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

Area of Science:

• Materials Science
• Condensed Matter Physics
• Computational Materials Science

Background:

• Materials with positive thermal expansion (PTE) and negative thermal expansion (NTE) are common, but zero thermal expansion (ZTE) materials are rare.
• Understanding thermal expansion in 2D materials is crucial for advanced electronics.

Purpose of the Study:

• To identify key mechanical descriptors for classifying thermal expansion properties of 2D crystals.
• To discover novel 2D materials exhibiting zero, large positive, or large negative thermal expansion.

Main Methods:

• Utilized high-throughput calculations to analyze 2D crystal properties.
• Employed symbolic regression to identify predictive mechanical descriptors.
• Calculated linear thermal expansion coefficient (LTEC) for various 2D monolayers.

Main Results:

• Identified in-plane tensile stiffness and out-of-plane bending stiffness as key descriptors for PTE and NTE 2D crystals.
• Discovered ZTE 2D Invar monolayers with LTEC within ±2×10⁻⁶ K⁻¹.
• Discovered 2D anti-Invar monolayers with large PTE and NTE (LTEC > ±15×10⁻⁶ K⁻¹).

Conclusions:

• Mechanical descriptors can effectively classify and predict thermal expansion in 2D materials.
• The findings facilitate the discovery of 2D materials with tailored thermal expansion for nanometer-scale electronics.
• This research advances the understanding of materials with extreme thermal expansion properties.