--- title: Comparison of RIR and Rietveld quantification description: Comparison of RIR and Rietveld quantification --- [Skip to content](https://help.momentum-transfer.com/comparison-of-rir-and-rietveld-quantification#main-content) English Show submenu for translations [![Momentum Transfer](https://help.momentum-transfer.com/hs-fs/hubfs/md2x.png?width=150&height=150&name=md2x.png)](https://momentum-transfer.com/) Open main navigation Close main navigation - English Show submenu for translations - [Contact us](mailto:team@momentum-transfer.com) [Contact us](mailto:team@momentum-transfer.com) Momentum Transfer Help Page - There are no suggestions because the search field is empty. 1. [Momentum Transfer Help Page](https://help.momentum-transfer.com/?hsLang=en) 2. [Data Processing & Analysis](https://help.momentum-transfer.com/data-processing-analysis?hsLang=en) # Comparison of RIR and Rietveld quantification **Summary** For major phases, RIR and Rietveld results often agree within a few wt% when the sample meets the RIR assumptions. For minor phases and for minerals with overlapping reflections, Rietveld is generally more accurate. It returns uncertainty values and a visual check of how well the model fits. **How RIR works** The relative intensity ratio (RIR) method gives a fast, almost instant estimate of mineral abundances. It scales the tabulated d/I values of reference patterns (e.g., ICDD PDF-5+) to the measured data. It then converts the scale factors into weight fractions using each phase's tabulated I/Icor value, which is its intensity relative to corundum in a 50:50 mixture by weight. The results are reliable when the following assumptions hold: The sample is fully crystalline. RIR normalises the result to 100%. Any amorphous or unidentified material is therefore spread across the identified phases, and all of them are overestimated. Peak profiles in the sample match those of the reference. Where scaling uses peak heights, phases with small crystallites or strain have broader, lower peaks and are underestimated (e.g., clays, poorly crystalline iron oxides). The reflections used for scaling don't overlap significantly with those of other phases. Reliable I/Icor values exist for all phases and suit the composition actually present. Tabulated values can differ a lot between database entries for the same mineral, and each refers to one specific composition. This is a limitation for solid-solution series such as plagioclase, chlorite, carbonates and garnet. Preferred orientation doesn't distort the intensities. RIR has no correction for it. The identified phase really is the phase in the sample. **How Rietveld addresses these points** The Rietveld method calculates the entire diffraction pattern from the crystal structures of all phases. It includes instrument and sample contributions to peak broadening (crystallite size and microstrain) and refines them for each phase. Taking the points in turn: Amorphous content can be quantified in absolute terms with an internal standard (spike) or an external standard. The external standard method needs the sample's mass absorption coefficient, which can be calculated directly from the XRF analysis, so no spiking is needed. Partially crystalline or disordered phases without a known structure can be included through calibrated models (PONKCS). Peak broadening is modelled for each phase, and quantification uses integrated intensities across the whole pattern. Differences in crystallite size and strain therefore don't bias the result. Overlap: every reflection of a phase contributes to its scale factor, not only the strongest peak. Where the main reflections overlap, the structural model separates the phases using their other reflections. Typical cases are kaolinite and chlorite at ~7 Å, quartz and mica at ~3.34 Å, and plagioclase and K-feldspar at ~3.2 Å. Overlap still reduces the information available and increases correlation between parameters, but this can be seen in the reported uncertainties. No I/Icor values are needed. Intensities are calculated from the crystal structure. Lattice parameters and site occupancies can be refined to match the actual composition (e.g., Fe/Mg substitution in chlorite or olivine). Preferred orientation (PO) does not occur in our measurements due to the experimental design. However for laboratory data PO can be corrected (March-Dollase or spherical harmonics). Phase identification is still a requirement for both methods and should be supported by chemical assays and mineralogical context. Rietveld helps here, though. A wrong or missing phase can't reproduce the full pattern, so it shows up in the difference curve and the fit statistics. RIR can match a few peaks without revealing the missing phase. **Minor phases** For minor phases, RIR usually depends on one or a few weak reflections that sit close to the background, so relative errors can be large. Rietveld uses all reflections of the phase and models the background at the same time, which improves both detection and quantification. The practical limit of quantification depends on scattering power, overlap and counting statistics. It is typically around \[0.5–1\] wt% under routine conditions, and lower for strongly scattering phases with optimised data collection. In any XRD method, relative uncertainty rises considerably below a few wt%. The standard deviations reported by Rietveld software reflect precision, not accuracy. We suggest accuracy be determined by performing replicate analyses. **Role of XRF reconciliation** In RIR–XRF workflows, XRF is often used to adjust abundances until they fit the bulk chemistry. When an element is hosted by several phases, that adjustment has more than one possible solution and depends on the mineral compositions assumed. Examples are Al, K, Fe and Mg spread across feldspars, micas, clays and chlorite. With Rietveld, the mineralogy is determined independently. The bulk chemistry calculated back from the phase abundances and mineral compositions is then compared with the XRF assay. Agreement within uncertainty confirms the result; a mismatch points to missing, misidentified or amorphous phases. XRF therefore works both as a quality check and, through the mass absorption coefficient, as an input for absolute quantification. Rietveld has its own sources of error: Results depend on suitable crystal structure models and on the analyst's experience. Clay minerals with stacking disorder (smectites, mixed-layer illite–smectite) need specialised models. Microabsorption from coarse, strongly absorbing particles affects both methods. The high energy of Momentum Transfer data mitigates this effect to the maximum. Careful sample preparation is essential either way, ideally by micronising to below 10 µm. In independent round robins such as the Reynolds Cup, full-pattern methods including Rietveld have generally produced the best results. 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