Mixed Mobile Ion Effect Research Articles

A cooperative model for the mixed mobile ion effect in covalent glasses

A thermodynamical model of the long–standing problem of the mixed mobile ion effect (MMIE) or the mixed alkali effect, respectively, in glasses is presented. The basic idea of the model is an internal dynamic interaction between the cations and the dynamics of the cooperative regions in glasses. Two types of cation traps due to structural disorder in the glassy network are assumed, in which the deeper traps mainly determine the glass relaxation properties and the cations with a reduced binding energy are responsible for the movement of ions. The modification of the usual diffusion coefficient of cations has been calculated under these considerations. That leads to a variation of dc-conductivity in dependence on the composition ratio, f, of the different cations introduced into a covalent network, i.e. the occurrence of the MMIE. The main result is a relation between the dc conductivity and temperature dependent relaxation time that is controlled by f. Furthermore, the conductivity properties of ion exchanged glasses can be predicted quantitatively if the exchange of ions take place either above or below the glass transition temperature.

Mixed mobile ion effect: A numerical study on the basis of a modified two-spin facilitated kinetic Ising model

A numerical simulation on the basis of a modified two-spin facilitated kinetic Ising model for the long-standing problem of the mixed mobile ion effect (or mixed alkali effect) in glasses is presented. The essential idea is an internal dynamical interaction between the cation motion and the dynamics of the cooperative regions of the glass. This interaction leads to a strong variation of the dc conductivity versus the composition ratio $f$ of the cations contained in the glass. Both the dependence on temperature and the dependence on the composition ratio can be obtained in good agreement with experimental measurements.

Ion exchange and the mixed mobile ion effect in micro-optics applications

Silver–sodium ion exchange in aluminosilicate glasses is reviewed in the context of micro-optics fabrication. The interdiffusion coefficient is more strongly concentration dependent in glasses with high non-bridging oxygen content. Radioactive tracer diffusion coefficients show unusual behavior in glasses devoid of nonbridging oxygen. The local environments of the silver and sodium ions are related to the changes in ion exchange behavior. The modified quasi-chemical (MQC) model links these structural details to the thermodynamic description of ion exchange. The MQC model accurately describes ion exchange behavior in silicate, aluminosilicate and aluminoborate glasses. Using this model, long experimental trials are no longer necessary, and fast identification of optimal glass types and process parameters results.

Low‐Temperature ac Conductivity of Mixed Mobile Ion Germanate Glasses

The conductivity of alternating current in the xAg2O: (1 ‐ x)Rb2O:4Geo2 glass series has been measured between 5.0 K and room temperature where x is varied from 0.0 to 1.0. The typical low‐temperature conductivity region is observed below 200 K. The temperature and frequency dependence of conductivity in this region can be explained by the thermal excitation of asymmetric double well potential configurations. Further, the classical mixed mobile ion effect is essentially absent, which shows that the effect is associated with the independent movement of the mobile ions.

Chemical structure and the mixed mobile ion effect in silver-for-sodium ion exchange in silicate glasses

The relationship between chemical structure and ion transport in silver-for-sodium ion exchange in the endpoints of a series of sodium aluminosilicate glasses is examined. It is shown that the non-bridging oxygen (NBO) content of the glass has a major impact on both the local environments of the mobile cations and the mixed mobile ion effect (MMIE). X-ray absorption fine structure studies of the local environments of the mobile cations are used to help formulate a structural picture of ion exchange, in which interactions between the mobile cations affect ion transport rates. Studies of the diffusion coefficient using energy dispersive microanalysis and the modified quasi-chemical (MQC) diffusion coefficient are used to obtain quantitative values for MMIE. Parameter fits of the MQC diffusion coefficient to experimentally obtained values are used to extract self-diffusion coefficients, excess interaction energies and cation-cation coordination numbers. It is found that the NBO-rich glass has the highest excess interaction energy and exhibits the greatest MMIE, consistent with the structural model.

Correlation between local structure and electrical response of Rb and (Rb,Ag) germanate glasses: dc conductivity

The relationship between ionic conductivity and local structure (interatomic distance, coordination number, structural disorder around the various cations and the fraction of non-bridging oxygen) is determined for xRb 2O · (1 - x)GeO 2 binary glasses with x = 0.01−0.20, and 0.2(Ag,Rb) 2O · 0.8GeO 2 mixed mobile ion glasses. The composition dependence of activation energy for dc conductivity is explained by the existence of an ‘unoccupied volume’. The cooperative ion movement model proposed for alkali silicate glasses is found inappropriate for describing ionic conduction in Rb germanate glasses, probably because elastic interactions in the latter are not duly accounted. The mixed (Rb,Ag) germanate glass series shows the classical mixed mobile ion effect in dc conductivity. The distance of the mobile cation from oxygen and the disorder around it are not important for the development of this effect.

Effective medium approach to the mixed mobile ion effect

A mathematical treatment using the effective medium approach (EMA) is applied to the mixed mobile ion (MMI) effect observed in the composition dependence of the conductivity of mixed ionic conductor glasses, by taking into consideration the pairing of unlike ions and blocking of transport paths by these pairs. In this model, the conductivity of a mixed conductor with a- and b-type mobile ions is given by σ=xσ a a D ∗ a (x) a ∗ a +(1−x)σ b b D ∗ b (x) D b ∗ b where σ a a and D a ∗ a , σ b b and D b ∗ b are, respectively, the conductivity and tracer self-diffusion coefficient in pure a- and b-glasses. D ∗ a (x) and D ∗ b (x) , tracer diffusion coefficients of a- and b-type ions, respectively, in the mixed glass, depend on the substitution rate x = a/(a + b) and are calculated using an EMA. It is proposed that the i ( i = a, b) ions can jump from a given site through z different directions in regions of ii-type, jj-type or ij-type with, respectively, the self- ( D i ∗i ), foreign-( D j ∗i ) and mixed ( D ij ∗i ) diffusion coefficients. The number of connections, z, for a given site and the diffusion coefficients in the mixed and foreign regions are used in the calculations as adjustable parameters. The model is tested with the mixed alkali glasses [ xNa 2O−(1 − x)Cs 2O]−5SiO 2. A satisfactory fitting is obtained as a function of substitution rate and temperature.