Chapter 10 Physics of Highly Compressed Matter

9.1 Equation of State of Matter in High Pressure

1.The pressure is equal to zero at the solid density and the experimental bulk modulus is reproduced. 2.The cold pressure at the density less than the solid density should be negative (tensile force). 3.The Fermi pressure of electron is reproduced to be a dominant term at high density in the limit of  F >> T e, when  F is the Fermi energy of electron. 4.The ideal gas EOS should be reproduced at high temperature T e >>  F. 5.The effective charge Z* is determined not only by the thermal ionization, but also by the pressure ionization. More’s QEOS

Formula of Equation of State Applicable to Wide Range of T and n Total Free Energy Thermodynamic Consistency

1.0 < T i <  D (low-temperature solid phase)  D < T i < T m (high-temperature solid phase) 3.T m < T i (fluid phase) Ion Equation of State (Cowan Model by More)

(eV) Melting Temperature

Electron Equation of State based on Thomas-Fermi Model

Thomas Fermi Model Takabe-Takami model,

 H is in the unit of g/cm 3

varies from  e = 2/3 for  to  e = 2/3  (= 0.821) for  << 1.

Bonding Correction where P b0 =  b0 b  s /3,  s the solid density, R/R s = (  s /  ) 1/3. The parameters  b0 and b are determined so that the total pressure is equal to zero at  s and T e = 0 and the bulk modulus defined by

Bulk Modulus

Equation of State of DD

16 Image of Atoms in Hot-Dense Plasmas (Pressure Ionization) 10.2 Atomic Physics of Hot Dense Plasam

rn =a0n2 / Zn Average Atom Model Screened Hydrogen Model

photo excitation cross-section  m,m' ∫f m,m' d = 1 x n = P n / g n

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10.3 Equation of State Experiments and Planetary Physics

28 Equation of State Giant Planet

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