Mechanical, structural, and thermodynamic properties of TaC-ZrC ultra-high temperature ceramics using first principle methods
Ali Reza Farhadizadeh, Hamid Ghomi
Abstract
Abstract In this research, a systematic investigation of the properties of stoichiometric ultra-high temperature ceramics <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>Z</mml:mi> <mml:msub> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> <mml:mi>T</mml:mi> <mml:msub> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>8</mml:mn> <mml:mo>−</mml:mo> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>8</mml:mn> </mml:mrow> </mml:msub> </mml:math> is carried out. The mechanical properties including elastic constants, shear modulus, bulk modulus, Zener ratio, Poisson ratio, Pugh’s index are calculated and then the hardness (H) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:mo stretchy="true">/</mml:mo> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> based on a semi-empirical approach are estimated. It exhibits that TaC possesses the lowest hardness equal to 22 GPa that increases to maximum hardness 30 GPa when a single Zr atom is substituted with Ta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>Z</mml:mi> <mml:msub> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mi>T</mml:mi> <mml:msub> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>8</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>.</mml:mo> </mml:math> Afterwards, the partial density of states (PDOS) of mentioned ceramics was calculated and plotted. Since the density of states at the Fermi level has some value, it is inferred that they all are electrical conductors. The p-d hybridization, the states at the Fermi level and the Mulliken charges of each atom indicate that the covalent, metallic and ionic nature of bonding exist simultaneously among constituent elements.