Mechanistic Quantification of Thermodynamic Stability and Mechanical Strength for Two-Dimensional Transition-Metal Carbides

Recently, two-dimensional (2D) materials with superior mechanical properties, unique electronic structures, and specific functionalities have stimulated considerable interest in designing novel flexible devices and multifunctional nanocomposites. However, high-throughput experiments and calculations, which are desirable for identifying those promising candidates with excellent strengths and flexibilities, remain a great challenge due to their difficulty and complexity. In the present work, a systematic investigation has been performed on the oxygen-functionalized 2D transition-metal carbides M₂CO₂ (M = Sc, Ti, V, Cr, Y, Zr, Nb, Mo, Hf, Ta, and W) to identify those with excellent thermodynamic stabilities and mechanical behaviors via high-throughput first-principle calculations. Our results suggest that the position and bonding/antibonding character of metallic d-band electrons play a vital role in stabilizing M₂CO₂, whose formation energy is below 0.2 eV/atom, a generally considered threshold observed for freestanding 2D materials, except for Sc₂CO₂, Y₂CO₂, and Cr₂CO₂. The synthetic effect from the surface stacking geometry and the delocalization character of d electrons provides a mechanistic quantification for periodic variation of elastic moduli and ideal strengths for M₂CO₂, whereas the strain-induced premature dynamic instabilities in different modes may intrinsically limit their achievable strengths, e.g., zone-center optical phonon instability for Hf₂CO₂ versus elastic instability for W₂CO₂. Detailed electronic structure analyses reveal that strong M-C bonds endow M₂CO₂ with excellent in-plane mechanical strengths but the appearance of different phonon instabilities when M changes from group IVB to group VIB may be attributed to the different filling characters of specific metal-d_xz orbital or metal-d_z² orbital. These findings resolve an apparent discrepancy for the preferred adsorption sites of the functional group and shed a novel view on the electronic origin of distinct mechanical strengths and flexibilities observed for different M₂CO₂.