CylinderAbsorptionCW v1#

Summary#

Absorption and multiple scattering calculation for cylindrical samples with constant wavelength and assuming in-plane scattering only.

Properties#

Name	Direction	Type	Default	Description
InputWorkspace	Input	`Workspace`	Mandatory	Input workspace
Wavelength	Input	number	Mandatory	Wavelength in Angstroms.
Radius	Input	number	Optional	Radius of the cylinder in cm. If not provided, it will be inferred from the workspace sample shape if it is a cylinder.
Height	Input	number	Optional	Height of the cylinder in cm. Only used for multiple scattering calculation. If not provided, it will be inferred from the workspace sample shape if it is a cylinder.
AbsorptionXSection	Input	number	Optional	Absorption cross-section in barn at 1.7982 Å. If not provided, it will be inferred from the workspace sample material.
ScatteringXSection	Input	number	Optional	Scattering cross-section in barn. If not provided, it will be inferred from the workspace sample material.
SampleNumberDensity	Input	number	Optional	Number density of the material in atoms/Å^3. If not provided, it will be inferred from the workspace sample material.
AbsorptionCorrectionMethod	Input	string	Sears	Method to calculate absorption correction. Allowed values: [‘Sears’, ‘Sabine’]
AbsorptionWorkspace	Output	`Workspace`	Mandatory	Absorption correction output workspace name
MultipleScatteringWorkspace	Output	`Workspace`	Mandatory	Multiple scattering output workspace name

Description#

This algorithm implements two simple analytical absorption corrections and a lookup table for multiple-scattering corrections for constant wavelength diffractometers. The absorption and multiple scattering are calculated assuming a cylindrical sample geometry, constant wavelength and in-plane scattering only.

Two methods are available for calculating the absorption correction: Using Equation 26 and Table 3 from Sears [1] and using Equations 1-6 from Sabine [2].

Multiple scattering is calculated using Equation 16 and Table 1 from Blech and Averbach [3], using a bilinear interpolation of the tabulated values. Equation 16 gives \(\sigma_m\) but the output from this algorithm is the multiple scattering factor, \(\delta\) = \(\sigma_m/(\sigma_s + \sigma_m)\).

The cross-sections and number density are either taken from the sample material of the input workspace, as set by SetSample v1 or SetSampleMaterial v1, or provided directly through the AbsorptionXSection, ScatteringXSection and SampleNumberDensity properties. As with the sample material, AbsorptionXSection is the value tabulated at the reference wavelength of 1.7982 Å and is scaled linearly to Wavelength, \(\sigma_a(\lambda) = \sigma_a(1.7982\,\text{Å}) \times \lambda / 1.7982\,\text{Å}\).

Usage#

Example:

ws = CreateSampleWorkspace()
# Using values for vanadium
result = CylinderAbsorptionCW(
         InputWorkspace=ws,
         Radius=0.5,  # cm
         Height=4.0,  # cm
         Wavelength=1.7982,
         AbsorptionXSection=5.08,  # barn at 1.798 Å
         ScatteringXSection=5.1,  # barn
         SampleNumberDensity=0.0723,  # atoms/Å^3
         AbsorptionWorkspace="Absorption",
         MultipleScatteringWorkspace="MultipleScattering"
     )
print(f"Absorption correction calculated value is {result.AbsorptionWorkspace.y(0)[0]:.2f} and multiple scattering value is {result.MultipleScatteringWorkspace.y(0)[0]:.2f}")

Output:

Absorption correction calculated value is 0.54 and multiple scattering value is 0.15

Example using SetSample:

ws = CreateSampleWorkspace()
# Using values for Vanadium
SetSample(
     ws,
     Geometry={"Shape": "Cylinder", "Height": 4.0, "Radius": 0.5},
     Material = {"ChemicalFormula": "V", "SampleNumberDensity": 0.0723}
 )
result = CylinderAbsorptionCW(
         InputWorkspace=ws,
         Wavelength=1.7982,
         AbsorptionWorkspace="Absorption",
         MultipleScatteringWorkspace="MultipleScattering"
     )
print(f"Absorption correction calculated value is {result.AbsorptionWorkspace.y(0)[0]:.2f} and multiple scattering value is {result.MultipleScatteringWorkspace.y(0)[0]:.2f}")

Output:

Absorption correction calculated value is 0.54 and multiple scattering value is 0.15

Categories: AlgorithmIndex | CorrectionFunctions\AbsorptionCorrection

Source#

Python: CylinderAbsorptionCW.py