Abstract
The influence of long range potentials on the stationary rate of diffusion controlled reactions is studied. It is shown that the concept of a reaction radiusR a can be retained but due to the potentialR a becomes temperature dependent, e.g. for attractive potentials decreases with increasing temperature. We give a perscription how to calculateR a . For spherically symmetric potentials the problem can be solved exactly whereas for anisotropic potentials approximate results are obtained with the help of a variational principle. For strong potentials of the formϕ(r)=−α f(Ω)/r n the powern alone determines the temperature dependence ofR a whereas the angular functionf(Ω) determines the absolute value. Purely attractive power potentials (f(Ω)=1) yield approximatelyR a ≅(α/kT)1/n.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Schroeder, K.: Diffusion Reactions of Point Defects, Report of the Nuclear Research Center Jülich (Germany) JÜL-1083-FF, July 1974
Waite, T.R.: Phys. Rev.107, 463 and 471 (1957)
Corbett, J.W., Smith, R.B., Walker, R.M.: Phys. Rev.114, 1460 (1959)
Simpson, H.M., Sosin, A.: Rad. Eff.3, 1 (1970)
Peak, D., Corbett, J.W.: Phys. Rev. B5, 1226 (1972)
Schroeder, K.: Rad. Eff.17, 103 (1973)
Brailsford, A.D., Bullough, R.: J. Nucl. Mat.44, 121 (1972)
Dworschak, F., Lennartz, R., Wollenberger, H.: J. Phys. F, to be published
Sonnenberg, K., Schilling, W., Dibbert, H.J., Mika, K., Schroeder, K.: Rad. Eff.15, 129 (1972)
Schroeder, K., Eberlein, E.: Z. Physik B22, 181 (1975)
Peak, D., Brosius, P., Lee, Y.H., Peters, M.St., Frisch, H.L., Corbett, J.W.: Rad. Eff.15, 61 (1972)
Debye, P.: Trans. Electrochem. Soc.82, 265 (1942)
Montroll, E.W.: J. Chem. Phys.14, 202 (1946)
Bullough, R., Newman, R.C.: Proc. Roy. Soc. London A249, 427 (1959)
Margvelashvili, I.G., Saralidze, Z.K.: Sov. Physics Sol. State15, 1774 (1974)
Heald, P.T.: Phil. Mag.31, 551 (1975)
Yoo, M.H., Butler, W.H.: To be published
Seeger, A.: phys. stat. sol. (b)41, 509 (1971)
Eshelby, J.D.: Sol. State Phys.3, 79 (1956) (Turnbull-Seitz, Eds.)
Siems, R.: phys. stat. sol.30, 645 (1968)
Dederichs, P.H., Pollmann, J.: Z. Physik255, 315 (1972) and JÜL-836-FF, Report of the Nuclear Research Center Jülich, Germany (1972)
Muggli, J.: Phys. kond. Mat.12, 237 (1971)
Masumura, R.A., Sines, G.: J. Appl. Phys.41, 3930 (1970)
Pollmann, J.: JÜL-1023-FF, Report of the Nuclear Research Center Jülich, Germany (1973)
Trinkaus, H.: Private communication
Ehrhart, P., Haubold, H.G., Schilling, W.: Advances in Solid State Physics, Vol. 14, p. 87 (O. Madelung and H.J. Queisser, Eds.), Braunschweig: Vieweg Verlag 1974
Schober, H.R.: Private communication
Koehler, J.S.: Phys. Rev.181, 1015 (1969)
Flynn, C.P.: Point Defects and Diffusion, p. 411ff. Oxford: Clarendon Press 1972
Scholz, A., Lehmann, Chr.: Phys. Rev. B1, 1306 (1970)
Profant, M., Walther, H.: JÜL-1027-MA, Report of the Nuclear Research Center Jülich, Germany (1973)
Profant, M., Wollenberger, H.: phys. stat. sol. (b) to be published
Becker, D.E., Dworschak, F., Wollenberger, H.: phys. stat. sol. (b)54, 455 (1972)
Abramowitz, M., Stegun, I.A.: Eds. Handbook of Mathematical Functions (Ntl. Bureau of Standards, 1968), p. 355ff.
Author information
Authors and Affiliations
Additional information
This paper is a condensed version of the second part of the report [1], Berichte der Kernforschungsanlage Jülich — Nr. 1083 FF (205 pages), available from: Zentralbibliothek der Kernforschungsanlage Jülich GmbH, D-517 Jülich 1 (Fed. Rep. Germany) Postfach 1913.
Rights and permissions
About this article
Cite this article
Schroeder, K., Dettmann, K. Diffusion reactions in long range potentials. Z Physik B 22, 343–350 (1975). https://doi.org/10.1007/BF01312804
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01312804