RE: absorption correction for neutrons

Jean Marc JOUBERT ( joubert@cnrs-bellevue.fr )
Thu, 23 Oct 1997 18:32:20 +0100

Absorption coefficients for neutrons are often neglected There are several
reasons for that :
- those coefficients as regard to X-rays' are generally very small
- when they are large (Eu, Gd, Cd), it is impossible to make neutron
diffraction
- absorption spectroscopy for neutron is far less rich than for X-rays -
they are a bit difficult to calculate (!!!)
They are several interests in doing this calculation before your experiment
or before your refinement of powder data
- you must keep always in mind that, like for X-ray in Debye-Scherrer
geometry, the value of muR must be kept below 1 because the fomula used in
Rietveld programs known as Hewat fomula (eg Fullprof) is only valid in that case
- you can be helped by the calculation if you intend to make neutron
diffraction with heavy absorber elements (B, Gd...) to select the adequate
diameter for your capillary, the appropriate wavelength or the appropriate
extent of isotopic enrichment you need
- finally the correct value for muR must be introduced in Rietveld
refinement programs, if not (because the effects on the intensities are the
same than thermal motion), your value for Bs can be all shifted downwards.

You calculate the cross-section for absorption (for each element) by making
the sum of the cross-sections of all the processes that reduce the neutron
beam :

- coherent scattering (i.e. diffraction)
- incoherent scattering
- magnetic scattering
- true absorption

The reference to be taken for cross sections is V.F. Sears, Neutron News,
3(3) (1992) 26-37.

The cross-section for true absorption is given in tables for lambda=1.798
(v=2200m/s). You must correct it depending on the wavelength you have used
following :
sigma true abs=sigma true abs (at 2200m/s).lambda/1.798

We suppose that true absorption depends on 1/v where v is the velocity of
neutrons. This is true only in the absence of any resonant effect. Resonant
absorption does exist also for neutrons : it can be dangerous to neglect it.
However absorption resonance peaks are difficult to find in literature. If
someone has a reference for that, it would be very interesting for me.

You add the different cross-sections :
sigma abs (in barn)=sigma coh+sigma incoh+sigma magn+sigma true abs

Then you can calculate the absorption coefficient for each element:
mu/rho=sigma abs*1E-24*Avogadro number/molar weight (in cm2/g)

You can easily now calculate the value of mu in cm-1 depending of the
concentrations of each element in your compound.

The value of muR is then calculated (R is radius not diameter, in cm) but
taking into account the packing of your sample in the capillary (generally
not more than 30-50%) (you can measure it) and you can enter it in the
proper place in FULLPROF.

I have written an EXCEL sheet making those calculations and I can send it to
you if interested.

If the value of muR is more than one, you have to face a great problem
because the correction is no more valid. However you can still use some
tricks...

It is strange that you didn't succeed in refining your data because normally
absorption correlates completely with overall thermal factors. Therefore you
should have fitted well with low (even negatives) B factors.

Hope this helps. Any comments appreciated.

Jean-Marc Joubert

---------------------------------------------------------------
Jean-Marc Joubert
Laboratoire de Chimie Metallurgique des Terres Rares
1, Place A. Briand
F-92195 MEUDON CEDEX

phone : (33)(0)1 45 07 52 80
fax : (33)(0)1 45 07 58 44
E-mail : joubert@cnrs-bellevue.fr