optmat.gas.virial#

The refractivity virial coefficient of each gas, from the curated data.

The refractivity of a real gas departs from Lorentz-Lorenz through the pair term of the virial expansion, (n^2 - 1)/(n^2 + 2) = A_R rho + B_R rho^2 + ...: a relative correction B_R rho / A_R of order 1e-6 (helium) to 1e-4 (SF6) at 1 atm, and of order 1e-3 to 1e-2 at the tens of bar of gas-filled fibres. Which measured B_R each gas uses is chosen in data/gas/refractivity_virial.toml, which points at curated datasets; the values themselves come from those datasets.

Module Attributes

VIRIAL_FILE

The per-gas choice of refractivity virial coefficient.

Functions

`like_term`(gas)	Return a gas's pair term with its uncertainty, or its declared scale.
`pair_rules`()	Return the rules for the unlike pairs of a mixture (OEP 4, section 7.2).
`third_term`(gas)	Return the bound on a gas's third refractivity virial term (OEP 4, 4.3).
`virial_ratio`(gas)	Return `B_R / A_R` for a gas, m^3/mol (0 where none is curated).
`virial_sources`()	Return, per gas, the dataset keys of its `B_R` and `A_R`.

Classes

`LikeTerm`(gas, b, sigma, status, source, ...)	A gas's own pair term, `B_R = b A_R`, as a mixture takes it.
`ThirdTerm`(gas, ratio, status, source)	The bound on a gas's third refractivity virial term, for the optical domain.

class optmat.gas.virial.LikeTerm(gas, b, sigma, status, source, temperature, frequency, contribution)[source]#

Bases: object

A gas’s own pair term, B_R = b A_R, as a mixture takes it.

Attributes:

gasstr: The species.
bfloat: B_R / A_R, m^3/mol; 0 for an uncurated term.
sigmafloat: Its standard uncertainty, m^3/mol; for an uncurated term the declared scale.
statusstr: curated, provisional (a published estimate, with its stated uncertainty: O2’s, egan_2026) or unknown.
sourcestr: The B_R dataset or formula, or empty.
temperaturefloat: The temperature it was measured at, K; NaN where there is none.
frequencystr: static, or the vacuum wavelength in nm.
contributionstr: induced: an optical value, or a static one whose induced part is stated.

b: float#

contribution: str#

frequency: str#

gas: str#

sigma: float#

source: str#

status: str#

temperature: float#

class optmat.gas.virial.ThirdTerm(gas, ratio, status, source)[source]#

Bases: object

The bound on a gas’s third refractivity virial term, for the optical domain.

Attributes:

gasstr: The species.
ratiofloat: |C_R| / A_R, m^6/mol^2; NaN for a gas with neither B_R nor C_R, which has no third-term bound (OEP 4, section 4.3).
statusstr: measured (a curated C_R), bound (a measured bound), scale (the declared third_ratio B_R^2 / A_R) or none.
sourcestr: The C_R dataset, or what gives the bound.

gas: str#

ratio: float#

source: str#

status: str#

optmat.gas.virial.VIRIAL_FILE: Final = PosixPath('/home/docs/checkouts/optmat/checkouts/7/src/optmat/data/gas/refractivity_virial.toml')#: The per-gas choice of refractivity virial coefficient.

optmat.gas.virial.like_term(gas)[source]#

Return a gas’s pair term with its uncertainty, or its declared scale.

Parameters:

gasGas or str: The species.

Returns:

LikeTerm: The curated b of virial_ratio(), or unknown with b = 0 and pair_rules()’ unknown_b as its scale.

Raises:

DataError: If a static B_R does not state that it is induced.

Examples

>>> like_term("D2").status
'unknown'
>>> like_term("O2").status
'provisional'
>>> f"{like_term('Ar').b * 1e6:.3f}"
'0.419'

optmat.gas.virial.pair_rules()[source]#

Return the rules for the unlike pairs of a mixture (OEP 4, section 7.2).

Returns:

Mapping: rule ("mean"), reason, uncertainty, unknown_b (cm^3/mol), third_ratio and density_fraction.

optmat.gas.virial.third_term(gas)[source]#

Return the bound on a gas’s third refractivity virial term (OEP 4, 4.3).

Parameters:

gasGas or str: The species.

Returns:

ThirdTerm: From its measured C_R, a measured bound, the declared scale on its B_R, or none.

Examples

>>> term = third_term("Ar")
>>> term.status, f"{term.ratio * 1e12:.2f}"
('measured', '20.64')

optmat.gas.virial.virial_ratio(gas)[source]#

Return B_R / A_R for a gas, m^3/mol (0 where none is curated).

Parameters:

gasGas or str: The species.

Returns:

float: The ratio the Lorentz-Lorenz functions take as virial.

Examples

>>> f"{virial_ratio('Ar') * 1e6:.3f}"
'0.419'
>>> virial_ratio("D2")
0.0

optmat.gas.virial.virial_sources()[source]#

Return, per gas, the dataset keys of its B_R and A_R.

Returns:

dict of Gas to tuple of str: (B_R key, A_R key) for every gas with a pair term.

Raises:

DataError: If an entry names a dataset that does not exist.