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    Interpretable machine learning reveals a structure-property trade-off between negative thermal expansion magnitude and temperature range in framework materials

    Yu Cai1,2, Xiaoyu Zhao3, Rui Zhu1, Yongqiang Qiao4, Liangliang Liu1, Liying Zhang1, Xianran Xing5,*, and Yu Jia1,4,†

    • *Contact author: xing@ustb.edu.cn
    • †Contact author: jiayu@henu.edu.cn

    Phys. Rev. Materials 10, 093609 – Published 28 September, 2026

    DOI: https://doi.org/10.1103/wk63-p83g

    Abstract

    Negative thermal expansion (NTE) materials with framework structures are of considerable interest due to their ability to mitigate thermal stress and enhance dimensional stability in composite systems. However, broader applications remain limited by the relatively small coefficients of negative thermal expansion (CNTE) and narrow operational temperature windows available in most materials. Here, we employ an interpretable machine-learning framework based on Shapley additive explanations to investigate the structure–property relationships associated with CNTE and the NTE temperature range. By analyzing physical and structural descriptors for a broad range of framework NTE materials, we identify mean electronegativity and electronegativity range, mass density, porosity, lattice parameters, and space-group symmetry as the main factors associated with these two properties. A symmetry-derived proxy descriptor, wfi_proxy, defined by the number of symmetry operations normalized by the number of atoms in the chemical formula, is also included in the CNTE analysis. We identify thresholdlike behavior in electronegativity and mass density, and show that their trends are nonmonotonic and may depend on other structural descriptors. Notably, the descriptors that favor large CNTE often act in the opposite direction for the NTE temperature range, revealing a trade-off between NTE magnitude and temperature window. We refer to this relationship as the approach–approach conflict. These findings extend our earlier correlation-based analysis and provide structure–property trends that may guide the discovery and design of framework NTE materials.

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