Abstract
By using the example of several typical thermally activated processes in atomic clusters, organic molecules, and nanostructures, it has been shown that calculations of the corresponding pre-exponential factors in the Arrhenius law according to the Vineyard formula are in good agreement with the molecular dynamics simulation data for temperature dependences of characteristic times of these processes. This “static” approach (together with the determination of the activation energy through the examination of the potential energy hypersurface) provides information on kinetic characteristics of the system without resorting to numerical simulation of the time evolution, which requires large computer resources.
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References
C. Wert and C. Zener, Phys. Rev. 76, 1169 (1949).
M. M. Maslov, Russ. J. Phys. Chem. B 4(1), 170 (2010).
F. Montalenti and A. F. Voter, Phys. Status Solidi B 226, 21 (2001).
A. I. Podlivaev and L. A. Openov, Phys. Solid State 54(7), 1507 (2012).
L. A. Openov and A. I. Podlivaev, JETP Lett. 84(2), 68 (2006).
M. M. Maslov, D. A. Lobanov, A. I. Podlivaev, and L. A. Openov, Phys. Solid State 51(3), 645 (2009).
A. I. Podlivaev and K. P. Katin, JETP Lett. 92(1), 52 (2010).
A. I. Podlivaev and L. A. Openov, Semiconductors 45(7), 958 (2011).
L. A. Openov, A. I. Podlivaev, and M. M. Maslov, Phys. Lett. A 376, 3146 (2012).
X.-L. Sheng, H.-J. Cui, F. Ye, Q.-B. Yan, Q.-R. Zheng, and G. Su, J. Appl. Phys. 112, 074315 (2012).
C. H. Xu, C. Z. Wang, C. T. Chan, and K. M. Ho, J. Phys.: Condens. Matter 4, 6047 (1992).
M. M. Maslov, A. I. Podlivaev, and L. A. Openov, Phys. Lett. A 373, 1653 (2009).
G. H. Vineyard, J. Phys. Chem. Solids 3, 121 (1957).
A. I. Podlivaev and L. A. Openov, Phys. Solid State 55(12), 2592 (2013).
A. Santana, A. M. Popov, and E. Bichoutskaia, Chem. Phys. Lett. 557, 80 (2013).
C. Lifshitz, Int. J. Mass Spectrom. 198, 1 (2000).
S. Tomita, J. U. Andersen, K. Hansen, and P. Hvelplund, Chem. Phys. Lett. 382, 120 (2003).
K. Hansen, E. E. B. Campbell, and O. Echt, Int. J. Mass Spectrom. 252, 79 (2006).
M. M. Maslov, A. I. Podlivaev, and L. A. Openov, Phys. Solid State 53(12), 2532 (2011).
P. E. Eaton and T. W. Cole, Jr., J. Am. Chem. Soc. 86, 962 (1964).
M. A. White, R. E. Wasylishen, P. E. Eaton, Y. Xiong, K. Pramod, and N. Nodari, J. Phys. Chem. 96, 421 (1992).
J. An, L.-H. Gan, X. Fan, and F. Pan, Chem. Phys. Lett. 511, 351 (2011).
H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, Nature (London) 318, 162 (1985).
A. J. Stone and D. J. Wales, Chem. Phys. Lett. 128, 501 (1986).
A. I. Podlivaev and L. A. Openov, JETP Lett. 81(10), 533 (2005).
J. Zhou, Q. Wang, Q. Sun, X. S. Chen, Y. Kawazoe, and P. Jena, Nano Lett. 9, 3867 (2009).
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science (Washington) 306, 666 (2004).
I. V. Davydov, A. I. Podlivaev, and L. A. Openov, Phys. Solid State 47(4), 778 (2005).
L. A. Openov, D. A. Lobanov, and A. I. Podlivaev, Phys. Solid State 52(1), 201 (2010).
M. M. Maslov, Russ. J. Phys. Chem. B 3(2), 211 (2009).
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Original Russian Text © M.M. Maslov, L.A. Openov, A.I. Podlivaev, 2014, published in Fizika Tverdogo Tela, 2014, Vol. 56, No. 6, pp. 1191–1196.
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Maslov, M.M., Openov, L.A. & Podlivaev, A.I. On the vineyard formula for the pre-exponential factor in the Arrhenius law. Phys. Solid State 56, 1239–1244 (2014). https://doi.org/10.1134/S1063783414060250
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DOI: https://doi.org/10.1134/S1063783414060250