Materials¶
Neutron scattering lengths and cross sections of the elements and their isotopes have been taken from NIST.
Chemical Composition with Examples¶
H2 O
- Isotopically averaged Hydrogen(H2)2 O
- Heavy waterD2 O
- Another way to specify heavy water
Enter a composition as a molecular formula of elements or isotopes.
For example, basic elements might be H
, Fe
or Si
, etc.
A molecular formula of elements might be H4-N2-C3
, which
corresponds to a molecule with 4 Hydrogen atoms, 2 Nitrogen atoms and
3 Carbon atoms. Each element in a molecular formula is followed by
the number of the atoms for that element, specified without a hyphen,
because each element is separated from other elements using a hyphen.
The number of atoms can be integer or float, but must start with a
digit, e.g. 0.6 is fine but .6 is not. This can be used to set elemental ratios
within a chemical composition. For example 95.1% Vanadium 4.9% Niobium can be
expressed as V0.951 Nb0.049
. Warning: Using this representation will
calculate all properties except for SampleNumberDensity which must be
set manually if required
Isotopes may also be included in a material
composition, and can be specified alone (as
in (Li7)
), or in a molecular formula (as in (Li7)2-C-H4-N-Cl6
).
Note, however, that No Spaces or Hyphens are allowed in an isotope
symbol specification. Also Note that for isotopes specified in a
molecular expression, the isotope must be enclosed by parenthesis,
except for two special cases, D
and T
, which stand for H2
and H3
, respectively.
Cross Section Calculations¶
Each of the cross sections (
where D2 O
Number Density¶
The number density is defined as
It can can be generated in one of several ways:
Specifying it directly with
NumberDensity
.Specifying the
ZParameter
and theUnitCellVolume
(or letting the algorithm calculate it from the OrientedLattice on theInputWorkspace
).If a chemical formula consisting of a single element has been supplied the number density will be looked up from Mantid tables
The default behaviour is to deduce it from an effective number density (see below) and an optional packing fraction supplied as
PackingFraction
(which is assumed to be 1 if not supplied)
The effective number density is defined as
where
It can be specified in one of several ways:
Specifiying it directly with
EffectiveNumberDensity
Specifying the mass density. In this case the effective number density is calculated as follows:
where
The default behaviour is to set it equal to the full number density multipled by the optional packing fraction (which is assumed to be 1 if not supplied)
The effective number density,
If both a number density and effective number density are supplied using the non-default behaviours then a packing fraction will be calculated from their ratio.
Attenuation Coefficients¶
The attenuation effect is calculated according to the following formula:
where
A detailed version of this is found in [2].
The sum of the two attenuation coefficients can be replaced by an externally measured profile of attenuation versus wavelength if the scattering effect is wavelength dependent eg if a material is crystalline and shows some Bragg edges in its attenuation profile. Mantid supports a space delimited text file format for the externally measured profile containing the following columns:
wavelength (in
)attenuation factor (in
)error (currently ignored)
The Xray Attenuation coefficients can also be provided by text file with the following columns containing:
energy (in
)attenuation factor (in
)error (currently ignored)
Any lines not following this format (eg header rows) are ignored. The file must have a .DAT file extension.
Normalized Laue¶
The low-
References¶
The data used in this algorithm comes from the following paper.
Varley F. Sears, Neutron scattering lengths and cross sections, Neutron News 3:3 (1992) 26 doi: 10.1080/10448639208218770
J. A. K. Howard, O. Johnson, A. J. Schultz and A. M. Stringer, Determination of the neutron absorption cross section for hydrogen as a function of wavelength with a pulsed neutron source, J. Appl. Cryst. (1987). 20, 120-122 doi: 10.1107/S0021889887087028
Category: Concepts