Isotropic sample handling multiple scattering and absorption for a general
S(q,w) (coherent and/or incoherent/self)

Identification

Author: E. Farhi, V. Hugouvieux

Origin: ILL

Date: August 2003

Version:(Unknown)

Modification history:

E. Farhi, Jul 2005: made it work, concentric mode, multiple use

E. Farhi, Mar 2007: improved implementation, correct small bugs

E. Farhi, Oct 2008: added any shape sample geometry

E. Farhi, Oct 2012: improved sampling scheme, correct bug in powder S(q)

Description

An isotropic sample handling multiple scattering and including as input the
dynamic structure factor of the chosen sample (e.g. from Molecular
Dynamics). Handles elastic/inelastic, coherent and incoherent scattering -
depending on the input S(q,w) - with multiple scattering and absorption.
Only the norm of q is handled (not the vector), and thus suitable for
liquids, gazes, amorphous and powder samples.
If incoherent/self S(q,w) file is specified as empty (0 or "") then the
scattering is constant isotropic (Vanadium like).
In case you only have one S(q,w) data containing both coherent and
incoherent contributions you should e.g. use 'Sqw_coh' and set 'sigma_coh'
to the total scattering cross section. Set sigma_coh and sigma_inc to -1 to unactivate.
The implementation will automatically nornalise S(q,w) so that S(q) -> 1 at
large q (parameter norm=-1). Alternatively, the S(q,w) data will be multiplied
by 'norm' for positive values. Use norm=0 or 1 to use the raw data as input.
The material temperature can be defined in the S(q,w) data files (see below)
or set manually as parameter T. Setting T=-1 disables detailed balance.
Setting T=-2 attempts to guess the temperature from the input S(q,w) data
which must then be non-classical and extend on both energy sides (+/-).
To use the S(q,w) data as is, without temperature effect, set T=-1 and norm=1.
Both non symmetric (quantum) and classical S(q,w) data sets can be given by mean
of the 'classical' parameter (see below).
Additionally, for single order scattering (order=1), you may restrict the
vertical spreading of the scattering area using d_phi parameter.
An important option to enhance statistics is to set 'p_interact' to, say,
30 percent (0.3) in order to force a fraction of the beam to scatter. This
will result on a larger number of scattered events, retaining intensity.
If you use this component and produce valuable scientific results, please
cite authors with references bellow (in Links).
E. Farhi et al, J Comp Phys 228 (2009) 5251
Sample shape:
Sample shape may be a cylinder, a sphere, a box or any other shape
box/plate: xwidth x yheight x zdepth (thickness=0)
hollow box/plate:xwidth x yheight x zdepth and thickness>0
cylinder: radius x yheight (thickness=0)
hollow cylinder: radius x yheight and thickness>0
sphere: radius (yheight=0 thickness=0)
hollow sphere: radius and thickness>0 (yheight=0)
any shape: geometry=OFF file
The complex geometry option handles any closed non-convex polyhedra.
It computes the intersection points of the neutron ray with the object
transparently, so that it can be used like a regular sample object.
It supports the OFF, PLY and NOFF file format but not COFF (colored faces).
Such files may be generated from XYZ data using:
qhull < coordinates.xyz Qx Qv Tv o > geomview.off
or
powercrust coordinates.xyz
and viewed with geomview or java -jar jroff.jar (see below).
The default size of the object depends of the OFF file data, but its
bounding box may be resized using xwidth,yheight and zdepth.
Concentric components:
This component has the ability to contain other components when used in
hollow cylinder geometry (namely sample environment, e.g. cryostat and
furnace structure). Such component 'shells' should be split into input and
output side surrounding the 'inside' components. First part must then use
'concentric=1' flag to enter the inside part. The component itself must be
repeated to mark the end of the concentric zone. The number of concentric
shells and number of components inside is not limited.
COMPONENT S_in = Isotropic_Sqw(Sqw_coh="Al.laz", concentric=1, ...)
AT (0,0,0) RELATIVE sample_position
COMPONENT something_inside ... // e.g. the sample itself or other materials
COMPONENT S_out = COPY(S_in)(concentric=0)
AT (0,0,0) RELATIVE sample_position
Sqw file format:
File format for S(Q,w) (coherent and incoherent) should contain 3 numerical
blocks, defining q axis values (vector), then energy axis values (vector),
then a matrix with one line per q axis value, containing Sqw values for
each energy axis value. Comments (starting with '#') and non numerical lines
are ignored and used to separate blocks. Sampling must be regular.
Some parameters can be specified in comment lines, namely (00 is a numerical value):
# sigma_abs 00 absorption scattering cross section in [barn]
# sigma_inc 00 coherent scattering cross section in [barn]
# sigma_coh 00 incoherent scattering cross section in [barn]
# Temperature 00 in [K]
# V_rho 00 atom density per Angs^3
# density 00 in [g/cm^3]
# weight 00 in [g/mol]
# classical 00 [0=contains Bose factor (measurement) ; 1=classical symmetric]
Example:
# q axis values
# vector of m values in Angstroem-1
0.001000 .... 3.591000
# w axis values
# vector of n values in meV
0.001391 ... 1.681391
# sqw values (one line per q axis value)
# matrix of S(q,w) values (m rows x n values), one line per q value,
9.721422 10.599145 ... 0.000000
10.054191 11.025244 ... 0.000000
...
0.000000 ... 3.860253
See for instance file He4_liq_coh.sqw. Such files may be obtained from e.g. INX,
Nathan, Lamp and IDA softwares, as well as Molecular Dynamics (nMoldyn).
When the provided S(q,w) data is obtained from the classical correlation function
G(r,t), which is real and symmetric in time, the 'classical=1' parameter
should be set in order to multiply the file data with exp(hw/2kT). Otherwise,
the S(q,w) is NOT symmetrised (classical). If the S(q,w) data set includes both
negative and positive energy values, setting 'classical=-1' will attempt to
guess what type of S(q,w) it is. The temperature can also be determined this way.
In case you do not know if the data is classical or quantum, assume it is usually classical
at high temperatures, and quantum otherwise (T < typical mode excitations).
The positive energy values correspond to Stokes processes, i.e. material gains
energy, and neutrons loose energy. The energy range is symmetrized to allow up
and down scattering, taking into account detailed balance exp(-hw/2kT).
You may also generate such S(q,w) 2D files using iFit Powder file format:
Files for coherent elastic powder scattering may also be used.
Format specification follows the same principle as in the PowderN
component, with parameters:
powder_format=
Crystallographica: { 4,5,7,0,0,0,0, 0,0 }
Fullprof: { 4,0,8,0,0,5,0, 0,0 }
Undefined: { 0,0,0,0,0,0,0, 0,0 }
Lazy: {17,6,0,0,0,0,0,13,0 }
qSq: {-1,0,0,0,0,0,1, 0,0 } // special case for [q,Sq] table
or: {j,d,F2,DW,Delta_d/d,1/2d,q,F,strain}
or column indexes (starting from 1) given as comments in the file header
(e.g. '#column_j 4'). Refer to the PowderN component for more details.
Delta_d/d and Debye-Waller factor may be specified for all lines with the
'powder_Dd' and 'powder_DW' parameters.
The reflection list should be ordered by decreasing d-spacing values.
Additionally a special [q,Sq] format is also defined with:
powder_format=qSq
for which column 1 is 'q' and column 2 is 'S(q)'.
Examples:
1- Vanadium-like incoherent elastic scattering
Isotropic_Sqw(radius=0.005, yheight=0.01, V_rho=1/13.827,
sigma_abs=5.08, sigma_inc=4.935, sigma_coh=0)
2- liq-4He parameters
Isotropic_Sqw(..., Sqw_coh="He4_liq_coh.sqw", T=10, p_interact=0.3)
3- powder sample
Isotropic_Sqw(..., Sqw_coh="Al.laz")
%BUGS:
When used in concentric mode, multiple bouncing scattering
(traversing the hollow part) is not taken into account.
%VALIDATION
For Vanadium incoherent scattering mode, V_sample, PowderN, Single_crystal
and Isotropic_Sqw produce equivalent results, eventhough the two later are
more accurate (geometry, multiple scattering). Isotropic_Sqw gives same
powder patterns as PowderN, with an intensity within 20 %.

E. Farhi, V. Hugouvieux, M.R. Johnson, and W. Kob, Journal of Computational Physics 228 (2009) 5251-5261 "Virtual experiments: Combining realistic neutron scattering instrument and sample simulations"

Hugouvieux V, Farhi E, Johnson MR, Physica B, 350 (2004) 151 "Virtual neutron scattering experiments"

Hugouvieux V, PhD, University of Montpellier II, France (2004).

H. Schober, Collection SFN 10 (2010) 159-336

H.E. Fischer, A.C. Barnes, and P.S. Salmon. Rep. Prog. Phys., 69 (2006) 233

P.A. Egelstaff, An Introduction to the Liquid State, 2nd Ed., Oxford Science Pub., Clarendon Press (1992).

S. W. Lovesey, Theory of Neutron Scattering from Condensed Matter, Vol1, Oxford Science Pub., Clarendon Press (1984).