Thermodynamics of dislocations within the harmonic approximation
by Schuck, Paul, Ph.D., ARIZONA STATE UNIVERSITY, 2008, 108 pages; 3302959

Abstract:

The vibrational spectra of straight screw and edge dislocations in several body-centered cubic (Mo and Fe) and face-centered cubic (Cu and Al) metals within the harmonic approximation were calculated. The translational symmetry of straight dislocations leads to Bloch-diagonal dynamical matrices, for which the phonon eigenstates can be obtained very efficiently. The heat capacities and free energies of screw and edge dislocations dipoles were calculated as a function of temperature and compared to point defects in those same systems. The results show that quantized vibrations lead to a non-negligible contribution of defects to the low-temperature specific heat of crystals. This translates into a surprisingly large decrease in the formation free energies of dislocations at high temperatures, due only to harmonic phonons. Localized and resonance modes associated with dislocations appeared in the vibrational spectra and were studied by the spatial spread of these modes around the dislocation cores by projecting vibrational eigenstates onto individual atoms. In this way, atom-decomposed free energies and entropies were obtained and show that the vibrational free energy of an isolated dislocation diverges due to its long-range strain field. The above analysis was also performed on screw dislocations in the same metals as a function of stress and shown to have little effect. Finally, the transition state of an iron screw dislocation from one Peierls valley to the next was investigated and the energy profile reported. The change of the core of the dislocation in atomistic detail is shown. These results were compared with molecular dynamic results for a mobility curve and found to have reasonable agreement.

 
Advisor
SchoolARIZONA STATE UNIVERSITY
SourceDAI/B 69-02, p. , May 2008
Source TypeDissertation
SubjectsMaterials Science
Publication Number3302959
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