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Metallurgical and Materials Transactions A

, Volume 50, Issue 6, pp 2978–2990 | Cite as

Effect of Solid Solution Elements on Solubility Products of Carbides and Nitrides in Ferrite: Thermodynamic Calculations

  • Xuan-Wei Lei
  • Da-Yong Li
  • Xue-Hui ZhangEmail author
  • Tong-Xiang LiangEmail author
Article
  • 73 Downloads

Abstract

Thermodynamic calculation based on the two sublattice model are used to evaluate solubility products of titanium, niobium, vanadium carbide, and nitride in ferrite under the effect of solid solution alloy elements Mn and Ni, respectively. The results show that the calculated solubility products of these binary compounds in pure ferrite are closer to the solubility products by experimental measurements than the solubility products by thermodynamic calculations in previous studies. The solubility products in ferrite, on the condition that the total solid solution alloy content is relatively small, are given as follows:
$$ \log ^{\alpha }K_{\text{TiC}} = 5.08 - \frac{11,048}{T} + 0.04\left[ {\text{wt pct Mn}} \right] + \frac{62}{T}\left[ {\text{wt pct Ni}} \right] $$
$$ \log ^{\alpha }K_{\text{NbC}} = 5.72 - \frac{12,249}{T} + 0.06\left[ {\text{wt pct Mn}} \right] + \frac{44}{T}\left[ {\text{wt pct Ni}} \right] $$
$$ \log ^{\alpha }K_{\text{VC}} \, = \,6.02\, - \,\frac{9563}{T} + \left( { - \,0.04 + \frac{79}{T}} \right)\left[ {\text{wt pct Mn}} \right] + \left( { - \,0.03 + \frac{80}{T}} \right)\left[ {\text{wt pct Ni}} \right] $$
$$ \log ^{\alpha }K_{\text{TiN}} = 5.41 - \frac{16,997}{T} + 0.03\left[ {\text{wt pct Mn}} \right] + \frac{32}{T}\left[ {\text{wt pct Ni}} \right] $$
$$ \log ^{\alpha }K_{\text{NbN}} = 5.51 - \frac{12,799}{T} + 0.05\left[ {\text{wt pct Mn}} \right] + \frac{13}{T}\left[ {\text{wt pct Ni}} \right] $$
$$ \log ^{\alpha }K_{\text{VN}} = 4.94\, - \,\frac{10,615}{T} + \left( { - \,0.05 + \frac{85}{T}} \right)\left[ {\text{wt pct Mn}} \right]\, + \,\left( { - \,0.03 + \frac{49}{T}} \right)\left[ {\text{wt pct Ni}} \right] $$

Nomenclature

\( X_{i} ,X_{{i^{\prime}}} \)

i-th and \( i^{\prime} \)-th (\( i^{\prime} \) < i) solid solution elements (not compound formed elements) in ferrite, of which atoms fill in the first sublattice

M

Binary compound formed element, of which atoms fill in the first sublattice

N

Binary compound formed element, of which atoms fill in the second sublattice

Va

Vacancy, which fills in the second sublattice

Gα

Gibbs energy of α phase (J/mol)

mgGa

Magnetic contribution to Gibbs energy, which is proposed by Inden[5] and modified by Hillert and Jarl[6] (J/mol)

GP

Gibbs energy of binary compound

j, j′

Element types in first sublattice (in the order of Fe, X1, X2, … and M; the sequence number of j′ is smaller than that of j)

k, k′

Element types in second sublattice (in the order of N and Va; the sequence number of \( k^{\prime} \) is smaller than that of \( k \))

\( {^\circ}G_{j:k}^{\text{bcc}} \)

Gibbs energy of body-centered-cubic (bcc) phase where the first and second sublattices are filled with j atoms and k atoms, respectively (J/mol)

\( {^\circ}G_{j:k}^{\text{fcc}} \)

Gibbs energy of face-centered-cubic (fcc) phase where the first and second sublattices are filled with j atoms and k atoms, respectively (J/mol)

\( \mu_{j:k}^{\text{bcc}} \)

Chemical potential of bcc phase where the first and second sublattices are filled with j atoms and k atoms, respectively (J/mol)

\( \mu_{j}^{\text{bcc}} \)

Chemical potential of j element in bcc phase

\( \mu_{k}^{\text{bcc}} \)

Chemical potential of k element in bcc phase

\( \mu_{j:k}^{\text{fcc}} \)

Chemical potential of fcc binary compound where the first and second sublattices are filled with j atoms and k atoms, respectively (J/mol)

Lbcc

Interaction parameter of bcc phase (in the subscripts of Lbcc, components in different sublattices are separated by a colon and, in the same sublattice, by a comma) (J/mol)

βbcc

Quantity related to total magnetic entropy of bcc phase

\( T_{c}^{\text{bcc}} \)

Critical temperature for magnetic ordering of bcc phase

\( _{ }^{0} T_{cj}^{\text{bcc}} \)

Magnetic interaction parameter of pure j atoms in bcc phase related to critical temperature for magnetic ordering (Kelvin)

\( _{ }^{0} \beta_{j}^{\text{bcc}} \)

Magnetic parameter of pure j atoms in bcc phase related to magnetic entropy

\( _{ }^{n} T_{{c j,j^{'} }}^{\text{bcc}} \)

The n-th binary magnetic interaction parameter between j atoms and j’ atoms in bcc phase related to critical temperature for magnetic ordering (Kelvin)

\( _{ }^{n} \beta_{{j,j^{'} }}^{\text{bcc}} \)

The n-th binary magnetic interaction parameter between j atoms and j’ atoms in bcc phase related to magnetic entropy

\( y_{j}^{\alpha } \)

Site fraction of j atoms in the first sublattice in ferrite

\( y_{k}^{\alpha } \)

Site fraction of k atoms in the second sublattice in ferrite

f(τ)

Polynomial function, which is obtained by Hillert and Jarl[6] based on the magnetic specific heat of iron

T

Temperature (K)

R

Universal gas constant (J/mol K)

τ

Ratio of T to \( T_{c}^{\text{bcc}} \)

p

Ratio of magnetic enthalpy due to short-ordering to the total amount of magnetic enthalpy, \( p = 0.4 \) for bcc structure[6]

xm

Mole fraction of m element in the system

[wt pct m]

Mass percent of m element in ferrite

\( A_{m} \)

Relative atomic mass of m element

\( { \log }_{ }^{\alpha } K_{MN}^{0} \)

Logarithmic solubility product of binary compound MN in pure ferrite in the Fe-M-N system

\( { \log }_{ }^{\alpha } K_{MN}^{{X_{i} }} \)

Logarithmic solubility product of binary compound MN in ferrite in the Fe-Xi-M-N system

\( \Delta { \log }_{ }^{\alpha } K_{MN}^{{X_{i} }} \)

Increment of logarithmic solubility product of binary compound MN in ferrite for solid solution element Xi addition

\( { \log }_{ }^{\alpha } K_{MN}^{ } \)

Logarithmic solubility product of binary compound \( MN \) in ferrite in the Fe-X1-X2- … M-N system

Notes

Acknowledgments

This work was supported by a start-up fund for new researchers of Jiangxi University of Science and Technology (Grant No. jxxjbs18037), the Department of Science and Technology of Jiangxi Province (Post-doctoral fund under Grant No. 3205700012 and High-level talent fund under Grant No. 3401223254), and the National Natural Science Foundation of China (Grant Nos. 51871114 and 51804138).

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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringJiangxi University of Science and TechnologyGanzhouP.R. China
  2. 2.Bohai Shipyard Group Co., Ltd.HuludaoP.R. China

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