The ionic conductivity and viscous flow data of , , have been collected in a large temperature range, below and above their glass transition temperatures ( ). A microscopic model is proposed, assuming that the ionic displacement would result from the migration of interstitial positively charged cationic pairs whose concentration is an activated function of temperature. Below , their migration is also an activated mechanism, but a “free volume” would prevail above this temperature. This discontinuity in the migration mechanism justifies a Dienes-Macedo-Litovitz (DML) relationship to be representative of conductivity data above and an Arrhenius law below. According to this model, the enthalpy deduced by the fit of high temperature data using a DML equation would correspond to the charge carrier formation, whose migration enthalpy, below , could be deduced by the difference between the activation energy measured in the Arrhenius domain and the charge carrier formation enthalpy. To reduce the number of adjustable parameters numerical values were physically justified. We also applied a complete test for conductivity below , using the so-called weak electrolyte model, splitting activation enthalpy into formation and migration enthalpies and also explaining the variation of pre-exponential term of conductivity with composition. 1. Introduction For glass-forming mixtures in the solid or supercooled liquid state, ionic transport due to alkali cations strongly depends on temperature . The variations of the conductivity-temperature product in an Arrhenius representation show two distinct behaviors. At the lowest temperatures, that product follows an activated relationship: where and are constants; is the gas constant. At higher temperatures, experimental data obey another temperature behavior: where , and are constants. This expression will be deduced in more details below. Such equation suggests an asymptotic decrease of conductivity towards and is similar to the empirical Vogel-Fulcher-Tammann-Hesse (VFTH) relationship originally established to describe the viscosity-temperature dependence of molten silicates [1–3]: where (the glass transition temperature) is an empirical constant at which the viscosity diverges, and has the same meaning of the preexponential constant of the Arrhenius expression: where and are constants. The regime of viscosity below follows (4) and is called isostructural (i.e., the viscosity of the glassy state where the structure is frozen). Unfortunately (4) was not used because there is no data in such temperature range. Some authors have
References
[1]
H. Vogel, “The law of the relationship between viscosity of liquids and the temperature,” Physikalische Zeitschrift, vol. 22, pp. 645–646, 1921.
[2]
G. Tamman and W. Hesse, “Die Abh？ngigkeit der viscosit？t von der temperatur bie unterkühlten flüssigkeiten,” Zeitschrift für Anorganische und Allgemeine Chemie, vol. 156, pp. 245–257, 1926.
[3]
G. S. Fulcher, “Analysis of recent measurements of the viscosity of glasses,” Journal of the American Ceramic Society, vol. 8, no. 6, pp. 339–355, 1925.
[4]
P. B. Macedo and T. A. Litovitz, “On the relative roles of free volume and activation energy in the viscosity of liquids,” Journal of Chemical Physics, vol. 42, p. 245, 1965.
[5]
A. K. Doolittle, “Studies in newtonian flow—II. the dependence of the viscosity of liquids on free-space,” Journal of Applied Physics, vol. 22, no. 12, pp. 1471–1475, 1951.
[6]
M. H. Cohen and D. Turnbull, “Molecular transport in liquids and glasses,” Journal of Chemical Physics, vol. 31, p. 1164, 1959.
[7]
G. J. Dienes, “Activation energy for viscous flow and short-range order,” Journal of Applied Physics, vol. 24, no. 6, pp. 779–782, 1953.
[8]
A. D. Akopyan, Issledovanie Fiziko-Khimicheskikh Svoistv Stekol Sistemy Na2O-RO-GeO2 i Razrabotka na ikh Osnove Novykh Sostavov dlya Vakuumnoi Tekhniki [Ph.D. thesis], Advisor: K. A. Kostanyan, Yerevan State University, 1973.
[9]
J. L. Souquet and W. G. Perera, “Thermodynamics applied to ionic transport in glasses,” Solid State Ionics, vol. 40-41, no. 2, pp. 595–604, 1990.
[10]
J. L. Souquet, M. Duclot, and M. Levy, “Ionic transport mechanisms in oxide based glasses in the supercooled and glassy states,” Solid State Ionics, vol. 105, pp. 237–242, 1998.
[11]
E. I. Kamitsos, M. A. Karakassides, and G. D. Chryssikos, “Cation-network interactions in binary alkali metal borate glasses. A far-infrared study,” Journal of Physical Chemistry, vol. 91, no. 22, pp. 5807–5813, 1987.
[12]
G. D. L. K. Jayasinghe, D. Coppo, P. W. S. K. Bandaranayake, and J. L. Souquet, “Electrical properties of TeO2 glasses with Na2O as network modifier,” Solid State Ionics, vol. 76, no. 3-4, pp. 297–300, 1995.
[13]
D. Ravaine and J. L. Souquet, “A thermodynamic approach to ionic conductivity in oxide glasses—part 1. Correlation of the ionic conductivity with the chemical potential of alkali oxide in oxide glasses,” Physics and Chemistry of Glasses, vol. 18, no. 2, pp. 27–31, 1977.
[14]
D. Ravaine and J. L. Souquet, “A thermodynamic approach to ionic conductivity in oxide glasses—part 2. A statistical model for the variations of the chemical potential of the constituents in binary alkali oxide glasses,” Physics and Chemistry of Glasses, vol. 19, no. 5, pp. 115–120, 1978.
[15]
S. W. Martin and C. A. Angell, “Dc and Ac conductivity in wide composition range Li2O.P2O5 glasses,” Journal of Non-Crystalline Solids, vol. 83, no. 1-2, pp. 185–207, 1986.
[16]
J. C. Reggiani, J. P. Malugani, and J. Bernard, “Etude des systèmes vitreaux AgPO3-AgX (X=I, Br, Cl) par calorimétrie de dissolution. Correlation entre l'actvite thermodynamique de AgX et la conductivité ionique du verre,” Journal de Chimie Physique, vol. 75, no. 9, pp. 849–854, 1978.
[17]
A. Pradel, F. Henn, J. L. Souquet, and M. Ribes, “Use of a thermodynamic model to interpret Li+ ionic conduction in oxide and sulphide binary glasses,” Philosophical Magazine B, vol. 60, no. 6, pp. 741–751, 1989.
[18]
C. I. B. Fincham and F. D. Richardson, “The behaviour of sulphur in silicate and aluminate melts,” Proceedings of the Royal Society of London, vol. 223, pp. 40–62, 1954.
[19]
G. W. Toop and C. Samis, “Part II—papers—hydride habit in zirconium and in unstressed and stressed zircaloy-4,” Transactions of the Metallurgical Society of AIME, vol. 224, p. 878, 1962.
[20]
O. Kubaschewski, F. E. Evans, and C. B. Alcock, Metallurgical Thermochemistry, Pergamon, 1967.
[21]
N. Umesaki, N. Iwamoto, M. Tatsumisago, and T. Minami, “A structural study of rapidly quenched glasses in the system Li2OSiO2,” Journal of Non-Crystalline Solids, vol. 106, no. 1–3, pp. 77–80, 1988.
[22]
M. L. F. Nascimento, “Test of the Anderson Stuart model and correlation between free volume and the universal conductivity in sodium silicate glasses,” Journal of Materials Science, vol. 42, pp. 3841–3850, 2007.
[23]
M. L. F. Nascimento and S. Watanabe, “Test of the Anderson Stuart model and correlation between free volume and the universal conductivity in potassium silicate glasses,” Materials Chemistry and Physics, vol. 105, pp. 308–314, 2007.
[24]
M. L. F. Nascimento, E. do Nascimento, and S. Watanabe, “Test of Anderson-Stuart model and the “Universal” conductivity in Rubidium and cesium silicate glasses,” Brazilian Journal of Physics, vol. 35, pp. 626–631, 2005.
[25]
M. L. F. Nascimento, A. C. M. Rodrigues, and J. L. Souquet, “Microscopic and thermodynamic interpretations of experimental data on ionic conductivity in lithium silicate glasses,” Physics and Chemistry of Glasses, vol. 51, no. 1, pp. 69–77, 2010.
[26]
M. L. F. Nascimento and S. Watanabe, ““Universal” curve of ionic conductivities in binary alkali silicate glasses,” Journal of Materials Science, vol. 40, no. 18, pp. 5079–5081, 2005.
[27]
M. L. F. Nascimento and S. Watanabe, ““Universal” curve of ionic conductivities in binary alkali borate glasses,” Journal of Materials Science, vol. 40, no. 16, pp. 4423–4425, 2005.
[28]
M. L. F. Nascimento, E. do Nascimento, and S. Watanabe, ““Universal” curve of ionic conductivities in binary alkali germanate glasses,” Materials Chemistry and Physics, vol. 96, pp. 55–58, 2006.
[29]
M. L. F. Nascimento and S. Watanabe, “Universal curve of ionic conductivities in binary alkali tellurite glasses,” Brazilian Journal of Physics, vol. 36, pp. 795–798, 2006.
[30]
M. L. F. Nascimento and C. Aparício, “Viscosity of strong and fragile glass-forming liquids investigated by means of principal component analysis,” Journal of Physics and Chemistry of Solids, vol. 68, pp. 104–110, 2007.
[31]
M. L. F. Nascimento and C. Aparicio, “Data classification with the Vogel-Fulcher-Tammann-Hesse viscosity equation using correspondence analysis,” Physica B, vol. 398, no. 1, pp. 71–77, 2007.
[32]
F. A. Kr？ger, The Chemistry of Imperfect Crystals, North Holland, Amsterdam, The Netherlands, 1964.
[33]
E. Caillot, M. J. Duclot, J. L. Souquet, M. Levy, F. G. K. Baucke, and R. D. Werner, “Unified model for ionic transport in alkali disilicates below and above the glass transition,” Physics and Chemistry of Glasses, vol. 35, no. 1, pp. 22–27, 1994.
[34]
I. Gutzow and J. W. P. Schmelzer, The Vitreous State, Springer, 1995.
[35]
J. L. Souquet, M. L. F. Nascimento, and A. C. M. Rodrigues, “Charge carrier concentration and mobility in alkali silicates,” Journal of Chemical Physics, vol. 132, Article ID 034704, 2010.
[36]
V. Clément, D. Ravaine, C. Déportes, and R. Billat, “Measurement of Hall mobilities in AgP03 Agi glasses,” Solid State Ionics, vol. 28–30, pp. 1572–1578, 1988.
[37]
A. C. M. Rodrigues, M. L. F. Nascimento, C. B. Bragatto, and J. L. Souquet, “Charge carrier mobility and concentration as a function of composition in AgPO3-AgI glasses,” Journal of Chemical Physics, vol. 135, Article ID 234504, 2011.
