Conductivity of a solid

Example Suppose one wants to measure the thermal conductivity of a solid (k). To do this, one needs to measure the heat flux (q), the thickness of the... 

Making use of Eq. (25), the maximum conductivity of a solid electrolyte with monovalent mobile species is given by... 

The thermal conductivity of a solid is determined by its form and structure, as well as composition. Values for the commonly used engineering materials are given in various handbooks. 

Example Suppose one wants to measure the thermal conductivity of a solid (k). To do this, one needs to measure the heat flux (q), the thickness of the sample (d), and the temperature difference across the sample (AT). Each measurement has some error. The heat flux (q) may be the rate of electrical heat input (< ) divided by the area (A), and both quantities are measured to some tolerance. The thickness of the sample is measured with some accuracy, and the temperatures are probably measured with a thermocouple to some accuracy. These measurements are combined, however, to obtain the thermal conductivity, and it is desired to know the error in the thermal conductivity. The formula is... 

Assuming identical conductivity mechanisms, the conductivity of a solid will be greatest if the cation charge carriers are ... 

From plots such as these, we find that the activation energies lie in the range of 0.05 to 1.1 eV, which is lower than the enthalpies of defect formation. As we have seen, raising the temperature increases the number of defects, and so increases the conductivity of a solid. Better than increasing the temperature to increase conductivity is to find materials that have low activation energies, less than about 0.2 eV. We find such materials in the top right-hand corner of Figure 5.7. 

The behavior of thermal conductivity with increasing temperature is highly material dependent—some examples are depicted in Figure 8.2. The thermal conductivity of a solid at the... 

The electrical conductivity of a solid may be defined by the following relationship... 

In Solids, heal conduction is due to two effects the lattice vibrational waves induced by the vibrational motions of the molecules po.sitioned at relatively fixed positions in a periodic manner called a lattice, and the energy transported via the free flow of electrons in the solid (Fig. 1—28). The Ihermal conductivity of a solid is obtained by adding the lattice and electronic components. The relatively high thermal conductivities of pure metals arc primarily due to the electronic component. The lattice component of thermal conductivity strongly depends on the way the molecules are arranged. For example, diamond, which is a liighly ordered crystalline solid, has the highest known thermal conductivity at room temperature. 

The thermal conductivity of a solid depends upon the solid s tetuperaiure ask aT + b where a and b are constants. The temperature in a planar layer of this solid as it conduchs heal is given by... 

The thermal conductivity of a solid whose density and specific heal are known can be determined from the relation k = cf/pc after evaluating the thermal diffusiviiy or. 

Electrical techniques primarily measure the electrical impedance of a mixed-phase medium. Because the dielectric constant or electrical conductivity of a solid phase differs from that of the fluid, one can measure electrical conductance or capacitance to determine phase distribution. To attain better sensitivity, conductance flowmeters are usually applied to conducting media, such as aqueous solutions or solids/water slurries, whereas capacitive flowmeters are applied to solid/gas flows and solid/nonconducting-liquid flows. Capacitance measurements are generally more reproducible because they are not affected by the ion concentration of the solution, which is difficult to control during processing. 

Typically the total thermal conductivity of a solid, k, can be considered to be the sum of the electronic, kg and phonon, kph, contributions that is ... 

A sum rule for the imaginary part of the conductivity establishes a connection between the spectrum of 02(01) and the dc conductivity of a solid which could be measured independently using a resistance probe ... 

Why don t substances like glass conduct electricity as metals do Figure 6.32 provides an answer to this question. Basically, the electrical conductivity of a solid depends on the spacing and the state of occupancy of the energy bands. In magnesium and other metals, the valence bands are adjacent to the conduction bands, and, therefore, these metals readily act as conductors. In glass, on the other hand, the gap between the valence band and that... 

E. J. W. Verwey [1935] Electrolytic Conduction of a Solid Insulator at High Fields The Formation of the Anodic Oxide Film on Aluminium. Physica 2, 1059-1063. 

Connection of in Ak (TJ with J, the separation of the first excited level from the ground state. Figure 91 shows data on 7 ax=/( T) for a number of materials with PLnIs. It turns out that T ax —So, it is possible to exclude from the heat transfer (thermal conductivity) of a solid that or another phonon group (cf. fig. 61), and to construct a material with certain thermal properties by selection of PLnIs. 

Thermal conductivity of a solid is written according to Fourier s law in one dimension (x) as... 

Nafe, H., Low temperature ion conductivity of a solid oxide electrolyte the role of electrode polarization, in Solid State Ionics, Balkanski, M., Takahashi, T, and Tuller, H.L., Eds., North-Holland, Amsterdam, 1992, 253-258. 

The conductivity of a solid is given by Eq. (1). If we assume that, as in conventional extrinsic semiconductors, the concentration of free carrier is simply given by the density of dope, the mobility would be proportional to the conductivity, and the measurement of the conductivity would be a very simple way to have access to the mobility of an organic material. Unfortunately, this is rarely the case, and an independent measurement of the free carrier density would be most often required. As rehable determinations of the latter is generally not available, a direct measurement of the mobility is generally the necessary counterpart to conductivity measurements. 

The Fourier rate equation for conductive heat transfer is used to determine the thermal conduction of a solid support member. 

This relationship can be used to calculate the maximum ionic conductivity of a solid electrolyte. Assuming that the carrier moves at the rate v, the hopping frequency o is... 

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