2D X-ray Diffraction Crystallite Size Distribution Analysis
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Solution Overview
Problem
Current methods for measuring crystallite size in polycrystalline materials, such as the Scherrer equation and γ profile analysis, can only determine average crystallite size and not the size distribution, which is crucial for understanding properties like solubility and stability in pharmaceuticals and other applications.
Innovation Solution
A method using an X-ray diffractometer with a two-dimensional detector to measure crystallite size distribution by rotating the sample relative to the X-ray beam and detector, measuring diffraction spot intensities at multiple rocking angles, and calculating crystallite volumes from peak intensities to determine size distribution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional methods (Scherrer equation or γ profile analysis) are used, then average crystallite size can be measured, but crystallite size distribution cannot be determined
Solution Approach 1:
The patent segments the diffraction pattern into individual spot profiles, each corresponding to a separate crystallite. By analyzing the intensity of each individual spot rather than the overall diffraction peak, the method can determine the size of individual crystallites and thus obtain the size distribution. This segmentation approach transforms the measurement from an average value to individual component analysis.
Solution Approach 2:
The patent transitions from one-dimensional diffraction peak analysis to two-dimensional spot profile analysis. By utilizing the two-dimensional detector and analyzing spots in the γ direction (azimuthal angle) rather than only in the 2θ direction, the method extracts additional dimensional information that enables size distribution determination while maintaining average size measurement capability.
2Productivity
If a single diffraction pattern image is recorded, then measurement time is reduced, but spot intensity and measurement quality are insufficient
Solution Approach 1:
The patent implements periodic rocking of the sample during data collection, where the sample is oscillated at a small amplitude around a central angle. This periodic motion distributes the diffraction spots across multiple detector positions, allowing the accumulation of intensity information for each spot from multiple rocking angles. The result is enhanced spot intensity and improved signal-to-noise ratio while maintaining relatively fast measurement times.
Solution Approach 2:
The patent merges diffraction data from multiple rocking angles into a single comprehensive analysis. By collecting and combining intensity information from spots measured at different rocking positions, the method accumulates sufficient signal strength for accurate size determination. This merging approach maintains productivity by processing the combined data through a unified analysis framework.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables accurate determination of crystallite size distribution, providing critical information for material properties and process control, particularly in the pharmaceutical industry, by effectively measuring the volume of each crystallite and analyzing intensity variations across a range of rocking angles.
Implementation Method 1
X-ray diffraction has been used for crystallite size measurement for over ninety years
Implementation Method 2
crystallites in the sample produce diffraction spots on a detection surface of the detector
Implementation Method 3
a two-dimensional X-ray detector... The intensities of the spots are measured within a defined detection window of the detector
Data Source
Figure 1A
Figure 1B~1C
Figure 2~3
AI summary
An X-ray diffraction method measures crystallite size distribution in a polycrystalline sample (106) using an X-ray diffractometer (100) with a two-dimensional detector (108). The diffraction pattern collected contains several spotty diffraction rings. The spottiness of the diffraction rings is related to the size, size distribution and orientation distribution of the crystallites as well as the diffractometer (100) condition. The invention allows obtaining of the diffraction intensities of all measured crystallites at perfect Bragg condition so that the crystallite size distribution can be measured based on the 2D diffraction patterns.