Direct determination of amorphous number density from the reduced pair distribution function

Area of Science:

• Materials Science
• Nanotechnology
• Physical Chemistry

Background:

• Accurate amorphous bulk density determination is challenging for industrial materials like melts, porous solids, and non-soluble organic pharmaceuticals.
• Traditional methods like the Archimedean principle and gas pycnometry have limitations for these materials.
• Gas pycnometry often yields skeletal density, overestimating true density due to blind pores.

Purpose of the Study:

• To present a novel method for inferring amorphous bulk density from diffraction experiments.
• To extend the capability of Pair Distribution Function (PDF) analysis beyond crystalline density estimation.
• To provide a viable alternative for density determination when conventional techniques are inapplicable.

Main Methods:

• Extracting the reduced Pair Distribution Function (PDF) profile via Fourier transformation of diffraction intensity data.
• Identifying a local minimum within the PDF profile, specifically between r_min = 2π/Q_max and the first coordination peak.
• Calculating amorphous density using the ratio of the reduced PDF value at the minimum to 4πr, where r is the real-space coordinate of the minimum.

Main Results:

• Amorphous density can be reliably inferred from the position of a specific local minimum in the reduced PDF profile.
• The method is applicable to materials where traditional density measurement techniques are not feasible.
• The PDF minimum's location is bounded by theoretical limits related to the scattering vector (Q_max).

Conclusions:

• The developed method offers a new pathway for accurate amorphous density determination in challenging materials.
• This technique enhances the utility of diffraction experiments in materials characterization.
• It holds significant implications for nanotechnology and life sciences applications requiring precise material property data.