Thermal conductivity due to s-s and s-d electron interaction

Thermal conductivity due to s-s and s-d electron interaction in nickel at high electron temperatures Yu.V. Petrov, N.A. Inogamov L.D. Landau Institute for Theoretical Physics XXVII International Conference onEquations of State for MatterMarch 1-6, 2012, Elbrus, Kabardino-Balkaria, Russia

Scatterng of electrons with momentum and transferred momentum Electrons interact through the screened Coulomb interaction with a screening length

Frequency of collisions of s-electron with momentum with other electrons is a statistical factor

In the case of ss->ss scattering the statistical factor has a form This case was presented in Elbrus-2010 Physics of Extreme States of Matter – 2010, Chernogolovka, 2010, pp. 129-132. Н.А. Иногамов, Ю.В. Петров, Теплопроводность металлов с горячими электронами. ЖЭТФ, 2010, т. 137, вып. 3, 505-529.

When considering sd->sd scattering At electron temperature Fermi functions are is a bottom of s-band are the bottom and top of d-band is a chemical potentiall

Within the effective mass approximation Energy conservation In terms of variables and

and In terms of variables the collision frequency of s-electrons having the momentum with d-electrons takes a form

Frequency of sd-sd collisions as a two-dimensional integral in plane At given introduce polar and azimuthal angles of vector and Is the angle between and ) ( and the variable introduce polar and azimuthal angles of vector At given and and the variable Then , ,

-function After integration over because of the presence of

introduce function When integrating over

Because of dependence and we obtain For given p the frequency of collisionsis a two-dimensional integral in plane Because of after scattering d-electron remains in d-band with respect to the interval In dependence on position of point two cases arise

Case I. . It leads to In this case and At the same time and Because of the presence of integration over depends on the relative positions of segments and . It defines the boundary , of integration in plane and arguments in a function It gives 3 variants of this relative positions. Variant 1. or , Here ,

In this variant For example, for : limits of integration over

Analogously Variant 2 and , Variant 3 , are considered. Case II. , , In this case

integration over Because of the presence of gives a result which differs from zero in 4 variants Variant 1 , Variant 2 , Variant 3 , Variant 4 ,

Average s-d electron collision frequency When having the frequency of collisions of the s-electron with given momentum p we can obtain the thermal conductivity coefficient due to s-d electron scattering: Then we define the average s-d collision frequency by using its Drude relation with thermal conductivity coefficient , mean squared velocity of s-electrons and their heat capacity per unit volume

Thermal conductivity coefficient of Ni and Al due to electron-electron scattering

Average frequency of electron-electron collisions in Ni and Al as a function of electron temperature

Thermal conductivity due to s-s and s-d electron interaction