Steels_ Metallurgy and Applications, Third Edition

Low-carbon strip steels 9

Table 1.1 Temperature dependence of solubility products (Wt%) for carbides,

nitrides, carbonitrides, 1~ sulphides and carbosulphides I I

Solubility product l og lok Solubility product l og lok

[B][N] - 13970/T + 5.24 [VI[N]

[Nbl[NI -10150/T + 3.79 [V][C] ~

[Nb][C] ~ -7020/T + 2.81 [Ti][S]

[Nb][C]~ ~ -9450/T + 4.12 [Ti][C]I/2[S] ~

[TiI[N] -15790/T + 5.40 [Mn][S]

[Ti][C] -7000/T + 2.75 -

.........................

-7700/T + 2.86

-6500/T + 4.45

• 16550/T + 6.92
  -15350/T + 6.32
  -9020/T + 2.93

where IX] and [Y] are the weight percentages of elements in solution, such
as titanium and carbon, T is the temperature in degrees Kelvin and A and B
are constants. Table 1.1, prepared mainly by Turkdogan, 1~ gives the solubility
products for a number of compounds in austenite, but additional data for the
sulphides have been added from a separate source. II
It is useful to note that a number of the precipitates are solid soluble in each
other and that the precise composition of such a precipitate depends on the
composition of the austenite matrix with which it is in equilibrium, as well as on
the temperature. Niobium carbonitride, for example, has a wide range of solid
solubility and an early theory 12 showed how the ratio of carbon to nitrogen in the
precipitate in equilibrium at a given temperature could be calculated for different
amounts of carbon, nitrogen and niobium in the steel.
In this model, a precipitate with formula NbC~N(l_x) was assumed to be in
equilibrium with a matrix according to the reaction:

Nbsot + x. Csol + (l - x). N = NbCxNtl_x)ppt

The solubility product K for this reaction was, therefore, written as

[Nb]. [C] x. [N](l-x)/[NbCxN(l_x)] = K

where [NbCxN~l_x)] was the activity of the carbonitride which was taken as unity.
It was assumed, however, that the effective activity of NbC in the precipitate
was x and the effective activity of NbN in the precipitate was (1 -x) and that
separate solubility product equations for the matrix would apply for NbC and
NbN as follows:

[Nb]. [C]/x = r l

and [Nb]. [N]/(1 - x) = K2

where K l and K2 are the solubility products for the pure carbide and nitride
respectively at the desired temperature. For a given steel composition and
temperature, these equations could be solved to give a value of x. The predictions
from the model were in good agreement with the compositions of the niobium
carbonitride precipitates that had been reported in the literature.
The model was later developed further to involve more than one precipitate 13
and a number of computer programs able to predict the equilibrium conditions for