[ Identification | Description | Input parameters | Links ]

# The `Isotropic_Sqw` Component

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

## Identification

- Site:
- Author: E. Farhi, V. Hugouvieux
- Origin: ILL
- Date: August 2003

## 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 %.

## Input parameters

Parameters in boldface are required; the others are optional.

Name | Unit | Description | Default |
powder_format | no quotes | name or definition of column indexes in file | {0,0,0,0,0,0,0,0,0} |
Sqw_coh | str | Name of the file containing the values of Q, w and S(Q,w) Coherent part; Q in Angs-1, E in meV, S(q,w) in meV-1. Use 0, NULL or "" to disable. | 0 |
Sqw_inc | str | Name of the file containing the values of Q, w and S(Q,w). Incoherent (self) part. Use 0, NULL or "" to scatter isotropically (V-like). | 0 |
geometry | str | Name of an Object File Format (OFF) or PLY file for complex geometry. The OFF/PLY file may be generated from XYZ coordinates using qhull/powercrust | 0 |
radius | m | Outer radius of sample in (x,z) plane. cylinder/sphere. | 0 |
thickness | m | Thickness of hollow sample Negative value extends the hollow volume outside of the box/cylinder. | 0 |
xwidth | m | width for a box sample shape | 0 |
yheight | m | Height of sample in vertical direction for box/cylinder shapes | 0 |
zdepth | m | depth for a box sample shape | 0 |
threshold | 1 | Value under which S(Q,w) is not accounted for. to set according to the S(Q,w) values, i.e. not too low. | 1e-20 |
order | 1 | Limit multiple scattering up to given order 0:all (default), 1:single, 2:double, ... | 0 |
T | K | Temperature of sample, detailed balance. Use T=-1 to disable it, and T=-2 to guess it from non-classical S(q,w) input. | 0 |
verbose | 1 | Verbosity level (0:silent, 1:normal, 2:verbose, 3:debug). A verbosity>1 also computes dispersions and S(q,w) analysis. | 1 |
d_phi | deg | scattering vertical angular spreading (usually the height of the next component/detector). Use 0 for full space. This is only relevant for single scattering (order=1). | 0 |
concentric | 1 | Indicate that this component has a hollow geometry and may contain other components. It should then be duplicated after the inside part (only for box, cylinder, sphere) [1] | 0 |
rho | AA-3 | Density of scattering elements (nb atoms/unit cell V_0). | 0 |
sigma_abs | barns | Absorption cross-section at 2200 m/s. Use -1 to unactivate. | 0 |
sigma_coh | barns | Coherent Scattering cross-section. Use -1 to unactivate. | 0 |
sigma_inc | barns | Incoherent Scattering cross-section. Use -1 to unactivate. | 0 |
classical | 1 | Assumes the S(q,w) data from the files is a classical S(q,w), and multiply that data by exp(hw/2kT) on up/down energy sides. Use 0 when obtained from raw experiments, 1 from molecular dynamics. Use -1 to guess from a data set including both energy sides. | -1 |
powder_Dd | 1 | global Delta_d/d spreading, or 0 if ideal. | 0 |
powder_DW | 1 | global Debey-Waller factor, if not in |F2| or 1. | 0 |
powder_Vc | AA^3 | volume of the unit cell | 0 |
density | g/cm^3 | density of material. V_rho=density/weight/1e24*N_A | 0 |
weight | g/mol | atomic/molecular weight of material | 0 |
p_interact | 1 | Force a given fraction of the beam to scatter, keeping intensity right, to enhance small signals (-1 unactivate). | -1 |
norm | 1 | Normalize S(q,w) when -1 (default). Use raw data when 1, multiplier for S(q,w) when norm>0. | -1 |
powder_barns | 1 | 0 when |F2| data in powder file are fm^2, 1 when in barns (barns=1 for laz, barns=0 for lau type files). | 1 |

AT ( | , | , |  | ) RELATIVE |  |
ROTATED ( | , | , |  | ) RELATIVE |

## Links

- Source code for `Isotropic_Sqw.comp`.
- 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).
- Cross sections for single elements
- Web Elements
- Fullprof powder refinement
- Crystallographica software
- Example data file He4_liq_coh.sqw
- The PowderN component.
- The test/example instrument Test_Isotropic_Sqw.instr.
- Geomview and Object File Format (OFF)
- Java version of Geomview (display only) jroff.jar
- qhull
- powercrust

[ Identification | Description | Input parameters | Links ]