Anisotropic elastic properties of the Ca–Pb compounds

• The Ca–Pb compounds are mechanically stable.
• Ca3Pb has the largest hardness, while CaPb3 possesses the smallest hardness.
• The elastic anisotropy follows the order Ca2Pb > Ca5Pb3 > CaPb > Ca3Pb > CaPb3.
• The order of ΘD is: Ca3Pb > Ca5Pb3 > CaPb > Ca2Pb > CaPb3.

To better clarify and understand the anisotropic elastic properties of Ca–Pb intermetallic compounds, the structural and elastic properties of the Ca–Pb compounds (Ca3Pb, Ca2Pb, Ca5Pb3, CaPb and CaPb3) have been investigated by using the first-principles calculations based on density functional theory. The calculated equilibrium structural parameters are in good agreement with the available experimental data. Elastic properties including bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio, are obtained by Voigt–Reuss–Hill approximation. All Ca–Pb compounds are mechanically stable. The brittle and ductile properties are discussed by using B/G and Poisson’s ratio. The elastic anisotropies of Ca–Pb compounds are investigated via the anisotropic index and the 3D figures of directional dependences of reciprocals of elastic moduli. Finally, the anisotropic sound velocities and Debye temperatures of the Ca–Pb compounds are predicted.

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