Adiabatic temperature profile - P-V-T measurement

Experimental methods

  • HP-apparatus: SPEED-Mk.II
  • Anvils
    • WC for Ol, Wd, Rw and Pv
      • In their stability fields and up to 30 GPa
    • SD for Pv
      • Up to 52 GPa
      • Focusing on taking good diffractions rather than high P.
  • Energy dispersive X-ray diffraction using white X-rays and a solid-state detector with a multi-channel analyzer
  • MgO P-marker
    • The most reliable
    • P calculated using Matsui et al.’s [2000] EOS
    • Separately loaded with the sample in WC experiment
    • Mixed with Pv in SD experiment
      • No enough space to load them separately

 

HP-cell for experiment with carbide anvils (Ol, Wd & Rw)

  • The cylindrical furnace with the axis parallel to the X-ray incidence
  • Half-disks of the sample and MgO sandwiching TC junction
  • Take diffractions of the sample and MgO separately.
  • TiB2 heater
    • transparent to hard X-rays
    • X-ray incidence normal to the heater axis
  • Very small sample for multi-anvil experiment
    • Thickness: 0.3 mm
    • Diameter: 0.6 mm

Profile analysis

  • Determine unit cell V by the whole powder pattern fitting
    • The diffraction patterns of the samples are complicated
      • Ol, Wd and Pv are orthorhombic
    • Fitting parameters
      • three unit cell parameters; a, b, c
      • 5 parameters for background
      • intensities of the peaks
      • two parameters for the peak width 
    • Put artificial errors to each channel data, which are square roots of counting
      • So that each channel data should contribute to the volume measurement with the same weight
      • Because peaks with higher intensity are not always more reliable
    • Using 30~50 peaks to determine the volumes

 

Equations of state

Draw the base using the Birch-Murnaghan EoS at 300 K

HT data are fitted to Mie-Grüneisen-Debye EoS.

P-dependence of thermal expansivity

(α/α0) = (V/V0)δT

α: thermal expansivity at high pressure

α0: thermal expansivity at ambient pressure

V: volume at high pressure

V0: volume at ambient pressure

δT: Anderson-Grueneisen parameter

logarithmic V dependence of α

 

Results: olivine

 

Results: wadsleyite

 

Results: ringwoodite

 

Results: Bridgimanite

 

EOS parameters

 

α = a0 + (T-300)a1

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