Mathematical approach to investigation of synthesis processes at high temperatures

• Authors: Mažvydas Mackevičius , Feliksas Ivanauskas , Aivaras Kareiva
• Languages of publication: EN

Abstracts

EN

In our work, we present a method for estimation of the diffusion and reaction rates of synthesis at high temperatures using limited information from laboratory experiments, such as synthesis time and dimensions of reactants. Synthesis by sol-gel and solid-state reactions is considered. The inverse modeling problem is solved for one- and two-dimensional models. Explicit formulas for the diffusion coefficient and reaction rate as functions of temperature are obtained. The activation energies are calculated, and the lower bounds of diffusion and reaction rates are estimated, thus obtaining conditions for occurrence of synthesis. [...]

Keywords

EN

Sol-gel and solid-state reactions; Diffusion coefficient; Reaction rate; Occurrence of synthesis; Activation energy

• Publisher: De Gruyter Open
• Journal: Open Chemistry
• Year: 2012
• Volume: 10
• Issue: 2
• Pages: 380-385

Dates

published

1 - 4 - 2012

online

29 - 1 - 2012

Contributors

author

Mažvydas Mackevičius

• Institute of Mathematics and Informatics, Vilnius, LT-08663, Lithuania

author

Feliksas Ivanauskas

• Department of Mathematics and Informatics, Vilnius University, Vilnius, LT-03225, Lithuania

author

Aivaras Kareiva

• Department of Chemistry, Vilnius University, Vilnius, LT-03225, Lithuania

References

• [1] B.N. Arzamasov, V.N. Simonov, Met. Sci. Heat Treat. 52(9–10), 403 (2011) http://dx.doi.org/10.1007/s11041-010-9291-9[Crossref]
• [2] P. Budrugeac, Thermochimica Acta 511(1–2), 8 (2010) http://dx.doi.org/10.1016/j.tca.2010.07.018[Crossref]
• [3] F. Ivanauskas, A. Kareiva, B. Lapcun, J. Math. Chemistry 37(4), 365 (2005) http://dx.doi.org/10.1007/s10910-004-1103-2[Crossref]
• [4] H.H. Mohamed, C.B. Mendive, R. Dillert, D.W. Bahnemann, J. Phys. Chem. A 115(11), 2139 (2011) http://dx.doi.org/10.1021/jp108958w[Crossref]
• [5] B. Adnadevic, B. Jankovic, D.M. Minic, J. Phys. Chem. Solids 71(7), 927 (2010) http://dx.doi.org/10.1016/j.jpcs.2010.04.009[Crossref]
• [6] H. Belhouchet, M. Hamidouche, N. Bouaouadja, V. Garnier, G. Fantozzi, Annal. Chimie-Sci. Mater. 35(1), 17 (2010) http://dx.doi.org/10.3166/acsm.35.17-25[Crossref]
• [7] C. Chen, W.L. Gong, W. Lutze, I. L. Pegg, J. Mater. Sci. 46(9), 3073 (2011) http://dx.doi.org/10.1007/s10853-010-5186-9[Crossref]
• [8] K. Muraleedharan, V.M.A. Mujeeb, M.H. Aneesh, T. Gangadevi, M.P. Kannan, Thermochimica Acta 510(1–2), 160 (2010) http://dx.doi.org/10.1016/j.tca.2010.07.010[Crossref]
• [9] F. Xia, J. Brugger, A. Pring, In: P.J. Williams et al. (Eds.), Smart Science for Exploration and Mining, Proc. 10th Biennial SGA Meeting of The Society for Geology Applied to Mineral Deposits, 2, 700 (2010)
• [10] C.J. Deng, J.M. Cai, R.H. Liu, Solid State Sci. 11(8), 1375 (2009) http://dx.doi.org/10.1016/j.solidstatesciences.2009.04.009[Crossref]
• [11] A. Perejon, P. E. Sanchez-Jimenez, J. M. Criado, L. A. Perez-Maqueda, J. Phys. Chem. B 115(8), 1780 (2011) http://dx.doi.org/10.1021/jp110895z[Crossref]
• [12] W. Preis, Montash. Chemie 140(9), 1059 (2009) http://dx.doi.org/10.1007/s00706-009-0124-8[Crossref]
• [13] J. Amami, D. Hreniak, Y. Guyot, W. Zhao, G. Boulon, J. Lumin. 130(4), 603 (2010) http://dx.doi.org/10.1016/j.jlumin.2009.11.003[Crossref]
• [14] J. Dong, P. Deng, J. Xu, Optics Commun. 170(4–6), 255 (1999) http://dx.doi.org/10.1016/S0030-4018(99)00519-2[Crossref]
• [15] A. Leleckait, A. Kareiva, H. Bettentrup, T. Justel, H.-J. Meyer, Z. Anorg. Allg. Chemie 631(15), 2987 (2005) http://dx.doi.org/10.1002/zaac.200500315[Crossref]
• [16] A. Katelnikovas, J. Barkauskas, F. Ivanauskas, A. Beganskiene, A. Kareiva, J. Sol-Gel Sci. Techn. 41(3), 193 (2007) http://dx.doi.org/10.1007/s10971-006-9002-6[Crossref]
• [17] X.D. Yang, Y. Bo, Q.J. Peng, A.C. Geng, OPTIK 122(6), 467 (2011) http://dx.doi.org/10.1016/j.ijleo.2010.03.007[Crossref]
• [18] F. Ivanauskas, A. Kareiva, B. Lapcun, J. Math. Chemistry 42(2), 191 (2007) http://dx.doi.org/10.1007/s10910-006-9092-y[Crossref]
• [19] F. Ivanauskas, A. Kareiva, B. Lapcun, J. Math. Chemistry 46(2), 427 (2009) http://dx.doi.org/10.1007/s10910-008-9468-2[Crossref]
• [20] A.A. Samarskii, The Theory of Difference Schemes (Marcel Dekker, New York, 2001) http://dx.doi.org/10.1201/9780203908518[Crossref]

Identifiers

DOI

10.2478/s11532-011-0159-7