Green's function formulation of conductivity of anisotropic two-dimensional materials containing metallic inclusions: Application to phosphorene

Published

August 31, 2020

Author(s)

Vinod Tewary, Edward Garboczi

Abstract

A semi-analytical expression is presented for the effective thermal/electrical conductivity of two-dimensional anisotropic host solids, such as phosphorene, containing a regular array of metallic inclusions of arbitrary shape. The expression is derived by using a new, computationally efficient representation of the Green's function for the steady-state Laplace/Poisson equation. The representation is based upon a semi-discrete model of the solid, which yields an analytical formula for the Green's function in terms of its partial Fourier transform. Numerical results are presented for phosphorene host and metallic inclusions having elliptic (different eccentricities and orientations) or square shapes. In the low concentration limit, the calculated values have excellent agreement with the exact analytical values. The effective conductivity should be useful as a single parameter for design and characterization of two-dimensional composites.

Citation

Physics Letters A

Pub Type

Journals

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DOI Link

Keywords

Keywords: Anisotropic Laplace equation, Composites, Conductivity, Green’s function, Materials characterization, Phosphorene, Two-dimensional materials

Citation

Tewary, V. and Garboczi, E. (2020), Green's function formulation of conductivity of anisotropic two-dimensional materials containing metallic inclusions: Application to phosphorene, Physics Letters A, [online], https://doi.org/10.1016/j.physleta.2020.126851 (Accessed November 21, 2024)