Intensive Lecture

Intensive lecturer series "Mineral Physics I"


In order to understand the structure, dynamics, and evolution of the Earth and planetary interiors, a proper understanding of the physical properties of constituent minerals is desired. However, the majority of geology courses provide no classes for understanding theories of mineral properties. This course series aims to provide basic theories of mineral properties for students who have graduated from a geology course and work in high-pressure-temperature experiments to understand the Earth and planetary interiors better. Students and other researchers interested in high-pressure mineral physics in other fields are also welcome. The background of mathematics and physics of the first-year bachelor students of natural science is assumed. This series of lectures will focus on mineral properties controlled by the crystal structure and major composition. In other words, properties related to crystalline defects such as point defects, dislocations, and grain interfaces will not be discussed in this series of lectures.


The details of the lectures are as follows.


0. Introduction

  1. Thermodynamic properties
    1. Background of thermodynamics
    2. Heat capacity
    3. Bulk modulus
    4. Grüneisen parameter
    5. Adiabat
  2. Elasticity
    1. Mathematical and physical backgrounds
    2. Strain
    3. Stress
    4. Linear elasticity
    5. Elastic constants of symmetric and isotropic solids
    6. Frequently used elastic constants
    7. Averaged elasticity of composite materials
    8. Elastic wave velocity of the isotropic body
    9. Acoustic impedance
  3. Lattice vibration
    1. Phase and group velocities
    2. Boltzmann distribution
    3. Dulong-Petit law
    4. Quantum one-dimensional harmonic oscillator
    5. Vibrational energy of the lattice
    6. Dispersion relation
    7. Debye model
    8. Thermal expansion
  4. Equation of State
    1. What is “equation of state”?
    2. Birch-Murnaghan equation of state
    3. Vinet equation of state
    4. Murnaghan’s equation of state
    5. Examination of Eulerian finite strain theory
      1. Eulerian or Lagrangian scheme?
      2. Why expansion of squared length?
    6. Thermal equation of state
    7. Mie-Grüneisen-Debye eqution of state
    8. Shock compression
  5. Heat transfer
    1. Physics of heat transfer
    2. Lattice thermal conductivity
    3. Radiative thermal conductivity

The theories of mineral properties controlled by defects will be argued in another series of lectures "Mineral Physics II" that will be held eventually.