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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 electronphonon coupling are evaluated for 7
metals (Al, Au, Cu, Fe, Ni, Pt, Ta).