly with the transverse thermal vibrations of bridging O atoms and, in turn, the low-frequency phonon modes possessing negative Grüneisen parameters. Three representative component designs, Sc_1.6(MgTi)_0.2Mo₃O₁₂, In₂Mo_2.5W_0.5O₁₂, and (Al_0.2Sc_0.2Fe_0.2Ga_0.2Cr_0.2)₂W₃O₁₂, were synthetized. As predicted, synchrotron XRD as a function of temperature showed that In₂Mo_2.5W_0.5O₁₂, which has the minimum CII value, exhibits negative thermal expansion behavior, while (Al_0.2Sc_0.2Fe_0.2Ga_0.2Cr_0.2)₂W₃O₁₂, with the maximum CII value, displays positive thermal expansion. This work establishes a simple and effective strategy to engineer thermal expansion properties in open-framework materials through the CII idea.