Wiedemann-Franz constant

Formerly these metallic properties were attributed to the presence of free electrons. The classical theory of this electron gas (Lorentz) leads, however, to absurdities for instance, a specific heat of 3/2 R had to be expected for this monatomic gas, contrary to the experience that Dulong and Petit s rule (atomic specific heat 6/2 R) holds for both conductors and non-conductors. The calculated ratio of heat conductivity to electrical conductivity (Wiedemann-Franz constant) also did not agree with observation. 

The sp-valent metals such as sodium, magnesium and aluminium constitute the simplest form of condensed matter. They are archetypal of the textbook metallic bond in which the outer shell of electrons form a gas of free particles that are only very weakly perturbed by the underlying ionic lattice. The classical free-electron gas model of Drude accounted very well for the electrical and thermal conductivities of metals, linking their ratio in the very simple form of the Wiedemann-Franz law. However, we shall now see that a proper quantum mechanical treatment is required in order to explain not only the binding properties of a free-electron gas at zero temperature but also the observed linear temperature dependence of its heat capacity. According to classical mechanics the heat capacity should be temperature-independent, taking the constant value of kB per free particle. 

Adequate predictions of thermal conductivity for pure metals can be made by means of the Wiedemann-Franz law, which states that the ratio of the thermal conductivity to the product of the electrical conductivity and the absolute temperature is a constant. High-purity aluminum and copper exhibit peaks in thermal conductivity between 20 and 50 K, but these peaks are rapidly suppressed with increased impurity levels and cold work of the metal. The aluminum alloys Inconel, Monel, and stainless steel show a steady decrease in thermal conductivity with a decrease in temperature. This behavior makes these structural materials useful in any cryogenic service that requires low thermal conductivity over an extended temperature range. 

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. 

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. 

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. 

Wiedemann-Franz law The ratio of the thermal conductivity of any pure metal to its electrical conductivity is approximately constant at a ven temperature. The law is fairly well obeyed, except at low temperatures. The law is named after Gustav Wiedemarm and Rudolph Franz, who discovered it empirically in 1853. 

The fact that the ratio of the thermal conductivity to the electrical conductivity of any metal is a constant times the absolute temperature was observed by Wiedemann and Franz and this relationship is known as the Wiedemann-Franz ratio. This relationship works because the collision time t for the electron carriers is the same in both models and cancels out when taking the ratio of the two conductivities. From Chapter 17, the classical electronic thermal conductivity was found in Equation 17.33 to be K = 4nl(fT/m n)T. The classical electrical conductivity from the Drude model is given by Equation 18.15 and the Wiede-mann-Eranz ratio becomes... 

Wiedemann-Franz law—for metals, the ratio of thermal conductivity and the product of the electrical conductivity and temperature should be a constant... 

The ratio of the thermal conductivity to the electrical conductivity times the absolute temperature is known as the Wiedemann and Franz ratio and involves only universal physical constants. Therefore, this ratio should be the same for any metal (provided that the heat is predominately carried by the electrons). This relationship depends on the fact... 

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