XRD Analysis in Cement: Complete Guide

X-ray diffraction analysis (XRD) has been used for nearly one hundred years to identify and characterize the crystalline phases in solid materials, and it is one of the three great instruments of cement quality control, standing beside chemical analysis and the microscope. Because it gives information about phases, X-ray diffraction is distinctly different from the determination of chemical composition using X-ray fluorescence: the XRF reports how much calcium, silicon, aluminium and iron are present, while the XRD reports how those elements are arranged into the crystals of alite, belite, aluminate, ferrite, lime and the sulfate phases. Powder diffraction is particularly well suited to the determination of phases in portland cement, because the clinker is a fine, polycrystalline powder whose phases can be identified and quantified from the diffraction pattern of a single prepared specimen. This complete technical guide, based on the authoritative chapter “X-Ray Diffraction Analysis” from the Innovations in Portland Cement Manufacturing series held in the Complete Cement Technical Package, explains the principles of crystal structure and diffraction, the instrumentation, the specimen preparation, the qualitative and quantitative analysis, and the applications of XRD throughout the cement manufacturing operation.

The method is built on a beautiful physical law: when a beam of X-rays of wavelength lambda strikes a family of parallel crystal planes separated by the distance d, the rays scattered by successive planes interfere constructively only when the angle theta satisfies the Bragg equation n times lambda equals two d sine theta. Every crystalline phase in the specimen diffracts according to its own unique set of plane spacings, producing a characteristic pattern of peaks that functions as the phase’s fingerprint. The cement analyst reads those fingerprints to identify the phases present, and measures the peak intensities to determine how much of each phase the sample contains. This guide walks the whole technique, from the unit cell and the Miller indices to the Rietveld refinement and the daily quality control applications, with the numbers, the peak data and the plant practice that make the method work.

1. Why XRD Is Different From Chemistry and From Microscopy

The position of X-ray diffraction in the quality control laboratory is defined by what it measures and what it does not. Each analytical family of the cement laboratory occupies its own level of information:

• X-ray fluorescence (XRF): determines the chemical composition of the bulk specimen, reporting the elements as oxides; it cannot distinguish the alite from the belite, because both are calcium silicates of nearly the same oxide ratio.
• X-ray diffraction (XRD): determines the crystalline phases of the bulk specimen, reporting the actual mineral forms; it answers the question XRF cannot, which of the possible compounds the elements have formed, and in what proportions.
• Microscopy: determines the microstructure, how the phases are arranged on the microscopic scale: their sizes, shapes, intergrowths and distribution; the next chapter of the source series treats this level.
• Electron microscopy with X-ray analysis: determines the chemical composition of small selected regions of the specimen, the local answer between the bulk method and the microstructure.

Other X-ray techniques complete the family: single crystal X-ray diffraction determines the crystal structure of a single crystal (the powder method can refine, but not unambiguously determine, a structure), electron diffraction and neutron diffraction serve structure analysis by other radiations, and small-angle X-ray scattering determines the surface area of a material. In the cement plant, however, the powder method is the tool, because the clinker and the cement present themselves as powders and the questions the plant asks (how much alite, how much free lime, which sulfate phases, how much glass) are phase questions.

2. Crystal Structure: The Lattice, the Unit Cell and the Miller Indices

The diffraction method rests on the structure of crystals, so the theory begins with the crystal itself. A crystal is a solid in which the atoms or molecules are arranged in a regular and repeating pattern; amorphous or glassy materials, by contrast, have no crystal structure because their constituents are arranged without a regular repeating pattern. Between the two extremes lie the partly crystalline materials, such as the partially glassy clinker of a rapidly cooled product, and this scale of crystallinity is itself an object of XRD measurement.

• The lattice: the distribution of atoms or molecules in a crystal is described by the lattice, obtained by the translational repetition in three dimensions of points representing the positions of the atoms or molecules.
• The unit cell: the smallest repeating unit of the lattice, whose repetition in three dimensions generates the entire crystal; the general unit cell is a parallelepiped whose edges (a, b and c) and angles (alpha, beta and gamma) may all be unequal, and the symmetry of the crystal often requires the unit cell to be more regular.
• The Miller indices (hkl): to describe how X-rays interact with crystals, the analyst refers to specific planes within the structure, each plane designated by the indices (hkl), obtained by finding where the plane intercepts each crystallographic axis, taking the reciprocal of each intercept (which avoids introducing infinity for planes parallel to an axis), and converting the reciprocals to the smallest integers.
• Properties of the indices: a plane parallel to a given axis has a zero intercept on that axis; planes with larger indices lie closer together, which means smaller interplanar spacings d, which diffract at larger angles.

The intellectual chain of the method is therefore: the crystal structure defines the plane spacings, the plane spacings define the diffraction angles by the Bragg equation, and the measured angles identify the phase. This is why the phase identification libraries (the powder diffraction file of the International Centre for Diffraction Data) are organised by the d-spacings and the relative intensities of the strongest peaks: every known crystalline phase has its own pattern, and the unknown specimen is matched against the library.

3. The Bragg Equation and the Physics of Diffraction

The diffraction of X-rays by a crystal is described by the Bragg equation, the most important relationship of the method: n times lambda equals two d sine theta, where lambda is the wavelength of the X-rays, d is the spacing of the diffracting planes, theta is the angle of incidence (and reflection) of the beam on the planes, and n is the order of the diffraction, an integer. The equation is the instrument’s calibration and its language: at the fixed wavelength of the instrument, each plane spacing d diffracts at a specific angle theta, and the measured angles of the pattern translate directly into the plane spacings of the phases.

• Constructive interference: the rays scattered by successive planes add up only when the path difference between them equals an integer number of wavelengths; otherwise they cancel, and no peak appears.
• Peak position and phase identity: because every phase has its own set of plane spacings, the angular positions of its peaks are unique; the pattern of a phase is as identifying as a fingerprint, and a mixture produces the superposition of the patterns of its phases.
• Peak intensity and phase amount: the intensity of a phase’s peaks grows with the amount of the phase in the specimen, which is the basis of the quantitative analysis; the proportionality is modified by the absorption of the specimen, which the quantitative methods must handle.
• Line broadening and crystal size: when the crystals of a phase are very small (below a few hundred nanometers), the peaks broaden, and the width of the peaks can be used to estimate the crystal size, a specialised application of the same pattern.

The beauty of the Bragg law for the cement laboratory is its simplicity of operation: the instrument measures the intensities of the scattered radiation as a function of the angle, the pattern is compared with the library, and the phases and their quantities follow. The cement analyst does not need to solve crystal structures; the analyst needs to measure patterns well and to read them carefully, and that is the discipline the remainder of this guide describes.

4. The Powder Diffractometer: Instrumentation and the Measurement Geometry

The working instrument of the method is the powder diffractometer, in which a prepared powder specimen is placed at the centre of the goniometer, the X-ray source and the detector sweep the angles, and the scattered intensities are recorded as the diffraction pattern. The components and the measurement practice are:

• The X-ray source: a sealed or rotating-anode tube producing the characteristic radiation of its target; copper is the standard choice for cement work, with the Cu K-alpha radiation of wavelength 1.5406 angstroms (0.15406 nanometers) as the working line, usually monochromatised or filtered to remove the K-beta component.
• The goniometer: the precision stage that moves the detector (and in some geometries the specimen) through the angular range, typically from about 5 to 70 degrees two-theta for cement phase work, recording the intensity at each step.
• The detector: the scintillation or solid-state detector converts the scattered photons into counts, and modern instruments use position-sensitive detectors that collect large angular ranges in a fraction of the time of the classical step scan.
• The specimen holder: the flat, front-filled or side-filled holder presents the powder with a flat surface at the centre of the geometry; the preparation quality, not the electronics, usually limits the quality of the data.
• Alignment and calibration: the instrument is aligned with standard materials (the silicon or quartz reference) and the angle calibration is verified, because a small angle error shifts every peak and corrupts every phase identification.

The modern diffractometer used in cement analysis is a robust, enclosed, computer-controlled machine that performs the scans, identifies the phases and, with the appropriate software, delivers the quantitative phase analysis with the Rietveld refinement as a routine function. The instrument shown in the source chapter is the standard laboratory configuration, and the operational expertise of the plant lies in the specimen preparation and the interpretation, not in the electronics.

5. Specimen Preparation: The Discipline That Determines the Data Quality

In powder diffraction, the specimen preparation is where the analysis is won or lost. The specimen must represent the sample, must present a statistically large number of randomly oriented crystals to the beam, and must have a flat surface at the correct position. The preparation practice of the cement laboratory includes:

• Grinding: the clinker or cement is ground to a fine powder, typically with a laboratory mill to below about 10 microns median, because coarse particles both bias the phase proportions (each particle contributes its own phases) and reduce the number of crystals in the beam.
• Random orientation: the flat specimen holder is filled and the surface is smoothed, taking care that the filling does not preferentially orient the plate-like or needle-like crystals of some phases; the preferred orientation would strengthen some peaks and weaken others, corrupting the quantitative results.
• Representativeness: the specimen is taken from a properly split subsample of the plant’s sample, because the diffraction pattern of a nonrepresentative handful of powder is the pattern of that handful, not of the production.
• Special preparation for quantitative work: the quantitative methods may require mixing the specimen with an internal standard or preparing a back-loaded holder to eliminate the surface effects; the Rietveld analysis works from the same specimen with its own corrections.
• Humidity and carbonation: the cement specimen reacts with the humidity and the carbon dioxide of the air; the prepared surface is scanned promptly and the specimen is stored in a desiccator, or the analysis will report the hydration products instead of the cement phases.

The preparation discipline is the same message the industry repeats for every instrument: the measurement is only as good as the specimen. A poorly prepared XRD specimen produces a pattern that the software will identify confidently and wrongly, and the analyst’s protection is the preparation protocol, the visual inspection of the specimen, and the periodic validation of the whole method against reference samples.

6. Qualitative Analysis: Identifying the Phases of Clinker and Cement

The qualitative analysis identifies the phases present in the specimen by matching the measured pattern against the reference patterns of the powder diffraction file. The phases of the portland cement system have well-documented patterns, and the everyday qualitative identification covers:

• Alite (tricalcium silicate, C3S): the dominant phase of the clinker, with its strongest reflections in the region around 32 to 34 degrees two-theta; the identification also covers the polymorphs and the modified forms stabilized by the alkalis and the sulfate.
• Belite (dicalcium silicate, C2S): the beta form is the usual phase of the cement clinker, with its characteristic pattern overlapping the alite in places, which makes the careful separation of the two silicate patterns a routine exercise of the quantitative work.
• Tricalcium aluminate (C3A) and the ferrite (C4AF): the aluminate appears with its strong low-angle reflections, and the ferrite solid solution shows a distinctive pattern whose position shifts with the iron content of the solid solution.
• Free lime (CaO): a few tenths to two percent of uncombined lime produces clearly measurable reflections, making the XRD an excellent free-lime check complementing the chemical titration.
• The sulfate phases: gypsum, hemihydrate and anhydrite in the cement, and the alkali sulfates in the clinker, are identified by their own patterns, giving the XRD a unique role in the sulfate balance questions of the plant.
• Periclase (MgO): the crystalline magnesia of the clinker, whose slow hydration causes the long-term expansion, is identified and quantified when the raw materials carry magnesia.

The qualitative scan of a cement or clinker specimen takes minutes with the modern instrument and delivers the phase inventory of the sample. For the routine control, the identification is the first step; for the investigations (a strength shortfall, a setting complaint, an expansion failure), the phase inventory is often the first hard evidence of what actually changed.

7. Quantitative Analysis: From Peak Intensities to Phase Proportions

The quantitative phase analysis converts the measured peak intensities into the mass fractions of the phases. The methods available to the cement laboratory form a ladder from the simple to the rigorous:

• The external standard (reference intensity ratio) method: the intensities of the phases’ strongest peaks are compared with the reference intensity ratios of the pure phases, giving the proportions directly; the method is fast and adequate for the semiquantitative screening.
• The internal standard method: a known amount of a standard phase (for example, corundum) is mixed into the specimen, and the ratios of the phase peaks to the standard peaks give the absolute amounts, compensating for the specimen absorption; the method is classical and accurate when the standard and the peaks are well chosen.
• The Rietveld method: the modern standard of quantitative cement analysis: the complete diffraction pattern is calculated from the crystal structures of all the phases and refined against the measured pattern, adjusting the phase scale factors, the lattice parameters, the peak shapes and the specimen effects until the calculated pattern matches the measured one; the refined scale factors give the phase proportions directly, including an estimate of the amorphous or unaccounted content.
• Amorphous and glass content: the Rietveld method can quantify the amorphous material (the glassy fraction of the clinker and the amorphous content of the fly ash and slag additions) when an internal standard is used, because the amorphous material scatters into the background and its amount is derived from the discrepancy.

The cement literature and the source chapter present the comparison of the methods with the caveats that govern their use: the reference intensity ratio method assumes no preferred orientation and no microabsorption differences, the internal standard method needs the standard to mix intimately, and the Rietveld method needs the crystal structures of all the phases, including the modified clinker phases, to be modelled correctly. In practice the modern plant laboratory runs the Rietveld refinement on the clinker and the cement as the routine quantitative method, and the results are validated against the Bogue calculations, the microscopy modal analyses and the free lime chemistry.

8. Comparing the XRD Results With the Bogue Calculation

No quantitative XRD result in a cement laboratory is complete without the comparison with the Bogue calculation, and the comparison is itself an item of information. The Bogue method calculates the phase composition of the clinker from the oxide chemistry using the classical equilibrium assumptions; the XRD measures the phases directly. The two agree when the clinker is a well-burned, slowly cooled, near-equilibrium material, and they disagree systematically when the real clinker departs from the assumptions:

• Alkali and sulfate modification: the alkalis and the sulfur modify the real clinker phases (the alite and the belite take up foreign ions, and the C3A reacts with the sulfates to form the alkali sulfates), so the Bogue C3A overestimates the true aluminate and the XRD reports the actual modified phases.
• Glass formation: rapid cooling freezes part of the liquid into glass, which the Bogue calculation assigns to the crystalline compounds it assumes; the XRD sees the glass as the amorphous content.
• Free lime: the Bogue calculation assumes full combination of the lime; the unburned free lime is measured directly by the XRD and by the titration, and the difference between the calculated and the measured combination is a measure of the burning quality.
• The practical synthesis: the plant uses the Bogue numbers for the daily chemical control (they come from the XRF, which runs continuously) and the XRD numbers for the phase truth (which the chemistry can only approximate), and the two are reconciled in the quality report.

The reconciliation is not a correction but an interpretation: where the Bogue and the XRD diverge, the divergence explains the behaviour of the cement (its setting, its strength, its sulfate response) better than either number alone. This is why the best laboratories report both, and why the source chapter treats the XRD as the complement, not the competitor, of the chemical method.

9. XRD in the Plant: Applications Across the Manufacturing Operation

The applications of X-ray diffraction in the cement manufacturing operation extend far beyond the clinker phase analysis, and the chapter reviews them in detail:

• Raw material characterisation: the identification of the mineralogy of the limestone, marl, clay, sand and corrective materials (the quartz content, the clay minerals, the dolomite, the free silica) is the foundation of the raw mix design and the burnability assessment.
• Clinker control: the routine phase quantification of the clinker (alite, belite, aluminate, ferrite, free lime, periclase, alkali sulfates) tracks the burning and the cooling shift by shift, supplementing the chemistry and the microscopy.
• Kiln problem diagnosis: the ring and coating samples from the kiln are identified by XRD, revealing the sulfate, chloride or liquid-phase mechanism that formed them, and guiding the removal and prevention strategy.
• Cement phase control: the sulfate phases of the finished cement (gypsum, hemihydrate, anhydrite), the limestone and the additions are quantified, verifying the mill’s sulfate balance and the declared composition of the blended cements.
• Complaint investigation: the strength, setting and durability complaints are investigated with the phase picture of the cement and the concrete materials involved, converting the speculation of the complaint meeting into the evidence of the pattern.
• Alternative materials and SCMs: the amorphous content of the slag and the fly ash, the calcined clay phases and the new low-carbon constituents are characterised by XRD as the industry moves toward the blended products of the low-carbon era.

Across these applications the common thread is the same: the XRD answers the phase questions that the chemistry cannot, at a speed and a cost that make it a routine instrument rather than a research one. The plant that runs the XRD on its clinker and its cement sees the mineralogical reality of its process, and the quality system that includes the phase picture is the quality system that understands its product.

10. The Limitations and the Careful Reading of the Pattern

The honest assessment of the method includes its limitations, and the chapter is explicit about where the XRD must be read with care:

• Detection limits: phases below about one percent (and often below two to three percent in a mixture) become difficult to quantify reliably, and the trace phases may escape detection entirely; the free lime at 0.5 percent, for example, is measurable but with a significant uncertainty.
• Peak overlap: the clinker phases overlap extensively (the alite and the belite share the 32-to-34 degree region), and the quantitative methods must separate the overlapping profiles, which is exactly why the Rietveld method has replaced the simple peak-area methods for the serious work.
• Solid solutions and polymorphs: the real phases are solid solutions, not the pure compounds of the reference patterns, so their peak positions and intensities shift; the analysis must model the actual compositions or accept the bias.
• Amorphous material: the glass and the amorphous phases scatter into the background, so the simple methods underreport the total; the Rietveld method with the internal standard recovers the amorphous content but at the price of the extra preparation and refinement care.
• Sampling and preparation: the specimen, not the instrument, sets the quality ceiling: the coarse particles, the preferred orientation and the humidity reaction of the cement powder all degrade the pattern, and the discipline of the preparation is the discipline of the method.

The careful reading of the pattern is therefore a craft: the analyst looks at the whole pattern (the background, the peak shapes, the low-angle scatter, the unexplained reflections) and not only at the software’s identification list, because the software reports what it was asked to find. The experienced analyst finds what the software missed, and the source chapter is a course in that reading.

11. XRD and the Other Instruments: The Integrated Laboratory

The position of the XRD in the integrated cement laboratory is defined by the division of labour among the instruments:

The integrated laboratory uses the XRF for the chemical chain, the XRD for the phase truth, the microscope for the microstructure, the wet chemistry for the referee values and the physical testing for the specification performance, and it reconciles all of them in the quality report. The instruments do not compete; they interrogate different levels of the same material, and the plant that runs all of them with discipline is the plant whose product understanding is complete.

12. Frequently Asked Questions

What is Bragg’s law and why is it the basis of XRD?

Bragg’s law, n lambda equals two d sine theta, states that X-rays of wavelength lambda diffract from crystal planes spaced d apart at the angle theta where the scattered rays interfere constructively. Because every crystalline phase has its own set of plane spacings, the angles of its diffraction peaks are unique, which is how the pattern identifies the phase and how the measured intensities quantify it.

What is the difference between XRF and XRD?

XRF determines the chemical composition of the specimen (which elements are present and in what amounts), while XRD determines the crystalline phases (how those elements are arranged into crystal structures such as alite, belite, aluminate and ferrite). The XRF cannot distinguish the alite from the belite because both are calcium silicates; the XRD can.

Which wavelength is used for cement XRD?

The copper K-alpha radiation, with a wavelength of 1.5406 angstroms (0.15406 nanometers), is the standard working line of cement analysis, usually filtered or monochromatised to remove the K-beta component. The patterns of the cement phases are all indexed on this wavelength in the reference libraries.

Why is the Rietveld method preferred for quantitative cement analysis?

Because the clinker phases overlap heavily and are modified solid solutions, the simple peak-intensity methods are biased. The Rietveld method calculates the entire pattern from the crystal structures of all the phases and refines it against the measured pattern, separating the overlapping peaks correctly and giving the phase proportions, the lattice parameters and an estimate of the amorphous content from a single analysis.

Can XRD measure the free lime of the clinker?

Yes: the free lime (CaO) produces its own reflections, and the XRD quantifies it in the clinker alongside the other phases. The sensitivity is limited for very low contents (below about one percent the uncertainty grows), so the plant typically uses the XRD for the phase picture and confirms the low-level free lime with the chemical titration when precision is required.

Why does the XRD show glass in rapidly cooled clinker?

Rapid cooling freezes part of the clinker liquid into an amorphous glass instead of allowing it to crystallise. The glass has no regular repeating structure, so it produces no sharp diffraction peaks; it scatters into the broad background of the pattern, and the Rietveld method with an internal standard converts that background elevation into a quantitative amorphous content.

13. Conclusion and Summary

X-ray diffraction analysis is the phase instrument of the cement laboratory: the method that reads the crystalline fabric of the clinker and the cement, identifying the alite, belite, aluminate, ferrite, free lime, periclase and sulfate phases and quantifying them by the Rietveld and the classical methods. The technique rests on the physics of the crystal (the lattice, the unit cell, the Miller indices) and on the Bragg equation that ties every plane spacing to its diffraction angle, and it is executed on the powder diffractometer with the discipline of the specimen preparation as the guard of the data quality.

In the plant, the XRD characterises the raw materials, tracks the clinker phase composition, diagnoses the kiln problems, verifies the sulfate balance of the cement, investigates the complaints and characterises the new supplementary materials of the low-carbon era. Its limitations, the detection limits, the peak overlap, the solid solutions, the amorphous content and the preparation sensitivities, are understood and managed, and its results are reconciled with the Bogue chemistry and the microscopy in the integrated quality laboratory. The method has been used for nearly a hundred years, and it remains, alongside chemistry and microscopy, one of the indispensable instruments of cement quality control, with the complete technical treatment of its principles, instrumentation and applications available in the Complete Cement Technical Package.

This file is part of the Complete Cement Technical Package (931 files) available from cementequipment.org. Respective rights holders; library copy for the licensed single user.