• Matter and Radiation at Extremes
  • Vol. 6, Issue 2, 026901 (2021)
Yong Hou1、a), Yang Jin1, Ping Zhang1, Dongdong Kang1, Cheng Gao1, Ronald Redmer2, and Jianmin Yuan1、3
Author Affiliations
  • 1Department of Physics, College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, People’s Republic of China
  • 2Institute of Physics, University of Rostock, A.-Einstein-Strasse 23–24, D-18059 Rostock, Germany
  • 3Graduate School, China Academy of Engineering Physics, Beijing 100193, People’s Republic of China
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    DOI: 10.1063/5.0024409 Cite this Article
    Yong Hou, Yang Jin, Ping Zhang, Dongdong Kang, Cheng Gao, Ronald Redmer, Jianmin Yuan. Ionic self-diffusion coefficient and shear viscosity of high-Z materials in the hot dense regime[J]. Matter and Radiation at Extremes, 2021, 6(2): 026901 Copy Citation Text show less

    Abstract

    High-Z materials exhibit a broad range of variation of the charge state in the hot dense regime, and so ionic structures become complex with increasing density and temperature owing to ionization. Taking high-Z uranium as example, we study its electronic and ionic structures in the hot dense regime by combining an average-atom model with the hypernetted chain approximation. The electronic structure is described by solving the Dirac equation, taking account of relativistic effects, including broadening of the energy levels, and the effect of other ions via correlation functions. On the basis of the electronic distribution around a nucleus, the ion pair potential is constructed using the modified Gordon–Kim model in the frame of temperature-dependent density functional theory. Because of the presence of ion–ion strong coupling, the bridge function is included in the hypernetted chain approximation, which is used to calculate the correlation functions. To take account of the influence on transport properties of the strong correlation of electrons with highly charged ions, we perform both classical and Langevin molecular dynamics simulations to determine ion self-diffusion coefficients and the shear viscosity, using the Green–Kubo relation and an ion–ion pair potential with good convergence. We show that the influence of electron–ion collisions on transport properties becomes more important as the free electron density increases owing to thermal ionization.
    dPnκ(r)dr+κrPnκ(r)=1c[ϵnκ+c2V(r)]Qnκ(r),(1)

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    dQnκ(r)drκrQnκ(r)=1c[ϵnκc2V(r)]Pnκ(r),(2)

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    V(r)=Zr+ρb(r)rrd3r+Vxcρb(r)+ρe0Vxc(ρe0)ρe0βCee(rr)hie(r)d3rρi0βCie(rr)hii(r)d3r.(3)

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    ρb(r)=14πr2jϵΔϵϵ+Δϵbj(ϵ)[Pj2(r)+Qj2(r)]dϵ,(4)

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    ρf(r)=1π2k0(r)k2dkexp{β[k2c2+c4c2V(r)μ]}+1,(5)

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    hii(r)=exp[βVii(r)+hii(r)Cii(r)+Bii(r)]1,(6)

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    Bii(r)=αΓβexpb1b0r2,(7)

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    b0=0.2580.0612lnΓ+0.0123(lnΓ)21/Γ,b1=0.0269+0.0318lnΓ+0.00814(lnΓ)2,(8)

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    VeeDeutsch(r)=1r1exprλee+kBTln2expln2πrλee2,(9)

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    hie(r)=ρf(r)ρe01,(10)

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    mid2ri(t)dt2=Fγmidri(t)dt+Ni,(11)

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    γ=2πZ*RWSmikBT,(12)

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    D=13N0i=1Nvi(t)vi(0)dt,(13)

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    η=VkBT0P12(0)P12(t)dt,(14)

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    P12(t)=1Vimivi1(t)vi2(t)+ij>irij1(t)Fij2(t).(15)

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    FSE[D,η]=DηkBTni1/3=CSE,(16)

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    Γii=Z*2RWSkBT.(17)

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    Yong Hou, Yang Jin, Ping Zhang, Dongdong Kang, Cheng Gao, Ronald Redmer, Jianmin Yuan. Ionic self-diffusion coefficient and shear viscosity of high-Z materials in the hot dense regime[J]. Matter and Radiation at Extremes, 2021, 6(2): 026901
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