收稿日期：31 January 2013
基金：financially supported by the National Natural Science Foundation of China (Nos. 51274083 and 51074062);
Balanced solubility product and enthalpies of formation of Nb compounds in 0.09 % oriented silicon steel
Abstract：
Balance solubility products and enthalpy of formation for NbC0.75 , NbC0.85 , NbC0.88 , NbC and NbN in oriented silicon steels were calculated and compared qualitatively. Meanwhile, the mixing enthalpies of these five Nb compounds were calculated based on Miedema Model. The results show that the solubility products of Nb compounds in ferrite and austenite meet the following relationship, NbC0.75＞NbC0.85＞ NbC0.88＞NbC＞NbN and NbN has the minimum enthalpy of formation. It indicates that NbN easily precipitate out, but it is more difficult for NbC 0.75 .
Keyword：
Oriented silicon steel; Nb compounds; Solubility formula; Enthalpy of formation;
Received： 31 January 2013
1 Introduction
Oriented silicon steel is mainly used in electric motor and transformer as iron core materials in industry, and sharp (110) [001]texture has a significant effect on magnetic performance.However, in normal oriented silicon steel production process, the growth of primary recrystallized grains are inhibited by inhibitor, which benefits secondary recrystallization for obtaining the Goss texture[1].In traditional oriented silicon steel production, Mn S and Al N?Mn S[2]are mainly used as inhibitors, which have high solution temperature.Its slab heating temperature is as high as 1, 673 K, which could cause rough grains and serious cracks.More seriously, this high slab heating temperature could dramatically reduce the metal yield and increase the energy consumption[3].Therefore, it is very important to develop the technology of orientated silicon steel with a low slab temperature.
In terms of the problems mentioned above, in recent years the researchers in academic and industrial fields at home and abroad have carried on lots of research on development and introduction of low temperature inhibitors.For example currently the method of low temperature slab heating production in industry is nitriding prior to secondary recrystallization, which can participate Al N as a inhibitor[4–10], or Al N as a primary inhibitor and Cu S?Mn S as auxiliary inhibitors[11, 12].So far, the feasibility studies on Nb (C, N) as a new lower temperature inhibitor have been accepted widely, while its solution and precipitation in oriented steel have rarely studied.According to related work on niobium compounds used as low temperature inhibitors in oriented silicon steel, 0.09%Nb oriented silicon is studied, deduced the solubility products formula of niobium compounds (Nb C0.75, Nb C0.85, Nb C0.88, Nb C, Nb N) , meanwhile, the mixing enthalpies of different niobium compounds have been calculated and analyzed by Miedema model.In theory it solves some important basis problems.This could be a useful theoretical guidance for related products.
2 Experimental
2.1 Reduced of balance solubility products formula for niobium carbide, niobium nitride in austenite, ferrite
At present, many researchers have deduced and calculated the balance solubility products formula for niobium carbide, niobium nitride in austenite, ferrite in low carbon steel by means of testing method, thermodynamic method, phase analysis, gas equilibrium method, and so on.The results are shown in Table 1.
However, there are carbon vacancies, whose chemical compositions are changed from Nb C0.686to Nb C in niobium carbide for oriented silicon.Therefore, Nb C0.75, Nb C0.85and Nb C0.88may precipitate from oriented silicon.In this article, based on the calculation of standard mole free energy change from dissociation of different niobium carbide by means of HSC Chemistry 5.1, the solubility products formulas of Nb C0.75, Nb C0.85and Nb C0.88are deduced by thermodynamic method.
2.2 Deduced of solubility products formula for Nb C0.75, Nb C0.85and Nb C0.88
Considered the chemical reactions as follows:
The reactants Nb Cxare pure substance, whose activity is 1.The standard Gibbs free energy in this reaction is:
DGHVIII??RT ln KHVIII??RT f?Nb]??C?xg
The standard Gibbs free energy of graphitic carbon dissolved in ferritic matrix are:
Table 1 Formulas (lg K=A?B/T) of solubility products for Nb C and Nb N in ferrite and austenite of low carbon steel 下载原图
Table 1 Formulas (lg K=A?B/T) of solubility products for Nb C and Nb N in ferrite and austenite of low carbon steel
In this article, the index a or c denote that the substance dissolved in austenite or ferrite.When x is 0.75, 0.85 and0.88, respectively, DGHcan be calculated as follows:
The changes of free energy of Nb Cx=0.75, 0.85, 0.88dissolving into Nb and graphitic carbon are:
Then the standard Gibbs free energy, at which Nb C0.75, Nb C0.85and Nb C0.88dissolve into ferritic matrix are:
Therefore, the solubility products formulas for Nb C0.75Nb C0.85and Nb C0.88dissolving into ferritic matrix can be introduced as follows:
Meanwhile, the equilibrium solubility products formulas listed in Table 1, from references[12, 13]for Nb C and Nb N in austenite and ferrite are listed, as follows:
3 Results and discussion
3.1 Analysis of solubility products formulas of niobium carbide/nitride
It is shown that the balance solubility products for Nb C0.75, Nb C0.85, Nb C0.88, Nb C and Nb N in ferrite and austenite are in Fig.1a, b.The balance solubility products for Nb C0.75, Nb C0.85, Nb C0.88and Nb C are less than 1 9 10-5orders of magnitude in ferrite, and more than 1 9 10-5orders of magnitude in austenite.The solid solubility limit of Nb N is about 1 9 10-7orders of magnitude in ferrite and 1 9 10-7orders of magnitude in austenite.The balance solubility products of niobide in ferrite is less than them in austenite, therefore, when the austenite form ferrite during cooling, a large number of niobium compounds are precipitated.It can be seen from Fig.1 that the balance solubility products for niobium compounds in ferrite and austenite satisfy the following relation, Nb C0.75[Nb C0.85[Nb C0.88[Nb C[Nb N.Therefore, the sequence of precipitation for niobide in ferrite and austenite is Nb N, Nb C, Nb C0.88, Nb C0.85, Nb C0.75.As a whole, the solubility products of niobium carbide/nitride are coincident with the basic rule that the solubility products increase with the increase of carbon atoms vacancy concentration.
3.2 Calculation of full solution temperature
It is valid to control the second phase precipitation by definiting the full solution temperature.In 0.062%C–0.0082%N–0.09%Nb oriented silicon, the full solution temperature of niobium carbide/nitride which is defined as MXxis calculated with the formula[14, 15]as follows:lg fx?M) ??x?X??xg?C?D=T
where C, D is the constant in solubility products formula for Nb Cx (Nb N) phase in ferritic matrix, x=0.75, 0.850.88, 1.00, and x (M) , x (X) is the mass fraction of niobium and carbon (or nitrogen) , respectively.
Combined with the secondary solubility products formulas, the above-mentioned solubilization temperatures are listed in Table 2.
Table 2 shows that the full solution temperature of inhibitors for Nb C0.75, Nb C0.85, Nb C0.88, Nb C and Nb N is lower than traditional inhibitors of Mn S and Al N?Mn S[16–18] (about 1, 673 K) .Thus, the niobium carbide/nitride which is used as a new inhibitor in oriented silicon, can effectively reduce the slab heating temperature and energy
Table 2 Solubilization temperatures of niobium compounds 下载原图
Table 2 Solubilization temperatures of niobium compounds
Fig.1 Comparison between balance solubility products for Nb C0.75, Nb C0.85, Nb C0.88, Nb C and Nb N in ferrite and austenite:a balance solubility products in ferrite, and b balance solubility products in austenite
3.3 Calculation of precipitation amount for niobium carbide/nitride
In 0.062%C–0.0082%N–0.09%Nb oriented silicon, the pattern and amount of second phases in oriented silicon steel can be adjusted via temperature, based on the calculation of balance solution and precipitation amount for secondary phases formation elements in ferritic matrix.
Take MXxfor instance, the volume fraction formula of MXxwhich participated balanced (Ref.[14]) , is as follows:
where[M], x (M) represents the balanced solution amount of niobium in ferritic matrix and the mass fraction of niobium in steel of niobium, respectively;AM, AXdenotes the atomic weight of niobium and carbon (or nitrogen) , respectively;dFeis the density of ferritic matrix;and dMXX is the density of MXx.
In 0.062%C–0.0082%N–0.09%Nb oriented silicon, the volume fraction of niobium carbide/nitride increases with temperature which is lower than the full solution temperature.The calculation results are shown in Fig.2.
From Fig.2, it is shown that below the niobium carbide/nitride full solution temperature, the volume fraction of niobide, which precipitate balanced, decreases as temperature drops.Niobide precipitates mainly in austenite area, and completely in ferritic area.Therefore, it is consistent with that the niobide solubility in ferritic area are less than in austenite area.Meanwhile, the volume fraction of niobium carbide is slightly higher than niobium nitride.Therefore, niobium carbide and niobium nitride are both active in inhibiting.
3.4 Calculation of formation enthalpy for niobium carbide/nitride
Miedema model is the well-known thermodynamic theory in recent years.It is proposed for the formation heats of binary alloy, and can calculate the formation heats and surface free energy[19]of any alloy except O, S, Se, Te via components properties such as molar volume of element, electronegativity, electron density.Other studies have shown that with the increase of the absolute value of the formation enthalpies the intermetallic compound preferentially precipitates and stably exist under the same heat treated condition[20].The formation enthalpies of niobide in steel alloy are calculated using Miedema theory.The precipitation order of niobide in the iron matrix is analyzed and compared to the above results of solid solubility product derivation.
Fig.2 Effect of temperature on niobium compounds in steel
The expression of formation enthalpy DH by Miedema model is as follows:
where A represents carbon atom (or nitrogen) , B represents niobium atom.fBAis a measure of the degree to which A atoms are surrounded by B atoms, DHsolAin Bis the enthalpy of solution which A atoms dissolves B atoms, and is the molar fraction of A atoms.Nb C, Nb N are ordered alloys because of the face-centred cubic structure, the concentration function fBAis given by:
The surface concentrations CASand CBSare defined by:
For the above atoms A and B, where xA;xBare the molar fractions of A and B, respectively, and, VA, VBare the molar volumes of A and B, respectively in an alloy.
Miedema regarded the heat of solution, in which A dissolves in B:
For the binary alloy system formed by transition metal and nontransition metal, the expression of DH is:
Table 3 Relevant thermodynamics parameters used for calculation[20] 下载原图
Table 3 Relevant thermodynamics parameters used for calculation[20]
Table 4 Enthalpies of formation for niobium compounds 下载原图
Table 4 Enthalpies of formation for niobium compounds
Thermodynamic parameters are shown in Table 3[21]Where nwsis the electron density at the boundary of the Winger–Seitz cell, uAand uBare Miedema electroneg ativities for components A and B, respectively.
In Miedema model, Q, P, r and a are empirical constants Q/P=9.4, P=12.3 for alloy system consisted of transi tion element and nontransition element, and a=1 for solid alloy system.The above parameters are induced in forma tion enthalpy formula, and the results are shown in Table 4
It can be seen from Table 4 that Nb N compound precipi tates easily due to the higher absolute value, and Nb C0.75precipitates more difficult than Nb–C intermetallic com pounds.The absolute value of formation enthalpies, from the maximum to minimum is Nb N, Nb C, Nb C0.88, Nb C0.85Nb C0.75.The sequence of precipitation for Niobide in the iron matrix is Nb N, Nb C, Nb C0.88, Nb C0.85, Nb C0.75.This result is consistent with the above solid solubility product derivation
4 Conclusion
In oriented silicon, the calculation of formation enthalpy and solubility products formulas for niobium carbide nitride show that the solubility products of Nb compounds in ferrite and austenite meet the following relationship Nb C0.75[Nb C0.85[Nb C0.88[Nb C[Nb N and Nb N has the minimum enthalpy of formation.It indicates tha Nb N easily precipitate out, but Nb C0.75precipitates more difficultly.That agrees with the results of qualitative comparison by solubility product formulas.Meanwhile, i is identified that the full solution temperature of inhibitors such as Nb C0.75, Nb C0.85, Nb C0.88, Nb C and Nb N are lower than traditional inhibitors of Mn S and Al N?Mn S (about 1, 673 K) , which can reduce the slab heat tempera ture and energy consumption.
参考文献
[19] Zhang BW.Miedema theory for formation heat of alloy system.Shanghai Met.1993;15 (5) :23.
