The thermodynamics of three-dimensional, single-component elastic crystalline
solids was developed by Slattery and Lagoudas (2005). Considering the inïnitesimal
deformations, the stress can be expressed as a function of the lattice vectors and
density in the reference configuration and ù(I;mn), which is defined as the derivative of
specific Helmoholtz free energy with respect to the I(mn). Using the Cauchy - Born rule
to connect the interatomic potential energy and the specific Helmholtz free energy, it is
possible to calculate the elastic properties of both nano-scale materials such as carbon
nanotubes and macro-scale materials such as diamond and silicon. In this study, we
used Tersoî (1988a) - Brenner (1990b) Potential, Tersoî (1988b) potential and Finnis
and Sinclair (1984) potential for carbon, silicon, and vanadium systems respectively.
Using the interatomic potentials to describe the specific Helmholtz free energy, the
elastic properties of graphite, diamond, silicon and vanadium were calculated. This
method was also extended to the calculation of Young's modulus of single-walled
carbon nanotubes (SWCNTs), which are composed of a two dimensional array of
carbon atoms. For SWCNT, we get good agreement with the available experimental
data. For diamond and silicon, C11 and C12 were consistent with both the superelastic
model and the experimental data. The difference of C44 between the calculation and
experimental data was due to accuracy of the potential functions.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/4252 |
| Date | 30 October 2006 |
| Creators | Tian, Yongzhe |
| Contributors | Slattery, John C. |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | 414331 bytes, electronic, application/pdf, born digital |
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