Wiedemann Franz law

Classical Free-Electron Theory, Classical free-electron theory assumes the valence electrons to be virtually free everywhere in the metal. The periodic lattice field of the positively charged ions is evened out into a uniform potential inside the metal. The major assumptions of this model are that (1) an electron can pass from one atom to another, and (2) in the absence of an electric field, electrons move randomly in all directions and their movements obey the laws of classical mechanics and the kinetic theory of gases. In an electric field, electrons drift toward the positive direction of the field, producing an electric current in the metal. The two main successes of classical free-electron theory are that (1) it provides an explanation of the high electronic and thermal conductivities of metals in terms of the ease with which the free electrons could move, and (2) it provides an explanation of the Wiedemann-Franz law, which states that at a given temperature T, the ratio of the electrical (cr) to the thermal (k) conductivities should be the same for all metals, in near agreement with experiment ... 

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. 

Usually, the electronic thermal conductance re can be calculated from the Wiedemann - Franz law, re TG/e2. However, as shown in Ref. [8, 9] for the ballistic limit f > d, this law gives a wrong result for Andreev wires if one uses an expression for G obtained for a wire surrounded by an insulator. Andreev processes strongly suppress the single electron transport for all quasiparticle trajectories except for those which have momenta almost parallel to the wire thus avoiding Andreev reflection at the walls. The resulting expression for the thermal conductance... 

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. 

Another ansatz used in the literature (Wtosewicz et al., 1979) assumes that the Wiedemann-Franz law holds for the total electrical resistivity... 

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 thermal conductivity (k) comprises electrical component (k ) and lattice component (Kj), k = -e Kj. The is related to the electrical conductivity through the Wiedemann-Franz law. That is... 

Returning to diamonds, the high thermal conductivity of diamonds is certairrly mysterious. In physics, a rale called the Wiedemann-Franz law states that the electric conductivity of a substance is proportiorral to the thermal conductivity. Briefly put, this law says that good thermal condrrctors are good electrical conductors attire same time. Strictly speaking, this is orrly true for metals. The best coimteiexarrrple... 

Ke(r) is generally estimated firom the temperature-dependent electrical resistivity using the Wiedemann-Franz law... 

Fig. 46. The temperature dependence of k in polycrystal-line CeCu2.02Si1.98 (Spam et al. 1985). The solid line gives Ke calculated using the Wiedemann-Franz law with L = Lo. The dotted line gives the experimental result at H — 0, points the experiment result at H = 2.5 T.

LaS and PrS are metals. For them = Kl-I-Ke> where is calculated from the Wiedemann-Franz law, and the Lorentz number is determined by eq. (4) (Oskotski and Smirnov 1972, Smirnov and Tamarchenko 1977, Wilson 1965). The influence of... 

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