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The elastic properties of the wurtzite-type aluminum nitride (w-AlN) are investigated by ab initio plane-wave pseudopotential density functional theory method. The pressure dependences of the normalized primitive cell volume V/V-0, the elastic constants c(ij), the aggregate elastic modulus (B, G, E), the Poisson's ratio (nu), and the Debye temperature circle minus(D) are successfully obtained. From the elastic constants of the w-AlN under pressure, we find that the w-AlN should be unstable at higher pressure than 61.33 GPa.

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