Ion Transport in Glass-Forming Calcium Potassium Nitrate: From Complex Behaviours to Unexpected Simplicities

Abstract:

Re-examination of published conductivity spectra for 2Ca (NO₃)₂∙3KNO₃ (CKN) in its molten and glassy states, in terms of the MIGRATION concept, has brought to light new links between elementary processes occurring within one picosecond and their successful outcomes, i.e. those which determine the DC conductivities. The starting point of this analysis is the transition at 378 K, which arises from a change from a decoupled to a coupled transport mechanism. Remarkably, while there is a change in the shape of the conductivity dispersion and a jump in its onset frequency, there is no change in the temperature dependence of DC conductivity. What emerges from the analysis is a surprising continuity in high-frequency behaviour, with the activation energy and volume for elementary displacements, E_ed and V_ed, remaining constant from 300 K in the glass up to 500 K in the melt. The ratio, E_ed/V_ed, turns out to be equal to our previously defined DC activation moduli for CKN, given by E_DC(T)/V_DC(T) and T_g/(dT_g/dp) for charge transport in the melt and structural relaxation at T_g, respectively. It seems that, at very short times, molten CKN behaves just like an elastic solid. The importance of elastic forces for ionic transport in CKN is corroborated by the finding that the published value of the high-frequency shear modulus of glassy CKN, G_¥, matches those of E_ed/V_ed and hence of both activation moduli. The detected continuity in the picosecond behaviour of CKN across the glass transition could provide a new link between fragile liquids and glassy materials in general.

• Periodical: Diffusion Foundations (Volume 22)
• Pages: 140-159
• DOI: https://doi.org/10.4028/www.scientific.net/DF.22.140
• Online since: May 2019
• Authors: Klaus Funke*, Radha D. Banhatti, Malcolm D. Ingram
• Keywords: Activation Energies, Activation Moduli, Activation Volumes, Coupled/Decoupled Transition, Elementary Displacements, Fragile Melts, Glass Transition, Glass/Melt Continuities, High-Frequency Shear Modulus, Ion Transport, MIGRATION Concept, Molten CKN, Successful Displacements

References

[1] C.A. Angell, Free volume model for transport in fused salts: electrical conductance in glass-forming nitrate melts, J. Phys. Chem. 68 (1964) 1917-1929.

DOI: 10.1021/j100789a042

[2] H. Vogel, The law of the relation between viscosity of liquids and the temperature, Phys. Z. 22 (1921) 645-646.

[3] G. Tammann, W. Hesse, Die Abhängigkeit der Viskosität von der Temperatur bei unterkühlten Flüssigkeiten, Z. Anorg. Allg. Chem. 156 (1926) 245-257.

DOI: 10.1002/zaac.19261560121

[4] G.S. Fulcher, Analysis of recent measurements of the viscosity of glasses, J. Am. Ceram. Soc. 8 (1925) 339-355.

[5] C.A. Angell, Oxide glasses in the light of the ideal glass, concept: I, ideal and nonideal transitions, and departure from ideality, J. Am. Ceram. Soc. 51 (1968) 117-124.

DOI: 10.1111/j.1151-2916.1968.tb11854.x

[6] R. Bose, R. Weiler, P.B. Macedo, Temperature dependence of conductance of a vitreous KNO3 -Ca(NO3)2 mixture, Phys. Chem. Glasses 11 (1970) 117.

[7] F.S. Howell, R.A. Bose, P.B. Macedo, C.T. Moynihan, Electrical relaxation in a glass-forming molten salt, J. Phys. Chem. 78 (1974) 639-648.

DOI: 10.1021/j100599a016

[8] M.C.C. Ribeiro, T. Scopigno, G. Ruocco, Computer simulation study of thermodynamic scaling of dynamics of 2Ca(NO3)2· 3KNO3, J. Chem. Phys. 135 (2011) 164510-(1-9).

DOI: 10.1063/1.3656872

[9] Z. Akdeniz, M.P. Tosi, Microstructure of mixed-nitrate melts and glasses, Phys. & Chem. Liquids 44 (2006) 361-365.

DOI: 10.1080/00319100600801785

[10] C. Tengroth, J. Swenson, A. Isopo, L. Börjesson, Structure of Ca0.4 K0.6 (NO3)1.4 from the glass to the liquid state, Phys. Rev. B 64 (2001) 224207-(1-9).

[11] C.A. Angell in: Relaxations in Complex Systems,, K.L. Ngai and G.B. Wright(Eds), GPO, Washington DC, U.S.A., 1985, pp.3-16.

[12] V.N. Novikov, A.P. Sokolov, Poisson's ratio and the fragility of glass-forming liquids, Nature 431 (2004) 961-963.

DOI: 10.1038/nature02947

[13] W. Götze, L. Sjögren, Relaxation processes in supercooled liquids, Rep. Prog. Phys. 55 (1992) 241-376.

[14] G. Li, W.M. Du, X.K. Chen, H.Z. Cummins, N.J. Tao, Testing mode-coupling predictions for α and β relaxation in Ca0.4 K0.6 (NO3)1.4 near the liquid-glass transition by light scattering, Phys. Rev. A 45 (1992) 3867-3879.

[15] F. Mezei, M. Russina, Intermediate range order dynamics near the glass transition, J. Phys. Condensed Matter 11(1999) A 341-A354.

DOI: 10.1088/0953-8984/11/10a/031

[16] K.L. Ngai, J. Habasaki, An alternative explanation of the change in T-dependence of the effective Debye-Waller factor at Tc or TB, J. Chem. Phys. 141(2014) 114502-(1-16).

DOI: 10.1063/1.4895554

[17] C.A. Angell, J.L. Pollard, W. Strauss, Transport in Molten Salts under Pressure. I. Glass‐Forming Nitrate Melts, J. Chem. Phys. 50(1969) 2694-2705.

DOI: 10.1063/1.1671431

[18] M.D. Ingram, C. T. Imrie, Z. Stoeva, S.J. Pas, K. Funke, H.W. Chandler, Activation Energy− Activation Volume Master Plots for Ion Transport Behavior in Polymer Electrolytes and Supercooled Molten Salts, J. Phys. Chem. B Letters 109 (2005) 16567-16570.

DOI: 10.1021/jp053400n

[19] M.D. Ingram, C.T. Imrie, J. Ledru, J.M. Hutchinson, Unified approach to ion transport and structural relaxation in amorphous polymers and glasses, J. Phys. Chem. B 112 (2008) 859-866.

DOI: 10.1021/jp0754482

[20] E. Williams, C.A. Angell, Pressure dependence of the glass transition temperature in ionic liquids and solutions. Evidence against free volume theories, J. Phys. Chem. 81 (1977) 232-237.

DOI: 10.1021/j100518a010

[21] M.D. Ingram, C.T. Imrie, New insights from variable-temperature and variable-pressure studies into coupling and decoupling processes for ion transport in polymer electrolytes and glasses, Solid State Ionics 196 (2011) 9.

DOI: 10.1016/j.ssi.2011.05.019

[22] Z. Wojnarowska, K.L. Ngai, M. Paluch, Invariance of conductivity relaxation under pressure and temperature variations at constant conductivity relaxation time in 0.4 Ca(NO3)2− 0.6 KNO3, Phys. Rev. E 90 (2014) 062315-(1-5).

DOI: 10.1103/physreve.90.062315

[23] P. Lunkenheimer, A. Pimenov, A. Loidl, Fast dynamics in CKN and CRN investigated by dielectric spectroscopy, Phys. Rev. Letters 78 (1997) 2995-2998.

DOI: 10.1103/physrevlett.78.2995

[24] J. C. Dyre, Aging of CKN: Modulus versus conductivity analysis. Phys. Rev. Letters 110 (2013) 245901-(1-4).

DOI: 10.1103/physrevlett.110.245901

[25] P. Singh, R.D. Banhatti, K. Funke, Correlation between viscosity and ion dynamics in a fragile ionic melt. Phys. Chem. Glasses 46 (2005) 241-244.

[26] K. Funke, R.D. Banhatti, Modelling frequency-dependent conductivities and permittivities in the framework of the MIGRATION concept, Solid State Ionics 169 (2004) 1-8.

DOI: 10.1016/j.ssi.2003.06.003

[27] K. Funke, R.D. Banhatti, Ionic motion in materials with disordered structures. Solid State Ionics 177 (2006) 1551-1557.

DOI: 10.1016/j.ssi.2005.12.037

[28] K. Funke, R. D. Banhatti, D. M. Laughman, L.G. Badr, M. Mutke, A. Šantić, W. Wrobel, E.M. Fellberg, C. Biermann, First and second universalities: Expeditions towards and beyond. Z. Phys. Chem. 224 (2010) 1891-1950.

DOI: 10.1524/zpch.2010.0025

[29] K. Funke, M.D. Ingram, R.D. Banhatti, P. Singh, S.J. Pas, Ionic conductivity of a fragile glass-forming molten salt: Modelling its dependence on frequency, temperature, and pressure, Z. Metallkunde 95 (2004) 921-927.

DOI: 10.1515/ijmr-2004-0170

[30] P. Singh, Fragility and the Coupled to Decoupled Transition in Supercooled Molten Calcium Potassium Nitrate Studied by Broad-Band Conductivity Spectroscopy, Ph.D. Thesis, University of Münster, Germany, (2005).

[31] R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12 (1957) 570-586.

DOI: 10.1143/jpsj.12.570

[32] T. Scopigno, G. Ruocco, F. Sette, G. Monaco, Is the fragility of a liquid embedded in the properties of its glass?, Science 302 (2003) 849-852.

DOI: 10.1126/science.1089446

[33] S. Summerfield, Universal low-frequency behaviour in the ac hopping conductivity of disordered systems, Phil. Mag. B, 52 (1985) 9-22.

DOI: 10.1080/13642818508243162

[34] A. Šantić, W. Wrobel, M. Mutke, R.D. Banhatti, K. Funke, Frequency-dependent fluidity and conductivity of an ionic liquid, Phys. Chem. Chem. Phys. 11 (2009) 5930-5934.

DOI: 10.1039/b904186a

[35] K. Funke, R.D. Banhatti, P. Grabowski, J. Nowinski, W. Wrobel, R. Dinnebier, O. Magdysyuk, Low-temperature α-AgI confined in glass: Structure and dynamics, Solid State Ionics 271 (2015) 2-9.

DOI: 10.1016/j.ssi.2014.09.033

[36] K.L. Ngai, R.W. Rendell, C. Leon, The crossover from the near constant loss to ion hopping ac conductivity in ionic conductors: the crossover times, J. Non-Cryst. Solids 307 (2001) 1039-1049.

DOI: 10.1016/s0022-3093(02)01570-3

[37] K. Funke, R.D. Banhatti, P. Singh, Conductivity dispersion in supercooled calcium potassium nitrate: caged ionic motion viewed as part of standard behaviour, Phys. Chem. Chem. Phys. 9 (2007) 5582-5590.

DOI: 10.1039/b618788a

[38] L.M. Torell, R. Aronsson, Brillouin scattering study of elastic properties in a glass forming KNO3–Ca (NO3)2 mixture, J. Chem. Phys. 78 (1983) 1121-1125.

DOI: 10.1063/1.444896

[39] D.H. Torchinsky, J.A. Johnson, K.A. Nelson, A direct test of the correlation between elastic parameters and fragility of ten glass formers and their relationship to elastic models of the glass transition, J. Chem. Phys. 130 (2009) 064502-(1-11).

DOI: 10.1063/1.3072476

[40] J.C. Dyre, T. Christensen and N.B. Olsen, Elastic models for the non-Arrhenius viscosity of glass-forming liquids, J. Non-Cryst. Solids 352 (2006) 4635-4642.

DOI: 10.1016/j.jnoncrysol.2006.02.173

[41] Z. Wojnarowska, M. Rams-Baron, J. Knapik-Kowalczuk, A. Połatyńska, M. Pochylski, J. Gapinski, A. Patkowski, P. Wlodarczyk, M. Paluch, Experimental evidence of high pressure decoupling between charge transport and structural dynamics in a protic ionic glass-former, Scientific Reports 7 (2017) 7084-(1-8).

DOI: 10.1038/s41598-017-07136-5

[42] N.S. Bagdassarov, J. Maumus, B. Poe, A.B. Slutskiy, V.K. Bulatov, Pressure dependence of Tg in silicate glasses from electrical impedance measurements, Phys. Chem. Glasses 45 (2004) 197-214.

[43] S. Mori, E. Ohtani, A. Suzuki,  Viscosity of the albite melt to 7 GPa at 2000 K, Earth and Planetary Science Letters 175 (2000) 87-92.

DOI: 10.1016/s0012-821x(99)00284-8