Equation of state data

From here you can download the eos parameters for many phases as '.eos' files. These files can be 'loaded' directly in to the EosFit7 software so that you can do calculations immediately. You can also use EosFit7c to modify the parameters within the files.

Important:
  • Most browsers will download these files. If your browser opens the file, just right-click on the link and select save link as (or save target as in IE).

  • If you use the data in these files, please read the comments and refer to the original literature; you can find the references in the table!




EoS useful for pressure measurement

Quartz The P-V EoS for quartz (SiO2) as determined by Scheidl et al (2016) Journal of Applied Crystallography, 49, 2129-2137. A reprint is available as a pdf file, Copyright International Union of Crystallography.

We use quartz as an internal pressure standard in single-crystal diamond-anvil cell experiments at room temperature. We measure the volume of the quartz by diffraction and use this EoS to convert the measured volume to pressure.

This new EoS extends to 19 GPa. It replaces the previous quartz EoS determined by Angel et al (1997).

Old quartz The P-V EoS for quartz (SiO2) as determined by Angel et al (1997) Journal of Applied Crystallography, 30, 461-466. A reprint is available as a pdf file, Copyright International Union of Crystallography.

You should no longer use this EoS. You should use the new EoS determined by Scherdl et al (2016).
If you want to convert the pressures previously determined by this EoS to the new pressure scale given by Scherdl et al (2016), download both eos files for quartz and use the pshift command in the Edit utility of EosFit7c to convert the pressures in your dataset.


EoS of example datasets distributed with EosFit

These eos files hold the results of fitting some of the example datasets distributed with EosFit7c. Details of how to fit the data and obtain these results are provided in the 'worked examples' section of the EosFit7 help system.

Quartz The P-V EoS for quartz (SiO2) as determined by Angel et al (1997) Journal of Applied Crystallography, 30, 461-466. A reprint is available as a pdf file, Copyright International Union of Crystallography.

We use quartz as an internal pressure standard in single-crystal diamond-anvil cell experiments. We measure the volume of the quartz by diffraction and use this EoS to convert the measured volume to pressure.

Birch-Murnaghan 3rd order EoS
K0 = 37.12(5) GPa
K' = 5.99(5)
Ferropericlase Equation of state obtained from the pressure-volume-temperature data (up to 2000K and 50GPa) using a BM3 EoS combined with a Berman-type thermal expansion. Beware that data have been only considered up to 50GPa (i.e. well below the spin transition).The original P-V-T data are taken from Mao et al. (2011) GRL 38, L23308
Birch-Murnaghan 3rd order EoS
K0 = 162(14) GPa
K' = 4.1(6)
dK/dT=-0.018(7) GPa/K
alpha0=4.0(6) x 10^-5 /K, alpha1=0.1(6) x 10^-8 K^-2
Kalsilite lowP

Kalsilite highP
Equations of state obtained from the pressure-volume data of kalsilite Gatta et al. (2011) Amer. Mineral. 96, 461. The two eos files are for the low-pressure and high-pressure phases, seperated by a phase transition at ~3.6 GPa. Birch-Murnaghan 3rd order EoS
Low P: K0 = 60 GPa, K' = 3.5
High P: K0 = 44 GPa, K' = 6.5



EoS useful for host-inclusion calculations

For details about host-inclusion piezobarometry see:
  • EntraPT: an online platform for elastic geothermobarometry. Mazzucchelli ML, Angel RJ, Alvaro M (2021) American Mineralogist, 106, 829-836. link
    and the local page about the EntraPT software or the EntraPT online software

  • Geobarometry from host-inclusion systems: the role of elastic relaxation. Angel RJ, Mazzucchelli ML, Alvaro M, Nimis P, Nestola F (2014) American Mineralogist, 99, 2146-2149. link

  • How large are departures from lithostatic pressure? Constraints from host-inclusion elasticity. Angel RJ, Nimis P, Mazzucchelli ML, Alvaro M, Nestola F (2015) Journal of Metamorphic Geology, 33, 801-813. link

  • EosFit-Pinc: A simple GUI for host-inclusion elastic thermobarometry. Angel RJ, Mazzucchelli ML, Alvaro M, Nestola F (2017) American Mineralogist, 102, 1957-1960. link



Pyrope

Grossular

Almandine

Spessartine

New Garnet EoS:

These PVT EoS are new determinations obtained by fitting all of the elasticity and volume data for these garnets that is published in the literature. We first used published heat capacity data to determine which published data sets are consistent, and then fitted the EoS parameters to all of those data together. These are the most internally consistent EoS that it is possible to obtain with currently-available data, and they should be used for all host-inclusion calculations.

The EoS are q-compromise Mie-Grueneisen-Debye thermal-pressure EoS. Therefore, in order to use the eos files, you need the June 2021 version of EosFit or a more recent version.

These EoS have been implemented in the EntraPT online software

For the details of how we determined these EoS, please read the open access paper Angel et al., (2022) Contributions to Mineralogy & Petrology, 177,54.
Diamond Our best estimate of the P-V-T EoS for diamond determined from a critical review of the most recent experimental data (elasticity, heat capacity, PV data) and DFT simulations (Angel et al., (2014) Russian Geology & Geophysics, 56,211).



BM3-MGD olivine

BM4-MGD olivine

BM3-Isothermal olivine

BM4-Isothermal olivine
Our best estimate of the P-V-T EoS for mantle composition olivine (Fo90-Fo92) determined from a critical review and a combined fit of elasticity and volume data from single-crystal measurements. Full details in Angel et al., (2018) Physics and Chemistry of Minerals, 45, 95-113.

There are four EoS:
  • BM3-MGD: No elastic softening.
  • BM4-MGD: Includes high-P softening at room temperature.
  • BM3-Isothermal: Includes HT/HP softening, but not the high-P softening at room T.
  • BM4-Isothermal: Includes both HP and HT/HP softening.


Quartz PVT This is a full P-V-T EoS for quartz, including the elastic softening in both alpha and beta quartz due to the alpha-beta phase transition, and a curved alpha-beta phase boundary to fit all available reversals and constraints. EoS parameters were determined by fitting simultaneously to both elastic moduli and P-T-V data. For details about this and the next two EoS for quartz see Angel et al (2017) Contribs. Min. Pet., 172:29 or contact us.

Quartz V and a This file contains the full P-V-T EoS of quartz and the EoS for the a-cell parameter, both in Angstroms. They can be used together to determine how the a,b,c and V of quartz change with P and T, in a self-consistent way in the CELL utility of EosFit7c. See Alvaro et al (2020) Geology, 48:24 and Angel RJ, Mazzucchelli ML, Gonzalez-Platas J, Alvaro M, F (2022) A self-consistent approach to determine unit-cell parameter variations with pressure and temperature. Journal of Applied Crystallography, 54, 1621-1630, which is available as a pdf file.

The PVT EoS is the same as the previous one, but with volumes in A3/cell. The EoS for the a-cell parameter was determined with the same transition model by fitting the same sources of data. Please reference Alvaro et al (2020) Geology, 48:24 as the source.

Quartz PVT This is a full P-V-T EoS for quartz, including the elastic softening in both alpha and beta quartz due to the alpha-beta phase transition, but with a linear alpha-beta phase boundary with slope of 240GPa/K, from Thermocalc. EoS parameters were determined by fitting simultaneously to both elastic moduli and P-T-V data. From Angel et al (2017) Contribs. Min. Pet., 172:29.

Quartz PVT This is a P-V-T EoS for quartz using a model similar to that in Thermocalc, with elastic softening only in alpha quartz. Linear alpha-beta phase boundary with slope of 240GPa/K, from Thermocalc. These EoS parameters were determined by fitting simultaneously to both elastic moduli and P-T-V data and can be used with Thermocalc. From Angel et al (2017) Contribs. Min. Pet., 172:29.

Rutile cell These are EoS for the cell parameters and the volume of rutile determined by fitting simultaneously to both elastic moduli and diffraction data in the literature. Full details in a manuscript by Zaffiro et al. (2019), Mineralogical Magazine, 83:339. The only difference from the published paper is that these files contain the cell parameters at the reference conditions to allow them to be used in the CELL utility.

All three EoS are loaded in one eos file. You can chose the individual eos (a, c, or V) out of the file with the load command of EosFit7c, or you can load them all simultaneously from this file into the CELL utility of EosFit7c. The EosFit-GUI and calculator will automatically read the first EoS in the file, which is for the volume.

You can try fitting the data yourself with the three dataset files for rutile formatted for EosFit:
cell parameters and volume dataset
adiabatic linear and bulk moduli at high T
adiabatic bulk moduli at high P
To use these data files, remove the '.txt' extension from the file name.

Rutile MGD

Rutile qcompMGD
These are two versions of the MGD EoS fitted to the same data for rutile. One is the general form of the MGD with a refined value of the q-parameter, and the other is the q-compromise version. Both provide a very similar PVT relationship as the 'isothermal' PVT EoS given above, but may be more reliable at more extreme P and T.

For a discussion of the role of the q-parameter in MGD EoS, the concept of q-compromise EoS, and a comparison of different EoS of rutile see Angel et al. (2020), Mineralogical Magazine, 84:355-357.

Spinel EoS This is an MGD EoS fitted to all consistent published volume and elasticty data for relatively well-ordered MgAl2O4 spinel. For calculations of volume at temperatures above 800C a correction for the effect of changes in the state of cation order is required. For full details of the data used, the refinement of the EoS and the corrections for cation ordering, see Hagiwara et al (2022) Contributions to Mineralogy & Petrology, 177, 108.

Zircon MGD This is an MGD EoS fitted to new PV and elasticity data for zircon, together with literature TV data. This EoS has been developed by Alix Ehlers of Virginia Tech. Full details of the data and fitting are in Ehlers et al (2022) American Mineralogist, 107, 74-81.

Zircon a,c,V EoS
These are isothermal-type EoS for the zircon volume and unit-cell parameters fitted to the same datasets as described for the MGD EoS for zircon in Ehlers et al (2022) American Mineralogist, 107, 74-81.

All three EoS are loaded in one eos file. You can chose the individual eos (a, c, or V) out of the file with the load command of EosFit7c, or you can load them all simultaneously from this file into the CELL utility of EosFit7c. The EosFit-GUI and calculator will automatically read the first EoS in the file, which is for the volume.

The c-axis of zircon is very incompressible. Therefore, in the CELL utility of EosFit7c we recommend using the EoS for the a-cell parameter and the volume to calculate the c-axis. See Journal of Applied Crystallography, 54, 1621-1630 or the reprint for more details.



Water

CO2

Fluid EoS:

The equations of state of fluids are far more complex than those of solids and there are many different algebraic formulations for them. It is therefore not practical to code all of these equations into EosFit. We provide an alternative with the IMPORT utility of EosFit7c. It allows you to import a text file containing a table of volumes as a function of P and T. You can generate the text file yourself with any suitable software. The properties of the fluid are then calaculated in EosFit7c by interpolation between the table values. They cannot be used in the GUI or the calculator. Full details are given in the EosFit7 help system, in the section about IMPORT.

Two examples are provided here:

To use these data files, remove the '.txt' extension from the file name.
Note that the information given at the top of these two examples are not used by the release version of EosFit7c.