Elastic Behavior of Group 13–Phosphide Nanosheets and Nanotubes: A Numerical Study

Group 13–phosphide nanosheets and nanotubes represent a family of nanostructures whose mechanical properties remain unevenly explored, particularly across the complete B–Al–Ga–In–Tl series. In this work, the elastic behavior of boron phosphide, aluminum phosphide, gallium phosphide, indium phosphide and thallium phosphide nanosheets and single-walled nanotubes is systematically investigated using nanoscale continuum modeling based on molecular structural mechanics and finite element analysis. The surface Young’s and shear moduli of the nanosheets are evaluated and their variation along the group 13–phosphide series is analyzed. The corresponding nanotubes are investigated considering zigzag, armchair and chiral configurations with diameters above 1.3 nm to assess the influence of geometry and chirality on their elastic response. The results reveal an overall decrease in the elastic properties along the B–Al–Ga–In–Tl series, although the trend is not uniform for all compounds and properties. The surface Young’s moduli of the nanotubes are found to be comparable to those of the corresponding nanosheets, whereas their surface shear moduli are consistently higher, despite the different deformation modes involved. Overall, this study provides a consistent assessment of the mechanical behavior of both 2D and 1D group 13–phosphide nanostructures within a unified modeling framework, while also providing reference data for compounds whose elastic properties remain scarcely reported.