Abstract
A simple theoretical model was developed to predict equilibrium between precipitate and matrix in a multicomponent microalloyed steel. The solute concentration in the matrix, the composition and the volume fraction of the precipitated second phases, and the reduction in critical precipitation temperature of AlN induced by carbonitride were quantified by the proposed thermodynamic model. The results predicted by the developed model and those by other approaches are in a good agreement. The main advantages of this model over the existing models are that the process of formulation derivation is simple and the model can be easily solved by a personal program.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42243-018-0173-5/MediaObjects/42243_2018_173_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42243-018-0173-5/MediaObjects/42243_2018_173_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42243-018-0173-5/MediaObjects/42243_2018_173_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42243-018-0173-5/MediaObjects/42243_2018_173_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42243-018-0173-5/MediaObjects/42243_2018_173_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs42243-018-0173-5/MediaObjects/42243_2018_173_Fig6_HTML.png)
Similar content being viewed by others
References
M. Gómez, L. Rancel, S.F. Medina, Mater. Sci. Forum 638 (2010) 3388–3393.
S.E. Kang, J.R. Banerjee, E.M. Maina, B. Mintz, Mater. Sci. Technol. 29 (2013) 1225–1232.
J. Moon, C. Lee, Acta Mater. 57 (2009) 2311–2320.
H. Pous-Romero, I. Lonardelli, D. Cogswell, H.K.D.H. Bhadeshia, Mater. Sci. Eng. A 567 (2013) 72–79.
A. Kundu, C.L. Davis, M. Strangwood, Solid State Phenom. 172 (2011) 458–463.
A. Kundu, ISIJ Int. 54 (2014) 677–684.
D.P. Dunne, Mater. Sci. Technol. 26 (2013) 410–420.
S.K. Badjena, J.K. Park, Mater. Sci. Eng. A 548 (2012) 126–133.
M. Gómez, L. Rancel, S.F. Medina, Mater. Sci. Eng. A 506 (2009) 165–173.
S.F. Tao, F.M. Wang, G.L. Sun, Z.B. Yang, C.R. Li, Metall. Mater. Trans. A 46 (2015) 3670–3678.
A. Karmakar, S. Kundu, S. Roy, S. Neogy, D. Srivastava, D. Chakrabarti, Mater. Sci. Technol. 30 (2013) 653–664.
B. Pereda, Z. Aretxabaleta, B. López, J. Mater. Eng. Perform. 24 (2015) 1279–1293.
T.W. Lee, S.I. Kim, M.H. Hong, W.Y. Kim, Y.G. Yoo, S.H. Lim, J. Alloy. Compd. 582 (2014) 428–436.
J. Fu, G. Li, X. Mao, K. Fang, Metall. Mater. Trans. A 42 (2011) 3797–3812.
Y. Funakawa, T. Shiozaki, K. Tomita, T. Yamamoto, E. Maeda, ISIJ Int. 44 (2004) 1945–1951.
C. Solenthaler, M. Ramesh, P.J. Uggowitzer, R. Spolenak, Mater. Sci. Eng. A 647 (2015) 294–302.
S. Zamberger, M. Pudar, K. Spiradek-Hahn, M. Reischl, E. Kozeschnik, Int. J. Mater. Res. 103 (2012) 680–687.
A. Deschamps, F. Danoix, F. De Geuser, T. Epicier, H. Leitner, M. Perez, Mater. Lett. 65 (2011) 2265–2268.
B. Dutta, E.J. Palmiere, C.M. Sellars, Acta Mater. 49 (2001) 785–794.
P. Maugis, M. Gouné, Acta Mater. 53 (2005) 3359–3367.
C.E.I.C. Ohlund, D.D. Ouden, J. Weidow, M. Thuvander, S.E. Offerman, ISIJ Int. 55 (2015) 884–893.
F. Perrard, A. Deschamps, P. Maugis, Acta Mater. 55 (2007) 1255–1266.
C. Zener, J. Appl. Phys. 20 (1949) 950–953.
H. Adrian, Mater. Sci. Technol. 8 (1992) 406–420.
K. Inoue, N. Ishikawa, I. Ohnuma, H. Ohtani, K. Ishida, ISIJ Int. 41 (2001) 175–182.
H. Zou, J.S. Kirkaldy, Metall. Mater. Trans. A 23 (1992) 651–657.
Y.L. Wang, L.C. Zhuo, M.W. Chen, Z.D. Wang, Rare Metals 35 (2015) 735–741.
P.R. Rios, Mater. Sci. Eng. A 142 (1991) 87–94.
Y. Xu, D. Tang, Y. Song, Steel Res. Int. 84 (2013) 560–564.
W. Wang, H.R. Wang, Mater. Lett. 61 (2007) 2227–2230.
Q.L. Yong, Second phase in steels, Metallurgical Industry Press, Bei**g, 2006.
M. Hillert, L.I. Staffansson, Acta Chem. Scand. 24 (1970) 3618–3626.
S.Q. Yuan, G.L. Liang, Mater. Lett. 63 (2009) 2324–2326.
S.G. Hong, H.J. Jun, K.B. Kang, C.G. Park, Scripta Mater. 48 (2003) 1201–1206.
J.G. Jung, J.S. Park, J. Kim, Y.K. Lee, Mater. Sci. Eng. A 528 (2011) 5529–5535.
M.J. Leap, E.L. Brown, Scripta Mater. 47 (2002) 793–797.
Y. Zeng, W. Wang, J. Mater. Sci. 43 (2007) 874–882.
Acknowledgements
This work is financially supported by National Key R&D Program of China under Grant No. 2017YFB0305300 and National Natural Science Foundation of China under Grant No. 51234002.
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Yang, Y., Li, Tr., Jia, T. et al. A simple calculation model for thermodynamic equilibrium information between precipitation and matrix. J. Iron Steel Res. Int. 25, 1156–1162 (2018). https://doi.org/10.1007/s42243-018-0173-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42243-018-0173-5