Constants Module¶

The constants module provides physical constants and conversion factors used throughout XRayLabTool.

Physical constants for X-ray calculations.

This module contains fundamental physical constants used throughout X-ray analysis calculations, translated from the Julia implementation with preserved numerical precision. All values are provided with explanatory docstrings describing their physical meaning and units.

The constants are defined with high precision to ensure accurate calculations in X-ray optical property computations.

xraylabtool.constants.ANGSTROM_TO_METER: Final[float] = 1e-10¶

Conversion factor from Angstroms to meters.

Value: 10⁻¹⁰ Units: m/Å Usage: length_m = length_angstrom * ANGSTROM_TO_METER

xraylabtool.constants.AVOGADRO: Final[float] = 6.02214199e+23¶

Avogadro’s number.

The number of constituent particles (atoms or molecules) per mole. Used in calculations relating molecular properties to bulk material properties.

Value: 6.02214199 × 10²³ mol⁻¹ Units: per mole (mol⁻¹) Reference: CODATA 2018 recommended values

Note: This value maintains compatibility with the Julia implementation. For the most current CODATA value, see: 6.02214076e23 mol⁻¹ (exact since 2019).

xraylabtool.constants.CM_TO_METER: Final[float] = 0.01¶

Conversion factor from centimeters to meters.

Value: 0.01 Units: m/cm Usage: length_m = length_cm * CM_TO_METER

xraylabtool.constants.DEGREES_TO_RADIANS: Final[float] = 0.017453292519943295¶

Conversion factor from degrees to radians.

Value: π/180 ≈ 0.017453292519943295 Units: rad/° Usage: angle_rad = angle_deg * DEGREES_TO_RADIANS

xraylabtool.constants.ELEMENT_CHARGE: Final[float] = 1.60217646e-19¶

Elementary charge.

The electric charge of a single proton, equal in magnitude to the charge of an electron. Used in X-ray calculations for energy unit conversions between Joules and eV.

Value: 1.60217646 × 10⁻¹⁹ C Units: coulombs (C) Reference: CODATA 2018 recommended values

Note: This value maintains compatibility with the Julia implementation. For the most current CODATA value, see: 1.602176634e-19 C (exact since 2019).

xraylabtool.constants.ENERGY_TO_WAVELENGTH_FACTOR: Final[float] = 1.2398417166827828e-09¶

Pre-computed factor for energy-to-wavelength conversion.

This constant combines fundamental constants to efficiently convert X-ray energies in keV to wavelengths in meters using: λ = ENERGY_TO_WAVELENGTH_FACTOR / E_keV

Mathematical derivation: λ = hc/E = (hc/e) / E_eV = (hc/e) / (1000 × E_keV)

Value: (SPEED_OF_LIGHT × PLANCK / ELEMENT_CHARGE) / 1000.0: = (2.998 × 10⁸ × 6.626 × 10⁻³⁴ / 1.602 × 10⁻¹⁹) / 1000 ≈ 1.240 × 10⁻⁶ m⋅keV

Units: meter-keV (m⋅keV) Usage: wavelength_m = ENERGY_TO_WAVELENGTH_FACTOR / energy_keV

xraylabtool.constants.EV_TO_KEV: Final[float] = 0.001¶

Conversion factor from eV to keV.

Value: 0.001 Units: keV/eV Usage: energy_keV = energy_eV * EV_TO_KEV

xraylabtool.constants.KEV_TO_EV: Final[float] = 1000.0¶

Conversion factor from keV to eV.

Value: 1000 Units: eV/keV Usage: energy_eV = energy_keV * KEV_TO_EV

xraylabtool.constants.METER_TO_ANGSTROM: Final[float] = 10000000000.0¶

Conversion factor from meters to Angstroms.

Value: 10¹⁰ Units: Å/m Usage: length_angstrom = length_m * METER_TO_ANGSTROM

xraylabtool.constants.METER_TO_CM: Final[float] = 100.0¶

Conversion factor from meters to centimeters.

Value: 100 Units: cm/m Usage: length_cm = length_m * METER_TO_CM

xraylabtool.constants.PI: Final[float] = 3.141592653589793¶

The mathematical constant π.

The ratio of a circle’s circumference to its diameter, appearing frequently in X-ray scattering calculations and Fourier transforms.

Value: 3.141592653589793… Units: dimensionless

xraylabtool.constants.PLANCK: Final[float] = 6.626068e-34¶

Planck constant.

The quantum of action, relating the energy of a photon to its frequency. Essential for X-ray energy-wavelength conversions through E = hc/λ.

Value: 6.626068 × 10⁻³⁴ J⋅s Units: joule-seconds (J⋅s) Reference: CODATA 2018 recommended values

Note: This value maintains compatibility with the Julia implementation. For the most current CODATA value, see: 6.62607015e-34 J⋅s (exact since 2019).

xraylabtool.constants.RADIANS_TO_DEGREES: Final[float] = 57.29577951308232¶

Conversion factor from radians to degrees.

Value: 180/π ≈ 57.29577951308232 Units: °/rad Usage: angle_deg = angle_rad * RADIANS_TO_DEGREES

xraylabtool.constants.SCATTERING_FACTOR: Final[float] = 270086523204316.84¶

Pre-computed factor for X-ray scattering calculations.

This constant combines the Thomson scattering length with Avogadro’s number and unit conversion factors, optimized for calculating dispersion and absorption coefficients in X-ray optical property calculations.

Mathematical derivation: Factor = (rₑ × Nₐ × 10⁶) / (2π)

Where: - rₑ: Thomson scattering length (classical electron radius) - Nₐ: Avogadro’s number - 10⁶: Unit conversion factor (cm³/m³ to account for density units) - 2π: Geometric factor from X-ray scattering theory

Value: THOMPSON × AVOGADRO × 10⁶ / (2π): ≈ 2.70 × 10¹⁴ m⁻¹⋅mol⁻¹

Units: per meter per mole (m⁻¹⋅mol⁻¹) Usage: Used in calculating δ = (λ²/2π) × rₑ × ρ × Nₐ × (Σf₁) / M

xraylabtool.constants.SPEED_OF_LIGHT: Final[float] = 299792458.0¶

Speed of light in vacuum.

The speed of electromagnetic radiation in vacuum, a fundamental physical constant that appears in many X-ray calculations involving wavelength-energy conversions.

Value: 299,792,458 m/s (exact by definition) Units: meters per second (m/s) Reference: SI base unit definition

xraylabtool.constants.SQRT_2: Final[float] = 1.4142135623730951¶

Square root of 2.

Mathematical constant that appears in geometric calculations and normalizations in X-ray crystallography.

Value: 1.4142135623730951… Units: dimensionless

xraylabtool.constants.THOMPSON: Final[float] = 2.8179403227e-15¶

Thomson scattering length (classical electron radius).

The Thomson scattering length represents the classical radius of an electron, which is the length scale characterizing the scattering of electromagnetic radiation by a free electron in the classical limit.

Value: 2.8179403227 × 10⁻¹⁵ m Units: meters (m) Reference: CODATA 2018 recommended values

xraylabtool.constants.TWO_PI: Final[float] = 6.283185307179586¶

Mathematical constant 2π.

Commonly appears in X-ray calculations involving angular frequencies, momentum transfer, and scattering theory.

Value: 6.283185307179586… Units: dimensionless

xraylabtool.constants.attenuation_length_cm(wavelength_angstrom, absorption)[source]¶

Calculate X-ray attenuation length from wavelength and absorption coefficient.

Parameters:

wavelength_angstrom (float | floating[Any] | ndarray[tuple[Any, ...], dtype[double]]) – X-ray wavelength in Angstroms
absorption (float | floating[Any] | ndarray[tuple[Any, ...], dtype[double]]) – Absorption coefficient β (dimensionless)

Return type:

float

Returns:

Attenuation length (1/e length) in centimeters

Example

>>> from xraylabtool.constants import attenuation_length_cm
>>> length = attenuation_length_cm(1.24, 1e-7)
>>> print(f"Attenuation length: {length:.2f} cm")
Attenuation length: 0.01 cm

xraylabtool.constants.critical_angle_degrees(dispersion)[source]¶

Calculate critical angle for total external reflection from dispersion coefficient.

Parameters:: dispersion (float | floating[Any] | ndarray[tuple[Any, ...], dtype[double]]) – Dispersion coefficient δ (dimensionless)
Return type:: float
Returns:: Critical angle in degrees

Example

>>> from xraylabtool.constants import critical_angle_degrees
>>> theta_c = critical_angle_degrees(1e-6)
>>> print(f"Critical angle: {theta_c:.4f}°")
Critical angle: 0.0810°

xraylabtool.constants.energy_to_wavelength_angstrom(energy_kev)[source]¶

Convert X-ray energy in keV to wavelength in Angstroms.

Parameters:: energy_kev (float | floating[Any] | ndarray[tuple[Any, ...], dtype[double]]) – X-ray energy in keV
Return type:: float
Returns:: Wavelength in Angstroms

Example

>>> from xraylabtool.constants import energy_to_wavelength_angstrom
>>> wavelength = energy_to_wavelength_angstrom(10.0)  # 10 keV
>>> print(f"Wavelength: {wavelength:.4f} Å")
Wavelength: 1.2398 Å

xraylabtool.constants.validate_constants()[source]¶

Validate that all constants are properly defined and have reasonable values.

Return type:: bool
Returns:: True if all constants pass validation
Raises:: ValueError – If any constant fails validation

xraylabtool.constants.wavelength_angstrom_to_energy(wavelength_angstrom)[source]¶

Convert X-ray wavelength in Angstroms to energy in keV.

Parameters:: wavelength_angstrom (float | floating[Any] | ndarray[tuple[Any, ...], dtype[double]]) – X-ray wavelength in Angstroms
Return type:: float
Returns:: Energy in keV

Example

>>> from xraylabtool.constants import wavelength_angstrom_to_energy
>>> energy = wavelength_angstrom_to_energy(1.2398)  # Cu Kα₁
>>> print(f"Energy: {energy:.4f} keV")
Energy: 10.0003 keV

Usage Examples¶

Energy-Wavelength Conversion:

from xraylabtool.constants import HC_EV_ANGSTROM

def energy_to_wavelength(energy_ev):
    return HC_EV_ANGSTROM / energy_ev

wavelength = energy_to_wavelength(8000)  # 1.55 Å

Critical Angle Calculation:

from xraylabtool.constants import MRAD_TO_DEGREE
import numpy as np

def critical_angle_degrees(delta):
    theta_mrad = 1000 * np.sqrt(2 * delta)  # Convert to mrad
    return theta_mrad * MRAD_TO_DEGREE

Unit Conversions:

from xraylabtool.constants import G_CM3_TO_KG_M3, ANGSTROM_TO_METER

# Convert density
density_si = 2.33 * G_CM3_TO_KG_M3  # g/cm³ to kg/m³

# Convert wavelength
wavelength_m = 1.55 * ANGSTROM_TO_METER  # Å to m

Material Properties:

from xraylabtool.constants import COMMON_MATERIAL_DENSITIES, SILICON_DENSITY

# Get standard material densities
materials = ['Si', 'Al', 'Cu', 'Fe']
for material in materials:
    if material in COMMON_MATERIAL_DENSITIES:
        density = COMMON_MATERIAL_DENSITIES[material]
        print(f"{material}: {density} g/cm³")

Energy Range Validation:

from xraylabtool.constants import MIN_ENERGY_EV, MAX_ENERGY_EV

def validate_energy(energy):
    if energy < MIN_ENERGY_EV:
        raise ValueError(f"Energy {energy} eV below minimum {MIN_ENERGY_EV} eV")
    if energy > MAX_ENERGY_EV:
        raise ValueError(f"Energy {energy} eV above maximum {MAX_ENERGY_EV} eV")
    return True

Constants Reference Table¶

Key Physical Constants¶
Constant	Symbol	Value	Unit
Planck constant	h	4.136e-15	eV·s
Speed of light	c	2.998e8	m/s
Classical electron radius	r₀	2.818e-15	m
Electron rest energy	mₑc²	510,999	eV
hc product	hc	12,398.4	eV·Å

Conversion Factors¶
Conversion	Factor	Usage
Å → m	1.0e-10	Length units
eV → J	1.602e-19	Energy units
mrad → deg	0.0573	Angular units
g/cm³ → kg/m³	1000	Density units

CODATA Standards¶

All physical constants are based on the 2018 CODATA internationally recommended values, ensuring compatibility with modern scientific standards and other physics software packages.