<i>Ab initio</i>characterization of the mechanical and electronic properties of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>-SiAlON (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>Si</mml:mi><mml:mrow><mml:mn>6</mml:mn><mml:mo>−</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>Al</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mrow><mml:mn>8</mml:mn><mml:mo>−</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>;<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>z</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mtext>–</mml:mtext><mml:mn>5</mml:mn></mml:mrow></mml:math>)

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Following a brief review of the past work published on the structural and mechanical properties of the $\ensuremath{\beta}$-SiAlON crystal, an ab initio computational method is outlined, which was employed to investigate the material properties and electronic structure of the $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Si}}_{6\ensuremath{-}z}{\mathrm{Al}}_{z}{\mathrm{O}}_{z}{\mathrm{N}}_{8\ensuremath{-}z}$, where $z=0\text{--}5$, single crystal configuration. Using data of preferred lattice configurations published previously, optimized lattice constants, elastic constants, the bulk modulus, bond length and angle, electronic band structure, and density of states were determined. The results, where possible, were compared to published works, with reasonable agreement obtained. The SiAlON system, for $z=0\text{--}5$, was found to exhibit lattice softening and the atomic structure was found to conserve directionality of the bond angles. Additionally, the bulk modulus was observed to decrease from 251 to 194 GPa, for $z=0$ to 5, respectively. The electronic structure exhibited a significant monotonic decrease in the band gap for an increasing $z$, along with a decrease observed for each $z$ configuration, as the applied strain was increased.

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