Peritheos
A Python library for thermodynamic equations of state calculations for solid materials.
Built-in EOS evaluation, inversion, bounded robust fitting, and uncertainty
statistics are implemented in Rust and exposed through the unchanged Python API.
NumPy broadcasting and user-defined EosBase subclasses remain supported.
Full model, fitting, units, and development documentation is available at peritheos.readthedocs.io. Release history is recorded in the changelog.
Features
- Room temperature equations of state (EOS) implementations
- Birch-Murnaghan
- Murnaghan
- Natural strain (orders 2-4)
- Modified Tait
- Vinet
- Holzapfel
- Thermal equations of state (EOS) implementations
- Mie-Gruneisen-Debye
- Mie-Gruneisen-Einstein
- Linear thermal pressure
- Holland-Powell thermal modified Tait
- Multi-oscillator Gruneisen thermal pressure
- P-V and P-V-T parameter fitting with covariance and diagnostics
- Joint reference-isotherm and thermal fitting with cross-covariance
- Correlated observation errors and robust least-squares losses
- Reproducible fit summaries and versioned JSON export
- EOS prediction uncertainty from fitted covariance or published parameter errors
- Thermoelastic derivatives, heat capacities, and vibrational potentials
- Versioned material and EOS-record catalog with explicit literature provenance, validity envelopes, inversion, and measurement/parameter uncertainty
- A Peritheos-owned
.eosmatschema and 115-material/146-record EOS library with optional diffraction structure, stable identifiers, and Dioptas 0.10 storage-read compatibility - Native wheels for supported CPython releases on Linux, macOS, and Windows
Unit conventions
- Public pressure and bulk-modulus values are in GPa.
- Temperatures are in K.
- Birch-Murnaghan, Murnaghan, modified Tait, and Vinet accept any consistent volume unit.
- Holzapfel and energy-based thermal EOS implementations require molar volume in J bar^-1 mol^-1, which is equivalent to cm^3/mol divided by 10.
- The volume-independent linear thermal-pressure correction uses the same volume convention as its reference isotherm.
Installation
pip install peritheos
The latest development version can instead be installed directly from GitHub:
pip install git+https://github.com/CPrescher/peritheos.git
Usage
Materials and EOS records
Materials group one or more literature-specific EOS records. The calculation API uses GPa, K, and conventional unit-cell volumes in angstrom cubed. Each EOS record carries its primary reference, parameter provenance, validity range, and uncertainty assumptions.
from peritheos import get_material
mgo = get_material("mgo_b1")
tange = mgo.get_eos_record("mgo_b1_tange_2009_vinet")
pressure = tange.pressure(volume=60.0, temperature=2000.0)
recovered_volume = tange.volume(pressure, temperature=2000.0)
prediction = tange.pressure_with_uncertainty(
volume=60.0,
temperature=2000.0,
volume_sigma=0.02,
temperature_sigma=20.0,
)
# Sokolova markers use the same cell-volume API although their composed EOS
# works internally with molar volume.
gold = get_material("au_fcc").get_eos_record("au_fcc_sokolova_2013")
hot_pressure = gold.pressure(volume=55.0, temperature=2000.0)
See Pressure standards for EOS records commonly
used in that application, and Dioptas and .eosmat
for the shared material library. The .eosmat schema reference
defines its fields, equation discriminators, defaults, units, and compatibility
rules.
Room-temperature equations of state
Third-order Birch-Murnaghan equation of state:
from peritheos.eos.rt import BM3
# V0 may use any volume unit for a room-temperature EOS; K0 is in GPa here.
eos = BM3(V0=50, K0=130, K0_prime=4.3)
# Calculate pressure and bulk modulus at a given volume.
pressure = eos.pressure(V=40)
bulk_modulus = eos.bulk_modulus(V=40)
# Invert the EOS to calculate volume at a given pressure.
volume = eos.volume(P=pressure)
print(f"Pressure: {pressure} GPa")
print(f"Bulk modulus: {bulk_modulus} GPa")
print(f"Recovered volume: {volume}")
Thermal equations of state
Mie-Gruneisen-Debye and Mie-Gruneisen-Einstein models can wrap any of the room-temperature equations of state:
from peritheos.eos.rt import BM3
from peritheos.eos.thermal import MieGruneisenDebye
# Thermal models require molar volume in J bar^-1 mol^-1.
rt_eos = BM3(V0=1.0, K0=160.0, K0_prime=4.0)
eos = MieGruneisenDebye(
rt_eos=rt_eos,
Tr=300.0,
theta0=800.0,
gamma0=1.5,
q=1.0,
n=2,
)
pressure = eos.pressure(V=0.9, T=2000.0)
volume = eos.volume(P=pressure, T=2000.0)
temperature = eos.temperature(P=pressure, V=0.9)
# Infer temperature from volumes measured before and during DAC heating.
ambient_volume = 0.80000
heated_volume = 0.80001
temperature_with_dac = eos.temperature_from_volumes(
V_ambient=ambient_volume,
V_heated=heated_volume,
f_dac=0.25,
)
ambient_pressure = eos.rt_eos.pressure(ambient_volume)
heated_pressure = ambient_pressure + 0.25 * eos.thermal_pressure(
heated_volume, temperature_with_dac
)
The two-volume method uses the empirical f_dac * thermal_pressure confinement
increment and requires 0 <= f_dac < 1; report and sensitivity-test the assumed
fraction.
Multi-oscillator thermal EOS with a freely chosen reference isotherm
from peritheos.eos.rt.holzapfel import Holzapfel
from peritheos.eos.thermal import MultiOscillatorGruneisenThermalEOS
# Diamond parameters from Sokolova et al. 2016.
# The thermal model requires molar volume in J bar^-1 (= [cm^3/mol] / 10),
# pressure parameters in GPa, and temperatures in K.
V0 = 0.3414
K0 = 441.5
K0_prime = 3.9 # pressure derivative of bulk modulus at reference volume
QE1o = 1561 # first Einstein characteristic temperature
mE1 = 2.436 # first Einstein number
QE2o = 684 # second Einstein characteristic temperature
mE2 = 0.564 # second Einstein number
delta = -0.506 # additive normalizing constant for the Gruneisen parameter
t = 1.085 # generalized Gruneisen parameter
a_0 = 0 # intrinsic anharmonicity parameter
m = 0 # anharmonic analogue of the Grüneisen parameter
e_0 = 0 # free electrons parameter
g = 0 # electronic analogue of the Grüneisen parameter
n = 1 # number of atoms in the formula unit
z = 6 # atomic number of the formula unit
Tr = 298.15 # in K - Reference temperature
# Initialize the Holzapfel EOS
holzapfel = Holzapfel(V0=V0, K0=K0, K0_prime=K0_prime, n=n, Z=z)
# Compose the thermal correction with the source's Holzapfel isotherm.
eos = MultiOscillatorGruneisenThermalEOS(
rt_eos=holzapfel,
Tr=Tr,
QE1o=QE1o,
mE1=mE1,
QE2o=QE2o,
mE2=mE2,
delta=delta,
t=t,
a_0=a_0,
m=m,
g=g,
e_0=e_0,
n=n,
)
# Calculate the thermal pressure at a given volume and temperature
V = V0 * 0.8
T = 3000 # in K
thermal_pressure = eos.thermal_pressure(V, T)
rt_pressure = holzapfel.pressure(V)
pressure = eos.pressure(V, T)
recovered_volume = eos.volume(pressure, T)
recovered_temperature = eos.temperature(pressure, V)
print(f"Thermal pressure: {thermal_pressure} GPa")
print(f"RT pressure: {rt_pressure} GPa")
print(f"Total pressure: {pressure} GPa")
print(f"Recovered volume: {recovered_volume} J bar^-1")
print(f"Recovered temperature: {recovered_temperature} K")
The equation class is named for its mechanism, not a paper. The validated
Sokolova et al. parameterizations remain available through author/year catalog
identifiers such as diamond_sokolova_2013; replacing the reference isotherm
creates a new user-composed model and does not inherit that validation claim.
Citation and support
Use the repository's CITATION.cff to cite Peritheos and cite the original
publication for each EOS used. Reproducible bugs and numerical discrepancies
can be reported through GitHub Issues.
See SUPPORT.md for the information needed to investigate a result.
Metadata
Release files for peritheos 0.6.0
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| Download URL | peritheos-0.6.0-cp39-cp39-macosx_11_0_arm64.whl |
|---|---|
| Size | 829.3 kB |
| Tags | CPython 3.9 macOS 11.0+ ARM64 |
|
SHA-256 checksum How to use checksums |
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BLAKE2b-256 checksum How to use checksums |
0710501664b6668f0f07371fbdb94dd61dec04fae251273ff0e83ed52c889c60
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Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
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twine/7.0.0 CPython/3.13.14
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Transparency logRelease files / peritheos-0.6.0-cp39-cp39-macosx_10_12_x86_64.whl
| Download URL | peritheos-0.6.0-cp39-cp39-macosx_10_12_x86_64.whl |
|---|---|
| Size | 839.6 kB |
| Tags | CPython 3.9 macOS 10.12+ x86-64 |
|
SHA-256 checksum How to use checksums |
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BLAKE2b-256 checksum How to use checksums |
072d1a46eaf8113b98068a70bafc7f38fa5b3239d9e26c41029a081268e98f87
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Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
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Provenance
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