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Isothermal Kinetics Model for Solid–Solid Reaction of Powders Through Surface Area and Size Distribution of Particles

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Abstract

Several industrial processes, such as those in metallurgical, chemical, ceramic, and cement industries, often involve solid–solid reactions. The solid reactions at high temperatures are often limited or controlled by solid diffusion, and some models have been suggested to describe the reaction behaviors. A model considering the particle shape, surface area, particle size distribution, and diffusion rate of reactants was established to develop a quantitative representation of the solid–solid reaction of powders in a binary reactant system. In this model, the interface of particles was divided into reaction and nonreaction surfaces, and the particle shape was divided into first- and second-level shapes. The area of the reaction interface was calculated, and the concentration distribution of the reactants was numerically expressed. The simulated kinetics curves of fractional conversion α with time for different average particle sizes and diffusion coefficients were shown to be useful for evaluating the kinetics of solid–solid reactions. The simulated kinetics curves and experimental data from the references were compared, and a good accuracy was achieved.

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References

  1. J.S. Sharp, G.W. Brindley, and B.M. Narahari Achar: J. Am. Ceram. Soc., 1966, vol. 49(7), pp. 379–82.

    Article  CAS  Google Scholar 

  2. S.F. Hulbert: Br. Ceram. Soc. J., 1967, vol. 6(1), pp. 11–20.

    Google Scholar 

  3. J.D. Hancock and J.H. Sharp: J. Am. Ceram. Soc., 1972, vol. 55, pp. 74–7.

    Article  CAS  Google Scholar 

  4. S.J. Kridelbaugh: Am. J. Sci., 1973, vol. 273, pp. 757–77.

    Article  CAS  Google Scholar 

  5. J.H. Taplin: J. Am. Ceram. Soc., 1974, vol. 57(3), pp. 140–2.

    Article  CAS  Google Scholar 

  6. C.H. Bamford and C.F.G. Tipper, eds.: Chemical Kinetics Reactions in Solid State, Elsevier, New York, 1980.

    Google Scholar 

  7. J.R. Frade and M. Cable: J. Am. Ceram. Soc., 1992, vol. 75(7), pp. 1949–57.

    Article  CAS  Google Scholar 

  8. P. Argyrakis: Comput. Phys., 1992, vol. 6(5), pp. 525–8.

    Article  Google Scholar 

  9. A. Maitre, P. Lefort, and H. Temp: Mater. Process., 2002, vol. 6, pp. 267–82.

    CAS  Google Scholar 

  10. D. Achilias and C. Piparissides: J. Appl. Polym. Sci., 1988, vol. 35, pp. 1303–23.

    Article  CAS  Google Scholar 

  11. D. Fatu: J. Therm. Anal., 1992, vol. 38, pp. 935–41.

    Article  CAS  Google Scholar 

  12. A.K. Suresh and C. Ghoroi: AIChe J., 2009, vol. 55(9), pp. 2399–413.

    Article  CAS  Google Scholar 

  13. W. Jander and Z. Anorg: Allg. Chem., 1927, vol. 163, pp. 1–30.

    Article  CAS  Google Scholar 

  14. A.M. Ginstling and B.I. Brounshtein: J. Appl. Chem. USSR (Engl. Transl.)., 1950, vol. 23, pp. 1327–38.

    CAS  Google Scholar 

  15. G. Valensi: J. Chim. Phys.-Chim Biol., 1950, vol. 47, pp. 489–505.

    Article  CAS  Google Scholar 

  16. R.E. Charter: J. Chem. Phys., 1961, vol. 34, pp. 2010–5.

    Article  Google Scholar 

  17. N. Ouchiyama and T. Tanaka: Ind. Eng. Chem. Fundam., 1980, vol. 19(4), pp. 338–40.

    Article  CAS  Google Scholar 

  18. Y.J. Hao and T. Tanaka: Can. J. Chem. Eng., 1988, vol. 66, pp. 761–6.

    Article  CAS  Google Scholar 

  19. Y.J. Hao and T. Tanaka: J. Soc. Powder Technol. Jpn., 1987, vol. 24, pp. 588–92.

    Article  Google Scholar 

  20. Y.J. Hao and T. Tanaka: Kagahu Kogahu Ronbunshu., 1987, vol. 13, pp. 764–72.

    Article  CAS  Google Scholar 

  21. Y.J. Hao and T. Tanaka: J. Assoc. Mater. End. Resour., 1988, vol. 1, pp. 52–8.

    Article  Google Scholar 

  22. A. Shimizu and Y.H. Hao: J. Am. Ceram. Soc., 1997, vol. 80, pp. 557–68.

    Article  CAS  Google Scholar 

  23. Shimizu: Powder Technol., 1998, vol. 100, pp. 24–31.

    Article  CAS  Google Scholar 

  24. C. Ghoroi and A.K. Suresh: AIChE J., 2007, vol. 53, pp. 502–13.

    Article  CAS  Google Scholar 

  25. C. Ghoroi and A.K. Suresh: AIChE J., 2007, vol. 53(9), pp. 2399–410.

    Article  CAS  Google Scholar 

  26. K. Suresh and C. Ghoroi: AIChE J., 2009, vol. 55, pp. 2399–413.

    Article  CAS  Google Scholar 

  27. R. Amaresh, M. Pathak, and A.K. Suresh: Ind. Eng. Chem. Res., 2014, vol. 53, pp. 11659–67.

    Article  CAS  Google Scholar 

  28. M. Phutke and H. Dedhia: Chem. Eng. J., 2019, vol. 377, pp. 1–10.

    Article  Google Scholar 

  29. P.G.Y. Huang, C.H. Lu, and T.W.H. Sheu: Mater. Sci. Eng. B., 2004, vol. 107, pp. 39–35.

    Article  Google Scholar 

  30. P.G.Y. Huang, C.H. Lu, and T.W.H. Sheu: Mater. Sci. Eng. B., 2003, vol. 103, pp. 77–82.

    Article  Google Scholar 

  31. S.K. Das, Y.M. Kim, T.K. Ha, and R. Gauvin: Metall. Mater. Trans. A., 2013, vol. 44A, pp. 320–2.

    Google Scholar 

  32. K. Meguro and M.O.M. Kajihara: J. Mater. Sci., 2012, vol. 47, pp. 4955–64.

    Article  CAS  Google Scholar 

  33. Y. Tanaka and M. Kajihara: J. Mater. Sci., 2010, vol. 45, pp. 5676–84.

    Article  CAS  Google Scholar 

  34. K. Motojima, T. Asano, W. Shinmei, and M. Kajihara: J. Electron. Mater., 2012, vol. 41, pp. 3292–302.

    Article  CAS  Google Scholar 

  35. M. Hashiba, W. Shinmei, and M. Kajihara: J. Electron. Mater., 2011, vol. 41, pp. 32–43.

    Article  Google Scholar 

  36. L. Gao, L. Zhou, C.S. Li, J.Q. Feng, and Y.F. Lu: J. Mater. Sci., 2013, vol. 48, pp. 974–7.

    Article  CAS  Google Scholar 

  37. H. Fukuyama, M.K. Hossain, and K. Nagata: Metall. Mater. Trans. B., 2002, vol. 33B, pp. 257–64.

    Article  CAS  Google Scholar 

  38. S. Tsuji: Metall. Mater. Trans. A., 2014, vol. 45A, pp. 5371–8.

    Article  Google Scholar 

  39. R. Paulson: Z. Anorg. Allg. Chem., 1973, vol. 401, pp. 172–8.

    Article  Google Scholar 

  40. J. Beretka and T. Brown: J. Am. Ceram. Soc., 1983, vol. 66, pp. 383–8.

    Article  CAS  Google Scholar 

  41. P. Zhang, J.K. Baczewska, S. Du, and S. Seetharaman: Metall. Mater. Trans. A., 1996, vol. 27A, pp. 2978–84.

    Article  CAS  Google Scholar 

  42. S. Shimada, K. Soejima, and T. Ishii: React. Solids., 1990, vol. 8, pp. 51–61.

    Article  CAS  Google Scholar 

  43. J. Y. Xiang, X. Wang, G. S. Pei, Q. Y. Huang, X. W. Lv. Int. J. Miner. Metall. Mater., 2020

  44. A. Shimizu and J. Saitou: Solid State Ionics., 1990, vol. 38, pp. 161–269.

    Article  Google Scholar 

  45. L. Fresh and J.S. Dooling: J. Phys. Chem., 1966, vol. 70, pp. 3189–202.

    Article  Google Scholar 

Download references

Acknowledgments

This study was supported by the Key Fund of Natural Science (Grant No. 1902217), Chongqing Outstanding Youth Project (Grant No. CSTC2019JCYJJQX0024), and State Key Laboratory of Vanadium and Titanium Resources Comprehensive Utilization. We also thank the Chongqing Key Laboratory of Vanadium-Titanium Metallurgy and New Materials, Chongqing University, Chongqing 400044, PR China.

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Authors and Affiliations

  1. Pangang Group State Key Laboratory of Vanadium and Titanium Resources Comprehensive Utilization, Panzhihua, P.R. China

    Mingrui Yang

  2. Pangang Group Research Institute Co., Ltd., Panzhihua, 617000, Sichuan, P.R. China

    Mingrui Yang

  3. Chongqing Key Laboratory of Vanadium-Titanium Metallurgy and New Materials, Chongqing University, No. 174 Shazheng Street, Shapingba District, Chongqing, 400044, P.R. China

    Xuewei Lv & Chenguang Bai

  4. College of Materials Science and Engineering, Chongqing University, No. 174 Shazheng Street, Shapingba District, Chongqing, 400044, P.R. China

    Xuewei Lv & Chenguang Bai

  5. Faculty of Engineering, University of Bristol, Queens Road, Bristol, BS8 1QU, UK

    Hanyuan Wang

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  1. Mingrui Yang
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  2. Xuewei Lv
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  3. Chenguang Bai
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Correspondence to Xuewei Lv.

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Manuscript submitted December 9, 2020, accepted November 16, 2021.

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Yang, M., Lv, X., Bai, C. et al. Isothermal Kinetics Model for Solid–Solid Reaction of Powders Through Surface Area and Size Distribution of Particles. Metall Mater Trans B 53, 968–980 (2022). https://doi.org/10.1007/s11663-021-02393-2

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  • DOI: https://doi.org/10.1007/s11663-021-02393-2

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