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Peer-reviewedCC BY 4.0Nanomaterials

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

  • Nataliya Sakharova1,2
  • André Pereira2
  • Jorge Antunes2,3
  1. 1UnIRE, Instituto Superior de Engenharia de Lisboa, Universidade Politécnica de Lisboa, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
  2. 2Centre for Mechanical Engineering, Materials and Processes (CEMMPRE)—Advanced Production and Intelligent Systems, Associated Laboratory (ARISE), Department of Mechanical Engineering, University of Coimbra, Rua Luís Reis Santos, Pinhal de Marrocos, 3030-788 Coimbra, Portugal
  3. 3Abrantes High School of Technology, Polytechnic Institute of Tomar, Quinta do Contador, Estrada da Serra, 2300-313 Tomar, Portugal
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@article{sakharova2026elastic,
  title = {{Elastic Behavior of Group 13–Phosphide Nanosheets and Nanotubes: A Numerical Study}},
  author = {Nataliya Sakharova and André Pereira and Jorge Antunes},
  journal = {Nanomaterials},
  year = {2026},
  month = oct,
  doi = {10.3390/nano16211398},
  url = {https://www.mdpi.com/2079-4991/16/21/1398},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Elastic Behavior of Group 13–Phosphide Nanosheets and Nanotubes: A Numerical Study
AU  - Nataliya Sakharova
AU  - André Pereira
AU  - Jorge Antunes
PY  - 2026
DA  - 2026/10/31
JO  - Nanomaterials
DO  - 10.3390/nano16211398
UR  - https://www.mdpi.com/2079-4991/16/21/1398
AB  - 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.
SN  - 2079-4991
ER  -