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Diffusion Coefficient of F − Ions in Perfect β‐PbF 2 Crystals
Author(s) -
Sekar P.,
Haridasan T. M.
Publication year - 1988
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221470205
Subject(s) - ion , kinetic energy , diffusion , arrhenius equation , atomic physics , activation energy , square (algebra) , chemistry , physics , thermodynamics , mathematics , quantum mechanics , geometry
In the quasi‐harmonic approximation, the mean square velocity of F − ions in β‐PbF 2 , along different directions is estimated. A critical square of the velocity is fixed by equating the experimental value of the migration energy to the minimum kinetic energy ( E kin min ) required by the F– ion to make the jump. The ratio of the calculated kinetic energy to E kin minis assumed to govern the probability term appearing in the Arrhenius equation. The diffusion coefficient is estimated for migration along 〈100〉 and 〈111〉 directions. The calculation is repeated in the reaction coordinate approach for migration along 〈111〉 direction. The estimated attempt frequencies of the ions in this approach are compared with that from Debye approximation. The diffusion coefficient thus calculated compares well with that of experiment. The requirement that the amplitude of the mobile ion should fluctuate to values just enough to cross the first ring of obstructing ions is found to be justified for these fluorite type crystals.