Effect of Size and Shape on Thermo-‎Elastic Properties of Nano-Germanium

Document Type : Research Paper


1 ‎Department of Physics, St. Xavier's College (Autonomous),‎ Ahmedabad-380009, Gujarat, India‎

2 ‎Department of Physics, Government Science College, Sec-15,‎ Gandhinagar-382415, India‎

3 ‎Department of Physics, St. Xavier's College (Autonomous),‎ Ahmedabad-380009, Gujarat, India


   Germanium is a semiconductor with varied applications in the field of nanoscience and other fields of science. With known information about the bulk properties of germanium, an effort has been made to investigate the characteristics of germanium when it is in nanoscale size. The effective use of germanium and its compound in nanotechnology and other fields requires an intensive study of the thermo-elastic properties in nano scale. Effect of size and shape on the melting temperature, thermal expansivity, and bulk modulus has been studied for pure nano germanium. An attempt has been made to compute Young's modulus using two different formalisms. A comparative study of both the formalisms with experimental values is presented in this work. The comparative study for Young's modulus brings out the most suitable formalism for germanium nano crystal to calculate this modulus.


Main Subjects

  1. Yonenaga Ichiro, "4-Germanium crystals in Single Crystals of Electronic Materials: Growth and Properties”, Woodhead Publishing, (2019) 89-127.
  2. Crain, J., Ackland, G. J., Clark, S. J., "Exotic structures of tetrahedral semiconductors", Prog.Phys., 58 (1995) 705-754.
  3. Pandya, Tushar C., Shaikh, Aasim I., Bhatt, Apoorva D., "Particle-size effect on the compressibility of nanocrystalline germanium", AIP Conf. Proc., 1349 (2011) 413-414.
  4. Stark W. J., Stoessel, P. R., Wohlleben, Hafner, W., A., "Industrial applications of nanoparticles", Soc. Rev., 44 (2015) 5793-5805.
  5. Patil, S. D., Shinde, P. B., Takale, M. V., "Effect of size and shape on Young's modulus of nano-structured Ag by Lindemann's criterion", International Journal of Chemical and Physical Sciences, 3 (2014) 150-154.
  6. Patel, Ghanshyam R., Pandya, Tushar C., "Effect of size and shape on Young modulus of semiconducting nanosolids”, AIP Conference Proceedings, 1837 (2017) 040024 (1-3).
  7. Yang, Po-Yu., Ju, Shin-Po., Lai, Zhu-Min., Hsieh, Jin-Yuan., Lin, Jenn-Sen., "The mechanical properties and thermal stability of ultrathin germanium nanowires", Royal Society of Chemistry Advances, 6 (2016) 105713.
  8. Smith, Damon A., Holmberg, Vincent C., Korgel, Brian A., “Flexible germanium nanowires: Ideal strength, room temperature plasticity, and bendable semiconductor Fabric”, American Chemical Society NANO, 4 (2010) 2356-2362.
  9. Qi, W. H., "Size effect on melting temperature of nanosolid", Physica B: Condensed matter, 368 (2005) 46-50.
  10. Kumar, Raghuvesh, Sharma, Geeta, Kumar, Munish, "Size and temperature effect on thermal expansion coefficient and lattice parameter of nanomaterials", Modern Physics Letters B, 27 (2013) 1350180 (1-11).
  11. Jaiswal, R., Pandey, B., Mishra, D., and Fatma, H., "Thermo-physical Behaviour of Nanomaterials with the Change in Size and Shape", International Journal of Thermodynamics, 24 (2021) 1-7.
  12. Jiang, Q., Aya, N., Shi, F. G., “Nanotube size-dependent melting of single crystals in carbon nanotubes”, Phys. A, 64 (1997) 627-629.
  13. Singh, Madan., Lara, Sekhants'o., Tlali, Spirit., "Effect of size and shape on the specific heat, melting entropy and enthalpy of nanomaterials", Journal of Taibah University for Science, 11 (2017) 922-929.
  14. Nanda, K. K., Sahu, S. N., Behera, S. N., "Liquid-drop model for the size dependent melting of low-dimensional systems", Rev. A, 66 (2002) 1-8.
  15. Qi, W. H., Wang, M. P., "Size and shape-dependent melting temperature of metallic nanoparticles", Chem. Phys., 88 (2004) 280-284.
  16. Jaiswal, R. L., Pandey, B. K., “Modelling for the study of thermophysical properties of metallic nanoparticles.” SN Appl. Sci., 3 (2021) 466.