Machine learning enables the discovery of 2D Invar and anti-Invar monolayers

Materials demonstrating positive thermal expansion (PTE) or negative thermal expansion (NTE) are quite common, whereas those exhibiting zero thermal expansion (ZTE) are notably scarce. In this work, we identify the mechanical descriptors, namely in-plane tensile stiffness and out-of-plane bending stiffness, that can effectively classify PTE and NTE 2D crystals. By utilizing high throughput calculations and the state-of-the-art symbolic regression method, these descriptors aid in the discovery of ZTE or 2D Invar monolayers with the linear thermal expansion coefficient (LTEC) within ±2×10⁻⁶ K⁻¹ in the middle range of temperatures. Additionally, the descriptors assist the discovery of large PTE and NTE 2D monolayers with the LTEC larger than ±15×10⁻⁶ K⁻¹, which are so-called 2D anti-Invar monolayers. Advancing our understanding of materials with exceptionally low or high thermal expansion is of substantial scientific and technological interest, particularly in developing next-generation electronics at the nanometer even Ångstrom scale.

在材料科学领域，展示正热膨胀（PTE）或负热膨胀（NTE）特性的材料颇为常见，而那些表现出零热膨胀（ZTE）特性的材料则尤为罕见。本研究中，我们确定了机械描述符，即平面拉伸刚度和法向弯曲刚度，这些描述符能够有效地区分PTE和NTE二维晶体。通过采用高通量计算和最先进的符号回归方法，这些描述符有助于发现具有线性热膨胀系数（LTEC）在±2×10⁻⁶ K⁻¹范围内的ZTE或二维Invar单层，这些单层位于温度的中值区间。此外，这些描述符还有助于发现具有大于±15×10⁻⁶ K⁻¹ LTEC的大尺寸PTE和NTE二维单层，即所谓的二维反-Invar单层。深入研究具有异常低或高热膨胀系数的材料，对于科学技术的进步具有重大意义，尤其是在纳米甚至埃级别的下一代电子器件的研发中。