Density-functional theory for vacancies in hard-sphere crystals

Area of Science:

• Computational Materials Science
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Calculating equilibrium vacancy concentrations in solids is crucial for understanding material properties.
• Traditional density-functional theory (DFT) methods face challenges with density profiles exhibiting less than one particle per lattice site, relevant for vacancy calculations.

Purpose of the Study:

• To adapt density-functional theory (DFT) for accurate computation of equilibrium vacancy concentrations in solids.
• To investigate the applicability and predictions of fundamental-measure theory (FMT) for vacancy concentrations in hard sphere crystals.
• To analyze the theoretical dependence of vacancy concentration on system density.

Main Methods:

• Employed density-functional theory (DFT) with modified density profiles allowing for less than one particle per lattice site.
• Utilized fundamental-measure theory (FMT) and asymptotic analysis of its functional.
• Calculated the prefactor of the exponential dependence using density profiles from quasifree minimization.

Main Results:

• Fundamental-measure theory (FMT) predicts reasonably small vacancy concentrations in hard sphere crystals, outperforming earlier DFT approaches.
• The number of vacancies exhibits an exponential dependence on the distance to the close packing density, consistent with theoretical expectations.
• Calculated prefactors for three FMT variants show good agreement with existing estimates and computer simulations upon extrapolation to melting density.

Conclusions:

• The adapted DFT approach, particularly using FMT, provides a robust framework for calculating equilibrium vacancy concentrations.
• The exponential relationship between vacancy concentration and density is theoretically validated and quantitatively supported by simulations.
• This work offers improved theoretical predictions for vacancy formation in crystalline solids.