Two-Dimensional X-Ray Diffraction Crystallite Size Measurement
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Solution Overview
Problem
Conventional X-ray diffraction methods are limited in measuring crystallite sizes larger than 100 nm, particularly in pharmaceutical systems where sizes range from micrometers to millimeters, as they are not suitable for determining particle sizes in these larger ranges.
Innovation Solution
A two-dimensional X-ray diffraction system performs quantitative γ-profile analysis on diffraction rings to determine crystallite size, extending the measurement range from below 100 nm to several millimeters by calibrating with a known sample and using the effective diffraction volume, grain size, and multiplicity of diffracting crystal planes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional 2θ profile analysis is used, then measurement is suitable for small crystallites (below 100 nm), but it cannot accurately measure larger crystallites (micrometers to millimeters) found in pharmaceutical systems
Solution Approach 1:
The patent transitions from conventional one-dimensional 2θ profile analysis to two-dimensional diffraction ring analysis by integrating diffraction patterns in the γ direction. This dimensional change enables accurate measurement of crystallite sizes from 0.1 μm to several millimeters, making the method suitable for pharmaceutical systems while maintaining capability for smaller crystallites.
2Measurement precision
If Scherer equation is used with significant broadening, then average size of crystallites smaller than 30 nm can be determined, but it fails when broadening is not significant enough (larger than 100 nm)
Solution Approach 1:
The patent employs two-dimensional diffraction ring analysis with γ-profile integration instead of relying on 2θ peak broadening. This approach measures the intensity distribution along the diffraction ring, enabling accurate crystallite size determination across a wide range from 0.1 μm to millimeters without requiring significant diffraction broadening.
Solution Approach 2:
The patent changes the measurement parameter from diffraction peak broadening (2θ domain) to diffraction ring intensity distribution (γ domain). This parameter change allows measurement of crystallite sizes where peak broadening is not significant, extending the measurable range to include larger pharmaceutical particles.
3Measurement precision
If microscopy techniques are used, then surface crystallite observation is possible, but special sample preparation is required and only surface measurement is achieved
Solution Approach 1:
The patent replaces mechanical microscopy techniques with X-ray diffraction methodology. This substitution eliminates the need for special sample preparation and surface polishing required by microscopy, while enabling non-destructive measurement of crystallite sizes throughout the entire sample volume, not just the surface.
Solution Approach 2:
The X-ray diffraction method provides universal applicability to various sample types without requiring special preparation procedures. It can measure crystallite sizes in bulk materials, powders, and pharmaceutical systems directly, making it more versatile and easier to implement than microscopy techniques.
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
This method allows for accurate measurement of crystallite sizes in a wider range, specifically from 0.1 μm to a few millimeters, making it suitable for pharmaceutical systems by integrating diffraction patterns in the γ direction and accounting for instrumental and sampling statistics, thereby overcoming the limitations of conventional 2θ profile analysis.
Implementation Method 1
X-ray diffraction has been used for crystallite size measurement for over ninety years since X-rays can penetrate a sample and measure crystallite size over the entire volume of the sample
Data Source
AI summary
Crystallite size in a sample is determined by performing a quantitative γ-profile analysis on a diffraction ring in a two-dimensional X-ray diffraction pattern. In particular, a two-dimensional X-ray diffraction system is first calibrated with a sample having a known crystallite size, crystal structure and X-ray absorption coefficient. For a given instrument window, the number of grains contributing to a selected diffraction ring is determined by the effective diffraction volume, grain size and the multiplicity of the diffracting crystal planes. The grain size of an unknown sample can then be determined by a quantitative analysis of the diffraction ring.