FPEOS#

With the goal in mind of making WDM computations more reliable and efficient, we make available our EOS tables for 11 elements and 10 compounds as well as the C++ computer codes for their interpolation. Python code is provided to generate graphs of shock Hugoniot curve, isentropes, isobars, and isotherms for compounds and user-defined mixtures. We put together this first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al and Si as well as the compounds LiF, B4C, BN, CH4, CH2, C2H3, CH, C2H, MgO, and MgSiO3. For all these materials, we provide the pressure and internal energy over a wide density-temperature range from ~0.5 to 50 g/cc and from ~104 to 109 K. This database encompasses the results from approximately 5000 different first-principles simulations. It allows one to compute isobars, adiabats, and shock Hugoniot curves in the regime of L and K shell ionization. Invoking the linear mixing approximation, one can study the properties of user-defined mixtures at high density and temperature.

Download the code#

Download the code here.

Download an FPEOS presentation slides by Burkhard Militzer#

Download a presentation about FPEOS here.

FPEOS: First-Principles Equation of State Code#

(1) Download the Latest Version#

Date

Description

Download Link

05-22-24

Figures are opened one by one.

fpeos_05-22-24.tar.gz

05-21-24

Added tutorial file: FPEOS_tutorial.pdf

fpeos_05-21-24.tar.gz

05-20-24

1. For oxygen, set default rho0=1.33416818
2. Added openCommand=... and pythonCommand=...
3. pylab → pyplot

fpeos_05-20-24.tar.gz

05-17-24

Minor updates in Python scripts

fpeos_05-17-24.tar.gz

02-12-22

Supports ternary mixtures like C10-H16-O8

fpeos_02-12-22.tar.gz

01-07-21

First public version of our FPEOS code.

fpeos_01-07-21.tar.gz

(2) Installation#

Download and untar the latest version, change into the directory, and compile:

tar -xzf fpeos_01-07-21.tar.gz
cd FPEOS
make

Expected compilation output:

g++ -O3 -c FPEOS_29.C
g++ -O3 -c EOSTableSimple.C
g++ -O3 -c Parser.C
g++ -O3 -c ReadInTable.C
g++ -O3 -c Standard.C
g++ -O3 -c Form.C
g++ -O3 -c Physics.C
g++ -O3 -c Spline.C
g++ -O3 -c FermiGas.C
g++ -O3 -c RelativisticFermiGas.C
g++ -O3 -c Debye.C
g++ -O3 -c GKIntegration.C
g++ -O3 -c RungeKutta.C
g++ FPEOS_29.o EOSTableSimple.o Parser.o ReadInTable.o Standard.o Form.o Physics.o Spline.o FermiGas.o RelativisticFermiGas.o Debye.o GKIntegration.o RungeKutta.o -lm -o fpeos

If compilation fails, try modifying the Makefile or using a different compiler.

Supported Compilers#

  • Linux: g++ version 7.5.0, 4.8.4

  • macOS: clang version 13.0.0, 12.0.0

  • Windows: Use Cygwin with g++ 10.2.1

Python is required only for plotting. C++ code works without Python.

(3) Files Included#

EOS Tables#

Sample filenames:

Al_EOS_09-18-20.txt   C10H40_EOS_09-18-20.txt   He_EOS_09-18-20.txt   O_EOS_09-21-20.txt
B4C_EOS_09-18-20.txt  C16H24_EOS_09-18-20.txt   LiF_EOS_09-18-20.txt  Si_EOS_10-19-20.txt
BN_EOS_09-18-20.txt   C18H18_EOS_09-18-20.txt   MgO_EOS_09-18-20.txt
B_EOS_09-18-20.txt    C20H10_EOS_09-18-20.txt   MgSiO3_EOS_09-18-20.txt
C_EOS_09-18-20.txt    H_EOS_09-18-20.txt        N_EOS_09-18-20.txt

Sample entry from carbon EOS:

f= C N= 1 rho[g/cc]= 0.100006 V[A^3]= 199.43071700 T[K]=  5000 P[GPa]= 0.053 0.007 E[Ha]= -37.66843800 0.00054900

Column description:

  1. Chemical formula (e.g., C, MgSiO₃)

  2. Number of atoms, N

  3. Density [g/cm³]

  4. Volume of N atoms [ų]

  5. Temperature [K]

  6. Pressure [GPa]

  7. 1-sigma pressure error

  8. Internal energy per N atoms [Ha]

  9. 1-sigma energy error

C++ Files#

Main file: FPEOS_29.C
Other headers and sources include: Parser.C, Form.h, Physics.C, RungeKutta.C, Spline.C, etc.

Python Plotting Scripts#

Examples:

FPEOS_P_T_plot03.py
FPEOS_T_E_Debye_plot03.py
FPEOS_comp_P_plot04.py
FPEOS_mixture_P_T_plot01.py
FPEOS_rho_T_plot03.py
FPEOS_up_us_plot01.py

These require:

from matplotlib.pylab import *
import numpy
import sys
import os

Compatible with Python 2.7 and 3.7+

(4) Execution#

Run:

./fpeos

This will print available EOS options:

1: Hydrogen     8: Sodium       15: CH4
2: Helium       9: Magnesium    16: CH2
3: Boron       10: Aluminum     17: CH1.5
4: Carbon      11: Silicon      18: CH
5: Nitrogen    12: LiF          19: CH0.5
6: Oxygen      13: B4C          20: MgO
7: Neon        14: BN           21: MgSiO3

Examples#

  • fpeos EOS=2 — helium

  • fpeos binaryMixture EOS1=1 0.92 EOS2=2 0.08 — H + He

  • fpeos binaryMixture EOS1=4 1.0 EOS2=6 2.0 rho0=1.6381 E0=-188.1576 — CO₂

  • Normalize per C2H6: EOS1=15 1.0 EOS2=16 1.0

  • Normalize per CH3: EOS1=15 0.5 EOS2=16 0.5

  • Normalize per atom: EOS1=15 0.125 EOS2=16 0.125

Optional Flags#

  • doNotCallPython

  • doNotOpenPDFFiles

  • processAllEOSs

  • processAllMixturesOfElements

  • processAllMixtures

  • hugoniotCompressionMaximum

  • noLogInterpolation

(5) Resulting Files#

Use ls -ltr to see the outputs. Example files for EOS=13:

FPEOS_convex_hull.txt
FPEOS_isobars.txt
FPEOS_Hugoniot.txt
FPEOS_T_P_Debye_plot03.pdf
FPEOS_T_P_Debye_plot03.png
FPEOS_T_E_Debye_plot03.pdf
FPEOS_T_E_Debye_plot03.png
FPEOS_P_T_plot03.pdf
FPEOS_P_T_plot03.png

  • .txt files from C++ code

  • .pdf/.png from Python scripts

(6) Remarks#

  1. Hugoniot curves assume non-bonded initial states unless rho0 and E0 are specified.

  2. E0 is in Hartrees per formula unit (FU).

  3. Ideal Fermi gas and Debye plasma routines included.

  4. C++ code is minimalist, avoiding large libraries.

  5. Python scripts are straightforward and produce high-quality plots.

Contact#

For feedback or questions, please contact:

Burkhard Militzer
📧 militzer[at]berkeley[dot]edu
📅 Last updated: May 20, 2024

Happy FPEOS computation!