Wiedemann-Franz-Lorenz

Estimated from electrical resistivity according to Wiedemann-Franz-Lorenz law b Arithmetic average of properties of alloy elements based on mole fractions c Properties of Ni... 

Use the modihed Wiedemann-Franz-Lorenz law to estimate the phonon contribution to the thermal conductivity of a semiconductor at 298 K whose total thermal conductivity is 2.2 W m if the electrical conductivity is 0.4 x 10 S m ... 

As Peierls obtains a law for the electrical resistance in the limiting case, he concludes that the ratio of the electrical and thermal resistances does not decrease proportionally to T, but to 7, or in other words at low temperatures the Wiedemann-Franz-Lorenz quantity pjTw should not be constant, but should decrease proportionally to 7. 

The Wiedemann-Franz-Lorenz Law and the Linear Law connecting Thermal Resistance, Electrical Resistance, and Temperature... 

Experimentally it was found that at constant temperature the increase in the thermal resistance caused by deformation or formation of mixed crystals static disturbances of the lattice) is to a remarkable degree of accuracy proportional to the increase of the electrical resistance divided by the absolute temperature. If we compare the above formula with the Wiedemann-Franz-Lorenz law for pure metals,... 

There is a close relationship between electrical and thermal conductivity. From the simple jBree-electron model for metals, the ratio of the thermal conductivity and the electrical conductivity (reciprocal of resistivity) for metals is directly proportional to the temperature. This is called the Wiedemann-Franz-Lorenz (WFL) relation and the constant of proportionality yields the theoretical (Sommerfeld) Lorenz number, L = 7 l3- kjef = 2.45 x lO" W ft K [67], which was predicted to be independent of temperature (for temperatures significantly larger than the Debye temperature) and of the material. Assuming a known uid/or constant value of Z, the WFL relation can be used to obtain the thermal conductivity from pulse-heating data. 

In solid materials that are not significantly electrically conductive, molecular vibrations known as phonons are the means of heat conduction. In metals that have free electrons available to conduct electric current, these same electrons provide another means of heat conduction. The electrical conductivity and electronic component of thermal conductivity are related by the Wiedemann-Franz-Lorenz ratio L, as shown in Eq. (1.10) ... 

As described above, quantum restrictions limit tire contribution of tire free electrons in metals to the heat capacity to a vety small effect. These same electrons dominate the thermal conduction of metals acting as efficient energy transfer media in metallic materials. The contribution of free electrons to thermal transport is very closely related to their role in the transport of electric current tlrrough a metal, and this major effect is described through the Wiedemann-Franz ratio which, in the Lorenz modification, states that... 

Figure 7. The Wiedemann-Franz ratio for solutions of lithium in ammonia at —33° C. The Lorenz number is 2.45 X 10 8 watt it/deg.2...

The thermal conductivities of U-ZrHi6o and U-ZrHi 90 by electronic conduction (/Le), plotted as (A, ) in Figs. 5 (a) and (b), were estimated from the relations of Zc=Tco7 , according to the Wiedemann-Franz rule. <7 is the electrical conductivity (a Mp), where p is the electrical resistivity, Le is the Lorenz number for the electronic conduction, assumed as fJ(p(n2/ i)(kH/e)2 A 2.45x 10 s [WO/K2], where kB and e are the Boltzmann constant and elementary electric charge. 

Estimate for thermal conductivity based on the Wiedemann-Franz relation with the Lorenz number, L Estimated thermal diftusivity based on the thermal conductivity or the electrical resistivity... 

Total thermal conductivity is a sum of the lattice and electronic parts, K = Ki + Ke- The lattice part of the thermal conductivity describes the scattering of phonons on the vibrations of atoms, whereas the electronic part describes thermal conductivity appearing due to conduction electrons and is related to the electrical conductivity Wiedemann-Franz equation, = a T Lo, where T is the absolute temperature and Lq is the ideal Lorenz number, 2.45 X 10 Wf2K [64]. The electronic part of the thermal conductivity is typically low for low-gap semiconductors. For the tin-based cationic clathrates it was calculated to contribute less than 1% to the total thermal conductivity. The lattice part of the thermal conductivity can be estimated based on the Debye equation /Cl = 1 /3(CvAvj), where C is the volumetric heat capacity, X is the mean free path of phonons and is the velocity of sound [64]. The latter is related to the Debye characteristic temperature 6 as Vs = [67t (7V/F)] . Extracting the... 

The fact that the thermal conductivity in a pure metal is dominated by the free electron contribution was Ulustrated in 1853 by Gustav Wiedemann (1826-1899) and Rudolf Franz (1827-1902), who showed that Xei and the electrical conductivity, (Tei, are proportionally related (Wiedemann and Franz, 1853). A few years later Danish physicist Ludvig Lorenz (1829-1891) realized that this ratio scaled hnearly with the... 

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