Module Evaluation Inelastic

# VITESS Module Evaluation Inelastic

This module supports the evaluation of the simulated inelastic scattering data for general prototypes of instruments:

1. Monochromator + Analyser,
2. Monochromator + TOF,
3. TOF + Analyser.

#### A. Monochromator + Analyser

In the case of monochromated and (crystal)analysed neutrons both the average initial and final wavevectors are fixed in the experiment and the momentum and energy transfers can be calculated: The corresponding scattering angle is: In this simple case, by integrating all detected neutron probabilities we obtain the value for S(q,w) in the point (q,w)=(Q, W).

The integral is written by this module to the log file (shown automatically in the Xcontrol window) as "INTEGRAL INTENSITY".

For the simulation of Triple Axis Spectroscopy or monochromator-analyser backscattering instruments, the user has to scan the incident and/or scattered neutron wavevectors, and to collect the integral intensity data for each single point (q,w), as in real experiments. For this case only the integral written to the log file is the output of interest, therefore no names for the 'TOF and energy spectrum files' should be given as an input, in order not to create them . All other input values or options excepting 'angle' and 'angle range' are not considered for calculating the "Integral Intensity", i.e. you can give some dummy values (e.g. 'divide by Bose factor' is not considered although if it is activated in the GUI).

B.+C. Monochromator + TOF or TOF + Analyser

These two cases comprise direct and inverted geometry instruments in which either the initial or the final average wavelength is selected by a crystal, chopper or other selector system. This wavelength has to be given in the input as "reference wavelength".

1. The input parameters are:

number of bins [-] | The number of time and energy channels to be considered;
primary and secondary flight path [cm] | Distance from the moderator to sample and from sample to detector.
reference wavelength [Å] | Initial or final wavelength of the neutrons which is known from the experimental setup.
time offset [ms] | If nonzero, start time at moderator is shifted: TOF' = TOF time offset.
minimal and maximal time [ms] | The TOF range in which the user is interested to bin intensities. If this range is not given it will be calculated from the energy transfer range.
minimal and maximal energy transfer [meV] | The energy transfer range in which the user is interested to bin intensities. If this range is not given it will be calculated from the TOF range.
gradient of timebins [-] | Derivative s of the time channel width in function of TOF (as described in the help manual, sec. 4) .
temperature [K] | Temperature according to the temperature of the sample (only used for the case 'divide by Bose factor').
angle and angle range [-] | The user can select those neutrons which cross a smaller area on the detector surface by giving the angular position ( 'angle' relative to the X-axis) and width ('angle range') of a window in horizontal direction. In vertical direction no restriction is possible.

2. Options:

geometry: direct or inverted | Choose geometry type of TOF instrument.
divide by Bose Factor | Choose whether the energy spectrum shall be normalised or not by the Bose Factor.

3. Files:

TOF spectrum file | Filename for the TOF spectrum datafile.
energy spectrum file | Filename for the energy spectrum datafile.

4. Expressions for TOF binning

For the case of constant channel-width spectra (number of bins: N), the TOF channel boundaries can be calculated in a simple way:

In this case the channel width is: For the case of increasing/decreasing channel width we have to choose a non-homogeneous form: The boundary conditions: t0 = tmin and tN = tmax are fulfilled if: It is convenient to define a small parameters : a = 1/(1 - s) so that: As it can be seen,s represents a gradient describing the channel width variation. A reasonable range for this parameter is: |s| < 0.01 .

5. Expressions for energy binning

This module also transforms constant angle TOF data into constant angle energy spectra.

Generally in TOF measurements, the total flight time of the neutrons is measured. By knowing the primary, secondary flight path (L1,2) and the average neutron velocity either before (direct geometry) or after (inverted geometry) interacting with the sample, both the primary and secondary TOF can be calculated. The kinetic energies E1,2 before or after the scattering can be calculated from the reference (known) wavelength l (given in Å):

E1,2= 81805.048 / l2meV. The following formula gives the energy transfers direct (first index and upper sign) and inverted (second index and lower sign) geometries: From this expression, the energy transfer range of interest can be calculated by taking t = tmin and t = tmax. In this module, the energy range is divided by the number of bins (N) yielding constant channel-width in the whole range.

In order to obtain a correct intensity distribution in energy, one has to take into account the derivative resulting from the TOF-energy transformation

dt anddw represent the time and energy channel width. Thus from the expression of energy transfer for direct (first index and upper sign) and inverted (second index and lower sign) geometries: Conforming to the master formula, for each neutron, the dynamic structure factor S(q,w) is multiplied in the sample module by the factor kf/ki. Thus, in the evaluation of S(f ,w) the intensity per channel has to be divided by the average of this factor: Consequently, the intensity has to be multiplied by the resulting factor:
In this module, the universal constants before the bracket are not considered in the normalization.

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Last modified: Thu Jan 29 15:23:30 MET 2004, G. Zs.