Kinetic coefficients of metals ablated under the action of femtosecond laser pulses.

Yu.V. Petrov*, N.A. Inogamov*, K.P. Migdal**

* Landau Institute for Theoretical Physics, Chernogolovka

** All-Russia Research Institute of Automatics (VNIIA)

DoS for nickel and its parabolic approximation

Also one constructed DoS for Al, Au, Cu, Fe, Pt, Ta using ABINIT* and Dmol³** *X. Gonze, B. Amadon, P.-M. Anglade et al., Computer Physics Communications, 2009. **http:\\www.accelrys.com\

2-parabolic DoS

• Based on simple dispersion laws

• 4 independent parameters for one metal

• Gives the electronic thermodynamic properties such as a t. Explicit separation of the s- and d-branches of 2p DoS allows to distinguish the contributions of 2 conduction bands.

• The electronic properties evaluated from 2p DoS are in good agreement with the data of DFT calculations.

f-zone for Ta

Data of Firefly* calculation** are used for the value of gap between f- and s-band

*Alex A.Granovsky, Firefly version 7.1.G, www http://classic.chem.msu.su/gran/firefly/index.html ** Andrei Mukhanov, private communication

Calculation of heat conductivity

• Solution of Boltzmann equation in time relaxation approximation leads to the expressions for frequency of collisions of electron with momentum .

• Frequencies of s-s and s-d collisions are used for calculation partial thermal conductivities.

Calculation of heat conductivity

• Thermodynamic values – from 2p partial DoS (s-branch).• Frequency of electron-ion collision – from the

experimental data* for electric resistivity (via Drude formula).

• Electron-electron collision frequencies find out from the expression in time relaxation approximation.

*G. Pottlacher, High Temperature Thermophysical Properties of 22 Pure Metals, Keiper (2010).

Heat conductivity for 5 metals

In 1T state and at room temperature heat conductivity is less than in order of magnitude ( )

Comparison with existing fitting*

*D.S.Ivanov, L.V.Zhigilei. Phys.Rev.B, 064114(2003).**N.A. Inogamov, Yu.V. Petrov. JETP, 137(3), pp. 505-529 (in Russian)

Calculation of electron-phonon coupling

• Bose-Einstein distribution for phonons

• The rate of energy exchange by Kaganov* et al formula

• Only longitudinal phonons are considered• Phonon dispersion law in Debye approach• The contributions of s- and d-band electrons in alpha are

derived* M.I Kaganov, I.M. Lifshitz, L.V. Tanatarov. JETP. 31(232), 1956

Electron-phonon coupling of Al and Au

for gold renormalized to experimental data at room T is in agreement with Lin*.

*Zh. Lin, L.V. Zhigilei, V. Celli, Phys. Rev. B 77, 075133 (2008).

Electron-phonon coupling for Fe,Ni,Ta

• Sufficient difference between alpha Fe(3d64s2) and Ni(3d84s2)

• Data for Ni compared with Lin*

*Zh. Lin, L.V. Zhigilei, V. Celli, Phys. Rev. B 77, 075133 (2008).

Conclusion

• The scheme for calculation of the electronic thermodynamic and kinetic properties for metals in 2T state.

• Electron heat conductivity and electron-phonon coupling are evaluated for 7 metals (Al, Au, Cu, Fe, Ni, Pt, Ta).