In the example above, all the atomic positions have site symmetry of '4a'. This means that there are 4 equivalent positions for each atom.

Therefore, a unit cell contains 4 formula units. (Z=4).

Step 2: Calculate absorption

Open the website of "Neutron activation and scattering calculator"  in NIST Center for Neutron Research.

In the "Material" section, write a chemical formula for a unit cell, specifically, CaBaCo4O7 x 4 = "Ca4Ba4Co16O28".

In the "Absorption and Scattering" section, input as follows

• Density : [Unit-cell volume in Angstrom^3 unit] A3

• Source neutrons : 2.4 Ang

By adding "A3" at the end of the unit-cell volume, the density will be automatically calculated.

At PONTA, we normally use thermal neutrons with a wavelength of 2.35-2.44 A. Please use "2.4 Ang" as a standard value.

And then, press "Calculate" button.

Check the 1/e penetration depth (cm) of "abs+incoh" (which means absorption and incoherent scattering).

This is the optimum scattering-path-length in the unit of "cm". In the present case, it is about 8 mm.

Wavelength dependence of absorption

Calculate the absorption coefficient assuming lambda = 1 A. 

The absorption cross section linearly depends on lambda. (The probability of absorption is inversely proportional to neutron velocity.) Incoherent scattering cross section does not depend on lambda. 

Therefore, the linear attenuation coefficient, μ(λ), is given by

The intensity of the neutron beam passing through the sample with the thickness of t (cm) is given by

I0 is the intensity of the incident neutron beam. t is the thickness or the scattering path length in the sample. Note that the unit of t is cm (not mm).