Frequency dependent conductivity and dielectric studies on RbSn 2 F 5 M.M. Ahmad * ,1 , K. Yamada, T. Okuda Department of Chemistry, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan Received 7 June 2002; received in revised form 25 June 2002; accepted 25 June 2002 by P. Wachter Abstract The ac electrical data of RbSn 2 F 5 are analyzed in the s p ð f Þ; M p ð f Þ and 1 p ð f Þ formalisms. The ac conductivity exhibited a power law behavior with the presence of low frequency dispersion at high temperatures. The conductivity relaxation time is determined from the maximum of the peaks of the modulus formalism associated with an activation energy of 0.56 eV, which agrees well with the dc conductivity activation energy, DE s ¼ 0:55 eV; suggesting a hopping mechanism for the ionic conduction. A huge increase of the dielectric permittivity is observed at low frequency due to space charge polarization. The dielectric relaxation phenomena were detected from the peaks of the frequency dependence of the dissipation factor, tan d. The activation energy and the relaxation time of the dielectric relaxation have been determined. q 2002 Elsevier Science Ltd. All rights reserved. PACS: 66.30.D; 77.22.G Keywords: Conductivity relaxation; Dielectric permittivity; Dielectric loss; RbSn 2 F 5 1. Introduction The electrical relaxation measurement is the most commonly used experimental technique to characterize the dynamics of diffusing ions in glasses, melts and crystals. It gives us the complex permittivity, 1 p ð f Þ¼ 1 0 ð f Þ 2 j1 00 ð f Þ; and complex conductivity, s p ð f Þ¼ s 0 ð f Þþ js 00 ð f Þ¼ 1=Z p ð f Þ; related to 1 p ð f Þ by the relation s p ð f Þ¼ jv1 0 1 p ð f Þ; ð1Þ where f is the frequency, 4 the angular frequency and 1 0 is the permittivity of free space. The complex electric modulus M p ð f Þ is related to 1 p ð f Þ and s p ð f Þ by M p ð f Þ¼ jvC 0 Z p ð f Þ¼ 1=1 p ð f Þ: ð2Þ Thus, 1 p ð f Þ; s p ð f Þ and M p ð f Þ are alternatives and interchangeable representations of the same dielectric relaxation data. Typically, the bulk ac conductivity, s 0 , of an ionic conductor exhibits a frequency independence at low frequencies, a low frequency plateau, identified with the true dc ionic conductivity, s(0), and at high frequencies an additional term increasing in a power law fashion such that s 0 ð f Þ¼ sð0Þþ Av s ; ð3Þ in which A is a constant and s is the power law exponent. In most cases, s is found to be between 0.6 and 1 for ion conducting materials [1]. In addition, ionic conductors exhibit a characteristic enhancement of the dielectric permittivity and a corresponding dielectric loss peak. The earlier experimental observations appear to be universal for solid ionic conductors. Accordingly, a detailed analysis of the frequency and tem- perature dependence of the ac conductivity and permittivity is necessary in order to characterize the microscopic mechan- isms and the accompanied relaxation phenomena of the charge carrier transport. RbSn 2 F 5 belongs to the MSn 2 F 5 -type compounds that are found in the MF–SnF 2 pseudo-binary system, where M is a monovalent cation. RbSn 2 F 5 has attracted considerable interest due to its high fluoride ion conductivity, 0038-1098/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S0038-1098(02)00300-9 Solid State Communications 123 (2002) 185–189 www.elsevier.com/locate/ssc 1 On leave from: Department of Physics, Faculty of Education, Assiut University, The New Valley, Egypt. * Corresponding author. Tel.: þ81-824-24-7419; fax: þ 81-824- 24-0727. E-mail address: mmahmad@sci.hiroshima-u.ac.jp (M.M. Ahmad).