Summary: | The structural, mechanical, electronic, and thermal properties, as well as the stability and elastic anisotropy, of <i>X</i>P (<i>X</i> = Al, Ga, or In) in the <i>P</i>6<sub>4</sub>22 phase were studied via density functional theory (DFT) in this work. <i>P</i>6<sub>4</sub>22-<i>X</i>P (<i>X</i> = Al, Ga, or In) are dynamically and thermodynamically stable via phonon spectra and enthalpy. At 0 GPa, <i>P</i>6<sub>4</sub>22-<i>X</i>P (<i>X</i> = Al, Ga, or In) are more rigid than <i>F</i><inline-formula> <math display="inline"> <semantics> <mrow> <mover accent="true"> <mn>4</mn> <mo>¯</mo> </mover> <mn>3</mn> </mrow> </semantics> </math> </inline-formula><i>m</i>-<i>X</i>P (<i>X</i> = Al, Ga, or In), of which <i>P</i>6<sub>4</sub>22-<i>X</i>P (<i>X</i> = Al or Ga) are brittle and <i>P</i>6<sub>4</sub>22-InP is ductile. In the same plane (except for (001)-plane), <i>P</i>6<sub>4</sub>22-AlP and <i>P</i>6<sub>4</sub>22-InP exhibit the smallest and the largest anisotropy, respectively, and <i>P</i>6<sub>4</sub>22-<i>X</i>P (<i>X</i> = Al, Ga, or In) is isotropic in the (001)-plane. In addition, Al, Ga, In, and P bonds bring different electrical properties: <i>P</i>6<sub>4</sub>22-InP exhibits a direct band gap (0.42 eV) with potential application for an infrared detector, whereas <i>P</i>6<sub>4</sub>22-<i>X</i>P (<i>X</i> = Al or Ga) exhibit indirect band gap (1.55 eV and 0.86 eV). At high temperature (approaching the melting point), the theoretical minimum thermal conductivities of <i>P</i>6<sub>4</sub>22-<i>X</i>P (<i>X</i> = Al, Ga, or In) are AlP (1.338 W∙m<sup>−1</sup>∙K<sup>−1</sup>) > GaP (1.058 W∙m<sup>−1</sup>∙K<sup>−1</sup>) > InP (0.669 W∙m<sup>−1</sup>∙K<sup>−1</sup>), and are larger than those of <i>F</i><inline-formula> <math display="inline"> <semantics> <mrow> <mover accent="true"> <mn>4</mn> <mo>¯</mo> </mover> <mn>3</mn> </mrow> </semantics> </math> </inline-formula><i>m</i>-<i>X</i>P (<i>X</i> = Al, Ga, or In). Thus, <i>P</i>6<sub>4</sub>22-<i>X</i>P (<i>X</i> = Al, Ga, or In) have high potential application at high temperature.
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