Vacancy diffusion and the hydrodynamics of crystals.

Area of Science:

• Condensed Matter Physics
• Thermodynamics
• Materials Science

Background:

• Understanding crystal hydrodynamics is crucial for materials science.
• Defects like vacancies significantly influence crystal properties.
• Local-equilibrium thermodynamics provides a framework for non-equilibrium phenomena.

Purpose of the Study:

• To develop a hydrodynamic theory for crystals containing vacancies.
• To establish microscopic foundations for transport coefficients related to vacancies.
• To identify and characterize the hydrodynamic modes in nonperfect crystals.

Main Methods:

• Application of local-equilibrium thermodynamics.
• Derivation of Green-Kubo and Einstein-Helfand formulas.
• Linearization of macroscopic equations to find dispersion relations.
• Numerical simulations of hard-sphere crystals with vacancies.

Main Results:

• Introduced the chemical potential of vacancies as a key variable.
• Derived formulas for vacancy conductivities and thermodiffusion coefficients.
• Established a relationship between vacancy conductivities and Fickian diffusion coefficients.
• Identified eight hydrodynamic modes, including a distinct vacancy diffusion mode.

Conclusions:

• The theoretical framework successfully describes crystal hydrodynamics with vacancies.
• The eighth hydrodynamic mode is confirmed to be vacancy diffusion.
• This work provides a microscopic basis for understanding defect-mediated transport in crystals.