Calculating temperature-dependent X-ray structure factors of α-quartz with an extensible Python 3 package

Area of Science:

• Solid-state physics
• Crystallography
• Materials science

Background:

• Accurate calculation of crystal structure factors is essential for designing X-ray optics.
• Temperature dependence of lattice parameters, atomic positions, and thermal vibrations in crystals is complex, being both anisotropic and nonlinear.
• α-Quartz presents significant challenges due to its anisotropic and nonlinear temperature-dependent properties and is considered for high-resolution X-ray spectroscopy.

Purpose of the Study:

• To develop a precise and flexible software package for calculating structure factors for dynamical X-ray diffraction.
• To address the temperature dependence of crystal properties, including anisotropic thermal vibrations.
• To provide a framework easily extensible to other crystalline materials.

Main Methods:

• Implementation of a software package in Python 3 for calculating structure factors.
• Utilizing α-Quartz as a test case to demonstrate the package's capabilities.
• Comparing results from anisotropic thermal vibration treatment with an isotropic Debye model.

Main Results:

• The software package enables precise and flexible calculation of structure factors for dynamical diffraction.
• Demonstrated significant discrepancies (up to 5% for strong, 100% for weak reflections) when comparing anisotropic thermal vibrations to isotropic models.
• Developed a script for identifying Bragg reflections relevant for X-ray backscattering within a specified temperature range.

Conclusions:

• Accurate anisotropic treatment of atomic thermal vibrations is critical for precise structure factor calculations in X-ray diffraction.
• The developed software package offers a robust and extensible solution for calculating temperature-dependent structure factors.
• The package facilitates advancements in X-ray optics design and high-resolution X-ray spectroscopy applications.