Grain boundary conductivity temperature dependence

Figure 33. Temperature dependence of total and partial conductivities (a) in bulk and (b) at the grain boundary. Note that the values of the ionic conductivity at the grain boundary are approximate.134 (Reprinted from X. Guo, J. Fleig and J. Maier, Sepa-ration of Electronic and Ionic Contributions to the Grain Boundary Conductivity in Acceptor-Doped SrTiOj. J. Electrochem. Soc., 148, J50-J53. Copyright 2001 with permission from The Electrochemical Society, Inc.)...

Grain boundaries offer some impedance to sodium ion conduction (i.e., approximately a factor of five increase for polycrystalline jS -alumina at 300 C) " . They also increase the activation energy for conduction by approximate factors of 1.6-2 depending on the temperature and grain size. Sodium ion grain boundary conduction is dominant in polycrystalline 8"-alumina when the grain size is very small (< 1-2 pm) and when the temperature is below 100°C. 

As Rgb decreases rapidly with increasing temperature because of high (Ea)GB to a comparable value with Rg at 300"C (Fig. 10), the total conductivities (Rg+Rgb) are dominated by grain boundary conductivity. The grain size-dependence of c is therefore explained by the decrease in the number of poorly conductive grain boundaries with increasing grain size. 

The thermopower is essentially a bulk-sensitive property. However, in the case of polycrystalline materials, the temperature gradient across the specimen is not uniform and thermopower exhibits higher values at grain boundaries (Figure 4.13). Consequently, the thermopower is sensitive to grain boundaries. The sensitivity depends on the grain size and the bulk-to-interface thermal conductivity coefficient ratio. 

The approximation of a constant G was dropped later130 and different heat conductivities of ice and water were used to calculate the temperatures of the interface at various distances y the convection in the liquid was, however, not taken into account. Moreover, the function y =f(x) was believed to depend on the distance between two nearest grain-boundary grooves. 

In a perfect crystal, all atoms would be on their correct lattice positions in the structure. This situation can only exist at the absolute zero of temperature, 0 K. Above 0 K, defects occur in the structure. These defects may be extended defects such as dislocations. The strength of a material depends very much on the presence (or absence) of extended defects, such as dislocations and grain boundaries, but the discussion of this type of phenomenon lies very much in the realm of materials science and will not be discussed in this book. Defects can also occur at isolated atomic positions these are known as point defects, and can be due to the presence of a foreign atom at a particular site or to a vacancy where normally one would expect an atom. Point defects can have significant effects on the chemical and physical properties of the solid. The beautiful colours of many gemstones are due to impurity atoms in the crystal structure. Ionic solids are able to conduct electricity by a mechanism which is due to the movement of fo/ 5 through vacant ion sites within the lattice. (This is in contrast to the electronic conductivity that we explored in the previous chapter, which depends on the movement of electrons.)... 

The defect concentrations and their dependence on p0l and temperature are derived from the law of mass action by procedures essentially the same as those outlined in Section 2.6.2. In the case of polycrystalline high-purity alumina, the electronic conductivity increases with decreasing grain size and is attributed to hole transport along grain boundaries. 

We discuss on the microscopic structure of our samples, in reference to the result of thermal conductivity measurements. A K. Collins et al. have reported that grain size of their polycrystal line sample could be estimated from the temperature dependence of low temperature thermal conductivity [6] with peak at around 200 K. They obtained values from several to 10 p m. The grain sizes in our samples are smaller than these value from SEM observations. Although the temperature of our measurement is higher the phonon scattering on the grain and pore boundaries may still be important. 

The velocity relevant for transport is the Fermi velocity of electrons. This is typically on the order of 106 m/s for most metals and is independent of temperature [2], The mean free path can be calculated from i = iyx where x is the mean free time between collisions. At low temperature, the electron mean free path is determined mainly by scattering due to crystal imperfections such as defects, dislocations, grain boundaries, and surfaces. Electron-phonon scattering is frozen out at low temperatures. Since the defect concentration is largely temperature independent, the mean free path is a constant in this range. Therefore, the only temperature dependence in the thermal conductivity at low temperature arises from the heat capacity which varies as C T. Under these conditions, the thermal conductivity varies linearly with temperature as shown in Fig. 8.2. The value of k, though, is sample-specific since the mean free path depends on the defect density. Figure 8.2 plots the thermal conductivities of two metals. The data are the best recommended values based on a combination of experimental and theoretical studies [3],... 

The increased metallic like screening which appears to occur at lower temperature siay indeed involve the grain boundaries, for it has been shown that the grain boundaries can strongly alter the conductivity and its dependence on temperature in these supercon-... 

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.

The variations of the conductance measured under specific gases depend on many parameters such as intrinsic resistance, grain size, grain boundary barriers, and detection temperature. 

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