Ionics (2021) 27:1177–1183 ORIGINAL PAPER Effect of local environment on stretching parameter in the mixed alkali oxyfluoro vanadate glasses: electrical modulus and structural analysis Gajanan V Honnavar 1,2 Received: 12 November 2019 /Accepted: 4 December 2020 # The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract A structural and electrical modulus study on the mixed alkali glass samples having general formula (in mol%) 40V 2 O 5 - 30BaF 2 - (30 - x) LiF – xRbF, where x =0 – 30, in steps of 5 mol% is presented in this communication. Various vibrational bands were identified in the infrared spectra spanning 400–1200 cm -1 . On the basis of shift in these bands, it was inferred that the glass network undergoes a noticeable change after 50 mol% of rubidium content. The analysis of the electrical modulus data is carried out using Kohlrausch-Williams-Watts (KWW) equation which describes the relaxation behavior of the mobile species. The variation of stretching parameter β with respect to alkali element concentration is analyzed on the basis of a combined effect of alkali ion distance and molar volume. It is found that the coupling between the mobile ions is better at 50 mol% of the alkali mixture when compared with single alkali concentrations. The contributions from fast and slow types of relaxation mechanisms were determined. Keywords Electrical modulus analysis . Oxyfluoride glasses . Vanadate glasses . KWW . Stretching parameter . Interaction between mobile ions . Infrared spectrum . Mixed alkali effect Introduction Electrical transport in disordered systems like glasses and polymers is an important and active field of research [1, 2]. Glasses have been used as fast ionic conductors [3], as battery materials [4], and as transparent solar energy harvesters [5]. The ionic transport in glasses is usually studied using im- pedance spectroscopy [6]. The predominant phenomenon of relaxation, in the frequency range of few hundred hertz to few megahertz, is through molecular orientation and reorientation, and hence, these ranges of frequencies are normally used for the study of conductivity relaxation. The AC conductivity spectra can be represented in different ways like complex admittance, complex permittivity, complex impedance, and complex electrical modulus [1]. Electrical modulus representation of the AC conductivity data, originally introduced by McCrum et al. [7], but exten- sively applied to study vitreous ionic conductors by Moynihan and co-workers [8–10], has gained popularity by settling down all the issues raised against its use as an analysis tech- nique [11]. It is a convenient method for analysis of electrical properties of the materials because in this representation, elec- trode polarization effects are suppressed and electrical effects related to bulk can be easily separated [8]. The complex elec- tric modulus spectrum presents the measure of the distribution in ion energies or configuration in the structure, and it also describes the electrical relaxation and microscopic properties. The complex form of electric modulus can be written in fre- quency domain as [9]: b M ω ð Þ¼ M ∞ 1-∫ ∞ 0 exp -iωt ð Þ dΦ dt   dt   ð1Þ where Φ(t) describes the relaxation of electric field E after the application of a step in the displacement D and M ∞ is high- * Gajanan V Honnavar gajanan.honnavar@gmail.com 1 Department of Physics, College of Science, Bahir Dar University, P.O. Box 79, Bahir Dar, Ethiopia 2 On sabbatical from PES Institute of Technology, Bangalore South Campus, Near Electronic City, Hosur Road, Bangalore 560 100, India https://doi.org/10.1007/s11581-020-03872-3 / Published online: 7 January 2021