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, Sc1.6(MgTi)0.2Mo3O12, In2Mo2.5W0.5O12, and (Al0.2Sc0.2Fe0.2Ga0.2Cr0.2)2W3O12, were synthetized. As predicted, synchrotron XRD as a function of temperature showed that In2Mo2.5W0.5O12, which has the minimum CII value, exhibits negative thermal expansion behavior, while (Al0.2Sc0.2Fe0.2Ga0.2Cr0.2)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.