Cement Manufacturers Association (CMA)

17 Rapid cooling (20–100°C/min) in modern plants creates small crystals with many defects and more amorphous material. Slow cooling does the opposite. This means two clinkers with the same Bogue numbers can have very different strengths and performance. In new low-carbon cements like LC³, Bogue becomes almost useless because extra phases form outside the kiln. A 2025 machine-learning study using two full years of real plant data achieved only 1.24 % error for alite — 88 % better than Bogue. These limitations are serious because cement performance and CO2 footprint now depend on crystal quality, not just bulk chemistry. 3. Alternatives to Bogue's Formula 3.1 Modified Bogue Equations These are improved versions of Bogue that include effects of minor oxides and real crystal compositions. They give about 5 % better accuracy than standard Bogue but still cannot handle cooling rate or amorphous content well. Implementation: Use daily XRF oxide results in spreadsheet or plant software and compare with standard Bogue. Validate every few months with XRD. 3.2 Thermodynamic Modelling This computer method calculates the most stable minerals by minimizing Gibbs free energy. It considers solid solutions, minor phases and temperature changes. Accuracy is usually better than 5 % when checked against XRD. It is especially useful for designing new low-lime cement. Implementation: Feed daily oxide data and kiln temperatures into software like FactSage, run the calculation, and use the results to adjust raw mix. Update the model once a year with plant-specific data. 3.3 Quantitative X-ray Diffraction (QXRD) with Rietveld Refinement X-ray Diffraction (XRD) works like taking a fingerprint of the clinker. X-rays pass through the powdered sample and create a pattern of peaks on a graph. Each mineral produces its own unique pattern. The Rietveld method is a smart computer technique that looks at the entire pattern, not just the tallest peaks. It starts with known crystal structures of the main clinker minerals (like digital blueprints). The computer creates a theoretical pattern and then adjusts many small details — such as the amount of each mineral, crystal size and background noise — until the calculated pattern matches the real one as closely as possible. This gives accurate quantities of each mineral and extra information about crystal quality. Because ordinary Rietveld assumes everything is crystalline, it misses amorphous (glass-like) material. Four improved versions solve this: Conventional Rietveld: Forces all phases to add up to 100 %. It overestimates crystalline minerals by the hidden amorphous amount (±3–8 % error). Not suitable for accurate work. Internal Standard Method (ISM): Mix a known amount (10–20 %) of pure crystal powder (like ZnO) into the sample. The software shows any extra standard, revealing the amorphous content. Accuracy: ±1–3 % for main minerals. Simple and popular for daily plant use.