(Warm Dense Matter) .. 15 2014 .. - PowerPoint PPT Presentation

ИНСТИТУТ ФИЗИКИ ВЫСОКИХ ДАВЛЕНИЙ им. Л.Ф.ВЕРЕЩАГИНА Российской Академии Наук XIII Конференция (Школа) молодых ученых ПРОБЛЕМЫ ФИЗИКИ ТВЕРДОГО ТЕЛА И ВЫСОКИХ ДАВЛЕНИЙ пансионат МГУ "Буревестник" (Сочи, Вишневка) Диэлектрические свойства разогретого плотного вещества (Warm Dense Matter) Саитов И.М. 15 сентября 2014

Саитов И.М. Диэлектрические свойства разогретого плотного вещества ( Warm Dense Matter)  2 2       4 1 e    2                   (2) lim 2 w f f       , , , , , , 2 k i k q j k i k e q j k i k q j k   0 q q , , i j k         (2) 2          (1) 1 P d          2 2 i 0       (1) (2) i Dielectric function DFT Kohn- Plasma frequency Reflectivity Conductivity Sham Effective free Absorbtion …… electron density Trasmission Electronic density of states

Outline 1.Calculation method. 2.Reflectivity. 3.Plasma frequency. 4.Conclusions.

1. Calculation method

Dielectric       (1) (2) i function Longitudinal expression for the imaginary part of dielectric function:  2 2     1 4 1 e               (2) lim 2 w f f     , , 2 k i k q j k  3 0 q q  , , , i j k   2             , , , , i k e q j k i k q j k    2 1 x      exp   x   2   2 2

Longitudinal expression  2 2     4 1 e              (2) lim 2 w f f     2 k i , k q j , k  q 0 q , , i j k   2             , , , , i k e q j k i k q j k          | | | 2 k u i u         n k n k q n k n k lim E E   n k q n k q m E E q 0  n k n k Kubo-Greenwood formula (transverse expression)  2 2 2   4   e            (2) 2 w f E f E     , , k i k j k 2 2 m i j , , k   2         | | E E , , , , i k j k i k j k M. Gajdoš , K. Hummer, G. Kresse, J. Furthm ű ller, F. Bechstedt, Phys. Rev. B 73 , 045112 (2006).

Kramers-Kronig transformation for the imaginary part of the dielectric function:         (2) 2          (1) 1 P d      2     2 i 0 The convergence in the upper limit of the integral is checked Density functional theory is used for calculation of ψ and E Т ~ 2.7 эВ for shocked xenon

  2                        *   r r r r r  n  f d V n d i i i ext   2 m i      2 n r n r e              d d r r E n r TS n r       xc 2 r r         2     E T  , r r n f i j ij i i i i   2                       V r V r V r r E r ext H xc i i i  2  m         E n r 2   n r e       xc V r V d r      H xc 2 r r n r G    max 2 2    G    i k G r  r C e max E n k k G n cut 2 m G

Pseudopotentional approach in DFT 46e – « core » 54 2 2 6 2 6 10 2 6 10 2 6 131 : 1 2 2 3 3 3 4 4 4 5 5 Xe s s p s p d s p d s p 8e - valent

Reflectivity and conductivity 2 2 2 2                             1 2 1 1 2 1 2          R 2 2 2 2                             1 2 1 1 2 1 2                 (2) (1)     1 (1) (2) 0 0

2. Reflectivity

Challenge R 1,0 Collisionless plasma   1064 nm Drude model [2] 0,4 Experiment [1] 0,2  г см 3 , / 0,0 1 2 3 4 [1] V.B. Mintsev, Yu.B. Zaporogets, Contrib. Plasma Phys. 29 , 493 (1989). [2] H. Reinholz, G. Röpke , A. Wierling, V. Mintsev, and V. Gryaznov, Contrib. Plasma Phys. 43 , 3 (2003)

Calculation parameters   1064 nm ρ , 𝑕/𝑑𝑛 3 T, 𝐿 0.51 30050 0.97 29570 1.46 30260 1.98 29810 2.7 29250 3.84 28810

Dependence of reflectivity on density R 1,0 Collisionless plasma   1064 nm Drude model [2] 0,4 DFT this work DFT [3] 0,2 Experiment [1] DFT with band gap corrections[3]  г см 3 , / 0,0 1 2 3 4 [1] V.B. Mintsev, Yu.B. Zaporogets, Contrib. Plasma Phys. 29 , 493 (1989). [2] H. Reinholz, G. Röpke , A. Wierling, V. Mintsev, V. Gryaznov, Contrib. Plasma Phys. 43 , 3 (2003) [3] M.P. Desjarlais, Contrib. Plasma Phys. 45 , 300 (2005).

3. Plasma frequency

Dependence of static conductivity of shocked xenon on density 20 experiment 4 Om -1 m -1  10 H.Reinholz, G.R ö pke, A.Wierling, V.Mintsev, V.Gryaznov // 15 Contrib. Plasma Phys., V.43, pp. 3 – 10 (2003) 10 DFT/QMD this work 5 3  g/cm 0 0 1 2 3 4

Method I. Conductivity of shocked xenon at density ρ = 𝟑. 𝟖𝐡/𝒅𝒏 𝟒 50 4 Om -1 m -1  10      (1) 40    0 30    2 2 1 DFT    2 20   0 p   2 2 1 10 Drude 0 0 10 20 30  eV

Method II. Sum rule. 1 Xe, 3eV S(  max )             2 2 3  , g/cm d p 2 0.53 0 S 1.1 1 1.6 0,1  2.2   2 max m              2 0 S d 2.8  max 2 N e e 0 3.4    max , eV      2 2 / N e m S 0 1 p e 1 10  2 2       1 4 1 e    2                    (2) lim 2 w f f       , , , , , , 2 k i k q j k i k e q j k i k q j k   3 0 q q  , , , i j k

Method III. Consideration of electrons with energies (E > E f ) as free particles      2 2 / n e m 0 p e

Dependence of plasma frequency in xenon on density 7 Method I Method II 6 Method III Mintsev et al 5  p  eV 4 3 2  , g /cm 3 1 1 2 3 4

Effective free electron density -3 n e , сm Method I Method II Method III Mintsev et al 22 10  , g / cm 3 21 10 0 1 2 3 4

Dependence of plasma frequency on density for H 10  , p eV 1  3 0,1 , / g cm 0,65 0,7 0,75 0,8 0,85 0,9 0,95

Dependence of plasma frequency on density for Se 7  , p eV 6 5  3 , / 4 g cm 4 5 6

Conclusions 1 S(  max ) Method of estimation of 3  , g/cm 0.53 plasma frequency and 1.1 1.6 effective free electron 0,1 2.2 number density is proposed, 2.8 3.4 based on using sum rule.  max , eV DFT is applied. 1 10 7  p  eV The dependence of plasma 6 frequency on density is 5 obtained for 4 warm dense Xe and H 2 3 and liquid Se. 2  , g /cm 3 1 1 2 3 4

Convergence (summary) in number of k-points in the Brillouin zone in number of particles in the supercell in frequency range in number of ionic configurations Relative error is ~ 5% - 30% depending on density

Dependence of reflectivity of shocked xenon on density   1064 nm DFT/QMD 0,5 M.P. Desjarlais, Contrib. Plasma Phys. 45 , 300 (2005) DFT/QMD 0,4 this work Reflectivity with transverse expression 0,3 DFT/QMD this work with longitudinal expression 0,2 experiment V.B. Mintsev, Yu.B. Zaporogets, 0,1 Contrib. Plasma Phys. 29 , 493 (1989). 0,0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0  ,g/cm 3

Dependence of reflectivity of shocked xenon on density   694 nm 0,5 DFT/QMD this work 0,4 experiment Yu. B. Zaporoghets, Reflectivity V. B. Mintsev, V. K. Gryaznov, 0,3 V. E. Fortov , Physics of extreme state of matter, P.188 (2002). 0,2 0,1 0,0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5  ,g/cm 3