Impedance spectroscopic studies on congruent LiNbO₃single crystal

Abstract

Electrical impedance measurements on a congruent LiNbO 3 single crystal were performed as a function of both temperature and frequency. The measurements were carried out in the directions along the cand a-axes of the crystal. The temperature and frequency dependence of various dielectric properties have been studied. The result has revealed two remarkable dynamic relaxations: dielectric dipolar relaxation and ionic conductivity relaxation. The dipolar relaxation peaks were found at frequencies around 4 × 10 6 and 2 × 10 6 Hz for the c-axis and a-axis, respectively, and they were only slightly temperature dependent. The ionic conductivity relaxation was found at the lower-frequency end but it was temperature dependent. The temperature dependence of the dc electrical conductivity follows the Arrhenius law. It corresponds to the longrange ionic motion of Li + ions which are thermally activated with activation energy of 0.90 and 0.87 eV along the cand a-axis directions, respectively. The dc conductivities measured along the cand a-axes are very close to each other, and the value increases from 1.7 × 10 −6 to 1.9 × 10 −3 −1 cm −1 as the temperature is raised from 300 to 700 • C. The sample crystal becomes an ionic conductor as the temperature is raised.

Conductivity and dielectric relaxation phenomena in (NH4)2SO4 single crystal

“…The obtained n values are nearly constant 1.32 for the temperatures below 403 K. The super-linear dependence, i.e. n N 1 has also been found in many materials [18][19][20][21][22][23][24].…”

“…If the response of the crystal under an ac field contained the dipolar reorientations and long-range mobile ions, it can be shown that the frequency variation of the dielectric constant is the linear combination of two contributions ⁎(ω) D and ⁎(ω) C , where ⁎(ω) D is the dielectric constant due to the dipolar response, and ⁎(ω) C is the dielectric constant due to long range migration of charge carrier. In this case, the equivalent circuit of the sample in the circuit is then modelled as a r − C s series in parallel with R and C ∞ , where r is the resistance due to the orientation of the dipoles in the sample, C s is the static capacitance of the sample crystal due to all charge carriers at zero frequency, R is the dc resistance of long-range mobile ions, and C ∞ represents the capacitance of the sample when the ac frequency approaches infinity [24]. The real and imaginary parts of ⁎(ω) have the following form [24]:…”

Dielectric Relaxation, Ionic Conduction and Complex Impedance Studies on NaNo3 Fast Ion Conductor

“…Table 1 summarizes the fitted values of A and n at different temperatures. It can be seen from the Table 1 that n is less than one for temperatures below 543 K and greater than 1 for the temperature at and above 543 K. The latter category corresponds to long-range diffusion of ions [26][27] .The observed frequency vs. conductivity behavior is explained by using jump relaxation model [28][29], according to which an ion jumps from a site to its neighbouring vacant site at low frequencies where as dispersion region is characterized by the random hopping of mobile ions and the conductivity is correlated to the forward-backward hopping of the ions leading to the long-range diffusion of ions at high frequency end [30][31]. The increase in ac conductivity could be attributed to the lowering of the activation barrier at higher frequencies as compared to that at lower frequencies [32].…”

AC and DC electrical conductivity in natural rubber/nanofibrillated cellulose nanocomposites

“…where σ(ω) is the measured AC conductivity, σ DC is the frequency independent DC limit of conductivity at ω = 0, A is the temperature dependent constant reflecting the polarizability, ω is the angular frequency and s(T) is the frequency exponent representing the degree of interaction between mobile ions and the surrounding environment [47]. The values of s (T) for an ideal Debye dielectric dipolar-type and ideal ionic-type crystal are 1 and 0, respectively.…”