Density Distribution in Soft Matter Crystals and Quasicrystals.

Area of Science:

• Materials Science
• Condensed Matter Physics
• Crystallography

Background:

• Traditional methods represent solid density distributions using Gaussian peaks or Fourier sums.
• These conventional approaches have limitations in accurately describing complex systems.

Purpose of the Study:

• To introduce and advocate for representing the logarithm of density distributions via Fourier sums.
• To demonstrate the accuracy and utility of this novel representation for crystalline and quasicrystalline systems.

Main Methods:

• Developing a Fourier sum representation for the logarithm of the density distribution.
• Applying this method to soft matter crystals and three-dimensional quasicrystal-forming systems.
• Utilizing accurate nonlocal density functional theory for phase diagram calculations.

Main Results:

• The logarithm-based Fourier sum representation achieves high accuracy for soft matter crystals with few terms.
• While not easily truncating for quasicrystals, this representation remains highly beneficial.
• Successfully calculated the phase diagram for a 3D quasicrystal-forming system.

Conclusions:

• Representing the logarithm of density distributions via Fourier sums is a more accurate and versatile approach.
• This method enhances the study of both soft matter crystals and quasicrystals.
• The approach facilitates advanced calculations like phase diagram determination.