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Cubic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Hf</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Zr</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">N</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>:</mml:mo></mml:math>A class of hard materials

Maurizio MattesiniCondensed Matter Theory Group, Department of Physics, Uppsala University, Box 530, SE-751 21 Uppsala, SwedenRajeev AhujaCondensed Matter Theory Group, Department of Physics, Uppsala University, Box 530, SE-751 21 Uppsala, SwedenB. JohanssonApplied Materials Physics, Department of Materials and Engineering, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
2003lv
ABI

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We report ab initio computer modeling of the high-pressure cubic forms of ${\mathrm{Zr}}_{3}{\mathrm{N}}_{4}$ and ${\mathrm{Hf}}_{3}{\mathrm{N}}_{4}.$ Equilibrium structural parameters were derived at 0 K and zero pressure for different exchange-correlation functionals. Single crystal elastic constants and bulk moduli were then computed at the athermal limit in order to quantify the stiffness of the investigated nitrides. We find that ${\mathrm{Hf}}_{3}{\mathrm{N}}_{4}$ should have a Vickers hardness similar to that of ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}.$

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