The theoretical elastic stiffness of Y(3)Si(5)N(9)O, the only Y-Si-O-N quaternary crystal that contains a framework of corner-sharing SiN(4) and/or SiON(3) tetrahedron in three dimensions, was investigated using the first-principles total energy calculations. The full set of second order elastic coefficients, polycrystalline bulk and shear moduli, and anisotropic elastic moduli were reported and further compared with those of Y(2)O(3) and beta-Si(3)N(4). The equation of state and compressibility of Y(3)Si(5)N(9)O were investigated at pressures up to 50 GPa. The crystal structure is stable up to 50 GPa and exhibits anisotropic compressibility under hydrostatic pressure. The relatively softer YN(6) and/or YN(5)O polyhedra are more prone to distort or deform than the SiN(4) and/or SiON(3) tetrahedra. Therefore, although the crystal structure of Y(3)Si(5)N(9)O contains a Si-N-O framework similar to that in beta-Si(3)N(4), it displays elastic stiffness between those of Y(2)O(3) and beta-Si(3)N(4).
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