Introduction to QXRD: Fundamentals and Applications

Introduction to QXRD: Fundamentals and Applications

What QXRD is

QXRD (Quantitative X-ray Diffraction) is an analytical technique that uses X-ray diffraction patterns to identify crystalline phases and quantify their amounts in multi-phase materials. It extends standard XRD by applying rigorous data-processing, calibration, and modeling to convert diffraction intensities into reliable quantitative phase fractions and crystallographic information.

Core principles

• Bragg’s law: X-rays scattered by crystal planes produce peaks at angles satisfying nλ = 2d sinθ; peak positions identify crystal structures.
• Peak intensity proportionality: Integrated peak intensities relate to phase abundance, atomic scattering factors, structure factors, multiplicity, and preferred orientation.
• Rietveld refinement: A full-pattern fitting method that models the entire diffraction pattern (peak positions, shapes, backgrounds) to refine structural, microstructural, and quantitative parameters simultaneously.
• Calibration and standards: Use of internal or external standards and calibration curves corrects for instrument factors, absorption, and sample preparation biases to improve absolute quantification.

Typical workflow

1. Sample preparation: Homogenize, grind, and pack to minimize preferred orientation and particle-size effects.
2. Data collection: Select appropriate radiation (Cu Kα common), step size, counting time, and scan range for sufficient peak statistics.
3. Preprocessing: Background subtraction, Kα2 stripping (if needed), and instrumental peak broadening correction.
4. Phase identification: Match peak positions to databases (ICDD PDF) to list candidate phases.
5. Quantification: Apply Rietveld refinement or the Reference Intensity Ratio (RIR) method to compute phase fractions.
6. Validation: Check goodness-of-fit metrics, residuals, and perform repeat measurements or standard addition tests.

Common applications

• Cement and concrete: Phase amounts (e.g., alite, belite, portlandite) for quality control and durability studies.
• Ceramics and minerals: Phase purity, polymorph identification, and stoichiometry.
• Metallurgy: Phase fractions in alloys, heat-treatment studies, and development of new materials.
• Battery materials: Quantifying active/inactive phases, degradation products, and lithiation states.
• Thin films & coatings: Phase composition and texture analysis (when combined with grazing-incidence XRD).

Strengths and limitations

• Strengths: Non-destructive; sensitive to crystalline phases; quantitative with proper calibration; provides crystallographic and microstructural parameters.
• Limitations: Insensitive to amorphous content without standards; subject to preferred orientation, particle-size, and absorption errors; requires good reference data and careful sample prep; low detection limits typically ~1–5 wt% depending on phase contrast and data quality.

Practical tips

• Use an internal standard (e.g., corundum) to quantify amorphous fractions.
• Minimize preferred orientation by side-loading or spray-drying powders.
• Increase counting time for low-concentration phases.
• Validate Rietveld results with complementary techniques (SEM/EDS, TEM, thermal analysis).
• Keep an instrument calibration file (zero error, peak broadening) and update regularly.

Further reading / resources

• Rietveld method textbooks and practical guides.
• ICDD PDF for phase identification.
• Software manuals: GSAS-II, TOPAS, FullProf, HighScore.