VOLUME 76, NUMBER 8 PHYSICAL REVIEW LETTERS 19 FEBRUARY 1996 Parameterless Explanation of the Non-Arrhenius Conductivity in Glassy Fast Ionic Conductors K. L. Ngai Naval Research Laboratory, Washington, DC 20375-5320 A. K. Rizos Department of Chemistry, University of Crete, Crete, Greece and FORTH, P.O. Box 1527, Heraklion 71409, Crete, Greece (Received 19 October 1995) Kincs and Martin [Phys. Rev. Lett. 76, 70 (1996)] have recently discovered a ubiquitous non- Arrhenius temperature dependence of the ionic conductivity in glassy fast ionic conductors when the conductivity exceeds the high level of 10 23 to 10 22 V 21 cm 21 . This important experimental discovery is readily explained and reproduced quantitatively by the coupling scheme without the use of any adjustable parameter. PACS numbers: 66.30.Dn, 61.43.Fs Recently Kincs and Martin (KM) [1] measured the ionic conductivity of many glassy fast ion conductors that were optimized to obtain the highest conductivity in the glassy state. At lower temperatures, the dc con- ductivity s dc has an Arrhenius temperature dependence s dc sT d › s ` exps2E s ykT d such as that in most glassy ionic conductors. However, with increasing tempera- ture as s dc increases and approaches high conductivity lOs10 22 V 21 cm 21 d, the conductivity starts to fall be- low the predicted values according to the Arrhenius for- mula and exhibits a strong non-Arrhenius temperature dependence. Quantitatively similar non-Arrhenius tem- perature dependence of s dc sT d was found in many glassy fast ionic conductors (GFICs). This has led KM to the important conclusion that the non-Arrhenius temperature dependence described above is a ubiquitous feature of all GFICs. In fact it has been seen before in Na b-alumina [2] which, although not a glass, is known to exhibit many of the characteristics of GFICs [3]. It is also seen in (AgI) 0.5 -(AgPO 4 ) 0.5 [4] and pointed out in [5]. The physi- cal meaning of the non-Arrhenius temperature dependence has been discussed [2,5,6]. Nevertheless, the importance of the work of KM lies in the clear demonstration that this effect is general and deserves a theoretical explana- tion. Currently there are several theories proposed to de- scribe the dynamics of ion transport in GFICs [7–12]. This ubiquitous non-Arrhenius behavior presents yet an- other challenge for these theories to explain. In this Letter we show one of these theories, the coupling scheme [2,3,5 – 7,13 – 16] can reproduce this non-Arrhenius temperature dependence quantitatively without the introduction of any unknown or indeterminable parameter. The coupling scheme or model was introduced a long time ago [13,14,17] and applied to the consideration of the dynamics of ions in glass [15]. It predicts the existence of a microscopic time t c , before which interactions between ions has no effect on the dynamics of an ion. The ion hopping correlation function for t , t c is then given by Cst d › expf2st yt 0 dg, t , t c , (1) where t 0 sT d › t ` expsE a ykT d (2) is the independent hopping relaxation time of an ion with attempt frequency t 21 ` over its energy barrier E a . Beyond t c , the effect of the nonintegrable (in the sense of non- linear classical mechanics) interactions between the ions sets in, slows down the relaxation rate, and modifies the correlation function to assume the Kohlrausch’s stretched exponential form, Cst d › expf2st yt s d 12n g, t . t c , (3) [16] where n, lying within the bounds 0 # n , 1, is a measure of the degree of slowing down and appropriately called the coupling parameter. The existence of the crossover time t c , the basic premise of the coupling model, has recently been confirmed by the high frequency ac conductivity measurement in a GFIC [18] and in a molten salt [19]. These measurements have located t c at 1 to 2 ps. Requirement of continuity of the correlation function at t › t c gives rise to the proven useful relation [17] t s › ft 2n c t 0 g 1ys12nd › ft 2n c t ` g 1ys12nd expf2E a ys1 2 ndkT g , (4) which have been used to explain quantitatively many experimental facts, including the isotope mass dependence of the conductivity [20] and the difference between NMR and conductivity relaxations [21,22]. From the correlation function Cst d given in two pieces by Eqs. (1) and (3), the frequency dependence of the conductivity ssvd can be obtained from the electric modulus formulation [21,22]. We formally express Cst d as Cst d › Z ` 0 gstd exps2t ytddt . (5) 1296 0031-9007y 96y 76(8) y1296(4)$06.00 © 1996 The American Physical Society