Resistance of grain boundary

Figure 2. Example of the impedance spectrum of a Ag/electrolyte/Ag cell at 350 °C. Separation of the resistance of the electrolyte bulk R uih resistance of grain boundaries Rgi, and polarization resistance of the electrodes R j is shown...

Fig. 2 presents typical hodograph curves of the cell impedance. The impedance spectroscopy measurements allowed separating contributions from electrode processes (Ri ), resistance of the grain bulk (Rbuik), and resistance of grain boundaries (Rgb) in a polycrystal. The experimental data were processed using a program [2,3], which was written by Bernard Boukamp. 

When the temperature increased, it was impossible to reliably separate the resistance of the electrolyte bulk Rbuik and the resistance of grain boundaries Rgb in the total resistance of the electrolyte. Flowever, reliability of separation of the electrolyte resistance and the polarization resistance of the electrodes R, was beyond doubt. 

Fig. 4 presents temperature dependences of the total specific resistance of some electrolytes based on cerium oxide. It is seen that the total electroconductivity of the ceramic under study is comparable with best conductivity values, which were obtained earlier for fiat samples prepared by magnetic pulse compaction (curves 6-7 in Fig. 4). Only the ceramic of the formula CeioGd, which was synthesized by Steele, had better characteristics (3, Fig. 4). His ceramic usually had a negligibly small resistance of grain boundaries.

Rt) = Ohmic reisistance of bulk species Rgb - Ohmic resistance of grain boundary Re = Kinetic resistance of the electrode C = Capacitance... 

Oo - approximate yield strength of monocrystal, for A1 amount to 11,1 MPa, k - material constant characterizing the resistance of grain boundaries for the movement of dislocations in the initial stage of plastic deformation (strength of grain boundaries), for A1 amount to 0,05 MN m"3/2, d - grain size, mm. 

From polarization curves the protectiveness of a passive film in a certain environment can be estimated from the passive current density in figure C2.8.4 which reflects the layer s resistance to ion transport tlirough the film, and chemical dissolution of the film. It is clear that a variety of factors can influence ion transport tlirough the film, such as the film s chemical composition, stmcture, number of grain boundaries and the extent of flaws and pores. The protectiveness and stability of passive films has, for instance, been based on percolation arguments [67, 681, stmctural arguments [69], ion/defect mobility [56, 57] and charge distribution [70, 71]. 

On top of this alloy development, turbine blades for the past two decades have been routinely made from single crystals of predetermined orientation the absence of grain boundaries greatly enhances creep resistance. Metallic monocrystals have come a long way since the early research-centred uses described in Section 4.2.1. 

The resistivity of the films increased from 10 O-cm for very low Cd content to a maximum of ca. 10 U-cm at 6% Cd and then slowly dropped again with increasing Cd. This maximum correlates with the minimum crystal size, suggesting a dominant role of grain boundaries in the conduction mechanism. The spectral response of the photoconductivity blue-shifted with increase Cd content up to a peak response at 1.35 p,m for 8.4% Cd. 

The PTC effect is seen to have its origins in the resistance of the grain boundary region which increases exponentially with temperature above the ferroelectric-paraelectric transition temperature. It therefore depends on the number of grain boundaries per unit volume of ceramic, i.e. on the microstructure, and of course on the acceptor and donor state densities Ns and n. 

A quantitative interpretation of grain boundary contributions to the overall impedance of polycrystals with highly resistive grain boundaries can be problematic (see... 

A quantitative analysis of grain boundary impedances measured with macroscopic electrodes can be rather problematic if grain boundary properties vary from boundary to boundary (cf. Sec. 3.2). Hence, additional information on the distribution of grain boundary resistivities is often desired. Microelectrode measurements can yield such additional information (Sec. 4.2) and below a microcontact impedance spectroscopic study of grain boundaries in a polycrystal is exemplarily presented. The material of choice is again SrTiCE (0.2 mol % Fe-doped), which represents a model material for the technologically highly important class of perovskite-type titanates (see also above). 

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