The Bogue calculation

In another approach, widely used in the USA and elsewhere, the quantitative phase composition is estimated using a procedure due to Bogue (B24). It is necessary also to know the content of free lime, which may be determined by a chemical extraction method (Section 4.3.3). The calculation is as follows  

This leads to the following equations, in which CaO is assumed to have been corrected for free lime  

As with LSF, the approach is applicable to cements if CaO is further corrected by deducting O.7SO3. Because minor oxide components are ignored, the total for the four main phases plus free lime will not add up to 100%. It is implicit in the approach that all the MgO is assumed to occur as periclase. The phase composition calculated by Bogue s method is related to the LSF in that a ratio of 38 to CjA 0.546, calculated without correcting the CaO content for free lime, corresponds to an LSF 1.0 (D2). 

---

The potential compound composition of a cement or cement clinker can be calculated from the oxide analyses of any given raw materials mixture, or from the oxide analyses of the cement clinker or finished cement. The simplest and most widely used method is the Bogue calculation (23). The ASTM C150 (24) calculation is somewhat modified. 

The calculated percentages of alite, belite, aluminate and ferrite are given by. v,-.V4, respectively. The Bogue calculation gives 60.3%, 16.1%, 9.4% and 9.7%, assuming that the Si02 and AI2O3 contents have been corrected for insoluble residue. 

Several early studies using QXDA gave results in fair agreement with j those of the Bogue calculation, but in the light of the above and other recent evidence are of doubtful validity. Odier et al. (09) found that alite contents ... 

Considering the low C3A content one should remember that the resistance of this phase in marine enviromnent depends on polymorph, which is present in cement clinker [286], Cement with cubic C3A gives more ettringite than chloroaluminate hydrates in sea water, while the inverse behaviour is observed in the case of cement with rhombohedral or monochnic C3A. Beside of the errors attributed to the Bogue calculation method, the occmrence of various C3A polymorphs can be the source of inadequate correlation between the C3 A content and resistance of concrete to the attack of aggressive solutions. 

Ono (1995) presented a series of correction factors in the calculation of phase percentages by the Bogue equations. The factors involve minor components,solid solution of CjS and C S, solid solution of C A F-C AF, and glass. Taylor (1990) also provided formulas for correcting the Bogue calculations. 

Weigand (1994) reported the point-count results of the ASTM microscopy task group on one of the Standard Reference Clinkers supplied by the National Institute of Standards and Technology (Gaithersburg, Maryland). Compared to the Bogue calculations, the microscopical data are roughly 5% higher for alite, 5% lower for belite, 4% lower for C A, and 0.5% lower for ferrite. It was further shown that 3000 points per sample would provide sufficient data for statistical acceptance of port-land cement clinker polished sections. 

If some of the lime remains uncombined, it must be subtracted from the total Ume content before performing the calculation it is for this reason that a clinker analysis normally contains a value for uncombined free lime. It should also be stressed that the Bogue calculation does not give the true amounts of the four main clinker phases present, but differs from them principally because the actual mineral compositions differ from those assumed in the calculation, particularly... 

QPA by XRD has become a prominent characterisation technique in cement science and more recently also in cement production. Properties such as strength development or durability are closely related to the cement phase composition. Early analyses were mostly based on the Bogue calculation... 

The demand for cement was stimulated by the growth of canal systems ia United States duting the nineteenth century. Process improvements were made ia the calciaation of certain limestones for the manufacture of natural cements, which were gradually displaced by Pordand cement. This latter was named ia a 1824 patent because of its color and resemblance to a natural limestone quarried on the Isle of Pordand ia England. Research conducted siace that time has provided a clear picture of the composition, properties, and fields of stabiUty of the principal systems found ia Pordand cement. These results led to the widely used Bogue calculation of composition based on oxide analysis (1). Details beyond the scope of this article may be found ia the Hterature (2). 

Indirect methods - these are usually based on the measurement of total chemistry which is then apportioned according to an assumed composition for each phase. A very widely used form of this normative calculation is the Bogue method for the estimation of Portland cement phases. The limitations in this approach arise when the actual compositions of individual phases vary from those assumed in the calculation. This frequently occurs in the cement industry, where variance in local materials and production conditions can affect detailed phase compositions. In addition, normative calculation has the potential to be unstable when several phases in the mixture have similar chemical composition. 

The calculation procedure is as follows. According to Bogue calculation CaO content must be corrected for free hme and bond in sulphates or CaCOj. Then, if there is no more accurate data, it can be assumed that 67 % of insoluble residue is composed of Si02 and 33 % of AI2O3. 

Theisen (1993) described a rapid method of mi croscopical determination of alite and belite size and approximation of visible pore space by recording the number of intercepts along a line of traverse in successive fields of view. The intercept numbers were used with Bogue calculations and related to power consumption (kwh/1) in grinding. Data can be gathered in less than an hour. 

To use the F. L. Smidth burnability equation, a lime saturation factor (LSF) of not greater than 100% or less than 88% is stipulated. If the LSF is greater than 100%, the free lime calculated by the Bogue equation must be added, and calculated as follows ... 

Midgley and Dharmadhikari (1964) described methods of point counting polished sections of clinkers, using an HF vapor etch and 1000 to 2000 points. These authors stated that the standard deviation of the alite and belite weight percentages were estimated at 1.0 and 1.5, respectively, and that the microscopical method is as accurate as that obtained from Bogue calculations and better than that from X-ray diffraction. 

Alite and belite percentages determined by microscopy are generally higjier and lower, respectively, than the values calculated by the Bogue equations. Major errors in microscopical percentages of matrix phases are mainly due to small crystal sizes. 

Heat of hydration can be converted approximately into degree of hydration if the hydration enthalpies of the different clinker phases are known. Values for the clinker phases can be taken from Taylor (1997) see Table 2.1. These values can be used to calculate the enthalpy of complete hydration if the phase composition of a portland cement is known, e.g. by (extended) Bogue calculation (Taylor 1997) or by quantitative X-ray diffraction (XRD) analysis (see Chapter 5). This value can be used to roughly estimate the hydration degree from the cumulated heat development. For... 

Note The XRD results are compared to a standard Bogue calculation of the phase content. As an additional check, a back calculation of the oxide chemical composition from the XRD results is carried out and compared to the XRF results. 

Bogue calculation Estimation of the phase composition of portland cement based on the oxide chemical composition. 

---