SOLUBILITY OF BORON AND CARBON IN FERRITE OF THE Fe-B-C SYSTEM ALLOYS

Investigation was carried out for Fe-B-C alloys with carbon content of 0.0001–0.01 % (wt.) and boron content of 0.0001–0.01 % (wt.), the rest is iron. To determine the structural state of alloys we use the microstructure analysis, X-ray microanalysis and X-ray structure analysis. The level of microstraines, dislocation density and the coercive force of ferrite is determined, and it is shown that structure imperfection grows with boron content increase in the alloy. The obtained results enable to suggest that boron atoms in a solid solution of α-iron occupy substitutional-interstitial positions depending on boron content. In the paper it is shown experimentally, that at room temperature solubility limit of boron and carbon in the ferrite is 0.00012 % (wt.) and 0.006 % (wt.). When boron and carbon content increases further, the following phases are formed: Fe2B, Fe3(CB) and Fe23(CB)6. In this paper by means of quasi-chemical method we obtain for the first time temperature dependence of the free energy for α-iron solid solution, as well as solubility limit of carbon and boron. Maximum mass fraction of carbon may be up to 0.016 % (wt.), and maximum boron mass fraction – up to 0.00025 % (wt.). At room temperature the boron solubility limit in ferrite is 0.0001 % (wt.), and carbon one is 0.004 % (wt.). The calculated numerical values of the solubility of boron and carbon in ferrite of the Fe-B-C system alloys are less than that of the experimental results. This can be explained by the fact that boron atoms interact more actively with structure imperfections than carbon atoms. At high temperatures the solubility of carbon and boron in given phase increases.

With boron content increase in alloy there boride are formed on the boundaries of ferrite grains, and with carbon content increase in alloy the formation of pearlite on the boundaries of ferrite grains occurs (Fig. 2).
If the content of boron or carbon in the alloy is greater than 0.0012 wt. % (boron) 0.004 wt. % (carbon), then the Fe 2 B, Fe 3 (CB), Fe 23 (CB) 6 phases are formed in the alloy [9].
It is known that the lattice parameter of bcc iron at room temperature is 2.862 Å [6]. Under boron and carbon doping of alloys the change in the lattice parameter of ferrite is observed ( Table 1).
The results shown in Table enable to qualitatively evaluate the structure imperfection of ferrite depending on content of boron and carbon in the alloy. As boron content increases in the alloy, the microstrain degree, the density of dislocations in ferrite and the coercive force grows.
An increase in the coercive force for alloys containing higher content of boron and carbon can be explained by change in the density of dislocations and decrease in the size of the crystallites. The results (Table 1) show unique correlation relationship between the characteristics of the Нс, on the one hand, and the microstrain degree and density of dislocations, on the other hand, in all the specimens examined.
In addition, the results represented in Table 1 show that doping of ferrite only with boron leads to increase in the size of crystallites L, the density of dislocations ρ, the microstrain degree and the coercive force Н с compared with carbon doping. The obtained results can be explained by the fact that boron atoms in α-iron solid solution occupy substitutional-interstitial positions depending on boron content, which is in line with the results of other authors [10][11].
The structure of ferrite represents as body-centered lattice and pertains to the space group 9 h O -Im3m with eight atoms in the first coordination shell [12]. For each atom of the bcc lattice there are six tetrahedral and three octahedral pores. Two of the six atoms surrounding the octahedral pore, are closest compared to others [13]. The arrangement of carbon atoms in the bcc lattice can be described as the arrangement of the atoms of carbon or boron in the octahedral pore, which have four nearest metal atoms at a distance of 2.02 Ǻ and two at the distance of 1.43 Ǻ, each metal atom has eight neighbors located at the distance of 2.48 Ǻ from each other (Fig. 3).  To calculate the solubility limit of carbon and boron atoms in the ferrite lattice, we use the quasi-chemical method with accounting for data on the boron and carbon position in α-iron solid solution [14].
The interaction of Fe-Fe, Fe-C, Fe-B and Fe-V atoms (where V is vacancy) can be taken into consideration as follows: the energy of interaction between eight atoms at the distance of 2.48 Å is For the values of the interaction energy of the atomic pairs, we use the results given in [9].
The free energy of ferrite can be determined by the formula where Е is the internal, W is the thermodynamic probability of the atom location in the sites of the ferrite crystal lattice, k=1.38·10 -23 J/K is Boltzmann constant, Т is absolute temperature.
Thus, the free energy of ferrite is found as: is the number of boron atoms. The obtained set of equations (1) is transcendental. Usually the solution of such equations can be obtained graphically or numerically. But within this problem there is a good reason to consider an asymptotic solution of the equations. For this we write the logarithm appeared in each equation of the system (1) as Taylor expansion (this is admissible in accordance with its convergence conditions):  To obtain an asymptotic estimate of the system (2) solution, it is quite sufficient to consider the first two terms of the logarithm expansion.
The results of solving of the set of equations are presented in Fig. 4. a b The solubility of carbon in δ-iron is estimated to be 0.062 % (wt.) and boron solubility is 0.15 % (wt.). The analysis of the results enables to determine the solubility of carbon and boron in ferrite: it was revealed that up to 0.016 % (wt.) of carbon atoms can get into the pores in the ferrite lattice depending on temperature. According to the