108 posts
TimePosted 23/01/2009 14:29:46
Dastgir says

### Re: LSF Formula

Dear Lalbatros,

This is simple derivation which may be derived how much c needed

to react with any of the three other components.The most teasing

part is how 1.18 and 0.65 comes.

Regard

Gulam Dastgir.

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138 posts
TimePosted 23/01/2009 22:26:03
lalbatros says

### Re: LSF Formula

Dastgir,

I think that pages 33-35-36-... in Taylor are giving suggestions to understand what happens. The three components and phases (sac) in this section is a better start and it is still applicable to white cement. The ideal (white) clinker made of (c3s,c2s,c3a) is only a simplified model. It assumes that all CaO combines if possible by stoechiometry. The physics might decide otherwise. The amount of free lime is an additional degree of freedom.

See also page 40 in Taylor which I will also read more carefully sometimes. I will see if the ternary diagram in the s-a-c system can lead to one of the coefficient, in the way this is explained in page 40 for the quaternary system.

If I make some progress I will tell you.

138 posts
TimePosted 24/01/2009 14:05:01
lalbatros says

### Re: LSF Formula

Dastgir,

Below I have reused the figure 2.3 from page 34 in the book of Taylor .

On Figure 1, I have superposed the (LSF=1) locus based on the standard formula

LSF = CaO/(2.8*SiO2+1.18*Al2O3).

As you can see, this locus matches very well the experimental boundary below which free lime will appear.

On Figure 2, I have superposed the (LSFb=1) locus based on the Bogue calculation that leads to

LSFb = CaO/(2.8*SiO2+1.65*Al2O3)

Clearly it falls well within the domain where free lime should appear, on the side of Alumina. This indicates clearly that the hypothesis of Bogue that all (s,a,c) would transform on (c3s,c2s,c3a) is wrong in the situation when LSFb=1. That's how this ternary system behaves actually. Therefore also, the Bogue calculation will be (potentially) right only as long as LSF<1.

This shows clearly that the LSF formula follows the experimental data depicted in the phase diagram. These experimental data are also systematically organised within thermodynamic data that can be found in the litterature as well as in some CALPHAD packages.

Furthermore this also shows that the Bogue calculations are not always valid. Specially when LSF>1, they will of course not be applicable, even though they could return positive values for the three phases (c3s,c2s,c3a).

Finally note that the quantity of free lime in industrial clinker depends on more parameters than those applicable to a thermodynamic equilibrium analysis.

Fig 1: LSF=1 locus, as based on LSF = CaO/(2.8SiO2+1.18Al2O3)

Fig 2: LSFb=1 locus, as based on LSFb = CaO/(2.8SiO2+1.65Al2O3)
(Observe where the locus crosses the c-s and the c-a axis! This just reflects how LSFb was obtained.)