Evaluating thermal expansion in fluorides and oxides: Machine learning predictions with connectivity descriptors

Open framework structures (e.g., ScF3, Sc2W3O12, etc.) exhibit significant potential for thermal expansion tailoring owing to their high atomic vibrational degrees of freedom and diverse connectivity between polyhedral units, displaying positive/negative thermal expansion (PTE/NTE) coefficients at a certain temperature. Despite the proposal of several physical mechanisms to explain the origin of NTE, an accurate mapping relationship between the structural-compositional properties and thermal expansion behavior is still lacking. This deficiency impedes the rapid evaluation of thermal expansion properties and hinders the design and development of such materials. We developed an algorithm for identifying and characterizing the connection patterns of structural units in open-framework structures and constructed a descriptor set for the thermal expansion properties of this system, which is composed of connectivity and elemental information. Our developed descriptor, aided by machine learning (ML) algorithms, can effectively learn the thermal expansion behavior in small sample datasets collected from literature-reported experimental data (246 samples). The trained model can accurately distinguish the thermal expansion behavior (PTE/NTE), achieving an accuracy of 92%. Additionally, our model predicted six new thermodynamically stable NTE materials, which were validated through first-principles calculations. Our results demonstrate that developing effective descriptors closely related to thermal expansion properties enables ML models to make accurate predictions even on small sample datasets, providing a new perspective for understanding the relationship between connectivity and thermal expansion properties in the open framework structure. The datasets that were used to support these results are available on Science Data Bank, accessible via the link .