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M 2 AX phases are a family of nanolaminate, ternary alloys that are composed of slabs of transition metal carbide or nitride (M 2 X) separated by single atomic layers of a main group element. In this combination, they manifest many of the beneficial properties of both ceramic and metallic compounds, making them attractive for many technological applications. We report here the results of a large scale computational survey of the elastic properties of all 240 elemental combinations using first-principles density functional theory calculations. We found correlations revealing the governing role of the A element and its interaction with the M element on the c axis compressibility and shearability of the material. The role of the X element is relatively minor, with the strongest effect seen in the in-plane constants C 11 and C 12. We identify several elemental compositions with extremal properties such as W 2 SnC, which has by …