Crystal Structure |
Simple Hexagonal (Space Group: P63/MMC) |
Simple Triclinic (Space Group: P1) |
Simple Cubic (Space Group: FM-3 M) |
Atomic Arrangement |
Ti atoms at simple cubic corner lattice points; hexagonal lattice in the basal plane |
Ti atoms at simple cubic corner lattice points, Al atoms at center, V atoms between Ti atoms along c-axis |
Zn atoms at simple cubic corner lattice points, forming connections with O atoms |
Electronic Band Structure |
Complete bandgap; Stable electronic structure with well-organized arrangement |
Complete bandgap; Presence of imaginary frequencies indicates instability |
Complete bandgap; Wider energy range suggests potential complex phonon structure |
Dynamic Stability |
Dynamically stable with absence of imaginary frequencies within specified energy range |
Presence of imaginary frequencies indicating instability |
Presence of imaginary frequencies indicating potential instability |
Fermi Surface |
Well-defined, nearly complete drum-shaped Fermi surface indicating good mechanical stability and interatomic bonding |
- |
- |
Stiffness Matrix |
Diagonal: 198.14 GPa, Off-diagonal: - |
Diagonal: 331.70–331.93 GPa, Off-diagonal: -0.0064 to -0.00605 |
Diagonal: 131.13 GPa, Off-diagonal: Relatively High |
Average Properties |
Bulk Modulus: 101–104 GPa, Young's Modulus: 64–88 GPa, Shear Modulus: 23–32 GPa, Poisson's Ratio: 0.358–0.394 |
Bulk Modulus: Higher, Young's Modulus: Higher, Shear Modulus: Higher, Poisson's Ratio: Similar Range |
Bulk Modulus: Relatively High, Young's Modulus: High, Shear Modulus: Relatively High, Poisson's Ratio: Limited Lateral Deformation |
Eigenvalues |
Eigenvalues: 13.485 GPa, 26.969 GPa, 44.526 GPa (Stiffness in Different Directions) |
Eigenvalues: 131.13 GPa (Identical in Principal Directions), 605.72 GPa, 892.33 GPa (Other Directions) |
Eigenvalues: 131.13 GPa (Isotropic in Principal Directions), 605.72 GPa, 892.33 GPa (Other Directions) |
Elastic Moduli Variations |
Young's Modulus Range: 64–88 GPa, Linear Compressibility: Range, Shear Modulus Range: 23–32 GPa, Poisson's Ratio Range: 0.358–0.394 |
Young's Modulus Range: 171.42 GPa to 313.59 GPa, Linear Compressibility: Constant, Shear Modulus Range: 57.122 GPa to 144.26 GPa, Poisson's Ratio Range: 0.059882 to 0.50054 |
Young's Modulus Range: 342.99 GPa to 678.35 GPa, Linear Compressibility: Constant, Shear Modulus Range: 131.13 GPa to 302.86 GPa, Poisson's Ratio Range: 0.069175 to 0.49224 |