Origin of Constant Loss in Ionic Conductors

Abstract

We have analyzed the constant loss contribution to the ac conductivity in the frequency range 10 Hz -1 MHz and temperatures down to 8 K, for two Li ionic conductors, one crystalline (Li 0.18 La 0.61 TiO 3 ) and the other glassy (61SiO 2 ? 35Li 2 O ? 3Al 2 O 3 ? P 2 O 5 ). As temperature is increased a crossover is observed from a nearly constant loss to a fractional power law frequency dependence of the ac conductivity. At any fixed frequency v, this crossover occurs at a temperature T such that v ഠ n 0 exp͑2E m ͞k B T͒, where n 0 is the attempt frequency and E m is identified with the barrier for Li 1 ions to leave their wells. DOI: 10.1103/PhysRevLett.86.1279 Much effort has been devoted during the last few decades to understand the dynamics of ionic transport in ionically conducting materials. In spite of the advances made, there is still no general agreement on interpretation of the experimental data [1][2][3][4][5][6][7][8][9][10][11]. Most research activity in this field has focused on the origin and properties of the long-range ion motion, and electrical relaxation is the most commonly used experimental tool to access the ion dynamics. The frequency dependence of the ionic conductivity can be usually well described by using Jonscher's expression [12]where s 0 is the dc conductivity, v p is a characteristic relaxation frequency, and n is a fractional exponent. Both s 0 and v p are thermally activated with about the same activation energy, indicating that the dispersive conductivity, s ‫ء‬ ͑v͒, originates from migration of ions. However, there is another ubiquitous contribution to dispersive conductivity that has received much less attention so far. This contribution consists of a nearly frequency independent dielectric loss,´0 0 ͑v͒ ഠ A, which corresponds to an almost linear frequency dependent term of the form s 0 ͑v͒ v´0 0 ͑v͒ ഠ Av in the real part of the complex conductivity. At sufficiently low temperature or high frequencies, the Av term dominates over the power law dependence of exponent n. The existence of this nearly constant loss (NCL) was suggested more than 20 years ago and subsequently verified [13,14]. Since then, few investigations of its properties have been made [15][16][17] and low temperature data with its dominant contribution are still scarce.Although, ultimately, mobile ions seem to be responsible also for the NCL, the experimental facts including its dependence on temperature and the effect of mixed alkalis point to a different origin than ionic hopping [18]. Experimentally, A is not thermally activated and has temperature dependence much milder than s 0 or v p [18][19][20]. Partial replacement by alkali ions of a different kind has the effect of reducing the NCL [3,18,21,22], but the reduction in A is much smaller than the decrease in s 0 due to the well-known mixed alkali effect [3]. From these facts, it has been very recently proposed [18] that local vibrational relaxation reflected in the mean-square displacement of ions could be the origin of the constant loss in ionic conductors...

Electrical properties of bulk and nano Li2TiO3 ceramics: A comparative study

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Electrical conduction and thermodynamic properties of K2NiP2O7

“…where σ dc is the dc conductivity, A is thermally activated, B involves only small temperature dependence, and s is an exponent function of temperature and frequency and is related to the degree of correlation among moving ions [25]. Two terms of the previous equation are denoted as, namely, universal dielectric response (UDR), in general, universal dynamic response, and nearly constant loss (NCL), respectively.…”

“…9 Temperature dependence of σ dc versus 1000/T potential energy minimum [24]. UDR and NCL terms are further categorized to occur in the high-temperature/low-frequency and the low-temperature/high-frequency regimes, respectively [25]. The crossover frequency from dc to the dispersive region of the ac conductivity is known as hopping frequency, ω h , and it can be calculated directly from ac conductivity data using the formula [26] …”

Crossover from a nearly constant loss to a superlinear power-law behavior in Mn-doped Bi(Mg1/2Ti1/2)O3–PbTiO3 ferroelectrics

“…The exponent n = 1 implies a negligible frequency dependence of the imaginary part of dielectric permittivity through the relation Љ͑ ͒ = Ј͑f͒ / 2 f. Nowick et al 3 named this behavior as the "nearly constant loss" ͑NCL͒. According to existing investigations on ionic conductors, [3][4][5][6] polymers, 7 polaronic conductors, and amorphous semiconductors, 8,9 the NCL response appears to be a universal feature in highly disordered materials. Up to now, however, interpretations of the NCL behavior remain speculative.…”

“…This type of behavior has been called the "universal dielectric response" ͑UDR͒ by Jonscher et al 1,2 At relatively low temperatures or high frequencies, a different power-law behavior has been found valid for a diverse range of materials [3][4][5][6][7] ͑2 f͒ = B͑2 f͒ n , ͑2͒…”