Continuum Mechanics and Thermodynamics

, Volume 30, Issue 5, pp 1027–1038 | Cite as

Phonon dispersion evolution in uniaxially strained aluminum crystal

  • Ranganathan ParthasarathyEmail author
  • Anil Misra
  • Sitaram Aryal
  • Lizhi Ouyang
Original Article


The influence of loading upon the phonon dispersion of crystalline materials could be highly nonlinear with certain particular trends that depend upon the loading path. In this paper, we have calculated the influence of [100] uniaxial strain on the phonon dispersion and group velocities in fcc aluminum using second moments of position obtained from molecular dynamics (MD) simulation at 300 K. In contrast to nonlinear monotonic variation of both longitudinal and transverse phonon frequencies along the \(\Delta \), \(\Lambda \) and \(\Sigma \) lines of the first Brillouin zone under tension, transverse phonon branches along the \(\Lambda \) line show inflection at specific wavevectors when the compressive strain exceeds 5%. Further, the longitudinal group velocities along the high-symmetry \(\Delta \) line vary non-monotonically with strain, reaching a minimum at 5% compressive strain. Throughout the strain range studied, the equilibrium positions of atoms displace in an affine manner preserving certain static structural symmetry. We attribute the anomalies in the phonon dispersion to the non-affine evolution of second moments of atomic position, and the associated plateauing of force constants under the applied strain path.


Anomalous phonon dispersion Non-affine thermal vibrations Local potential energy Non-monotonic evolution of phonon group velocities 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, Box 9616Tennessee State UniversityNashvilleUSA
  2. 2.Department of Civil, Environmental and Architectural EngineeringUniversity of KansasLawrenceUSA

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