Thermodynamics data of Alkali Feldspars from FPMD simulations

We computed the thermodynamic properties (pressure, temperature, internal energy, heat capacity) and thermoelastic coefficients (isobaric expansivity, isothermal compressibility, thermal pressure coefficient) on the two alkali feldspars end-members using ab initio molecular dynamics simulation in the 2000-20000 K temperature range and in the 0.5-6 g.cm-3 density range.

Simulations are performed using the Vienna Ab Initio Simulation Package (VASP) (Kresse and Furthmuller, 1996) in the canonical (NVT) ensemble with a timestep of 0.5-2 fs for 5-20 ps depending on the temperature and density. We model the feldspar end-members in a cubic cell containing 208 atoms (16 formula units) and 1024 or 1152 electrons for the Na- and K-feldspars respectively. For simulations at low density we used pseudopotentials which require a lower plane wave energy cutoff, set to 370 eV. For Na-end-member, we also used  hard pseudopotentials at high density in order to reduce the overlap of electronic spheres, in particular for Na-Na pairs. The energy cutoff for this set of pseudopotentials is 950 eV. Additional details can be found in the manuscript.

There is one dataset for each different composition and set of pseudopotentials used:

kobsch-ds01.txt    -->    NaAlSi3O8

kobsch-ds02.txt    -->    NaAlSi3O8 and set of pseudopotentials with a lower plane wave energy cutoff than in 01

kobsch-ds03.txt    -->    NaAlSi3O8 and harder pseudopotentials than in 01

kobsch-ds04.txt    -->    KAlSi3O8

kobsch-ds05.txt    -->    KAlSi3O8 and set of pseudopotentials with a lower plane wave energy cutoff than in 04

Each file present the arithmetic time averages of the pressure (P), temperature (T) and internal energy (E). The standard deviation of the data to the mean is indicated by stdev_X, where X is P, T or E. The statistical error to the mean (err_X) is computed using the blocking method as described by Flyvbjerg and Petersen (1989). The sign '>' is indicated before the value of the statistical error when no convergence  was reached during the estimation of this error. The heat capacity Cv is computed using fluctuations on both potential and kinetic energies (Allen and Tildesley, 1989) and its statistical error stdev_Cv is computed using the bootstrap method. 

We computed the thermoelastic coefficients only for densities (\(\rho\)) above 1.5 g.cm-3. The thermal pressure coefficient (TPC = \(\frac{\partial P}{\partial T}\big|_V\)) is  the slope of linear fit of P vs. T isochores. The isothermal compressibility (\(\beta = -\frac{1}{\rho} \frac{\partial \rho}{\partial P}\big|_T\)) is computed using central finite differences on our P vs. \(\rho\) isotherms. The isobaric expansivity (\(\alpha = \frac{1}{\rho} \frac{\partial \rho}{\partial T}\big|_P\)) is computed using the previously computed \(\beta\) and TPC.