Module Inelastic Sample

# VITESS Module Inelastic Sample

This module simulates a cylindrical, spherical or cuboid sample which scatters conforming to a scattering function S(q,w). It makes possible to compute inelastic energy transfers along a linear dispersion curve or plane dispersion surface within a finite momentum transfer range. This form can also be used for a local approach of non-linear energy dispersion relations.

The probability weight P provided by the former module is multiplied by the known factors:

P' = (sr) x pathlength x attenuation x |kf|/|ki| x S(q,w) x (solid angle/4pi) x P,

where (sr) is the scattering coefficient [cm-1] i.e. scattering cross section multiplied with density. Attenuation means two wavelength and path length dependent exponential factors before and after the scattering: exp(-(s + sabsorbtion)r x pathlength), where is sabsorbtion ~ l, and the usual tabular value for 1.8 Angstrom has to be converted to 1 Angstrom and used in order to calculate the input value absorption coefficient. The (sr) scattering coefficient [cm-1] contributes to the attenuation ('self-shielding').

The sample structure is considered as homogeneous and absorbent. The geometrical parameters of the sample are: position, horizontal and vertical offset angles with reference to the final coordinate system of the antecedent module, and size of the sample.

Detailed parameter definitions can be read from the tables in section B. The functions used to approximate S(q,w) are given in section C.

In the output frame X'Y'Z', all neutron coordinates are referring to the moment when the neutrons are just crossing the sample walls after the scattering . Multiple scattering is not yet included. The effect of sample size and geometry on the scattered intensity can be calculated by calibration taking into account that I / I' = V/V' (V - illuminated sample volume).

A. Options

1. No Bose Factor: | No detailed balance considered (BF = 1).
2. Bose Factor: | Detailed balance included.

B. Parameter and file descriptions

File | Format | Examples Attached
Parameter File | Includes FILE INPUT PARAMETERS. This file can be read or created/modified by the VITESS shell. Values are read from separate rows i.e. 1 value/row for scalar and 3 values/row for vector type variables. | sampleinelast_default.ine

- MAIN PARAMETERS

Parameter | Physical Symbol, Description | Range, Examples
P1, P2 [microeV] P3 [1/microeV] P4 [-] | Parameters of the S(q,w) function as defined in section C. The HWHM parameter P2 should be > 0.0001 microeV. If P4=0. one obtains Lorentzian function and P4 =1. gives symmetrized Lorentzian which works for P1 > 0. | e.g. quasielastic: P1 = 0.0, P2 = 10.0, P3 = 0.5, P4 =0.0
D1, D2, D3 [Å] | Cartesian coefficients defining the dispersion relation of excitations as given in section C. | if 0.0, 0.0, 0.0 no dispersion
temperature [K] | Temperature of the sample controlling detailed balance. If T = 0, Bose Factor is set to 1 for w>0 and 0 for w<0. | e.g. 0.0 1000. K
repetition [-] | If this integer > 1, the neutron is used multiple times to obtain better statistics. | >= 1

- FILE INPUT PARAMETERS

Parameter | Description | Range, Examples
lambda final [Å] | Gives centre position of the scattered wavelength interval which is considered in the computation. It is recommended to choose e.g. the main analyser wavelength. | e.g. 6.27 for Si(111) analyser
delta lambda final [Å] | Gives the length of the scattered wavelength interval which is considered in the computation. | e.g. ~0.02 for Si(111) and ~0.2 for PG(002);
angle horiz/vert final [deg] | horizontal and vertical components of the main scattering angle | -180° - 180°
delta angle horiz/vert [deg] | angular intervals around the horizontal and vertical components of the main scattering angle | 0° - 180°
absorption coefficient [1/cm/ Å] | Attenuation constant per unit wavelength (corresponding to 1 Angstrom) which is 1/ (density * absorbtion cross section). | > 0.
scattering coefficient [1/cm] | 1/ (density * scattering cross section) | from tables
position [cm] | Position of sample center in the frame provided by the former module. | e.g. 10.0, 0.0, 0.0
thickness, height, width [cm] | Thickness, height and width give dimensions of a cuboid sample. For cylinder only diamter and height are relevant parameters. For hollow cylinder, inner diameter is given by the third parameter.For spherical samples only the first value is considered as radius. | e.g. cylinder: 1.0, 6.0
offset angle horizontal, vertical [deg] | A rotation first around the Z axis and then around the (new)Y axis gives the orientation of the sample. It has no relevance for a spherical sample geometry. | e.g. 0.0, 0.0
lambda and angle horiz., vert. initial [Å], [deg],[deg] | These data only are necessary for setting "standard frame generation". It gives the initial wavevector (e.g. the most probable initial wavevector) to calculate the main scattering angle from the scattering triangle (by considering the centre of the q-transfer range). The corresponding energy transfer is also calculated and written to the log file (respectively to the X-control window). Generally, the initial k-vector should be set parallel to X, however the vectorial input makes possible a non-parallel choice in order to analyse the effect of divergence on the instrument resolution. The initial k-vector has to be given for formal reasons even if "user defined output frame" is activated . Nevertheless it can be used to obtain in the log file the corresponding energy transfer and scattering angle with respect to the vector q-transfer. | e.g. data corresponding to the most probable initial neutron wavevector
output angle horizontal, vertical [deg] | In case of "user defined output frame", a rotation about the Z axis and then a rotation about the (new)Y axis defines a new orientation for the neutrons written to the output. If "standard frame generation" is activated, the coordinate system is rotated until the new X axis is parallel to the scattering direction which is determined by the reference k-vector and the vector 'q-transfer' defined above. This option is recommended for all direct geometry or (quasi)elastic inverted geometry simulations, the reference (i.e average incident) k-vector being fixed for all q-transfers. | e.g. forward scattering: 0.0, 0.0
output frame X',Y',Z' [cm] | The position of the output frame origin in the original frame. It represents the translation vector applied to shift the origin of the original (input) frame to the new (output) position. Default setting (standard frame) is the main position of the sample. | one point on the scattered beam axis

Quasi-elastic scattering

Set P1=P4=0 for quasi-elastic scattering and lambda final equal to lambda initial. Delta lambda final should be matched to the HWHM parameter P2: lambda and delta lambda final determine the wavelength/energy range in which neutrons are simulated, while the P parameters determine the Lorentzian shape via the neutron weight. The delta lambda final should cover several times the FWHM to see the tails of the Lorentzian distribution. Note that in order to see a broadening of the elastic peak, the width of the incoming neutron wavelength has to be smaller than the energy transfer / delta lambda final.

C. Functions used

1) Scattering function:

Here a HWHM-independent normalization was defined as: S(q,w)max=2xBFxP3(1-P4) i.e. the (symmetrized) Lorentzian amplitude multiplied by P2 the HWHM of the Lorentzian. The user can properly set P3 as function of P2 in order to obtain the 'normal' Lorentz normalization. For continuity reasons exact w = 0 events are skipped and P2 > 0.0001 meV. For computation of non-coupled multipeak dynamic structure factors it is recommended to run separate simulations for each single peak and add the resulting TOF or energy spectra.

2) Dispersion function:

By considering P1 as a reference energy, the dispersion relation E(q) is:

with

3) Bose factor:

If option 'No Bose factor' has been chosen, BF is set to 1 for all cases.

If T = 0, BF = 1 for w > 0 and BF = 0 for w < 0.

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Last modified: Thu Jan 29 15:36:03 MET 2004, G. Zs.