April 23, 2021

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Broad-band Conductivity Spectroscopy

  Funke specializes in the theoretical treatment of ion dynamics in disordered materials. He is the Director of the Sonderforschungsbereich SFB 458 “Ionic Motion in Materials with Disordered Structures.” This research center, sponsored by the German Science Foundation, is one of the leading research centers in the world in this field. By collaborating with this research group, our MWN will be able to use their experience and progress in understanding the details of ionic motion in binary glasses and this will provide an excellent foundation for this project that will examine ternary MGF glasses.

     Broad-band conductivity spectroscopy is a powerful tool to obtain time-resolved information on the dynamics of mobile ions in disordered materials. At the SFB 458 Munster, we determine complex conductivities of such materials at frequencies ranging from 10-4 Hz to 1014 Hz, reflecting the ion dynamics over eighteen decades. In particular, the elementary steps of non-vibrational, thermally activated ionic motion as well as the non-trivial short-time correlations between the movements of different ions and between successive displacements of individual ions can be detected by measuring conductivities below ~1012 Hz in a continuous fashion.

         This requires very-far-infrared FT spectroscopy and sets of waveguide systems and vectorial network analyzers for swept measurements in several millimeter wave, microwave and radio-frequency bands. Frequency-dependent complex transmission and reflection factors are transformed into spectra of the complex conductivity. Our expertise in the field of broad-band centimeter, millimeter and sub-millimeter wave conductivity measurements is based on thirty-eight years of experience, and we are presently very well equipped for such measurements.

         In ion-conducting glasses, complete high-frequency conductivity data allow the removal of the frequency-squared low-frequency flank of the vibrational component from the conductivity to expose the thermally activated high-frequency plateau of that part of the conductivity that is caused by the hopping motion of the ions. In a conductivity spectrum, the high-frequency plateau is of particular importance for understanding the ion dynamics since it reflects all the ionic hopping processes in the system. Here, the experimental time window is so short that another hop of an ion (normally in the opposite direction) would not fit in. The frequency dependence of the non-vibrational ionic conductivity typically observed below1011 Hz reveals additional information. Two distinct local scenarios have been detected and in most glasses both of them are present simultaneously. The local scenario depends on the connectivity of the target site. In case (i), the target site belongs to an interconnected system of passageways along which mobile ions may diffuse translationally throughout the sample. In case (ii), the target site does not have this connectivity and the surrounding glassy network confines the ion to a localized structural pocket consisting of only very few sites. Of course, hopping processes within such pockets will not contribute to translational diffusion. Complete conductivity spectra of glassy electrolytes normally consist of the three components corresponding to scenarios (i) and (ii) and to vibrations, all three of them being collective and cooperative in character. Proper analysis of a given conductivity spectrum yields components (i) and (ii), plus the vibrational contribution, which governs the spectrum in the infrared.

          In the last few years, we have developed a physical model, called the MIGRATION concept, which can reproduce those conductivity components that correspond to scenario (i). This is achieved by tracing them back to their physical origin, the acronym providing an explanation in terms of the essential phenomena involved: MIsmatch Generated Relaxation for the Accommodation and Transport of IONs. The central function is the normalized time derivative of the mean square displacement, W(t), which is one at time zero and W(Â¥) = sDC/sHF in the limit of long times, with sDC and sHF denoting the DC and the high-frequency conductivity, respectively. According to linear response theory, the complex conductivity at angular frequency w , s*(w), is then sHF times the complex FT of the time derivative of W(t). In scenario (ii), each of the ions moving locally within a structural pocket may be regarded as a fluctuating dipole. Describing an assembly of localized fluctuating dipoles that interact with each other, we only need to modify one equation of the MIGRATION concept by adding a Debye-type rate. The resulting conductivity spectrum deviates from the Debye shape by displaying an additional s(w) µ w regime between the w2-regime at low frequencies and the constant-conductivity regime at high frequencies. As s(w) µ w implies e”(w) = const., i.e., a constant loss function, this feature has come to be known as NCL (nearly constant loss) behavior.

         Taking conductivity spectra over wide frequency ranges and using our physical models to describe scenarios (i) and (ii), we are now in a position to study ion-conducting glasses of any composition with regard to the dynamics of their mobile ions. In particular, we wish to contribute to the present MWN by detecting, describing, and understanding the variations in the dynamics of the mobile ions as one glass former is gradually substituted by another, thus forming a ternary system. Specific questions to be answered are:  (i) How does the strictly localized motion of the ions vary with network composition? Are more local “pockets” created? Are the elementary frequencies and activation energies of these processes influenced by the compositional variation?  (ii) How does the (potentially) translational hopping motion of ions along conduction pathways vary with network composition? Here, we are not only interested in variations of the elementary hopping rates and their activation energies, but also in variations of the energies required for the rearrangement of the neighborhood.

   The results of this study will be complementary to those of the structural investigations of XRD (CMU), ND (Chalmers) and NMR (Munster). It will be important to see how variations of the dynamic features are explained in terms of variations of the structural properties. It is also important to know how the dynamic information from this study will compare with the dynamic information obtained from computer simulations (Ilmenau). Computer simulations provide information that is not available from conductivity spectroscopy, such as the detailed character of dynamic heterogeneities, whereas measurements of frequency-dependent complex conductivities (Munster, ISU) are indeed irreplaceable and will always remain the basis to judge the validity of models and simulations. Likewise, tracer diffusion data (Cornell) also provide irreplaceable pieces of information which, together with sDC, yield the Haven ratios. The latter will be used to provide a realistic assessment of multi-particle phenomena like “ions moving in a row”. Last but not least, the MGF glasses must be systematically synthesized. It is most important that the different groups in the network use glasses from the same batches. Therefore, we all rely on the preparation of ternary MGF glasses by the ISU group. Munster will support one post-doctoral research fellow to carry out their conductivity research.