Investigation of local stiffness inside Ti₃AC₂ (A = Al, Ga, In, Si, Ge, Sn) MAX phase using first-principles atomic stress calculation

Abstract

In recent advances in structural materials, a fundamental strategy for achieving strength and durability involves controlling microscopic heterogeneity, where different microstructures coexist within a single material. At the nanoscale level, the MAX phase, with general formula M_n+1AX_n (M = an early transition metal, A = an element typically from the 13th to the 16th group, X = C or N, and n = 1, 2, 3) exemplifies such a heterogeneous structure. It consists of a hard ceramic layer (M-X-M-X-M) and a relatively softer monatomic layer (M-A-M). The elastic state is also spatially inhomogeneous in such structures; however, a computational method to reveal this inhomogeneous elastic state at the atomic level has not yet been established. We have developed a local stiffness calculation scheme based on first-principles atomic stress calculations and applied it to the analysis of the MAX phase Ti₃AC₂ (A = Al, Ga, In, Si, Ge, Sn). The results confirmed the presence of elastic heterogeneity in the hard and soft layers. Specifically, it was observed that the soft layer stiffens when the element A moves from Period 5 to Period 3. For comparison, the elastic constants and the crystal orbital bonding index (COBI) of a single phase (Ti-A-Ti) were calculated to assess the influence of the interface and the electronic structure within the MAX phases. The elastic constants and ICOBI values in the soft layer within the MAX phase were generally larger than those in the single phase, clearly indicating the influence from the interface of the hard layer.