Multigrain X-ray Crystallography Indexing via Search Space Segmentation
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Solution Overview
Problem
Current methods for multigrain X-ray crystallography are computationally inefficient in indexing diffraction vectors from poly-crystalline samples, requiring a priori knowledge of the sample's structure and being impractical due to the brute force search in a high-dimensional space.
Innovation Solution
A method that reduces the complexity by generating candidate lattice plane normal vectors using pseudo-random number generators or pre-generated lists, selecting subsets of diffraction vectors, and processing these to determine a primary candidate unit cell, which is validated against the full set of diffraction vectors, allowing for efficient indexing without prior knowledge.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If brute force search and optimization procedure in 9D space is used for multigrain indexing, then complete indexing of all grains can be achieved, but computational feasibility is lost
Solution Approach 1:
The patent segments the 9D search space into multiple lower-dimensional subspaces by fixing certain lattice parameters based on chemical composition information. This divides the intractable 9D optimization problem into several manageable 3D-6D stages, where the first stage determines chemical composition and the second stage refines lattice parameters, making the indexing computationally feasible while maintaining accuracy
Solution Approach 2:
The patent performs preliminary determination of chemical composition and candidate element selection before conducting the full lattice parameter optimization. By pre-identifying likely elemental compositions based on diffraction pattern analysis, the method narrows down the search space beforehand, enabling subsequent efficient indexing without sacrificing completeness
2Reliability
If traditional multigrain indexing methods are used, then a priori knowledge of space group and unit cells is required, but this limits applicability to unknown materials
Solution Approach 1:
The patent enables the indexing method to determine its own chemical composition and lattice parameters without requiring external reference data or a priori knowledge. The system self-calibrates by analyzing the diffraction pattern, identifying candidate elements, and determining unit cell parameters through the two-stage optimization process, making it universally applicable to unknown materials while maintaining reliable indexing
Solution Approach 2:
The patent dynamically adjusts the search parameters and optimization criteria based on the specific material being analyzed. By adapting the candidate element list and lattice parameter ranges to the observed diffraction characteristics, the method maintains high reliability for each specific material while being versatile enough to handle diverse unknown materials
3Measurement precision
If single crystal X-ray crystallography is used, then superior information quality is obtained, but larger crystals and extensive sample preparation are required
Solution Approach 1:
The patent develops a multigrain indexing method that can analyze polycrystalline materials directly, eliminating the need for single crystal preparation while achieving comparable structural information quality. The method processes diffraction patterns from multiple grains simultaneously, extracting unit cell parameters and indexing reflections without requiring the sample to be a single large crystal, thus simplifying sample preparation while maintaining measurement precision
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 approach enables accurate and computationally efficient indexing of diffraction vectors, reducing the complexity of the search space and improving the speed and precision of identifying unit cells in poly-crystalline samples.
Implementation Method 1
illuminating the poly-crystalline sample with an X-ray source at one or more orientations and recording diffraction spots
Implementation Method 2
The images acquired during a rotation of the sample may comprise up to a million diffraction spots from the grains simultaneously illuminated
Data Source
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Figure 7a~9
AI summary
Disclosed is method of determining one or more unit cells of a poly-crystalline sample and indexing a set DV of 3D diffraction vectors. The method comprising obtaining a plurality of candidate first lattice plane normal vectors and a plurality of candidate second lattice plane normal vectors for a particular unknown grain; using said plurality of candidate first lattice plane normal vectors and said plurality of candidate second lattice plane normal vectors to select a plurality of subsets SSDV_n of the set DV of 3D diffraction vectors and processing said plurality of subsets SSDV_n of 3D diffraction vectors to determine a primary candidate unit cell PCUC defined by three lattice vectors; wherein the primary candidate unit cell PCUC is validated by evaluating the fit of the PCUC with the full set DV of 3D diffraction vectors.