Rietveld Refinement and Cluster Analysis for Standardless Processing of Large Datasets

Table of Content

Case Study: Shale Rock Analysis
Case Study: Copper Ore


X-ray diffraction (XRD) provides a large amount of structural information, especially in geological formations of nature, where more than one phase can exist in the sample. Drilling and mining operations to obtain high sample throughput can benefit from standardless analysis tools, especially in instances where most samples have similar compositions. These tools include clustering of diffractograms (DIFFRAC.EVA) and batch processing of quantitative mineralogy (DIFFRAC.TOPAS).

XRD is a powerful tool to analyze the structure of mineralogical species. In addition to identifying polymorphs and distinct crystalline phases, XRD facilitates the detection of structural changes including; cationic substitution in carbonates, and lattice expansion in swelling clays, and quantification of complex mixtures. Data analysis of complete unknowns consists of two steps: (1) matching observed reflections to a database of known patterns for phase identification, and (2) using structural information for every identified phase to quantify specific phases, often with Rietveld refinement.

Intense processing of each diffractogram is not easy for several mining operations, especially at mining sites that generate large data and in automation settings. Here, the main objective could be the identification of statistical outliers or the routine analysis for quality control.

This article discusses the analysis of two sets of mineral samples – shale rock formations, and copper ore bodies. In the rock formations, different carbonate and clay concentrations can result in specific well treatments or steering decisions. For the copper ore bodies, diffraction approaches can be used to detect high concentration locations of sought-after ore minerals.

Individual refinement models were created for both of the sample sets, and they were applied to the diffractograms through batch processing with DIFFRAC.TOPAS. Quantitative Rietveld Techniques are ideal and powerful as several variables are taken into account such as; contrasts in absorption, preferred orientation effects, and peak broadening observed during disorder or crystallite size reduction. Structural databases or literature references can be used to import crystallographic data to quantify mineral mixtures, even when physical standards are non-existent. A large numbers of scans can be easily processed with the help of well-defined, robust models.

The clustering algorithms in DIFFRAC.EVA were used to process the two datasets. This can be considered a “standardless” technique, as information on specific crystalline phases is unknown or cannot be applied. Instead, scans are assigned into groups according to similarity, for a fast and easy identification of the samples of interest. For instance, outliers might be marked during quality control when aberrant peak intensities or considerable variation in peak location are noticed. DIFFRAC.EVA enables prescreening of >10,000 scans and allows single dataset grouping of up to 2,000 patterns, making the tool ideal for performing quick identification of patterns requiring detailed evaluation, and high-throughput analysis.


Wet-milling in ethanol with a McCrone micronizing mill and agate media were used to prepare samples. Fine powders were used to prepare diffraction specimens, utilizing backloading sample holders to reduce the preferred orientation effects.

Figure 1 shows a D8 ENDEAVOR process diffractometer, combined with a robotic sample handling system and a motorized anti-scatter screen for collecting data. A floor-standing instrument, the D8 ENDEAVOR performs well in laboratory environments, and can handle up to 72 samples in one load. A LYNXEYE XE silicon strip detector forms a part of the diffractometer, and enables a quick collection of data and reduction in sample fluorescence. Scans were collected in coupled Theta/Theta mode to enable the samples to be maintained in a horizontal position during data collection, reducing cross-contamination and sample spillage.

Figure 1. D8 ENDEAVOR process diffractometer.


DIFFRAC.EVA, in combination with the ICDD PDF-4+ database was used to perform phase identification. DIFFRAC.EVA also has cluster analysis tools and graphical functionalities, which were utilized to handle the data visualizations. Rietveld analysis with DIFFRAC.TOPAS was employed to quantify the identified crystalline phases.

Case Study: Shale Rock Analysis

This study is based on earlier research on shale rock in the Duvernay formation. Earlier work was devoted to the creation and testing of quantification models with a small quantity of samples. In this case study, the data is based on drill cuttings collected at 10 minute intervals, in a horizontal well more than 1200 m deep.

Figure 2 displays the collected data. Resembling a waterfall, it highlights the almost identical diffraction patterns, showing concomitant similarities in the composition of minerals. The 2D intensity map illustrates the differences in peak intensities, with bright spots representing the maximum intense calcite reflection (1 0 4).

Figure 2. (a) Waterfall plot and (b) 2D intensity map of data collected from shale rock cuttings. Diffractograms demonstrate similarity in both observed peak locations and intensities, indicating similar mineralogical compositions.

Figure 3 shows the metric multidimensional scaling (MMDS) view of several sets of outliers that were detected when processing the clustering algorithms. The red group is a cluster of the majority of the samples, indicating a high degree of similarity. Several outliers are allocated to separate clusters, this includes many with a more intense diffraction from calcite. This shows that clustering techniques can easily and quickly detect statistically different specimens, even before or in the absence of detailed crystallographic analysis.

Figure 3. 3D MMDS plot for cluster analysis and data similarity. The majority of samples are assigned to the central (red) group, indicating strong correlation. Groups assigned to blue and green are identified at statistical outliers, which correspond to higher calcite concentrations relative to the average.

The refinement model created in the earlier study was employed using batch processing with DIFFRAC.TOPAS. A tabular format output shows the results of phase quantification; this type of output can be easily changed into mineralogy tracks, as shown in Figure 4, by utilizing third-party software. Analysis of the blue and green clusters yields calcite concentrations, which range from 17-38 wt%, in comparison to the average calcite value for all samples (10 wt%).

Figure 4. Mineralogy track for all shale samples generated by batch processing with Rietveld refinement. Phase quantification is plotted along the X-axis, and measured depth is plotted along the Y-axis.

Case Study: Copper Ore

In this study, 20 samples of copper ore from various mine sites were taken and examined for compositional variance. Crystalline phases were first identified with DIFFRAC.EVA, as a prior quantification model for the samples was absent. Later, the phases were added to a fresh refinement model in DIFFRAC.TOPAS. Diffractograms were handled in a similar manner as the shale rock samples (clustering according to similarity, and batch quantification by employing a single model).

Figure 5 shows a waterfall plot for the collected diffractograms. In contrast to earlier example of shale cuttings, obvious differences exist in the diffraction data.

Figure 5. Waterfall plot for data collected from copper ore samples. Stark differences in relative peak intensities indicate large compositional variances.

Clustering allocates the data into four categories, as illustrated in the dendrogram plot in Figure 6. Representative diffractograms for all of the clusters are displayed below the dendrogram, highlighting the considerable peak intensity differences for various reflections. These differences show the variance in composition.

Figure 6. Dendrogram plot for cluster analysis of copper ore samples, indicating four distinct groups. Selected diffractograms are shown below the dendrogram for reference, highlighting the differences in diffraction data between groups.

Figure 7 shows the quantitative Rietveld refinement of one sample. Identified phases include ore minerals and common minerals such as; chalcopyrite, calcite, and quartz. Weight percentages were exported in tabular form after a refinement model was utilized for each diffractogram.

Figure 7. Quantitative Rietveld refinement with DIFFRAC.TOPAS for a single copper ore sample. The contribution of each mineralogical phase to the total diffraction pattern is indicated in the colored traces below the diffractogram.

Extensive Rietveld examination shows significant correlations between clustering and composition. Table 1 shows the weight percentages and specified phases. For instance, an average pyrite content of 23.7 wt% is found in the yellow cluster; this value is more than twice the average concentration for all samples, which is 12.1 wt%. Another good example for clustering effectiveness is shown in the case of chalcopyrite. Green and blue clusters have a significant quantity of this mineral (28.9 wt% and 52.3 wt%), while the red and yellow clusters are much less than 10 wt%. This research work can form the basis of future investigation in this mining location, as an extended sample group can be quickly sorted according to the similarity to the current clusters. This process can be automated, and does not require expert knowledge.

Table 1. Quantification for selected minerals with calculated averages for each identified cluster.

  Total Average Red Average Yellow Average Green Average Blue Average
Quartz 31,4 49,9 33,5 19,7 3,9
Pyrite 12,1 4,7 23,7 17,3 10,3
Chalcopyrite 18,6 2,3 7,1 28,9 52,3


The characterization of high volumes of samples involves several challenges, which can be resolved using software tools that can handle large data sets. With a combination of batch processing of refinement models and clustering approaches, several diffractograms can be handled, samples of interest or outliers can be identified, mineral composition can be quantified, and correlations between sample clusters can be drawn up.

This information has been sourced, reviewed and adapted from materials provided by Bruker AXS Inc.

For more information on this source, please visit Bruker AXS Inc.

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