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  • CV
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  • Research
    • Technologies
      • UHP generation
      • UHT generation
      • Homogeneous temperature
      • In situ X-rays observation
      • Rapid quench
    • Phase transitions
      • Akm-Brg transition and depression of D660
      • Sharp post-spinel transition
      • Post-spinel pressure
      • Binary ol-wd transition
      • Psp transition in Mg2SiO4
    • Mineral chemistry and structure
      • P dependence of Fe3+ in Brg Mg-rich
      • Brg is dry
      • T dependence of Fe3+ in Brg Mg-rich
      • Al in Brg at 3000 K
      • T dependence of MgAlO2.5
      • MgAlO2.5 vs bulk Mg/Si
      • Clustering of O vacancies
      • MgSiO3-Al2O3 at P-T
      • MgAlO2.5 in Brg with P
      • High H2O in Rw
      • H+ substitution mechanism in Fo
      • LiNbO3-type Mg3Al2Si3O12
      • LiNbO3-type (Mg,Fe3+)(Al3+,Si)O3
    • Melt
      • Zero-temperature gradient
      • Rapid quench
    • Electrical conductivity
      • H2O enhancement of ionic conductivity
    • Rheolgical properties
      • E-type slip
      • P-dependence of [100](010) and [001](010) dislocations
      • T-dependence of [100](010) and [001](010) dislocation mobility
      • Si and O diffusion mechanism
      • Si grain-boundary diffusion in Fo
      • H2O Effect of O diffusion in Fo
      • H2O effect on Si lattice diffusion in Fo
    • Thermoelastic properties
      • PVT measurement
      • Adiabatic temperature profile
      • Re-evaluation of T at D410
      • Adiabat
    • Developement of HPT technology
      • SPEED-Mk.II
      • Ultrahigh-pressure MAP
    • Material Science
  • Lecture Note
    • Mineral Physics 2021-22
    • Thermodynamics
      • 1st law and internal energy
    • Thermochemistry
      • G change of ideal gas with P
      • multi-comonent chemical potential
      • Standard pressure, single-component
      • Standard pressure, multi-component
      • High pressures, multi-component
    • Equation of state
      • What is EOS?
      • Isothermal EOS
      • Simplest EOS
      • Finite Strain
      • BM2 EOS
      • Proof a in BMEOS
      • BM3 EOS
      • Proof 3b/2a in BMEOS
      • Vinet EOS
      • Murnaghan EOS
      • Comparison of EOS's
      • Why squared length
      • Why not L but E
      • Thermal EOS
      • Thermal expansion
      • Path HC
      • Grüneisen parameter
      • Path CH
      • A-G parameter
    • Physics of the Earth's interior
    • Mineral Physics 2020
      • Background of thermodynamics
      • Heat capacity
      • Bulk modulus
      • Adiabat
      • Grüneisen paramter
      • Background for elasticity
      • Strain
      • Linear elasticity
      • Stress
      • Elastic constants of crystals
    • Geotherm Table
  • Home
  • CV
  • Publications
  • Research
  • Lecture Note
    • Mineral Physics 2021-22
    • Thermodynamics
    • Thermochemistry
    • Equation of state
      • What is EOS?
      • Isothermal EOS
      • Simplest EOS
      • Finite Strain
      • BM2 EOS
      • Proof a in BMEOS
      • BM3 EOS
      • Proof 3b/2a in BMEOS
      • Vinet EOS
      • Murnaghan EOS
      • Comparison of EOS's
      • Why squared length
      • Why not L but E
      • Thermal EOS
      • Thermal expansion
      • Path HC
      • Grüneisen parameter
      • Path CH
      • A-G parameter
    • Physics of the Earth's interior
    • Mineral Physics 2020
    • Geotherm Table

Equation of State

  • Equation of state
    • Isothermal equation of state
      • The simplest equation of state
      • Finite strain
      • Why not Lagrangian but Eulerian?
      • Why do we consider change in squared length?
      • 2nd-order Birch-Murnaghan equation of state
        • Derivation of the parameter a
      • 3rd-order Birch-Murnaghan equation of state
        • Derivation of the parameter 3b/2a
      • Vinet equation of state
      • Murnaghan's equation of state
      • Comparison of various equations of state
    • Thermal equation of state
      • First heating then compression
      • First compression then heating
      • Thermal expansion
      • Grüneisen parameter
      • Anderson-Grüneisen parameter
Return to Lecture Note

 

Tomoo Katsura, Ph.D.

Professor of Structure and Dynamics of Earth Materials

Bayerisches Geoinstitut, University of Bayreuth
95440 Bayreuth, GERMANY
TEL: +49-921-55-3791
FAX: +49-921-55-3769
E-mail: tomo.katsura@uni-bayreuth.de

Visiting professor

Graduate School of Science and Faculty of Science, Tohoku University

6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai 980-8578, Japan

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