Generalized dynamics of moving dislocations in quasicrystals

Area of Science:

• Materials Science
• Solid Mechanics
• Condensed Matter Physics

Background:

• Quasicrystals exhibit unique mechanical properties due to their complex atomic structures.
• Understanding dislocation dynamics is crucial for predicting material behavior and failure.
• Existing theories often do not fully capture the complexities of quasicrystal mechanics.

Purpose of the Study:

• To establish a comprehensive theoretical framework for dislocation dynamics in quasicrystals.
• To derive and generalize key mechanical quantities within the continuum theory of dislocations.
• To investigate the influence of phason fields and dynamical terms on quasicrystal behavior.

Main Methods:

• Application of the continuum theory of dislocations.
• Formulation of dislocation density and current tensors for phonon and phason fields.
• Derivation of equations of motion for incompatible elastodynamics and elasto-hydrodynamics.
• Development of balance laws for pseudomomentum and energy.

Main Results:

• Generalized forms of Eshelby stress tensor, pseudomomentum vector, and Peach-Koehler forces derived.
• Balance law of energy formulated, yielding generalized field intensity and elastic power density.
• Specific form of dynamical Peach-Koehler force for straight dislocations determined.
• Differences between two theoretical models and their implications analyzed.

Conclusions:

• The developed framework provides a robust theoretical foundation for studying dislocation mechanics in quasicrystals.
• Phason fields and dynamical terms significantly influence the mechanical response of quasicrystals.
• The generalized quantities offer new tools for analyzing deformation and fracture in these materials.