ResLibCal: a tool to compute triple-axis neutron spectrometer resolution

ResLibCal

E. Farhi, ILL/DS/CS - Version 1.3 - Mar. 22, 2017

using parts from ResLib, ResCal5, Res3ax and ResCal


  1. Purpose
  2. Obtaining the package
  3. Installation - starting
  4. Available computational methods
  5. Usage to compute the TAS resolution function (with plots)
    1. ResLibCal: the main interface
    2. ResCal standard nomenclature for configurations
    3. The lattice and spectrometer coordinate frames
    4. Plotting the TAS resolution function
    5. Handling computation along a scan (measurement sequences)
    6. Loading previous configurations
    7. Exporting the results, saving the configuration
    8. Non interactive mode (compute only)
  6. Convolution of the TAS resolution function with a model, in 4D
    1. Dispersion model: 4D dynamic structure factors S(q,w)
    2. Planned in the future
  7. Help
  8. Credits and disclaimer



Purpose

This ResLibCal application gathers a set of analytical computation methods to estimate the resolution function of a triple-axis neutron spectrometer (TAS). ResLibCal is based on Matlab. The Cooper-Nathans and Popovici methods are proposed [1-7], in different implementations from:

Obtaining the package

Source code
The package can be obtained here [ZIP 220 ko]. You can also browse the source code here or get a copy.
It does not depend on any other toolbox/library, except Matlab. Simply extract the application archive.
In addition, the legacy RESCAL code is also made available as [Fortran code].

Binary pre-compiled (no need for Matlab)
It comes pre-installed in the iFit standalone distribution.
ResLibCal does not require iFit to be installed, and can be used as a separate application. However, to benefit from the 4D convolution feature, it is advised to install iFit, which includes ResLibCal.

Installation - starting

Just launch ResLibCal with:
>> ResLibCal;
If you use the source code distribution (requires a Matlab license), type:
>> addpath(genpath('/path/to/ResLibCal'))
If you use the standalone (binary compiled, no need for a Matlab license) application, launch the application from iFit by starting:
from the terminal:
% ifit ResLibCal
from iFit standalone:
>> ResLibCal

Available computational methods

There are basically two analytical methods to compute the resolution function of a TAS instrument:
The Cooper-Nathans [1] method handles a conventional description of the instrument, with collimations and homogeneous mosaic spread.
The Popovici method [3] handles similarly collimations and mosaic spreads (but here with separate horizontal and vertical components), but also much more geometrical details, including the optical elements size, and the radius of curvature of the monochromator and analyzer. Modern TAS machines mostly use optics focusing so that this method is probably more suited to model today's spectrometers.
The Full Monte-Carlo uses a Monte-Carlo instrument simulation with McStas (templateTAS instrument) to evaluate the resolution as a cloud of points in the reciprocal space. This cloud can then be used for 4D convolution.
The analytical methods, Cooper-Nathans and Popovici, define the resolution matrix as [3]:

M = [B.A. [C'.F.C+G]-1 A'.B']-1
where:
The term C'.F.C is often labeled as H, and has a slightly more developed expression in the Popovici formalism, with additional geometrical terms involving distances and dimensions of the spectrometer parts.

The intensity pre-factor R0 can be estimated as (in Cooper-Nathans formalism) [3]:

R0 = [RM RA (2π)4 det(F) ] / [ 64π2 sinM) sin(θA) det(H) ]

where RM and RA are the monochromator and analyzer reflectivity. A similar expression holds for Popovici.

From there, the resolution Gaussian distribution is obtained from

R(q,w) = R0 e -x'.M.x

where x = [qx qy qz w] is the offset to the center of the resolution, in the HKLE 4D space.

The following computational methods are available (top left red pop-up menu):
Tip: If you do not know which method to use, prefer any of the Popovici methods. The Cooper-Nathans method is not recommended (highly approximate). The most accurate method is the full Monte-Carlo, but it is slower.
Intensity:
The Cooper-Nathans/AFILL method uses the Chesser and Axe intensity estimate [2], whereas all the other methods use the Popovici formulation [3]. The intensity estimate is given w.r.t the source, and is given in [a.u.]. The monochromator and analyzer reflectivity is assumed to be ideal (1).
The intensity with the Full Monte-Carlo model provides the best estimate.
Collimation:
In all methods, the alpha/beta collimation parameters support guide m-coating specification (negative values e.g. -2) which are then converted to equivalent critical angles 0.1 m λi [deg]. The alpha/beta collimations are also limited by the effective divergence set from the geometry, e.g. atan(width or height/distance) [rad].
The collimations with the Full Monte-Carlo model provides the best estimate, as they are indeed modeled as Soller type collimators.
Mosaic spread:
The sample mosaic spread is also taken into account, as well as a correction for the sample orientation w.r.t. the incoming beam.
In the legacy Cooper-Nathans formalism, all mosaic spreads are isotropic (monochromator, analyzer, sample). In the Cooper-Nathans/Popovici formalism, mosaicity supports separate vertical and horizontal components, including correction [7].
In the Popovici formalism, all mosaicities are taken into account with separate vertical and horizontal components (monochromator, analyzer, sample).
The mosaicities with the Full Monte-Carlo model are assumed with a gaussian reflectivity profile.

Computation takes a few 10ms, whatever be the analytical method used.The Full Monte-Carlo takes a few 100 ms.

Usage to compute the TAS resolution function (with plots)

The normal use of the application is through its GUI, which is a single window.
It is also possible to use the application from a Matlab script or prompt, without starting the GUI (see below).
The computation of the resolution is carried-out in about 11 ms, but the display can be slightly longer when using the GUI (few 100 ms).

ResLibCal: the main interface

The main interface present all parameters required to configure a Cooper-Nathans or Popovici computation. All items have a contextual help (bring the mouse pointer over to display a short tool-tip, with signification and units). Parameters indicated in blue are used only in for the Popovici method. Parameters in red are those which the user should mostly change (incident energy, position of measurement HKLE) once the instrument configuration has been set.

The Q and Energy transfer are defined as:

Q = HKL = Ki - Kf
w = E = Ei - Ef

where Ki,Kf and Ei,Ef are the wavevectors [e.g. in rlu or Angs-1] and energies [e.g. in meV] in initial (incoming) and final (after sample) states.

The main parameter categories are:

When any value is changed, an automatic re-computation is performed if the View/Auto-update menu item is checked (which is the default).
The result of the computation can be displayed from the View menu in 2D and 3D, as well as the instrument geometry.

The resolution matrix is then shown in reciprocal lattice units (rlu) [a*,b*,E] or inverse Angstroem (Angs-1) [Qx,Qy,E or A,B,E] . You can select the coordinate frame used for displaying the resolution in the Un-checking the Resolution in ... sub-menu in the View menu. See below for a description of the available coordinate frames. It is also possible to plot the resolution function projections in the vertical [Qz, c* or C]  axis instead of the energy E axis by toggling the View menu, e.g. Resolution in [Qx,Qy,E] item.
The resolution matrix is always computed in [Angs-3.meV], but it can be shown in [rlu3.meV] in the 2D and 3D views.

The ResLibCal main interface
The ResLibCal main interface. All items have contextual help. When the View/Auto-update menu item is checked, any change in the interface triggers a re-computation of the resolution, and an update of opened plots.

The collimations are given in [arcmin], but are bound between 0 and the geometrical angular aperture defined by the distances and dimensions of the spectrometer parts. The source-monochromator collimations (ALF1 and BET1) can be defined as a wavelength dependent divergence when given a negative value '-m' for a guide m-coating reading: 0.1 m λi [deg] where λi is the incident wavelength.

The monochromator and analyser curvatures can be given as the curvature radius [in cm], or set to 0 for a flat geometry, or to a negative value (e.g. -1) to request an automatic computation using the following expressions (for both monochromator and analyser):

RV = 2*L*sin(θ)
RH = 2*L/sin(θ)

where θ is the tilt angle, and 1/L=1/Lbefore + 1/Lafter is the effective focal distance.

ResCal standard nomenclature for configurations

The user interface and configuration files lists parameters with the legacy ResCal naming. The meaning of the configuration parameters is the following
DM Monochromator d-spacing
DA Analyzer d-spacing
ETAM Monochromator mosaic
ETAA Analyzer mosaic
ETAS Sample mosaic
SM scattering sense frocdm monochromator +1=right, -1=left
SS scattering sense from sample +1=right, -1=left
SA scattering sense from analyzer +1=right, -1=left
KFIX fixed neutron wavevector in Ang.-1
FX index for fixed wavevector 1=incident 2=final (10)
ALF1 horizontal source-mono. collimation in min (FWHM)
ALF2 horizontal mono.-sample collimation in min (FWHM)
ALF3 horizontal sample-analyser collimation in min (FWHM)
ALF4 horizontal analyser-detector collimation in min (FWHM)
BET1
vertical source-mono. collimation in min (FWHM)
BET2
vertical mono.-sample collimation in min (FWHM)
BET3
vertical sample-analyser collimation in min (FWHM)
BET4
vertical analyser-detector collimation in min (FWHM)
AS
sample lattice parameter a in Angs.
BS sample lattice parameter b in Angs.
CS sample lattice parameter c in Angs.
AA (alpha) angle in deg. between axes b and c
BB (beta) angle in deg. between axes a and c
CC (gamma) angle in deg. between axes a and b
AX First wavevector in scattering plane coordinate H (rlu). angle <KI,A>=A3
AY First wavevector in scattering plane coordinate K (rlu)
AZ First wavevector in scattering plane coordinate L (rlu)
BX Second wavevector in scattering plane coordinate H (rlu)
BY Second wavevector in scattering plane coordinate K (rlu)
BZ Second wavevector inou scattering plane coordinate L (rlu)
QH Position of resolution wavevector (center of measurement) H (rlu)
QK Position of resolution wavevector (center of measurement) K (rlu)
QL Position of resolution wavevector (center of measurement) L (rlu)
EN (W) Position of resolution wavevector (center of measurement) W (meV)
DQH Increment of Q,E defining general scan step along QH (rlu)
DQK Increment of Q,E defining general scan step along QK (rlu)
DQL Increment of Q,E defining general scan step along QL (rlu)
DEN Increment of Q,E defining general scan step along EN (meV)
GH Gradient of the dispersion (planar) direction along QH (rlu)
GK Gradient of the dispersion (planar) direction along QK (rlu)
GL Gradient of the dispersion (planar) direction along QL (rlu)
GMOD Gradient of the dispersion (planar) direction along EN (meV)
BeamShape =0 for circular source, =1 for rectangular source
WB width/diameter of the source (cm)
HB height/diameter of the source (cm)
Guide =0 No Guide, =1 for Guide
GDH horizontal guide divergence (minutes/Angs)
GDV vertical guide divergence (minutes/Angs)
SampleShape =0 for cylindrical sample, =1 for cuboid sample
WS sample width/diameter perp. to Q (cm)
TS sample width/diameter along Q (cm)
HS sample height (cm) (10)
DetectorShape =0 for circular detector, =1 for rectangular detector
WD width/diameter of the detector (cm)
HD height/diameter of the detector (cm)
TM thickness of monochromator (cm)
WM width of monochromator (cm)
HM height of monochromator (cm)
TA thickness of analyser (cm)
WA width of analyser (cm)
HA height of analyser (cm)
L1 distance between source and monochromator (cm)
L2 distance between monochromator and sample (cm)
L3 distance between sample and analyser (cm)
L4 distance between analyser and detector (cm)
RMH horizontal radius of curvature of monochromator (cm)
RMV vertical radius of curvature of monochromator (cm)
RAH horizontal radius of curvature of analyser (cm)
RAV vertical radius of curvature of analyser (cm)

The lattice and spectrometer coordinate frames

The resolution can be obtained and displayed in 2 coordinate frames:coordinate frames
The usual definition of the sample reciprocal lattice orientation vectors A and B (defined by the user), are so that the spectrometer angle A3 is the angle between KI and A=(AX,AY,AZ). The B=(BX,BY,BZ) vector defines a second lattice vector in the scattering plane. This is why, in order to properly define the [A,B] basis, an initial measurement is done in practice on a Bragg signal with Q=[QH,QK,QL]=[AX,AY,AZ]. For such a measurement, the [rlu] and [spec] frames are equivalent in a cubic lattice. Then the A3 angle offset is set to the signal maximum.

Plotting the TAS resolution function

To compute and plot the resolution function, select the View/Resolution Ellipsoid (2D and Matrix) or View/Resolution Ellipsoid (3D) menu item. The 2D view also prints the resolution function, its projection (flat phonon width) and intersection (Bragg width), and equivalent ResCal parameters. The 3D view also shows the ellipsoid projections. The corresponding full width values are indicated.

The Q// (parallel to Q) axis is along the longitudinal (radial) direction Q=[HKL], Q⊥ is the transverse (tangential) direction in the scattering plane, and Q↑ is vertical, w.r.t the scattering plane, in the laboratory coordinate frame.
In the sample coordinate frame, a*, b* and c* and the reciprocal lattice vectors.

If no resolution view is active, the results are sent to the console (as text).
These view can also be displayed with:
>> ResLibCal('view2')
>> ResLibCal('view3')
>> ResLibCal('geometry')
For the 2D and 3D view, it is possible to display the resolution volume as a cloud of points computed randomly with a gaussian distribution from the resolution matrix. When using the Full Monte-Carlo computational method, the cloud is ontained directly from the TAS model (McStas), and the resolution matrix is computed from the half width distribution. The cloud view is shown when selecting the Overlay Monte-carlo cloud item in the View menu. The number of points computed can be set with the Set Monte-Carlo iterations item (e.g. 200), but in all cases, in order to render the plot faster, the distribution is shown with not more than a few hundred points.

ResLibCal Resolution function: 2D plot and text
        output
The 2D plot of the TAS resolution function, with a text box containing the computation results and detailed configuration.

The ResLibCal resolution in 3D
The 3D plot of the TAS resolution function. The axis has a contextual menu allowing to change the plot rendering.

A geometric representation of the TAS can be shown in real space, using the instrument configuration parameters. This view is generated from the View/Instrument geometry menu item. It is automatically updated upon change of instrument parameters, as the other views.
The signification of the angles shown is as follows:
A1  rotation angle of the monochromator. A1=0 means the crystal is in grazing incidence.
A2 scattering angle (take-off) from the monochromator, usually A2=2*A1 in scattering condition.
A3 orientation angle of the crystal lattice in real space. This is the angle between KI and vector A=(AX,AY,AZ)
A4 scattering angle (take-off) from the sample. Usually A4 is NOT 2*A3.
A5 rotation angle of the analyser. A5=0 means the crystal is in grazing incidence.
A6 scattering angle (take-off) from the analyser, usually A6=2*A5 in scattering condition.  

The TAS geometry view
The 3D plot of the TAS geometry. The axis has a contextual menu allowing to change the plot rendering.

Handling computation along a scan (measurement sequences)

A computation along
            an energy scanAny HKLE setting can be assign a vector, so that the resolution will be computed, and plotted in GUI mode for all measurements. The vector should be set as values separated by spaces.
An example is for instance
H=1 K=0 L=0
W=-5 0 5
which shows a 3 steps scan along the energy axis.

Loading previous configurations

The 'File/Open...' menu item allows to read a saved ResLibCal configuration (*.m, *.ini, see below), a ResCal5 configuration (*.par, *.cfg, 42 or 27 numbers), or any file with named Rescal parameters, such as in an ILL TAS data ascii file and from ResTrax (*.res). SPEC (AFIT) files from LLB can also be read (do not contain sample information).
Getting configuration from other packages:
The *.res files can be generated by ResTrax. This is a list of NAME=VALUE pairs.
The *.par and *.cfg files can be generated by ResCal5.
The *.par files can be generated by the legacy ResCal code (42 values in a column).
ResTrax can also generate *.cfg files (different format than ResCal5), which only specify a reduced set of parameters (we refer to these as 'rtx' files when exporting to avoid confusion).
In addition, the 'File/Open Instrument...' menu item allows to read a predefined TAS instrument configuration. These instruments are stored in the ResLibCal/instruments directory. Such files should preferably be '.ini' files, but any other supported configuration format also works. We currently provide such files for IN1 IN8 IN14 IN20 IN22  MLZ_TRISP. You may add files in this location with your preferred configurations by just copying and renaming e.g. any ResLibCal.ini file.

Exporting the results, saving the configuration

The results can be saved using the 'File/Save as...' menu item. Enter a '.m' or '.ini' filename, and the full ResLibCal configuration (instrument, sample, position, method) is saved as a Matlab script. An example of such a  configuration file is available here.
You can further edit this file and change manually values in the 'EXP' ResLib-compatible structure.

Other file formats are available, which can all be read back into ResLibCal:
Rescal legacy format (*.dat):
If the output file name you specify has a 'dat' extension, the generated configuration uses the ResCal legacy format, which consists in 42 numbers.
Rescal legacy format (*.par and *.cfg) with comments:
If the output file name you specify has a 'par' or 'cfg' extension, the generated configuration uses the ResCal legacy format, which consists in 42 numbers. Comments are added for easier parameter identification. An additional cfg file with Popovici parameters will also be written. These files can be read by the legacy ResCal and ResCal5.

ResTrax/ResCal format (*.res):
If the output file name you specify has a 'res' extension, the generated configuration uses a simple 'NAME = value' list of parameters. Such files can be read by ResTrax.

ResTrax legacy format (*.rtx):
If the output file name you specify has a 'rtx' extension, the generated configuration uses the ResTrax legacy format. This type of file only exports a reduced number of parameters.
The main ResLibCal GUI can also be exported as graphics image in a set of formats (File/Export menu item), including PDF, EPS, PNG, TIFF, BMP, and Matlab Fig. Plot windows can be exported using their File/Saveas menu item, and printed.

When exiting the application, the current configuration is saved in the Matlab preferences directory.

Non interactive mode (compute only)

It is possible to compute the resolution without launching the GUI, which is then very fast.
For this, send the configuration file from which the computation is defined as an argument to ResLibCal:
>> out = ResLibCal('config_file')
ans =
Title: 'ResLibCal configuration'
handle: 173.0160
EXP: [1x1 struct]
resolution: [1x1 struct]
ResCal: [1x1 struct]
The file can be a saved ResLibCal configuration (see below), a ResCal5 configuration (42 or 27 numbers), or any file with named Rescal parameters, such as in an ILL TAS data ascii file. Alternatively, an EXP ResLib or full ResLibCal configuration structure can be sent, as well as a ResCal parameter list.
>> out = ResLibCal('DA=3.355; DM=3.355; ...')	% change the configuration and recompute resolution
In order to modify an existing configuration ResLib EXP or full ResLibCal out, use:
>> out = ResLibCal(out or EXP structure, 'DA=3.355; DM=3.355; ...')
>> out = ResLibCal(out or EXP structure, 'file')
For a given configuration (from file, or GUI), the resolution can be computed in the reciprocal space with e.g. :
>> out = ResLibCal(2,0,0,5) 	% computes at HKLE=[2 0 0 5] coordinates in r.l.u
>> out = ResLibCal('QH=2 W=5') % same as above but giving configuration as a string with named parameters
The resolution result is then available in 'out.resolution' and more specifically in its Bragg and RM fields of the [rlu] and [spec] sub-structures, depending on the reference frame used (see above):
>> out.resolution
focus: [80.0088 439.4046 49.7513 136.3181]
R0: 16.5334 % the intensity
HKLE: [2 1 0 5] % the HKLE rlu.meV coordinate of this point
method: 'Popovici (ResLib)'
README: {2x1 cell}
spec: [1x1 struct] % spectrometer frame
rlu: [1x1 struct] % lattice frame [a*, b*, c*]
cart: [1x1 struct]
rlu_ABC: [1x1 struct]
ABC: [1x1 struct]
angles: [25.2592 50.5184 14.3768 -70.9737 37.1658 74.3316] % A1-6 angles in a TAS machine
Q: 2.2361

>> out.resolution.rlu
cart2frame: [3x3 double]
rlu2frame: [3x3 double]
Q: [3x1 double]
RM: [4x4 double]
README: '[R] rlu lattice frame, xyz=[a* b* c*]'
unit: 'rlu'
frame: [3x3 double]
frameUnit: '1/\C5'
frameStr: {1x3 cell}
Bragg: [5x1 double]
cloud: {[2000x1 double] [2000x1 double] [2000x1 double] [2000x1 double]}
The resolution matrix is computed in the laboratory frame x//Q [spec] and the lattice frame x//a* [rlu]. These two computations are stored in the [spec] and the [rlu] fields. In these fields, such as out.resolution.rlu above, 'RM' is the resolution matrix, and the 'Bragg' holds the width along frame axes as well as the the Bragg energy width (4-th value) and Vanadium width (5-th value).
In practice, the Vanadium energy width out.resolution.spec.Bragg(5) is a good measure of the instrumental energy resolution.

The parameters used for the computation are listed in the 'out.EXP' structure (ResLib-like), but are also shown in the Rescal terminology in 'out.ResCal'.
>> out.ResCal
ans =

DM: 3.3542
DA: 3.3542
ETAM: 30
ETAA: 25
ETAS: 5
SM: -1
SS: 1
SA: -1
KFIX: 2.6620
FX: 2
ALF1: 40
ALF2: 40
ALF3: 40
ALF4: 40
BET1: 120
BET2: 159.9648
BET3: 120
BET4: 120
AS: 6.2800
BS: 6.2800
CS: 6.2800
AA: 90
BB: 90
CC: 90
: 1
AY: 0
AZ: 0
BX: 0
BY: 1
BZ: 0
QH: 2
QK: 0
QL: 0
EN: 0
DQH: 0
DQK: 0
DQL: 0
DEN: 1
GH: 0
GK: 0
GL: 1
GMOD: 0
BeamShape: 1
WB: 10
HB: 10
Guide: 0
GDH: 0
GDV: 0
SampleShape: 1
WS: 1
TS: 1
HS: 4
DetectorShape: 1
WD: 2.5400
HD: 5
TM: 0.2000
WM: 10
HM: 10
TA: 0.2000
WA: 10
HA: 10
L1: 150
L2: 150
L3: 150
L4: 150
RMH: 0.0067
RMV: 0.0067
RAH: 0.0067
RAV: 0.0067
You can change any configuration parameter, including the method for the computation:
>> out=ResLibCal;	% contains the ResLib structure as out.EXP
>> out.EXP.method = 'Cooper-Nathans ResCal'
The method should mention 'Cooper-Nathans' or 'Popovici', with a flavour 'ResLib','ResCal', 'AFILL' or 'Res3' as free text.
The position of the measurement is [ QH QK QL W ]:
>> [ out.EXP.QH out.EXP.QK out.EXP.QL out.EXP.W ]
ans =
2 0 0 0
>> out.EXP.W = 1; % change the position in reciprocal space
>> out = ResLibCal(out); % request a new computation with modified choices
The full list of ResLib parameters are described in the ResLib package documentation.

The following ResLibCal actions are available:
ResLibCal('action')
Description
open
open a configuration file (par, cfg, res, ini, m): ResLibCal('open','file')
save
save the configuration in the Preference directory (ini format)
saveas
save the configuration into a specified file/format: ResLibCal('saveas','file')
exit
close all active views, and save current configuration
reset
re-load the default configuration
create
open the main GUI (start interface), and read last saved configuration
compute
only compute the matrix (no plotting/printing)
update
compute, and then update open views, or send result to the console
view2
display the 2D view (resolution projections)
view3
display the 3D view (resolution)
geometry or tas
display the spectrometer geometry
close
close the 2D, 3D and TAS view windows
default
same as create, but does not read last configuration (using reset configuration)
resol
print-out the resolution matrix a la RESCAL
bragg
print-out the Bragg widths a la RESCAL
list
print-out the list of parameters a la RESCAL
version
print-out the ResLibCal version
export
dump the main ResLibCal window into a file
print
print the main ResLibCal window
quit
same as exit, but does not save the configuration
silent
Consecutive commands (in the same call) are executed in silent mode, with only computation of the resolution, and no plot nor text display.
hkle
Returns the current HKLE location, or empty when the interface is not opened.
config
Returns the current ResLibCal configuration.

Convolution of the TAS resolution function with a model, in 4D


The measured signal from a TAS can be schematically described as:

I(q0,w0) = ∫ S(q,w) R(q-q0,w-w0) dq dw

where S(q,w) is the dynamic structure factor of the measured sample, and R(q,w) is the resolution function (response) of the neutron TAS. The resolution function is directly obtained from the resolution matrix M detailed above.

Once ResLibCal can properly describe a TAS setting, it is possible to use the computed resolution to convolve a model dispersion in materials. The methodology is (for each QH,QK,QL,W location in the reciprocal space):
  1. compute the resolution function
  2. build a Monte-Carlo cloud of points which is a random statistical description of the TAS response
  3. evaluate the dispersion for all points in the resolution cloud, and sum it to get an estimate of the integrated counts on the detector arising from the 'capture' of the dispersion by the TAS resolution function.
All these steps are automated, and the use of iFunc objects allow to build a 'symbolic' representation of an ideal S(q,w) dispersion with the TAS resolution, in 4D (QH,QK,QL,W).

If we assume we have a dispersion model 's' in 4D, the syntax to convolve this model with the current ResLibCal TAS configuration is any of:
>> s_tas = conv(s, 'tas')
>> s_tas = ResLibCal(s);
The convolved model 's_tas' has the same parameters as the initial model 's', but includes the 4D convolution. When typing this command, ResLibCal is started if not already opened. To properly use this feature, you need iFit to be fully installed (the ResLibCal application alone is not enough). When ResLibCal is opened, its configuration is used to compute the resolution. If it is closed, the last saved configuration is used.

The number of Monte-Carlo points used for each convolution step is by default 200. This can be changed, e.g. to speed-up the computation at the cost of a coarser results (more noisy), by changing it from the menu item 'View/Set Monte-Carlo iterations...', or from the EXP.NMC ResLib structure (out.EXP.NMC when returned from ResLibCal). When using the Full Monte-Carlo computation, more than NMC points can be generated in the cloud, so that the resolution matrices can be computed with enough accuracy.

The data sets can also be processed by ResLibCal in order to convert them into 4D data sets that can be compared (and fit) with 4D models. The syntax is similar to that of models:
>> d_4d = ResLibCal(d);
will search for (Qhkl E) Axes and extend the data set dimensionality. In addition, if the data set contains a 4D model (as 'Model' alias), it will also be convoluted by the 4D TAS resolution.

Dispersion model: 4D dynamic structure factors S(q,w)

As we have seen the 4D convolution procedure seems straight-forward, as long as we have a reasonable description of the dynamic structure factor S(q,w) to model the excitations in the sample crystal. This is clearly not an easy task, as it highly depends on the physics taking place.

To demonstrate what can be done, we here list a few available 4D S(q,w) as part of iFit, and building iFunc models. More information about these models can be found in the iFit/Models page.

S(q,w)
Description
Dimensionality
Parameters
sqw_sine3d Phonon dispersions as sine wave in HKL (3D) with a damped harmonic oscillator energy dispersion  4D (HKLw)
sqw_sine3d
zone center, energy gaps, periodicity
sqw_vaks Phonon dispersions in perovskite cubic crystals using the Vaks parameterisation  4D (HKLw)
sqw_vaks
acoustic and optical , coupling parameters, soft mode frequency
sqw_cubic_monoatomic Phonon dispersions in a monoatomic cubic crystal using the Dynamical matrix. 4D (HKLw)
sqw_cubic_mono
acoustic force constant ratio and scaling energy
sqw_phonons Phonon dispersions from the Dynamical matrix, using forces estimated by ab-initio usingASE and a selection of DFT codes (EMT, GPAW, ABINIT, Elk, Dacapo, NWChem, QuantumEspresso, VASP). 4D (HKLw)
sqw_phonons Al fcc
Creation: POSCAR, CIF, or PDB, ...
Then, only the DHO line shape. ab-initio implies no (few) tunable parameter.
sqw_spinw Spin-wave dispersion in HKL using SpinW. Ann initial SpinW object must be given, or defaults to the 'squareAF' with J1=2, J2=0
4D (HKLw)
sw
energy broadening, Temperature, Amplitude, coupling parameters J...
sqw_linquad A phenomenological dispersion which can describe an acoustic or optical mode. This model can be considered as a local expansion in series of any dispersion. 4D (HKLw)
sqw_linquad
Energy and location of 'gap', slopes, directions of slopes, DHO width, temperature, background
sqw_acoustopt
A phenomenological dispersion which can describe an acoustic or optical mode.Acoustic slope and 'optical' minimum energy can be specified.
4D (HKLw)
sqw_acoustopt

Energy and location of 'gap', slopes, directions of slopes, DHO width, temperature, background

In the following example, we wish to estimate the excitation spectrum along a line at QH=0.3 rlu, varying the energy from 0 to 20 meV.
    s=sqw_sine3d; % create a 4D S(q,w) for a cubic pure material, using default parameters
t=ResLibCal(s); % convolute it with a TAS resolution, and open ResLibCal.
Then we evaluate both the ideal S(q,w) and its convolution with the 4D TAS resolution function, along the trajectory:
    w=linspace(0.01,10,50); qh=1.1*ones(size(w)); qk=0*qh; ql=0*qh; % an E-scan around the [1 0 0] Bragg
signal0=iData(s, [], qh,qk,ql,w); % the ideal model evaluated along the HKLE line
signal1=iData(t, [], qh,qk,ql,w); % the convoluted model evaluated along the HKLE line
The resulting signals are along the QH,QK,QL,W line, which is in 4D. To squeeze the singleton dimensions (which are constant) and generate 1D data sets along the energy axis, we use:ResLibCal 4D convolution
    figure; plot(squeeze([signal0 signal1/100])); % plot the dispersion and simulated measurement
Then we can plot the whole dispersion curve and the simulated signal along the given scan trajectory.
    QH=linspace(0,1.5,50); QK=linspace(-.25,.25,50);; QL=QK; W=linspace(0.01,10,51);	% a 4D grid
f=iData(s,[],QH,QK,QL,W); % evaluate the model on the 4D grid
figure; plot3(log(f(:,:,25,:))); % plot dispersion
hold on; scatter3(log(signal1(:,:,1,:)),'filled'); % overlay the simulated scan

Planned in the future

We wish to go further in the development of ResLibCal, and in particular its 4D convolution feature. The following features are envisaged:

Help

If you find bugs please send them to me [farhi (at) ill.fr] with:
  1. your Matlab version
  2. the ResLibCal version which you can get from the Help/About menu item.
  3. the TAS configuration you use and the associated procedure to reproduce the error
  4. a copy of the error messages produced by the script/command.
  5. a smile ;-)

Credits and disclaimer

This application was written by E. Farhi (c) ILL/DS/CS 2013 <farhi@ill.eu> using
Some bugs have been corrected in ResLib, ResCal5/rc_popma, and Res3ax by cross comparing codes and independent benchmarking. The results from ResTrax and RESCAL are in good agreement with ResLibCal.
The ellipsoid plot (2D, 3D) are contributed from Ellipse_plot by 2009, Nima Moshtagh.
A similar tool with the Cooper-Nathans method exists in the DAVE software (menu Planning => TAS Tools => Rescal2).

The application is distributed with an EUPL license (GPL compatible).

If you use this application, we would appreciate that you cite in your work:
E. Farhi, Y. Debab and P. Willendrup, J. Neut. Res., 17 (2013) 5. DOI: 10.3233/JNR-130001
References:

[1] M. J. Cooper and R. Nathans, Acta Cryst. 23, 357, (1967) [doi:10.1107/S0365110X67002816]. See [Fortran code].
[2] N. J. Chesser and J. D. Axe, Acta Cryst. A29, 160, (1972) [doi:10.1107/S0567739473000422].
[3] M. Popovici, Acta Cryst A31, 507 (1975) [doi:10.1107/S0567739475001088].
[4] G. E. Bacon and R. D. Lowde, Acta Cryst. 1, 303 (1948) [doi:10.1107/S0365110X48000831].
[5] S. A. Werner and R. Pynn, J. Appl. Phys. 42, 4736, (1971) [doi:10.1063/1.1659848].
[6] Gen Shirane, Stephen M. Shapiro, John M. Tranquada, Neutron Scattering with a Triple-axis Spectrometer: Basic Techniques, Cambridge University Press (2006).
[7] S. A. Werner R. Pynn, J. Appl. Phys. 42, 4736, (1971) [doi:10.1063/1.1659848]
[8] K. Lefmann and K. Nielsen, Neutron News 10, 20, (1999) ; P. Willendrup, E. Farhi and K. Lefmann, Physica B, 350 (2004) 735.

Disclaimer:
This software is experimental, and should not be considered bullet-proof. In particular, expect bugs - which should be reported to me [farhi (at) ill.fr] if you want them to be fixed quickly. There is no guaranty that the resolution computation is correct, but as we propose a set of methods, we expect that it gives a fair representation of its accuracy.



 E. Farhi - ResLibCal - Mar. 22, 2017 1.9 The
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