• Matter and Radiation at Extremes
  • Vol. 8, Issue 4, 046901 (2023)
Leonid Burakovskya), Dean L. Preston, Scott D. Ramsey, Charles E. Starrett, and Roy S. Baty
Author Affiliations
  • Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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    DOI: 10.1063/5.0124555 Cite this Article
    Leonid Burakovsky, Dean L. Preston, Scott D. Ramsey, Charles E. Starrett, Roy S. Baty. Shock standards Cu, Ag, Ir, and Pt in a wide pressure range[J]. Matter and Radiation at Extremes, 2023, 8(4): 046901 Copy Citation Text show less

    Abstract

    Although they are polymorphic (multiphase) materials, both copper and silver are reliable Hugoniot standards, and thus it is necessary to establish an accurate analytic model of their principal Hugoniots. Here we present analytic forms of their principal Hugoniots, as well as those of iridium and platinum, two “pusher” standards for shock-ramp experiments, over a wide range of pressures. They are based on our new analytic model of the principal Hugoniot [Burakovsky et al., J. Appl. Phys. 132, 215109 (2022)]. Comparison of the four Hugoniots with experimental and independent theoretical data (such data exist to very high pressures for both copper and silver) demonstrates excellent agreement. Hence, the new model for copper and silver can be considered as providing the corresponding Hugoniot standards over a wide pressure range. We also suggest an approach for calculating the Grüneisen parameter along the Hugoniot and apply it to copper as a prototype, and our results appear to be in good agreement with the available data.
    Us=C+BUp+AUp2,0UpUp*=2(cC)Bb,c+bUp+aUp2,Up*UpUp**=nUp*,df+43Up+dUp1+fUp,UpUp**.

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    P=4ρ0C2η(η1)ηB(η1)+[ηB(η1)]24AC(η1)22,0UpUp*,4ρ0c2η(η1)ηb(η1)+[ηb(η1)]24ac(η1)22,Up*UpUpmax=ca,4ρ0c2η(η1)ηb(η1)[ηb(η1)]24ac(η1)22,UpmaxUpUp**,ρ04f2ηη112dη1η4+112,UpUp**,

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    c+b43Up**+aUp**22=Lb43+2aUp**.

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    L875Z2.42Z+0.006Z2kms2.

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    Us=c+bUp+aUp2,c,b>0,0<a1,

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    ηmax=1+1b+2ac1,UpmaxUp(ηmax)=ca,UsmaxUs(ηmax)=2c+bca

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    f=a(43b)can3c(1+n2)3aL+ccan(1+n2)c(43b)n2,d=La(43b)can3c(1+n2)3aL+ccan(1+n2)c(43b)n22,

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    ηnc/a=1+1b+n+1/nac1.

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    n+1n<43bac,

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    43bac>2,

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    n<N43bacac43b.

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    Up**nUpmax,n2343bac23N,

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    Up**2343ba.

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    f=9a[2(43b)281ac]729a2L+162ac(43b)4(43b)3,d=Lf2.

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    Y227(43b)3/2aL1/2=1.

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    BsPCUp=3S1+S(2S2γ)UpC,

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    γγ(Up)=2(b1)+3aUp+cUp.

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    γ(Up)=γ0+g1Up+g2Up2,g1<0,

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    g1=3a+cUp*22γ02(b1)Up*,

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    g2=γ02(b1)Up*22cUp*3.

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    γ(Up)=23d/f3Up3+g4Up4+g5Up5.

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    g4=2df3Up**+4cUp**3+10b43Up**4+18aUp**5,

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    g5=df3Up**2+3cUp**4+8b43Up**5+15aUp**6.

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    Leonid Burakovsky, Dean L. Preston, Scott D. Ramsey, Charles E. Starrett, Roy S. Baty. Shock standards Cu, Ag, Ir, and Pt in a wide pressure range[J]. Matter and Radiation at Extremes, 2023, 8(4): 046901
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