Clinker C3S Content (Bogue)
Estimates the tricalcium silicate content, the alite or C₃S, of a clinker using the Bogue equation, the mass balance that splits the four main oxides among the mineral phases: C₃S = 4.071 × CaO − 7.600 × SiO₂ − 6.718 × Al₂O₃ − 1.430 × Fe₂O₃, with contents as mass percentages. Alite is the phase that gives cement its early strength, and ordinary Portland clinker sits between 50% and 65% — below that the 3-day and 7-day strengths collapse, above that kiln fuel consumption rises and the heat of hydration becomes a problem in mass concrete. The negative coefficients are large, so the result is very sensitive to the chemical analysis: half a point more silica knocks 3.8 points off C₃S, and a composition outside the clinker range can even return a negative value, which simply means that mixture has not enough lime to form alite. The classic four-term Bogue equation was adopted, the one for clinker without gypsum; for finished cement the ASTM C150 version also subtracts 2.852 × SO₃ and discounts free lime from CaO. Enter the CaO, SiO₂, Al₂O₃ and Fe₂O₃ contents.
Result
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Clinker alite: reading C3S from the Bogue equation
The plant lab turns X-ray fluorescence around in a couple of hours, while X-ray diffraction with Rietveld refinement, the method that actually measures alite, takes far longer and many kilns simply lack the instrument. Meanwhile the kiln keeps burning and someone has to decide whether the raw meal is drifting. The Bogue equation fills that gap: given the four main oxides, it estimates how much of the clinker ended up as tricalcium silicate, the phase behind the 3-day and 7-day strength of the cement.
The arithmetic is C3S = 4.071 × CaO − 7.600 × SiO₂ − 6.718 × Al₂O₃ − 1.430 × Fe₂O₃, every content as a mass percentage of the clinker. The coefficients come from the mass balance among the four phases: available lime pushes the figure up, while silica, alumina and iron subtract whatever gets committed to belite, aluminate and ferrite. Ordinary Portland clinker lands between 50% and 65% alite. Below 50% early strength drops with it; above 65% kiln fuel and heat of hydration climb, and the latter turns into cracking in a massive pour. With the values already on screen — 65, 21.5, 5.2 and 3 — the answer is 61.99%.
Bogue assumes full equilibrium on cooling and chemically pure phases, neither of which a real kiln gives: field alite carries magnesium and aluminium in solid solution, and Rietveld usually reads 3 to 8 points higher than the calculation. The classic four-term form was adopted here, the one for clinker with no gypsum; for finished cement, ASTM C150 further subtracts 2.852 × SO₃ and strips free lime out of the total CaO. The commonest unit slip is feeding a raw meal analysis instead of a clinker one: with 35% loss on ignition still in the numbers, the formula returns something plausible and meaningless. A negative answer flags no defect in the maths, only a mixture short of lime for alite.
Frequently asked questions
Where does the 61.99% on the opening screen come from?
My result came out negative. What did I get wrong?
Can I use this for the cement leaving the mill?
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