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Virtual experiments in a nutshell : simulating neutron scattering from

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1. 8 COMPONENT FC FermiChopper nu frequency w w height 0 05 Nslit 200 length L AT 0 0 1 RELATIVE PREVIOUS COMPONENT FC Mon Monitor nD xwidth 0 064 yheight 0 05 options auto time AT 0 0 0 1 RELATIVE PREVIOUS END Example 4 A simple Fermi chopper setup which computes automatically the rotation frequency and sets time for neutrons to reach the chopper time window This example makes use of the DECLARE and INITIALIZE blocks to handle internal variables and of the EXTEND block to act on the neutron event time ft and weight p FC Mon 1285677581 t o o o T y m FS o T Intensity n s bin 20r 085 09 095 1 105 11 115 12 125 TOF s x10 Figure 9a A Fermi chopper geometry from the Example 4 Slitsidth s m lengths L rotation frequency f Figure 9b Time distribution from the Fermi chopper spectrometer at A 4 The Example 4 shows a simple use of the FermiChopper component with some additional McStas grammar features such as the component instance extension with the EXTEND keyword The geometry as well as the obtained result are shown in Figures 9a and 9b It appears that a disk chopper system may be replaced with an equivalent Fermi chopper when the condition L7 w d JDN 18 13 is satisfied Both devices are mainly used on time of flight spectrometers in order to obtain a highly monochromatic neutron beam with typically a wavelength range of a fe
2. Define home csguest mcstas hosts or usr local lib mcstas tools perl hosts or use option machines file Clustering methods Single MPI Grid Your system has MPI SSH parallelisation available To make use of this please go to the Tool menu and select Install DSA key Figure 2 The McStas main interface McGUT 4 1 Installing McStas The McStas software runs on all common operating systems including Windows XP Vista and 7 Linux flavours and Mac OSX Installer packages are available 9 Currently McStas only requires a C compiler but higher level user interfaces make use of Perl Perl Tk PGPLOT and Perl DL We optionally recommend to install Scilab a VRML viewer MPI libraries for multi processor and cluster support and Matlab Support for the common X ray and neutron data format NeXus 10 is also available 4 2 Starting a simulation with McStas Starting the McStas software will typically result in showing up the main McGUT interface mcgui command as shown in Figure 2 We then recommend to start by selecting an instrument example in the Neutron Site menu such as the Templates templateDIFF one which is a standard diffractometer model Pressing the Run button will assemble the instrument model and request instrument parameters which are for this example the incident neutron wavelength A defaulting to 1 the monochromator lattice spacing DM defaulting to 3 355 A and curvature RV the s
3. T In the case were the u values are regularly sampled this corresponds with the well known mid point integration rule The Monte Carlo integration technique considers the case where the u values are randomly but uniformly sampled and the random integration step du converges to b a n As random number generators are not perfect we rather talk about pseudo Monte Carlo technique In principle Monte Carlo methods converge to the f function expectation by summing up a large number of infinitesimal random values in which case we state that the Monte Carlo estimate is consistent The Monte Carlo computer techniques require that the random numbers be unbiased independent variables The choice of the random number generator is essential to ensure a proper estimate consistency and the development of the Monte Carlo techniques have triggered much effort in the computational pseudo random number generator algorithms such as the well known linear congruential generator using modulus One way to quantify the efficiency of these random number generators resides in their periodicity that is the maximum pseudo random sequence length before it repeats itself and their maximum dimensionality that is the maximum sequence length that can be thrown and considered to hold independent equidistributed numbers Currently the Xorshift 4 and the Mersenne Twister 5 algorithms are among the most efficient pseudo random number generators 2 2 Error estimate
4. The Example 7 has diffraction on a monochromator at A 2 36 as a function the same geometry of the transverse position in the diffracted spot Intensity is shown as color scale from blue low to red high In the Example 6 we use a flat instance of the Monochromator curved component for which the rotation angle 0 is computed automatically from the desired wavelength The model geometry is shown in Figure 11a and the position wavelength distribution in Figure 11b for A 2 36 neutrons and a 002 graphite reflection This shows that the monochromating effect depends on the position in the diffracted beam where one side is more energetic than the other A better neutron beam focusing could be achieved e g to increase the intensity on the sample position by specifying the curvature radius RH and RV parameters in the component instance see section 6 2 below TRACE COMPONENT SX Single crystal xwidth 0 002 yheight 0 1 zthick 0 1 mosaic 30 reflections C_graphite lau barns 0 ax 0 ay 2 14 az 1 24 bx 0 by 0 bz 2 47 cx 6 71 cy 0 cz 0 absorption 0 014 incoherent 0 004 AT 0 0 0 5 RELATIVE PREVIOUS ROTATED 0 theta 0 RELATIVE PREVIOUS Example 7 A more advanced monochromator setup which also takes into account multiple scattering and blade thickness This example is derived from Example 6 MC Mon tt MC_Mon_1285771808 x_L X0 0 000695944 dX 0 005 2 YO 2 36185
5. in order to understand and label observed features for instance to separate contributions from sample environment or parasitic scattering signals such as multiple scattering Last but not least virtual experiments are invaluable for teaching The embedded model can be shown without actually travelling to neutron facilities and help in understanding both how instruments are built operated and the type of data which they generate 4 INTRODUCTION TO MCSTAS File Simulation Neutronsite Tools Help McDoc The McStas software package 6 7 9 is a European effort to bring an open source common frame work for modelling of all kinds of neutron scattering instruments diffractometers spectrometers reflectometers small angle back scattering for both continuous and pulsed sources It is based on a meta language specially designed for neutron scattering simulation Instrument descriptions are written in this language by users and automatically translated into efficient simulation codes in ANSI C The present version McStas 1 12b July 15 2010 supports both continuous and pulsed source instruments and includes a library which contains around 110 components and 70 instrument examples Mcs version 1 12b Jul 15 2010 N Copyright C Risoe National Laboratory 1997 2010 Additions C Institut Laue Langevin 2003 2010 All rights reserved Plotters Scilab PGPLOT McStas HTML VRML NeXus Warning No MPI grid machine list Running locally
6. 0 ABSOLUTE large incoming beam COMPONENT MC_in Progress_bar AT 0 0 0 5 RELATIVE PREVIOUS ROTATED 0 theta 0 RELATIVE PREVIOUS EXTEND flag_holder 0 neutron events entering here have not scattered yet 8 COMPONENT HoldIn 2 PowderN reflections Al laz xwidth 0 01 zthick 0 01 yheight 0 1 AT 0 0 0 055 RELATIVE MC in this is the pillar EXTEND flag holder SCATTERED set to true when scattering events happen in the pillar 8 COMPONENT SX Single crystal xwidth 0 002 yheight 0 1 zthick 0 1 mosaic 30 reflections C graphite lau barns 0 ax 0 ay 2 14 az 1 24 bx 0 by 0 bz 2 47 cx 6 71 cy 0 cz 0 absorption 0 014 incoherent 0 004 AT 0 0 0 RELATIVE MC_in COMPONENT HoldOut COPY HoldIn the same pillar but for outgoing neutrons AT 0 0 0 055 RELATIVE MC in EXTEND if SCATTERED flag holder 1 set to true when scattering events happen in the pillar 8 COMPONENT MC crystal Monitor nD xwidth 1 yheight 1 options sphere theta limits 180 180 y bins 180 AT 0 0 0 5 RELATIVE Source COMPONENT MC holder COPY MC crystal WHEN flag holder AT 0 0 0 5 RELATIVE Source END Example 13 An advanced monochromator setup which estimates the background generated from the crystal mount In this model we use the EXTEND keyword which enables to customize the behaviour of instrument components In this case we set a
7. The more intense peaks around 30 60 and 100 degrees angles correspond with the S q structural information of the diffraction pattern on the right side Faint arches can be seen to converge to these peaks scattered by phonons in the liquid This latter plot can not be measured directly with current detectors as we have used a neutron energy sensitive monitor With real instruments an angle time distribution would provide a similar but indirect result when using e g a time of flight spectrometer Such a model is already quite realistic even though no proper primary spectrometer is actually modelled here to provide a monochromatic beam This demonstrates the essential role of sample kernels in virtual experiments which should be complemented with an accurate description of the neutron optics which compose the instrument This will be achieved in section 6 1 JDN 18 19 RRR RRR ERR RRR che e e ke che e RK KKK KKK KR KK RK KK RK KR KKK KR KKK KK KK KKK KKK KKK KR RRR KKK KR KKK ERK k k k KEK KEK KK RK ckck KK KKK k k k Instrument liquid simple instr Description A liquid scattering example Parameters lambda Angs incoming neutron wavelength monochromatic material Angs liquid or powder description file lazy fullprof crystallographica qSq Sqw RRR ERK RRR RRR KK RR KK RR KKK KR KK KR KK KK KEK KK RK ck KK KR KK RK KK RK KK KR KKK KKK KR KKK KKK RRR k k k k k k k k k ck k k k ck k k k k k KK KKK KK FF F DEFINE INSTRU
8. components the Component Manual which lists most of the available components and the Component Library Index which shows a compact list of all available data files components and example instruments We also encourage users to register on the mcstas users mcstas org mailing list 9 to which they can post questions and follow discussions with many other McStas users When you feel confident with McStas using existing example instruments and components you can start to build your own instrument descriptions as shown Figure 5 Instrument model geometry as shown with below in sections 5 5 5 6 and 6 and eventually McStas McDisplay The neutron beam tube is shown in green modify existing or implement new components We followed by the multi blade monochromator which deflects shall not discuss this latter matter in the frame of this the neutron to a collimator just before the sample A radial paper but rather point you to the McStas User Manual collimator precedes a banana shaped detector in magenta Feel free to send your new data files instruments and components to the mailing list and the McStas core team so that they can be included in further releases and benefit the whole McStas and neutron community 5 VIRTUAL EXPERIMENT COMPONENTS In the following sections we introduce a number of common instrument simulation components to be used with McStas 1 12b In each case usage examples are listed as well as the corresp
9. dY 0 0428278 The Monochromator curved component only considers a gt e 0 000123184 Err 2 03861e 07 N 384846 single d spacing in the diffracting crystal infinitely thin blades However it does take into account multiple diffraction order n which corresponds to d n atomic plane spacing in the Bragg law In order to consider all possible reflections in the crystal we may use a more advanced single crystal model such as in Example 7 derived from Example 6 by replacing the Monochromator_curved component instance by a Single_crystal one A data file containing the structure factors gt of graphite is used instead of a single d spacing value For more details about this component refer to the section 5 3 3 wet 0 01 0 0 01 Figure 11c The Example 7 with a thick crystal monochromator The upper border of the spot is blurred from crystal thickness and multiple scattering The wavelength distribution shows a dip at 2 32 from higher order scattering Monochromators are essentially used on diffractometers back scattering and crystal time of flight spectrometers and triple axis inelastic spectrometers The selected wavelength range is typically about 1 around the diffracted wavelength 16 Collection SFN 5 3 Samples In this section we shall present the most common material types to be included in instrument models As explained in section 3 scattering materials are an essential part of virtual experiments In real
10. file extension qSq in which case no inelastic scattering is then modelled In order to model the dynamical part S q tables must be provided extension sqw and prepared for instance from molecular dynamics or experiments as explained in section 8 2 below Powders are handled less accurately in sotropic Sqw than with the PowderN component Gas dynamical structure factors may be approximated as a liquid with very low density The Example 9 lists an instrument model that makes use of this component in the spirit of the powder Example 8 The model geometry is similar to the one shown in Figure 12a Running this example is somewhat longer than the previous ones due to the fact that the sample model is much more complex and includes multiple scattering The simulation results are shown in Figure 13 when using as material information the dynamic structure factor S q c prepared from a liquid rubidium classical molecular dynamics simulation 19 The liquid structure for a liquid rubidium sample can be analysed from a diffraction pattern as shown in Figure 13 left which may actually be obtained on real diffractometers The arcs are portions of Debye Scherrer rings in a liquids and their radial integration provides the S q structure factor which characterizes the atomic distances in the liquid The angle energy spectrum is shown in Figure 13 right The elastic line is the horizontal one around the neutron incident energy of about 14 meV
11. h 0 05 theta 0 10 n 1 IsFirst 1 AT 0 0 1 RELATIVE PREVIOUS COMPONENT guide Guide w1 0 03 h1 0 05 w2 0 03 h2 0 05 1 d cc 0 1 AT 0 0 0 05 RELATIVE PREVIOUS COMPONENT Chop2 COPY Chopl IsFirst 0 phi 0 2 PI frequency d cc lambda 3956 RAD2DEG AT 0 0 d cc RELATIVE Chopl COMPONENT CG Mon Monitor nD xwidth 0 03 yheight 0 05 options auto time AT 0 0 0 1 RELATIVE PREVIOUS SPLIT COMPONENT sample Isotropic Sqw Sqw coh coh Sqw inc inc radius 0 005 yheight 0 05 AT 0 0 0 5 RELATIVE PREVIOUS COMPONENT detect Monitor nD xwidth 2 5 yheight 1 options banana auto time bins 256 angle limits 10 130 bins 120 AT 0 0 0 RELATIVE PREVIOUS END Example 11 A liquid scattering time of flight spectrometer virtual experiment This simulation requires a longer computing time to produce the Figure 15b Of course in this virtual experiment a similar information has been used from the coherent and incoherent parameter files But these obtained here from a molecular dynamics simulation see section 5 3 2 and 19 do not include any instrumental effects In practice no instrument is perfect so that the measured dynamical structure factor will not match exactly the simulated one The differences are related to the imperfections which hinder any measurement In the case of this liquid spectrometer virtual experiment we may notice a number of differences The most striking one is the parallax effect which is
12. ky o E S g w dQdE E f 158 q 0 4 Qd where E is the incident neutron energy and q are the energy and momentum exchange between the material and the neutron is the material bound cross section d is a solid angle and S q is the dynamic structure factor which is the double Fourier transform of the spatial and time atomic position distributions in the material This quantity is characteristic of each material and exhibits for instance the structure factors IF Q I introduced in the powder section 5 3 1 above as peaks along the 0 elastic line The inelastic spectrum 0 shows dispersion curves such as phonons and broad quasi elastic lines In liquids the structural information is fuzzy and phonon lines are broad The Isotropic_Sqw component models any isotropic density material such as liquids polymers and amorphous materials gas and powders It handles coherent and incoherent scattering both with elastic and inelastic processes Multiple scattering and secondary extinction are taken into account The material volume may be a box a sphere and a cylinder which all can be bulk or hollow geometries including concentric arrangements An additional complex geometry enables to use any point set to describe the material volume geomview OFF file The material is specified e g with a data file which is either a structure file such as for the PowderN component extension az or lau or a S q liquid structure factor
13. using McStas The two lower plots show the angular diffractogram and the 2D detector Run simulation templateDIFF instr Instrument source templateDIFF instr HTML docs Instrument parameters D floating point I integer S string lambda D 1 DM D 3355 Powder S Na2Ca3Al2F RV D a up 17 u 2 D 32 L3 D 1471 ALPHA1 D 5 ALPHA2 D 60 ALPHAS D 5 ETA D 12 verbose D THETA M D 0 swox Ouputo dr tore Browse Neutron count 10d i gravity BEWARE Randomseed Trace 3D view Plot results Format HTML VRML Clustering None singe CPU Numberofnodes 2 Inspect component perra E First component E Last component ene B E Figure 4 The Run simulation dialog set to the Trace 3D mode in order to visualize the model geometry with VRML Pressing again the Run button from the main interface but changing the Simulate mode into the Trace 3D mode with a HTML VRML plotter format see Figure 4 the Start button generates an interactive 3D view see Figure 5 The corresponding McStas instrument description will be discussed in section 5 6 It can be displayed by pressing the Edit New button 4 4 Getting help and going further 6 Collection SEN The Help menu on the right side of the main McStas File Navigate Preferences Help interface links to the User Manual which indicates how to use McStas write instruments and new
14. 0 0 ABSOLUTE COMPONENT VS V selector width 0 03 height 0 05 10 0 30 r0 0 12 phi phi ll d vs tb 0 0004 rot 3956 phi DEG2RAD 2 PI lambda d vs 60 nb 72 AT 0 0 1 RELATIVE PREVIOUS COMPONENT VS Mon Monitor nD xwidth 0 064 yheight 0 05 options auto wavelength AT 0 0 d vs 0 1 RELATIVE PREVIOUS END Example 5 A simple velocity selector setup which computes automatically the rotation frequency It can be seen that a velocity selector follows the same behavior as a double chopper system but with many input channels It does not select monochromatic pulses but ensures a continuous monochromated beam better suited for steady state neutron sources The transmitted neutron wavelength A follows a similar rule as the double chopper 13 vs _ 3956 _ 3956 rad Ans OFC bd Ving 27 fidi where f is the rotation frequency d is the length of the drum and is the twist angle The Example 5 shows a simple implementation of the V selector component and the resulting wavelength range typically 10 around A 5 These neutron optics devices are mainly used on small angle neutron scattering instruments which do not require a highly monochromatic neutron beam and as pre monochromators in front of e g monochromators see below A 14 Collection SEN velocity_selector VS Mon 1285690271 L Intensity n s bin x m z m 9 35 36 37 38 39 4 41 12 43 a4 45 Figure 10a A velocity sel
15. 100r 100 f gt b E Lh 80 ee prea eee PPP cS 80 3 ME Hj o c W ep 60 E AUF ne ARE RPR 40 20 e rere ry PED 20 4 4 5 5 4 4 5 5 5 5 3 3 TOF s 49 TOF s 49 Figure 22 The time of flight angle signal acquired from the liquid spectrometer with sample environment model The total signal from liquid rubidium in a Nb container and Al external shield is shown on the left whereas the sample only contribution is shown on the right Intensity is shown in log scale with colors ranging from blue low to red high 30 Collection SFN 7 4 Gas detectors Up to now all the models we have simulated use perfect monitors as explained in section 5 4 Their efficiency is ideal and does not depend on the neutron energy They do not saturate when neutron flux is too high and they have a perfect spatial response They are meant to analyse the neutron beam without introducing additional measurement imperfections Most current neutron detectors in the cold thermal range use a gas technology Neutrons that enter e g a He cell create charges proton triton pairs when absorbed by the atoms These charges drift in the gas until stopped and collected by high potential wires The PSD Detector has been designed in order to model most of the gas detector physics that takes place in the thermal neutron scattering instruments The Example 15 is based on the powder sample Example 8 section 5 3 1 which we extend with a 1 mm alu
16. 14 1laz TRACE COMPONENT Source Source simple dist 1 radius 0 01 xw 0 01 yh 0 01 Lambda0 lambda dLambda lambda 0 01 AT 0 0 0 ABSOLUTE COMPONENT powder PowderN reflections material radius 0 005 yheight 0 05 AT 0 0 0 5 RELATIVE PREVIOUS COMPONENT banana Monitor nD xwidth 1 yheight 0 3 options banana theta limits 10 130 bins 240 y bins 50 AT 0 0 0 RELATIVE PREVIOUS END Example 8 A simple powder diffraction example The equations from 14 relating to powders have been directly implemented in the PowderN component 15 This handles single coherent scattering and many d spacing structure factors with absorption correction and incoherent elastic scattering However no multiple or inelastic scattering is taken into account which the Jsotropic Sqw component can cope with in its powder mode see section 5 3 2 below In the Example 8 we present a usage example which produces so called Debye Scherrer rings from a structure factor list The model geometry is shown in Figure 12a and the 2D ideal diffraction detector in Figure 12b for a NazCa3ALbF reference powder The choice of the material may be any file adapted from Lazy Pulverix implemented in the ICSD database 16 and Fullprof 17 extension az or Crystallographica extension lau also used for crystals Currently McStas includes a material data base of about 60 powder and crystal definitions commonly used in neutron scattering These can be lis
17. 2 reflection direction at A 2 36 A this background intensity amounts to about 0 1 LOG MC ceryetel t4 MC_erystal_1266334546 th y LOG MC older t MZ ho der 1286354543 1h y 1 961899 dX 21 6927 YO 2 87279e O5 CY C O6HUS385 01969 dX 107 753 13 0 000994458 4dY 0 3032 0 780079 Err 4 6782 72 05 N 8 6831e 26 1 D 00868749 Err 4 0 4 8 y m o Lu 7 10 0 106 1600 0 100 Longitude deg lengilude deg Wy ADN 142 Figure 20 Results from the monochromator Example 13 around 2 36 A showing the total contribution with crystal diffraction on the left side and the pillar contribution on the right side Intensity is shown in log scale with colors ranging from blue low to red high 7 2 Sample environment An important source of background which appears on acquired scattering signals originates from the sample environments that is any material close to the sample which also scatters the neutron beam This particularly holds for furnaces cryostats magnets pressure cells and sample containers A way to circumvent this contribution is to make use of radial collimators which select a small gauge volume around the sample and remove most of the outer scattering However real experiments usually also include acquisitions with an empty container which is afterwards subtracted from the total signal in order to extract the sample contribution 28 Collection SFN R
18. ENT curved guide lambda 4 dlambda 3 5 R 2700 L 14 DECLARE double n 10 1 number of straight guide elements double d 1e 3 m spacer in between adjacent straight elements 8 TRACE COMPONENT Source Source simple dist 1 radius 0 03 xw 0 03 yh 0 2 Lambda0 lambda dLambda dlambda AT 0 0 0 ABSOLUTE COMPONENT CG 1 Guide 1 L n w1 0 03 hl 0 2 w2 0 03 h2 0 2 AT 0 0 1 RELATIVE PREVIOUS ROTATED 0 L n d R 180 PI 0 RELATIVE PREVIOUS COMPONENT CG 2 COPY CG 1 AT 0 0 L n d RELATIVE PREVIOUS ROTATED 0 L n d R 180 PI 0 RELATIVE PREVIOUS make it so with a total of n 10 elements COMPONENT CG 10 COPY CG 1 AT 0 0 L n d RELATIVE PREVIOUS ROTATED 0 L n d R 180 PI 0 RELATIVE PREVIOUS COMPONENT CG Mon Monitor nD xwidth 0 03 yheight 0 2 options x y AT 0 0 L n d RELATIVE PREVIOUS END Example 1 A curved guide example made of straight elements Simple bits of C language are used in the DECLARE block to define internal constant values n and dt The default guide coating is Nickel m 1 To assemble this Example type the description in the McGUI editor save it into the curved cuide instr file and press the Run button Curved guide Figure 6a The curved guide Example 1 geometry shown with Matlab left and PGPLOT right plotters Some neutron trajectories are displayed as a series of straight lines These views are obtained by starting the simulatio
19. JDN 18 1 Collection SFN 12 2010 Owned by the authors published by EDP Sciences 2010 Virtual experiments in a nutshell simulating neutron scattering from materials within instruments with McStas E Farhi P Willendrup 1 Institut Laue Langevin BP 156 38042 Grenoble Cedex 9 France 2 Rise National Laboratory Frederiksborgvej 399 P O Box 49 DK 4000 Roskilde Abstract We introduce Monte Carlo methods for neutron scattering with step by step examples using the McStas simulation tool A selection of neutron instrument components are presented as well as available sample scattering kernels All these parts are assembled into more advanced instrument models in order to produce so called virtual experiments that is simulations which produce results comparable with experiments Ways to couple such simulations with other simulation software including molecular dynamics are discussed 1 INTRODUCTION Building and improving neutron scattering instruments is a long and thorough process And all existing instruments suffer imperfections which show up in sample scattering measurements such as broadening asymmetry background and additional contributions Neutron scattering ray tracing simulation tools such as McStas offer the possibility to model many of these effects which in the end help to understand the instrument pitfalls and improve their usage The object of this paper is to present what can be achieved today with Monte Carlo
20. K KERR KKK KK KK KKK KK KK RK KR k k k KKK KR KKK k k KK k k k KKK ERK k k kk k ck KK ck ck k k k Instrument fermi_chopper instr Description A Fermi chopper example The rotation frequency is computed automatically and the initial time distribution is set by an EXTEND after the source Parameters from IN6 ILL Fermi Chopper Parameters lambda Angs neutron wavelength selected by the chopper system RRR ERK RRR RRR KR KR e ke KK RK KR RK KR KK KR KR KK RK KR KKK KR KR KK KR RRR KK KR KKK RK KR KKK KR KKK KKK RRR ckck ck ckckck ck ckck ck k k ck k k ck k k k kk k ck KKK DEFINE INSTRUMENT fermi chopper lambda 4 DECLARE double w 0 064 200 width of a single slit in the Fermi chopper package double L 0 012 length of the Fermi chopper package double frequency dt declare internal variables to be used afterwards 8 INITIALIZE frequency 3956 w 2 PI lambda L L dt w L 2 PI frequency Fermi chopper time window printf s frequency g Hz time window dt g s n NAME CURRENT COMP frequency dt 8 TRACE COMPONENT Source Source simple dist 1 radius 0 03 xw 0 064 yh 0 05 Lambda0 lambda dLambda lambda 0 01 AT 0 0 0 ABSOLUTE EXTEND double v sqrt vx vxtvy vytvz vz neutron velocity t randpml dt 1 v set neutron event time in Fermi chopper time window and shift to Fermi chopper at 1 m p p dt correct intensity which is set for 1 s
21. K ek KR KKK ce ck KK ck ck KK KKK KK k k k KR KKK k k KK k k k k k k KR k k k k k k k k k k k k k k ck ck ck ck ck KE KK KKK KK DEFINE INSTRUMENT monochromator simple lambda 2 36 DM 3 355 DECLARE double theta half take off used further in the instrument TRACE 8 INITIALIZE theta asin lambda DM 2 RAD2DEG also called Al on triple axis machines printf s 2 theta g deg take off angle n NAME CURRENT COMP 2 theta 8 TRACE COMPONENT Source Source simple dist 1 radius 0 01 xw 0 01 yh 0 01 Lambda0 1ambda dLambda lambda 0 04 AT 0 0 0 ABSOLUTE COMPONENT MC Monochromator curved width 0 10 height 0 10 DM DM AT 0 0 0 5 RELATIVE PREVIOUS ROTATED 0 theta 0 RELATIVE PREVIOUS COMPONENT MC_out Arm AT 0 0 0 RELATIVE PREVIOUS ROTATED 0 theta 0 RELATIVE PREVIOUS COMPONENT MC_Mon Monitor_nD xwidth 0 01 yheight 0 01 options auto wavelength x AT 0 0 0 5 RELATIVE PREVIOUS END Example 6 A simple monochromator setup which computes automatically the take off angle JDN 18 15 monochromator_simple MC_Mon tt MC_Mon_1285749754 x_L X0 1 1425e 06 dX 0 00451901 YO 2 35966 dY 0 0406231 1 5 96492e 05 Err 1 369e 07 N 18985 6x10 7 4x10 2x1077 xim Figure 11a Geometry of the Example 6 simple 0 01 0 0 01 monochromator setup showing a few diffracted neutron Figure 11b Wavelength distribution obtained by trajectories with take off angle 20
22. MENT liquid simple lambda 2 36 string coh Rb liq coh sqw string inc Rb liq inc sqw TRACE COMPONENT Source Source simple dist 1 radius 0 01 xw 0 01 yh 0 01 Lambda0 1ambda dLambda lambda 0 01 AT 0 0 0 ABSOLUTE COMPONENT sample Isotropic Sqw Sqw coh coh Sqw inc inc radius 0 005 yheight 0 05 AT 0 0 0 5 RELATIVE PREVIOUS COMPONENT banana Monitor nD xwidth 1 yheight 0 3 options banana abs theta limits 10 130 bins 240 y bins 50 AT 0 0 0 RELATIVE PREVIOUS COMPONENT bananE Monitor nD xwidth 1 yheight 0 3 options banana angle limits 10 130 bins 120 auto energy bins 100 AT 0 0 0 RELATIVE PREVIOUS END Example 9 A simple liquid scattering example which also works with powders and gases 0 15 0 1 0 05 y m Energy me 0 05 20 40 60 80 100 120 20 40 60 60 100 120 onaitiide deal Anale deal Figure 13 Neutron scattering from a liquid rubidium sample obtained from the Example 9 at A 2 36 A The left plot shows the liquid Debye Scherrer rings as obtained from a diffractometer 2D detector whereas the right one shows a radial angle energy signal with inelastic contribution Intensity is shown in log scale with colors ranging from blue low to red high 5 3 3 Single crystal structures When the sample is a single crystal the averaging on many crystallites that is responsible for the scattering rings in a powder does not apply The Bragg law is still valid but
23. Press 1978 15 Willendrup P Filges U Keller L Farhi E Lefmann K Validation of a realistic powder sample using data from DMC at PSI Physica B Cond Matt 385 2006 1032 16 K Yvon W Jeitschko and E Parth LAZY PULVERIX a computer program for calculating X ray and neutron diffraction powder patterns J Appl Cryst 10 1977 73 see also lt http icsd ill fr gt 17 J Rodriguez Carvajal Physica B 192 1993 55 18 V F Sears Adv Phys 24 1975 1 19 E Farhi V Hugouvieux M R Johnson W Kob Virtual experiments Combining realistic neutron scattering instrument and sample simulations Journal of Computational Physics 228 2009 5251 20 Theo Siegrist J Appl Cryst 30 1997 418 21 D Richard M Ferrand G J Kearley http www ill fr computing 22 T Rog K Murzyn K Hinsen G R Kneller J Comput Chem 24 2003 657 23 V Hugouvieux E Farhi MR Johnson et al Phys Rev B 75 2007 104208 24 25 N 24 Material Studio from Accelrys lt http accelrys com products materials studio gt San Diego CA 92121 USA 25 G Kresse and J Hafner Ab initio molecular dynamics for liquid metals Phys Rev B 47 1993 558 26 X Gonze B Amadon P M Anglade J M Beuken F Bottin P Boulanger F Bruneval D Caliste R Caracas M Cote T Deutsch L Genovese Ph Ghosez M Giantomassi S Goedecker D R Hamann P Hermet F Jollet G Jomar
24. R RK KERR KKK RRR KR KKK KKK KK KR KR KK e ck KK RK KR KK KKK KKK KK KK KK KK KKK RK KR KKK KKK KR RK k k k KK RK k k k KEK KK KEK KE ck ck KKK KEK Instrument disk choppers instr Description A disk chopper example made of two instances The phase is automatically set SParameters lambda Angs neutron wavelength selected by the chopper system frequency Hz chopper rotation frequency omega 2 PI frequency rpm 60 frequency d cc m distance between the two choppers Chopper opening slits is 10 deg here RRR RR KR RK RRR KK RR KK KR KR KEK KR KK KR ce ke KK RR RK RK KR KK KR KR KKK KK KK KK KR KKK KKK KR KKK KERR KEK k k k k k k ck ckck ck k k ck ck k k k KKK KKK KKK DEFINE INSTRUMENT disk_choppers lambda 4 frequency 200 d_cc 5 TRACE COMPONENT Source Source simple dist l d_cc radius 0 03 xw 0 03 yh 0 2 Lambda0 lambda dLambda lambda 0 01 AT 0 0 0 ABSOLUTE COMPONENT Chopl DiskChopper omega 2 PI frequency R 0 3 h 0 2 theta 0 10 n 1 IsFirst 1 AT 0 0 1 RELATIVE PREVIOUS COMPONENT Chop2 COPY Chopl IsFirst 0 phi 0 2 PI frequency d cc lambda 3956 RAD2DEG AT 0 0 d cc RELATIVE Chopl COMPONENT CG Mon Monitor nD xwidth 0 03 yheight 0 2 options auto time AT 0 0 0 1 RELATIVE PREVIOUS END Example 3 A simple disk chopper system after a continuous source A similar instrument using a pulsed source such as the ESS moderator long would require IsFirst 0 This instrument des
25. RR RRR ERR KEK che e ke ke che e KKK KK KKK KKK KKK KR KKK KR KK KKK KKK KKK KKK KK KKK KKK RR KK KEK KR KEK KR k k k k k KK KKK KKK KEK k k ck k k ck ck k k k Instrument liquid sample environment instr Description A disk chopper spectrometer with liquid sample and large detector including a sample environment Parameters lambda Angs neutron wavelength selected by the chopper system frequency Hz chopper rotation frequency omega 2 PI frequency rpm 60 frequency d cc m distance between the two choppers Chopper opening slits is 10 deg here coh str liquid or powder coherent scattering Sqw or powder format inc str liquid or powder incoherent scattering Sqw or NULL for isotropic elastic RRR ERK RRR RR KKK e ke KK e ck KR ek KR KKK KKK KKK KK RK ke ck KK KR RK RK KK RK KK KR KKK KKK KR KKK KKK RRR KR KR k k k KK k ck ckck ck ck k k k k k KK KKK ck k DEFINE INSTRUMENT liquid sample environment lambda 2 36 frequency 200 d cc 5 string coh Rb liq coh sqw string inc Rb liq inc sqw DECLARE double flag sample 3 TRACE COMPONENT Source Source simple dist 1 radius 0 03 xw 0 03 yh 0 05 Lambda0 lambda dLambda lambda 0 01 AT 0 0 0 ABSOLUTE COMPONENT Chopl DiskChopper omega 2 PI frequency R 0 3 h 0 05 theta 0 10 n 1 IsFirst 1 AT 0 0 1 RELATIVE PREVIOUS COMPONENT guide Guide w1 0 03 h1 0 05 w2 0 03 h2 0 05 1 d cc 0 1 AT 0 0 0 05 RELATIVE PREVIOUS COMPONEN
26. T Chop2 COPY Chopl IsFirst 0 phi 0 2 PI frequency d cc lambda 3956 RAD2DEG AT 0 0 d cc RELATIVE Chopl SPLIT COMPONENT sample Progress bar AT 0 0 0 5 RELATIVE PREVIOUS EXTEND flag sample 0 neutron events reaching the sample area have not scattered yet on it 8 COMPONENT Env In PowderN reflections Al laz radius 0 035 radius i 0 035 0 002 yheight 0 1 concentric 1 tfrac 0 9 AT 0 0 0 RELATIVE sample COMPONENT Con In PowderN reflections Nb laz radius 0 005 50e 6 radius i 0 005 yheight 0 1 concentric 1 tfrac 0 9 AT 0 0 0 RELATIVE sample COMPONENT liquid Isotropic Sqw Sqw coh coh Sqw inc inc p interact 0 9 radius 0 005 yheight 0 05 AT 0 0 0 RELATIVE sample EXTEND flag sample SCATTERED sets flag when scattering occurs in the liquid 8 COMPONENT Con Ou COPY Con In concentric 0 AT 0 0 0 RELATIVE sample COMPONENT Env Ou COPY Env In concentric 0 AT 0 0 0 RELATIVE sample COMPONENT total Monitor nD xwidth 2 5 yheight 1 options banana auto time bins 256 angle limits 10 130 bins 120 AT 0 0 0 RELATIVE sample COMPONENT detect COPY total WHEN flag sample AT 0 0 0 RELATIVE sample END Example 14 A liquid scattering time of flight spectrometer virtual experiment with a sample container and outer environment We could even add a last similar monitor to be used WHEN flag_sample gt 1 to record only the multiple scattering part from the liquid sample Th
27. ach event and in the previous case p p n and count them all in a weighted expression of E f n n E f lim 1 De pf u with gt D p n gt Il j 1 a lt u lt b i l which in this case uses the n events and the standard deviation is amp An This is an extremely common trick in Monte Carlo integration referred to as importance sampling and it actually lowers random number casting For instance most of the absorption estimate in McStas is taken into account that way Among the other variance reduction techniques one is to identify u space regions that have larger weight in the final result Suppose we aim at estimating the scattered intensity from a sample hitting a detector The integral E f may then be written as E f E f events that will probably hit the detector E f events that may not hit the detector It is reasonable to assume that the second term is substantially smaller than the first one in the total result If we now choose to cast more random numbers in the first term than in the second we shall probably improve the statistical accuracy on the result This is known as stratified sampling which favours regions of the phase space w r t other parts which are assumed to contribute less to the result This trick requires that we are able to in a way define the high importance regions which implies to define a choice criteria hit or miss sample and detector In the sample scattering example cited above these event
28. ample powder structure definition file Powder defaulting to Sapphire and instrument distances L L2 and L3 For a start just press the Start button and wait for the simulation completion which should be shorter than a minute From the main interface press the Plot button in order to display the simulation results which are in this case some histograms built from the neutron beam distribution at various places in the instrument In our case we shall focus on the two last monitors which present the angle dispersed diffractogram as well as a 2D detector showing portions of the sample scattering Debye Scherrer cones 14 as shown in Figure 3 You may of course change the instrument simulation parameters from the Run Dialogue without actually touching the model itself for instance the incoming neutron wavelength or sample structure file 4 3 Viewing the instrument model JDN 18 Xovelength Angs monitor Xovelength Angs monitor be t1 Ditt Kone Lambda 1284 308MLParnple Lambdo 1 Dit i 0995 1 Movelength Anga 0995 1 1005 Wevelength Anga 5x10 a 1 005 x m p ie 4eg monitor Intensity Angle Position Monitor rename out per bin D t i204 itt BonaneTheta iff BonanaTheta_1204130585 Apift_Bonagol thy 3000 Intensity n s bin 2000 1000 o 100 Angle deu so Longitude deg 100 150 Figure 3 Results from a typical diffractometer model simulation
29. and convergence Even though the convergence of the Monte Carlo estimate for the finite continuous integrable function fis guaranteed for infinite number of random evaluations n it may be appropriate to estimate the associated error for finite values of n The variance of the estimator is defined as the averaged square deviation of the f u values from its expectation E f V f Elf ECF F The law of large numbers and the central limit theorem state that the Monte Carlo estimate follows a normal distribution when n is large In this case the standard deviation of the estimate is W P o Vn which indicates that the error on the estimate follows a n law independent of the dimensionality d of the integration that is the number of independent variables to integrate in order to obtain the integral estimate This result is essential JDN 18 3 compared with other integration techniques such as the trapezoidal rule which behaves as n and the Simpson s rule n In a few words the Monte Carlo technique is guaranteed to converge faster than the trapezoidal and the Simpson s rule for dimensionality d larger than 4 and 8 respectively and more generally any usual quadrature integration rule will be slower than the Monte Carlo estimate at some point In the case of the McStas Monte Carlo neutron scattering ray tracing software 6 7 we use a d 10 phase space position velocity spin and time from which we integrate measurabl
30. attering which usually shows quite sharp features in momentum and energy transfer The incoherent scattering corresponds to interaction with disordered matter that is for instance impurities and isotopic composition crystal twining and boundaries Brownian motion and heat diffusion Such interactions often appear as broad momentum and energy transfer contributions The details of the scattering laws which apply in samples are beyond the scope of this paper and we re direct the reader to reference books 14 for more information 5 3 1 Powder structures Among the most common materials measured with neutron scattering techniques are powders which are composed of a large number of tiny single crystals The scattering intensity by means of constructive interference and averaging over all crystallites appears as well defined rings around the out going direct beam direction These rings are also present in liquids but are much smoother as we shall see in next section Let us consider a material of density p made of N scattering units each with a unit cell volume Vo arranged with lattice spacings dg 27 Q associated to structure factors F Q with equivalent reflection multiplicities jg These structure factors characterize the efficiency of the reflection with momentum exchange Q Following Squires 14 the scattering probability for an incoming neutron with wavelength penetrating along a distance x into the material is about exp Oc X Where Oco
31. but just flush neutron events into a file for further analysis Such feature may be obtained from the Monitor nD with the options source parameter or the Virtual output component A much more advanced model will be introduced in section 7 3 with the PSD Detector gas detector component 6 VIRTUAL EXPERIMENT SIMULATION EXAMPLES We shall now use the items presented in the section 5 sources neutron optics samples detectors to describe simple but realistic virtual experiment models For more advanced components and usage examples refer to section 7 Running these models will be slightly longer than those demonstrated in section 5 lasting a few minutes on current computers 6 1 A time of flight spectrometer for liquids 22 Collection SEN The idea is here to model a disk chopper time of flight spectrometer with a liquid sample and a large banana shaped detector This consists essentially in assembling the disk chopper Example 3 section 5 2 3 and the isotropic sample Example 9 section 5 3 2 as shown in the Example 11 The model geometry is shown in Figure 15a The SPLIT keyword at the sample position defines a partitioned sampling mechanism to be applied in order to greatly improve the simulation efficiency see section 2 3 The instrument detector image result is shown in Figure 15b and resembles in many ways Figure 13 but with a time axis in place of the energy axis This distribution can be directly measured on existing time of
32. cription makes use of the Monitor nD with its automatic histogram limits feature for the neutron time parameter f w ean n m CG Mon 1285668502 o x o D o a o BR Intensity n s bin o o b 6 o i 5 05 54 5 15 5 2 5 25 5 8 5 35 TOF s x10 Figure 8a A double chopper spectrometer from the Example 3 Figure 8b Time distribution from the double chopper Disks are de phased by angle 6 rotating with frequency f tromet ting at A 4 A separated by distance d EM 2M E The Fermi choppers are a more compact alternative to disk chopper arrangements They consist in a rotating short collimator In order for neutrons to be transmitted they have to pass the entry window of the collimator and propagate directly to the exit window without touching the collimator side walls All of this takes place in a rotating frame which makes the model slightly more complex 11 12 The neutron wavelength A selected by the Fermi chopper can be found to be close to rc 3996 Win Angs 2 2T finz Lim with w being the slit width and L its length The opening time of the Fermi chopper is about Ar2w L 2 7 f and the beam divergence is restricted to w L The Fermi chopper wavelength resolution will get narrower as the frequency increases and the slit width decreases which also leads to a decrease in intensity 12 Collection SFN RRR RRR ERR RRR che e ke ke che e KR KKK KK KR ce ke KK KKK KKK KR K
33. cylinder which all can be bulk or hollow geometries including concentric arrangements An additional complex geometry enables to use any point set to describe the material volume geomview OFF file In order to demonstrate its usage we re use the Examples 6 and 7 with a wider incoming wavelength range and add a larger detector as shown in Example 10 The instrument geometry resembles the Figure 12a with a tilted graphite plate at the sample As expected the scattering shows a number of spots which each select a single wavelength The central spot is the direct transmitted beam Currently McStas does not provide simple ways to add inelastic scattering on top of a mono crystalline structure even though there is a way to simulate the neutron scattering on a a simple phonon dispersion 5 3 4 Other sample models A number of other sample types may be modelled with McStas and we shall thus present some possibilities without actually demonstrating their usage in the frame of this paper We point the reader to the McStas Component Manual 9 and the Library Index for more details The sample models such as PowderN Isotropic Sqw and Single crystal may be used for small angle scattering as long as the data files do include large scale structure data However no special form factors will then be taken into account The Sans sphere component may be used to model dilute colloids of hard spheres the SANS Guinier models a scattering unit with a gyrati
34. d S Leroux M Mancini S Mazevet M J T Oliveira G Onida Y Pouillon T Rangel G M Rignanese D Sangalli R Shaltaf M Torrent M J Verstraete G Zerah J W Zwanziger Computer Phys Commun 180 2009 2582 27 P Giannozzi et al J Phys Condens Matter 21 2009 395502 28 K Parlinksy http wolf ifj edu pl phonon
35. e 8 e 7 o c X D q z o l A 4 st ed o ree Py u a s 1 o 1 50 100 50 100 Longitude deg abs Angle deg Figure 17 The Na2Ca3A12F14 powder diffractogram simulated with the Example 12 obtained at A 1 4 A Left side shows the angle height diffractogram with Debye Scherrer arcs and right side shows the radially integrated angle diffractogram 7 ADVANCED NEUTRON OPTICS SIMULATION EXAMPLES It is possible to use the previous examples in order to estimate other effects such as a background level from an instrument part The models presented in this section are certainly the most advanced presented in this work and their execution requires a longer simulation time up to 15 minutes on a current desktop computer However the corresponding descriptions remain very compact and focus on non trivial effects which do arise when performing 26 Collection SFN neutron scattering experiments 7 1 Monochromators thickness and background sources The use of heavy shielding around monochromator housings can be understood as a large portion of the incoming beam scatters in all directions and the following neutron instrument usually only collects one see Figure 14 in section 5 3 3 The remaining scattered beams generate additional scattering when hitting again other materials In the end a significant amount of background may arise In order to get an insight into this effect we shall start from the monochromator Example 7 with a si
36. e Example 14 is assembled from the liquid spectrometer Example 11 section 6 1 but adds two outer cylinders made of niobium and aluminium to model the sample container and the first sample environment thermal shield A few dedicated monitors are added at the end of the instrument description making use of the WHEN keyword which activates a component instance depending on a condition This way we are able to separate contributions from the sample itself and the sample environment The concentric geometry implemented in most McStas sample components enables to place components within others to model e g sample environments It consists of repeating a component instance symmetrically w r t the central position e g the sample one The model geometry is shown in Figure 21 The resulting plots are shown in Figure 22 Such results are invaluable in order to understand the meaning of a measurement and the ratio between the sample signal and the other contributions often labelled as background The intense contribution from the sample environment and the container justifies the JDN 18 29 installation of radial collimators on most spectrometers liquid_sample_environment z m 7 0 x Iml Figure 21 The Example 14 liquid spectrometer with sample environment geometry insert A few neutron trajectories are displayed with multiple scattering events IntTOF angle monitor TOF angle monitor Total signal Sample contribution 120
37. e quantities In this space we have estimated the number of random numbers to cast in order to obtain a given accuracy in the integral E f Basically throwing 10 neutron events ensures an error bar within a percent for most simulations Such simulations usually run within a few seconds The most advanced examples in this work may require up to 10 neutron events which then produce accurate results even for low probability processes e g scattering in materials within minutes Records in E f 10 104 105 10 10 Accuracy O E f 10 2 5 1 0 25 0 05 Table 1 Uncertainty estimate in percents as a function of the number of statistical events used to compute an integral with McStas 2 3 Variance reduction techniques improving the computation efficiency Even though the Monte Carlo techniques all use random numbers there are many ways to implement the method Suppose a given physical process has a probability p to occur and thus be counted in an integral One easy solution is to cast n equally distributed random numbers 0 lt 7 lt 1 and only count events that satisfy z lt p After n initial random numbers the E f integral only counts np events and the relative standard deviation is o ec AInp Clearly this is not efficient especially when p is small We may then label this method as a hit or miss algorithm An other way to obtain exactly the same estimate is to assign a statistical weight p to e
38. ector geometry from Example 5 Wavelength Angs showing drum length d rotation frequency f and twist Figure 10b The wavelength distribution around A 4 A angle obtained after a velocity selector on a continuous neutron source 5 2 5 Monochromators The previous monochromating neutron optics all use movable parts filtering the neutron velocity with a propagation time in between slits The crystal monochromators are static devices which select the neutron energy from the reflection constructive interferences on atomic planes following the Bragg s law nA 2dsin where A is the incident neutron wavelength d is the distance which separates the diffractive atomic planes 0 is the incidence angle w r t the plane surface and n is the order of the reflection In practice as a crystalline material contains many atomic planes a polychromatic neutron beam will be reflected in many directions providing narrow scattered beams each of which will correspond with a single diffracted wavelength RRR RK KERR KEK che e ke KR KKK KKK KK KR KR KK KKK KKK KR KK KR KR KKK KKK KKK KR KKK KKK KR KER KK KEK k k ck k k k k k k k k k ck ckck ck ckck ck KK KKK KKK k k k Instrument monochromator simple instr Description A monochromator example Parameters lambda Angs neutron wavelength selected by the monochromator DM Angs Monochromator d spacing default is 002 Graphite KKK ERK KR RK KR RK KR RK KK e ck KR KK KKK ce ke K
39. ent can also read tabulated spectrum flux The next sections demonstrate a number of usage examples of source components Detailed source models may be imported from neutron transport codes such as MCNP and FLUKA as explained in section 8 1 5 2 Neutron optics Once neutron particles have been emitted by a neutron source model they propagate to other model components which we label as neutron optics except for samples and detectors see dedicated sections 5 3 and 5 4 We only present the most common optics components but others are available from the McStas library e g refractive lenses and prisms statistical choppers filters polarized components 5 2 1 Guides Apart from beam tubes which have non reflective surfaces and thus effectively act as simple slits guides enable to transport neutron beams far away from the reactor State of the art multi layer coated guides have a very good transmission and also drastically lower the neutron source background noise level on the distant instruments by transporting neutrons far away from the neutron source There are many ways to model neutron guides which essentially depend on the complexity of the guide geometry Most of the available guide components model straight guide sections including the simplest and recommended Guide component A curved guide may be built by appending a series of Guide components along a curved line such as in the Example 1 A small gap d in between straight elements ha
40. entering the gas Also the inner side of the rings is well defined because it corresponds to events detected just when entering the gas cell whereas the outer ring side is blurred by the penetration is the gas The resulting contrast on the ideal monitor left side of Figure 24 appears to be unfortunately unreachable in reality right side 8 COUPLING MCSTAS WITH OTHER TOOLS 32 Collection SEN The McStas software is a open source community based package It has benefited from a large number of user contributions including some which interface with other simulation packages Some of the most important interfaces are certainly those which couple McStas with the world of reactor and particle physics and with the world of molecular dynamics to obtain S q 8 1 Reactor particle physics transport codes Most reactors that have been built today were designed using MCNP see section 2 1 and some accelerators have been simulated with e g MCNP X These codes handle the high energy physics which takes place in fissile materials and occur when high energy particle beams collide with matter This kind of interaction may generate neutrons which are then slowed down by e g successive Compton scattering processes in moderators Other codes such as FLUKA which is closely related to MCNP X GEANT4 or TRIPOLI provide the same functionality and actually all share the wide ENDF material database The MCNP type codes can produce neutron event records
41. experiments materials are primarily used as samples and also contribute as crystal monochromators or beam filters graphite sapphire beryllium But they also give a parasitic signal appearing as a background that is all we do not want or do not understand for instance in sample environment cryostat furnace sample containers or radiological shielding concrete polyethylene boronated materials wood cadmium lead The neutron scattering from all these materials where ever they are positioned in the model may be simulated with McStas Neutron scattering may be categorized into two types of processes Schematically coherent scattering takes place when neutrons encounter ordered matter This is the case mostly on the material atomic molecular structure crystalline liquid or gas where atoms are arranged with preferred distances d that neutrons will interact with following the Bragg law seen in section 5 2 5 This type of interaction is labelled as elastic as the neutron does not exchange energy but only momentum that is change its direction but not its velocity An energy transfer may also be considered when the material either gives or pumps energy to from the neutron This energy corresponds to propagating waves in the atomic molecular structure such as phonons sound waves or magnons spin waves or coherent fluctuations of the structure when reaching material phase transitions All these cases correspond with inelastic coherent sc
42. flag when a scattering event occurs in the aluminium pillar This flag is then used to monitor both the JDN 18 27 signal from the monochromator crystal blade and the pillar and the part that has scattered in the aluminium bar only The beam image is recorded on a m diameter sphere centred on the monochromator position with its angle centred on the direct transmitted beam The resulting total scattering is recorded and shown in Figure 20 The graphite crystal scatters the 002 reflection around 41 2 take off angle on the left plot corresponding to a wavelength A 2 36 A The strongest spot in the centre of the plot is the transmitted and attenuated beam through the crystal A large number of weaker diffraction spots are scattered both in and out of the scattering plane The shape of these spots depends on the crystal thickness and tilt as well as the beam attenuation from the neighbouring pillar Below the Laue Bragg scattering from the wide incoming neutron wavelength range appears the pillar powder scattering pattern as a large distribution of Debye Scherrer rings The background is essentially backward scattering and at 90 degrees centred on the incoming direction The total additional background from the aluminium structure aside the graphite blade can be estimated to around be 0 7 96 of the intensity scattered by the crystal but may be locally stronger for some angles which correspond to diffraction in aluminium In the vicinity of the 00
43. flight spectrometers As a standard data analysis procedure the time axis is usually processed and converted into the energy transfer whereas the angle axis provides the momentum transfer g so that it actually provides the sample dynamic structure factor S q RRR RRR ERR KEK RRR KK RRR KKK KKK KR KK RRR KKK RRR KER RK RK KK RK KK KR KR KR KKK KR KKK KKK KR EK KR KKK KR KKK ck k k ck k k k k k k KK k k k KEK Instrument liquid spectrometer instr Description A disk chopper spectrometer with liquid sample and large detector Parameters lambda Angs neutron wavelength selected by the chopper system frequency Hz chopper rotation frequency omega 2 PI frequency rpm 60 frequency d cc m distance between the two choppers Chopper opening slits is 10 deg here coh str liquid or powder coherent scattering Sqw or powder format inc str liquid or powder incoherent scattering Sqw or NULL for isotropic elastic RRR RR KR RE KR RR RK che ek KK RR KR RK KR KK KR KKK KKK KR KKK KR KK RR KR KKK KKK KKK KR KR KKK KEK KR RRR KEK KR KEK k k k k k k ck ckck ck k k k ck k k k k k KK KKK KK DEFINE INSTRUMENT liquid spectrometer lambda 4 frequency 200 d_cc 5 string coh Rb liq coh sqw string inc Rb liq inc sqw TRACE COMPONENT Source Source simple dist 1 radius 0 03 xw 0 03 yh 0 05 Lambda0 lambda dLambda lambda 0 01 AT 0 0 0 ABSOLUTE COMPONENT Chopl DiskChopper omega 2 PI frequency R 0 3
44. half take off used further in the instrument TRACE 8 INITIALIZE theta asin lambda DM 2 RAD2DEG also called Al on triple axis machines printf s 2 theta g deg take off angle n NAME CURRENT COMP 2 theta 8 TRACE COMPONENT Source Source simple dist 1 radius 0 1 xw 0 1 yh 0 1 Lambda0 1ambda dLambda lambda 0 04 AT 0 0 0 ABSOLUTE COMPONENT MC Monochromator curved width 0 10 height 0 10 DM DM RV 2 sin theta DEG2RAD RH 2 sin theta DEG2RAD AT 0 0 1 RELATIVE PREVIOUS ROTATED 0 theta 0 RELATIVE PREVIOUS EXTEND if SCATTERED ABSORB absorb non scattered events direct beam 8 COMPONENT MC out Arm AT 0 0 0 RELATIVE PREVIOUS ROTATED 0 theta 0 RELATIVE PREVIOUS SPLIT COMPONENT sample PowderN reflections material radius 0 005 yheight 0 05 d_phi atan2 0 3 1 RAD2DEG AT 0 0 1 RELATIVE PREVIOUS COMPONENT radial Collimator radial radius 0 6 yheight 0 3 length 0 30 divergence ALPHA theta min 5 theta max 140 AT 0 0 0 RELATIVE PREVIOUS COMPONENT psd Monitor nD xwidth 2 yheight 0 3 options banana abs theta limits 5 140 bins 270 y AT 0 0 0 RELATIVE PREVIOUS COMPONENT banana Monitor nD xwidth 2 01 yheight 0 3 options banana angle limits 5 140 bins 270 AT 0 0 0 RELATIVE PREVIOUS END Example 12 A powder diffractometer virtual experiment This simulation requires a longer computing time to produce the Figure 17 The re
45. ket Monte Carlo methods are all around us 2 Collection SEN The Monte Carlo computing method was invented by John von Neumann Nicholas Metropolis and Stanislaw Ulam 1 and actually named by reference to the well known Casino Figure 1 from Ulam who was obsessed by randomness in life and games such as solitaire and poker This method was first implemented in order to estimate the neutron diffusion in fissionable materials in the frame of the Manhattan Project and resulted in the first version of Monte Carlo N Particle code MCNP in 1945 More specifically for the purpose of this paper this computing technique may be applied to numerical integration methods which we shall mainly use for neutron scattering simulations in order e g to estimate macroscopic measurable values intensities spatial Figure 1 The Monte Carlo Casino distributions by summing up microscopic quantities Photograph Source GALE FORCE Archive Mathematically the Monte Carlo method is an application of the law of large numbers 2 3 Let f u be a finite continuous integrable function of parameter u for which an integral estimate is desirable The discrete statistical mean value of f computed as a series in the uniformly sampled interval a lt u lt b with n values converges to the mathematical f mean value E f also known as the expectation of f over the same interval lim y f u noc N i 1 a lt u lt b b a f u du E f a
46. minium window plate followed by a gas volume 3 cm thick 6 bars cell We have used a perfect beamstop after the powder sample which absorbs all non scattered neutrons in an EXTEND block RRR kk check e k k ek che e ke ke che e KR KKK KK KKK KKK KKK ERK KR KKK KR KKK KK RK KKK KKK KKK KR KKK KKK KR k k k k k k k k KK KKK KKK k k kk k KK KKK k k k Instrument powder detector instr Description A powder scattering example with a realistic gas detector SParameters lambda Angs incoming neutron wavelength monochromatic material Angs Powder structure file lazy fullprof crystallographica KKK ERK KER KR KEK RRR KKK KR KR KK KKK KR KK RK KR KR KR KR KK k k RRR KKK KK KKK KKK KKK KR RRR KKK k k k KR k k k k ck k k k ck k k ck k k ck ckckck KK KKK KK DEFINE INSTRUMENT powder detector lambda 2 36 string material Na2Ca3Al2Fl14 laz TRACE COMPONENT Source Source simple dist 1 radius 0 01 xw 0 01 yh 0 01 Lambda0 lambda dLambda lambda 0 01 AT 0 0 0 ABSOLUTE COMPONENT powder PowderN reflections material radius 0 005 yheight 0 05 AT 0 0 0 5 RELATIVE PREVIOUS EXTEND if SCATTERED ABSORB 8 COMPONENT Perfect Monitor nD options x y bins 512 xwidth 0 26 yheight 0 26 restore neutron 1 AT 0 0 0 15 RELATIVE powder COMPONENT Window PowderN xwidth 0 26 yheight 0 26 zthick 0 001 reflections Al laz tfrac 0 9 frac 0 01 AT 0 0 0 15 RELATIVE powder COMPONENT BIDIM26 PSD Detect
47. n in Trace mode JDN 18 9 In principle this type of polygonal guide may model most geometries including ballistic elliptic and parabolic guides made of flat surfaces More advanced geometries may be described using for instance the Guide gravity the Guide channeled the Guide curved and the Guide tapering components 5 2 2 Collimators 0 The primary role of a collimator is to restrict the neutron 0 005 beam divergence that is absorb all neutrons with trajectories 0 01 inclined by more than a given angle from the main axis Only ae exes neutrons which do not hit the collimator channel sides will Figure 6b Results from the Example 1 obtained from remain with a divergence lower than w L with w being the the neutron beam cross section at the end of the curved channels width and L their length Most neutron instruments guide Obtained by running the simulation and pressing tend to restrict the incoming neutron divergence in the he plo button Intensity is shown as color scale from horizontal plane with such components but usually leave the plue low to red high vertical divergence unaffected in order not to reduce too much the neutron intensity beyond We present in Example 2 a typical use of the Collimator linear component to be part of a McStas instrument simulation description The Guide channeled and the Guide gravity components may also be used to model collimators Radial collimator models such as the Collima
48. nances Compton scattering 19 No polarised neutron component is considered even though McStas provides a set of optic and sample components 5 1 Sources Source components generate neutron particles that is a random distribution in space source volume area velocity neutron energy time especially for pulsed sources and possibly spin Additionally the particle Monte Carlo weight integrates as the total source flux We shall not go into the details of the neutron generation in sources but only consider on the simulation side that neutron events are evenly generated on a surface with given energy divergence and time distributions JDN 18 7 Component name Description Source_simple A simple flat spectrum source steady state Source_Maxwell_3 and Source_gen A black body steady state source Parameters for the ILL and PSI are available Moderator Simple pulsed source ESS_moderator_long An ESS parametrized long pulsed source SNS_source An MCNP X based SNS USA short pulsed source ISIS moderator An MCNP X based ISIS England pulsed source Table 2 A short list of some common neutron source components available in McStas McStas provides a set of steady state sources e g for reactor based instruments as well as some other components more suited for pulsed sources refer to Table 2 As a start we recommend new McStas users to use the Source simple component The more advanced Source gen compon
49. ne is the so called coherent elastic cross section of the ring Nx jolF Q cone VQ Oo This relation is only valid under certain conditions among which do gt A 2 from the Bragg law As the possible lattice spacings d in the material can not exceed a maximum value for instance the inter atomic distance it appears that as the neutron wavelength increases the number of visible rings in the diffractogram will decrease until no more scattering is possible above the so called Bragg edge where materials become transparent to neutrons except for absorption and incoherent scattering This is why most of the diffractometers use thermal and hot neutrons Cold neutrons can only scatter on large distance arrangements in materials e g in larger molecules and proteins JDN 18 17 RRR RRR ke khe e ke RRR ke che e ck che e KK KKK KR KK KKK KR KR KR KK KKK KKK KKK KKK KR KKK KKK KR KKK KKK k k KK ERK k k k k k ck k k k k k k ck ckck ck k k ck ck k k k Instrument powder simple instr Description A powder scattering example Parameters lambda Angs incoming neutron wavelength monochromatic material Angs Powder structure file lazy fullprof crystallographica RRR ERK RRR RRR KK e KK KR KR KR RK KR KK KR KR KK RK KR ck ck KR KR KK KR KK ck ck KK RK KK KK KR KEK KR KER KK KEK KR k ck k k k k k k ck ckck ck ckck ck k k ck k k k kk k ck KKK DEFINE INSTRUMENT powder simple lambda 2 36 string material Na2Ca3Al2F
50. nelastic contributions a full atom trajectory must be simulated Lattice dynamics codes such as PHONON 28 only provide the inelastic part Ab initio based on DFT codes provide the most accurate results but classical molecular dynamics using parametrized interaction potentials are required for larger systems The space time atom trajectories should then be Fourier transformed into a momentum energy space to evaluate the dynamic structure factor These operations may be performed using e g the nMoldyn package 22 This procedure was used to produce the liquid rubidium 19 and germanium 23 dynamic structure factors included in the Mcstas data base 9 CONCLUSION AND OUTLOOK We have demonstrated a number of instrument simulation models which may be assembled in order to exhibit non trivial results for neutron scattering experiments All of these models even though rather concise still produce data which compare with actual measurements In particular a number of measurement imperfections are reproduced and help in understanding the required corrections and care that should be given during both the measurements and the 34 Collection SEN further data analysis In the near future such models will undoubtedly closely couple with the data analysis procedures to correct most of the instrumental effects and help to identify unknown features in measurement data It may also become possible to evaluate the feasibility of submitted experime
51. ngle crystal model section 5 2 and add an aluminium mount aside as crystal blade holder model In order for the scattered beam on the crystal to eventually be scattered again on the mount we copy the bar instance after the single crystal The model geometry is very similar to the Figure lla but with an additional pillar beside the diffractometer crystal RRR RR KERR KEK RRR ke che e ke KKK KR KKK KKK KKK KK RK KR KK ER RK RK KK RK KEK KK KR KKK KR RRR KKK RRR KK RK KKK KR KKK ERK KEK k k KK k k k KEK Instrument monochromator background instr Description A monochromator example Parameters lambda Angs neutron wavelength selected by the monochromator DM Angs Monochromator d spacing default is 002 Graphite RRR RRR RRR RRR KK RK KK RR KR RK KR KK KR ce ck KK RK KR KKK KR RK ER RK RK KKK KKK RK KKK KEK KR ERK KKK KEK k k k k k k ck ckck ck ckck ck k k ck k k k kk k kkk k DEFINE INSTRUMENT monochromator background lambda 2 36 DM 3 355 DECLARE double theta half take off used further in the instrument TRACE double flag holder flag which is set when a scattering event occurs on the crystal pillar 8 INITIALIZE theta asin lambda DM 2 RAD2DEG also called Al on triple axis machines printf s 2 theta g deg take off angle n NAME CURRENT COMP 2 theta 8 TRACE COMPONENT Source Source simple dist 1 radius 0 05 xw 0 1 yh 0 1 Lambda0 lambda dLambda lambda 0 4 AT 0 0
52. not corrected here due to the fact that for a cylindrical detector the time of flight from the sample to the detector is shorter in the equatorial plane and longer when hitting the top and bottom detector sides This results in a broadening of the time distribution which can easily be corrected in practice Also the neutron beam reaching the sample position suffers a number of artefacts In particular the neutron energy and pulse length defined by the choppers are not perfect so that it also broadens the time axis on the detector And as the neutron beam is not strictly parallel a distribution of incoming neutron momentum directions will result in a broadening of the angular axis Finally a variation of the time of flight originates from the sample volume itself which introduces an additional path length to travel to the detector All of these effects are common on all neutron scattering instruments and may be analysed and corrected But the addition of all imperfections may not be easily corrected as they are usually cross correlated The more complex the instrument is the more measurement artefacts appear and the harder it is to apply JDN 18 23 simple analytic corrections Besides the instrument parasitic effects the incoherent and multiple scattering can hardly be removed from experiments where they often partly hide the coherent scattering contribution In the Figure 15b these are mainly visible at low scattering angle around the elas
53. nt proposals based on simple models References 1 N Metropolis and S Ulam The Monte Carlo method Journal of the American Statistical Association 44 1949 335 341 2 F James Rep Prog Phys 43 1980 1145 3 Grimmett G R and Stirzakerand D R Probability and Random Processes 2nd Edition Clarendon Press Oxford 1992 4 Marsaglia George Random number generators Journal of Modern Applied Statistical Methods 2 2003 2 5 Matsumoto M Nishimura T Mersenne twister a 623 dimensionally equidistributed uniform pseudo random number generator ACM Transactions on Modelling and Computer Simulation 8 1998 3 30 6 K Lefmann and K Nielsen Neutron News 10 20 1999 7 P Willendrup E Farhi and K Lefmann Physica B 350 2004 735 8 K Lefmann et al Virtual experiments the ultimate aim of neutron ray tracing simulations Journal of Neutron Research 16 2008 97 111 9 McStas web site lt http www mcstas org gt 10 NeXus format web site lt http www nexusformat org gt 11 J Peters Nucl Instr Meth A 540 2005 419 12 M Marseguerra and G Pauli Nucl Instr Meth 4 1959 140 13 C D Clark E W J Mitchell D W Palmer and I H Wilson The design of a velocity selector for long wavelength neutrons J Sci Instrum 43 1966 1 14 G L Squires Introduction to the theory of thermal neutron scattering Dover edition 1996 and Cambridge University
54. on radius and the SANS DebyeS models a simple highly ordered diblock copolymer As we have already mentioned the sotropic Sqw component may model inelastic scattering for powders and liquids But the Single crystal component does not implement inelastic scattering from crystals A way to overcome this is to use the Phonon simple component which handles a single dispersion relation in cubic crystals Last we mention dedicated samples for reflectometry The simplest SiC component models a single bulk plate and the more advanced Multilayer sample can be used to model any layered arrangement 5 4 Detectors Most of the detector models used in the McStas instrument descriptions are ideal and they record events in space and time as this is the case for real devices but also monitor a wide range of other beam parameters energy divergence spin There is a large list of so called monitor components which usually require to specify some histogram tally recording bounds and binning A more unified specification of these monitoring parameters resides in the Monitor nD component in which an option parameter specifies explicitly what to record and the monitor geometry All of the previously shown Examples make use of this component often with the option auto parameter to determine the best histogram bounds from incoming neutron events An other class of monitors are the event type ones These monitors do not create histograms
55. onding model geometry when appropriate We present some simple neutron source models most common neutron optics samples and ideal detectors Each example is fully described as a plain text file in which we have highlighted the McStas grammar keywords in blue the McStas components in green the instance names defined by the user in red the McStas pre defined symbols in italic and the pure C keywords in bold To use these examples you may type them into instrument description files plain text format with instr extension open them with McStas McGUI and press the Run button The usual simulation time is within seconds with 10 neutron events and possibly reaches a few minutes when higher statistics are required In the following sections a number of standard notations are used for wavelength A E and for the energy meV k for the momentum A and v for the velocity m s These quantities are related by the simple relations E 81 804 22 2 072 k k 27 A v 3956 A for neutrons The coordinate system used in McStas defines the Y axis as vertical the X axis left bound when looking forward and the Z axis in the forward direction of propagation This frame is used for positioning and rotating instrument components in space In the latter case rotations apply around each axis in the order X Y and Z This work considers neutrons in the cold thermal energy range neglecting higher energy nuclear physics processes fission reso
56. or xwidth 0 26 yheight 0 26 depth 0 03 FN Conv Gas tables He3inHe table FN Stop Gas tables He3inCF4 table nx 512 ny 512 filename BIDIM26 psd restore neutron 1 AT 0 0 0 03 RELATIVE Window END Example 15 A simple powder diffraction example which uses a realistic gas detector JDN 18 31 powder_detector ym Figure 23 The Example 15 powder diffractometer with a realistic gas detector model Scattering events are detected within the gas volume LOG Perfect tt Perfec z 12863870 3 x y Loc BtbtMz6 amp tt B DIM26 pec 2 000105905 4X 0 073944 Y0 6 000164249 dY 0 0859860 00247612 X 8 C4 e Ye 0 010352 Y 8 C055 1 B249 06 z ozi 76 1 8364 1179e406 0 1 10 0 25 y m o posiliou cau u 14 5 0 05 16 0 1 1U X pos tien en Xy B CN 45 Figure 24 The image recorded from the Example 15 on an ideal monitor left and a gas detector model right The Example 15 geometry is shown in Figure 23 and the powder rings recorded by both a perfect and a more realistic gas detector are shown in Figure 24 Comparing the ideal and actually detected image we notice that the ring diameter is larger in the gas detection than in the ideal monitor which is just a thin plate This originates from the fact that events in the gas are detected with an exponentially decreasing efficiency in the cell volume due to absorption so that a Debye Scherrer cone opens when
57. ray tracing neutron scattering codes After introducing the Monte Carlo method principle section 2 we recall the definition and applications of virtual experiments section 3 A short introduction to the Mcstas simulation package is presented in section 4 We then demonstrate the use of the various parts that may enter in the description of a complete virtual experiment including usual neutron optics components and sample models section 5 Short reminders about the typical use of these components on real instrument are discussed as well as a schematic description of the underlying physics implemented in sample kernels These instrument parts are then assembled into simple virtual experiment models section 6 The most advanced instrument models section 7 make use of virtual experiments to reveal some of the common artefact inherent to neutron instrumentation and often enter in the definition of the resolution function Each concept discussed in this work is demonstrated with a simple McStas instrument description example 2 MONTE CARLO METHODS FOR NEUTRON SCATTERING In this section we present a short introduction to the Monte Carlo techniques that is those that use random numbers 2 1 Definition The Monte Carlo technique is simply any process making use of random numbers In this respect most processes in nature are random based DNA and species evolution within time traffic jams weather forecast flies in the kitchen stock exchange mar
58. ructure factor as shown in Figure 25 This requires to subtract the empty can contribution correct for detector efficiency and cell absorption The time of flight data should be converted to momentum energy space using e g the LAMP software 21 The total dynamic structure factor is then obtained In some cases the use of polarized neutron beam experiments provides a way to separate the coherent contribution from the incoherent one at the cost of measurement statistics Triple axis instruments may provide a direct measurement of a portion of the dynamical structure factor by mapping the momentum energy space Instrument resolution corrections must then be accounted for on top of the usual data corrections The final data should then be formatted accordingly to be read by e g the Jsotropic_Sqw component Alternatively powder and crystal structures may be refined using e g Fullprof 17 and formatted for use by the PowderN and Single crystal McStas components 8 2 2 From molecular dynamics Molecular Dynamics VASP Material Studio Figure 26 From molecular dynamics to dynamical and structural information With ever increasing computer power it has become quite usual to simulate complex materials using atomistic simulation codes such as Material Studio 24 VASP 25 AbInit 26 or Quantum Expresso 27 However in order to obtain a full description of the material including coherent and incoherent processes with elastic and i
59. s been added to permit a small rotation without actually over lapping adjacent components Running this instrument description will provide a single neutron beam image at the end of the guide It is intended to be used as an initial part of an instrument The Figure 6a shows the guide geometry see section 4 3 as produced by running the model in the Trace mode see section 4 3 or issuing the mcdisplay curved guide instr R 2700 command The Figure 6b shows the simulation results recorded by the monitor component In practice a guide with a constant width w m a Ni reference coating m value and a curvature radius R m should have a minimum length L V8wR m to bring the neutron beam out of direct sight of the source The neutrons are then transmitted when their wavelength is greater than 1 780 0 1 mz V2w R 8 Collection SFN RRR RRR ERR KEK che e ke ke che e KR KKK KK KK KKK KKK KR KKK KR KK KK RK RK KKK KKK KK KKK KKK KKK KKK KR k k k k k KK KKK KKK ERK k k kok k KK k k k k k k Instrument curved_guide instr Description A curved guide example made of straight elements Parameters lambda Angs neutron wavelength dlambda Angs neutron wavelength spread half width L m guide total length Rs m curvature radius KKK ERK RRR KR KR KR RK KK RK KR KK KKK KR KK RK KK RK RR KK KR KR k k k KR KK KKK KKK k k k KR k k k KKK k k KK k k k k k k k k k ckck ck k k ck ck ckck ck kck ck KKK DEFINE INSTRUM
60. s could simply be defined as neutron rays that actually hit the sample and thus have a chance to reach the detector whereas the second part could be those that miss the sample and mostly contribute to the background Finally up to now we essentially use equi distributed random numbers that is regularly sampled within a range In some cases we may directly estimate the probability distribution assigned to a given process which will count in the result Then there are ways to modify the initial flat equi distributed random number generator into a more efficient focused distribution Coming back to the hit or miss example above with probability p this boils down to choosing more random numbers z that satisfy m lt p than 72 gt p This is known as adaptive variance reduction 4 Collection SEN We encourage the reader to refer to James 2 for a detailed review on the Monte Carlo method 3 VIRTUAL EXPERIMENTS 3 1 Definition of virtual experiments Following 8 a neutron scattering Virtual Experiment is a simulation which 1 models a complete instrument including a detailed sample description 2 provides absolute intensity results that compare with actual measurements and 3 can be controlled like a real instrument The key point in these requirements is certainly the availability of advanced and accurate sample and neutron optics descriptions We may summarize mathematically a virtual experiment as a convolution Virtual experimen
61. similarly as a mirror each atomic plane selects a single reflected monochromatic ray As there are many structural planes available a polychromatic neutron beam will be scattered as a large number of distinct rays forming spots on detectors This happens in the monochromators discussed in section 5 2 5 but in this case only one reflection of interest is used the others are scattered around generating background 20 Collection SEN The scattering cross section from a set of reflections t follows a similar law as the one used for powders in section 5 3 1 However this time the momenta exchange are vectors instead of just norms Then the coherent elastic cross section is o k f X Of si E IERO which simply indicates that the beam is only scattered by the reflections which satisfy the momentum conservation T k k f that is the Bragg law again on all possible outgoing directions SE K K k e KERR KEK KER ke che e RRR KR KKK ce ke KK KERR KKK KR KKK RR KKK KKK KKK KR KKK KKK KKK KK KEK KR KEK RK RK KKK KR KE KK ERK KEK KE KK k k k KEK Instrument single crystal instr Description A single crystal scattering example Parameters lambda Angs neutron wavelength selected by the monochromator RRR RR KR RRR RK RK KR ek KK RK KR RK KR KKK ce ke KK RK RK RK KR RK KR KR KR KKK KK KK KK KR KR KKK RK KR KKK KKK KERR k k KK k k k k k k k k k ck k k k kkk k ckck k k f DEFINE INSTRUMENT single crystal lambda 1 string ma
62. sults from the powder diffractometer simulation are shown in Figure 17 as two diffractograms The left one corresponds to the position sensitive detector image where Debye Scherrer ring arcs are seen see section 5 3 1 The radial integration of these rings produces the second plot on the right side which is a typical powder diffraction pattern which implicitly includes instrumental resolution function In practice using a curved monochromator results in a broadening of the diffraction rings out of the equatorial scattering plane Replacing the PowderN instance with an Isotropic_Sqw one would even bring an estimate of the multiple scattering as well as support for liquids possibly with inelastic background when given proper S q data JDN 18 25 powder_diffractometer 0 5 o oo y m e 1 5 0 5 2 5 z m x m Figure 16 A powder diffractometer geometry obtained from the Example 12 for an incoming neutron wavelength of 1 4 A psd tt psd 1286452247 th y banana tt banana 1286452247 A 73 884 dX 34 1247 YO 6 40621e 05 dY 0 0791221 Angle deg monitor 128 70178e 05 Er 78375e 08 N 4 71 242 T05e 05 Err 2 7842le 08 N 4 72607e 06 X0 74 0201 dx e T T n 3 x v lt I 4 Si 4 o x T Ne o x o e EOR a i5 SE Bo CES m E d i x 2 2
63. t Instrument simulation amp Advanced sample model Compared with other neutron propagation Monte Carlo codes the Mcstas package 6 7 has put much effort in these fields and achieved a significant breakthrough towards effective Virtual Experiments for all classes of neutron scattering instruments and materials 32 Applications of virtual experiments Once we assume that a virtual experiment is available it may be used in many ways The neutron facilities staff will mainly use this tool in order to upgrade or design new instruments In this case the simulation results will enable to estimate the main instrument characteristics including intensity resolution signal to noise ratio not only on the integrated neutron beam but also on a realistic neutron scattering signal such as diffractograms and inelastic spectra This approach may be complemented with pure neutron transport codes such as MCNP in order to study fast neutrons and gamma background e g for shielding design Another use of virtual experiments deals with experiment planning An accurate virtual experiment model may be used to estimate the feasibility of a real experiment proposal in order for instance to estimate if a scattering process in the sample will effectively be measurable within an experiment An estimate of the acquisition time may also be obtained at this stage During an experiment one may compare the measured data with the corresponding data from the virtual experiment
64. ted from the McGUI Help Component Library Index menu item and you may easily add your own materials The material volume may be a box a sphere and a cylinder which all can be bulk or hollow geometries including concentric arrangements as we shall see in section 7 2 powder simple x 60 80 Longitude deg abs Figure 12b Diffraction pattern obtained from a 100 Figure 12a Geometry of the Example 8 simple z powder diffraction setup showing a few diffracted z neutron trajectories The beam is attenuated and Na Ca Al F powder at A 2 36 A showing intensity vs scattered in the sample horizontal angle vs vertical position along the detector 5 3 2 Liquid powder and gas elastic and inelastic scattering There is no periodic arrangement in liquids as atoms and molecules move continuously However there are still preferred distances for instance the one between two atoms seen as hard spheres that would slip one on the other but can not inter penetrate or the various coordination sphere radii The Bragg law still applies on such distances and will result in somewhat blurred Debye Scherrer rings compared with powders In the following we focus on liquid 18 Collection SFN materials but the same formalism can be transposed from liquids to powders where structural lines are sharper and gas Following the literature again 14 18 19 we find out that the total scattering cross section reads with usual notations No ce
65. terial C graphite lau TRACE COMPONENT Source Source simple dist 1 radius 0 01 xw 0 01 yh 0 01 Lambda0 lambda dLambda 0 2 lambda AT 0 0 0 ABSOLUTE COMPONENT SX Single crystal xwidth 0 002 yheight 0 1 zthick 0 1 mosaic 30 reflections material barns 0 ax 0 ay 2 14 az 1 24 bx 0 by 0 bz 2 47 cx 6 71 cy 0 cz 0 absorption 0 014 incoherent 0 004 AT 0 0 0 5 RELATIVE PREVIOUS ROTATED 0 45 0 RELATIVE PREVIOUS COMPONENT banana Monitor nD xwidth 1 yheight 1 options banana theta limits 10 130 bins 240 y bins 100 AT 0 0 0 5 RELATIVE Source END Example10 A single crystal scattering example with a large banana shaped detector The graphite crystal is tilted by 45 LOG banana tt banana 1285863265 th y X0 0 146922 dX 4 0076 YO 8 69158e 06 dY 0 0330731 100 0 100 Figure 14 Neutron scattering from a single crystal of graphite from a neutron beam around A 1 A obtained from the Example 10 Intensity is shown as a function of the horizontal angle and vertical coordinate in log scale with colors ranging from blue low to red high JDN 18 21 The Single crystal component is used the same way as the PowderN but only accepts au type files from Crystallographica 20 This component models coherent and incoherent elastic scattering with multiple scattering and secondary absorption The material volume may be a box a sphere and a
66. tic line We shall present a method in section 7 2 to estimate some of the contributions which contribute in an experimental measurement Time Of Flight Angle Detector liquid_spectrometer y m Angle deg 6 5 6 6 6 7 6 8 6 9 7 73 72 73 74 TOF s Figuxe 15a A disk chopper liquid spectrometer Figure 15b the radial angle time of flight signal geometry obtained from Example 11 obtained with a liquid rubidium sample for A 4 The vertical central line corresponds to the elastic 6 2 A powder diffractometer scattering One of the most widely used neutron instrument is the powder diffractometer It mainly consists of appending the crystal monochromator Example 6 section 5 2 5 and the powder sample Example 8 section 5 3 1 However most of the diffractometers make use of an additional radial collimator such as the Example 2 section 5 2 2 in between the sample and the banana shaped detector in order to improve the angular resolution of the instrument The resulting powder diffraction instrument description is listed as Example 12 and its geometry is shown in Figure 16 This example makes use of the partitioned sampling variance reduction technique SPLIT keyword see section 2 3 and 6 1 Also we are using the monochromator in a double focusing geometry to increase the neutron flux on the sample by setting the curvature radius from optical formulas In the instrument description we are using two detectors which are symme
67. tor radial component are to be used e g after the sample position Such collimators are usually made on real instruments from a set of linear component modules stacked side by side Both geometries are shown in Figure 7 ALPHA arc min collimator divergence One arc minute is 1 60 degree DEFINE INSTRUMENT ALPHA 60 TRACE COMPONENT linear Collimator linear xwidth 0 07 yheight 0 15 length 0 70 divergence ALPHA AT 0 0 0 05 RELATIVE PREVIOUS COMPONENT radial Collimator radial radius 0 3 yheight 0 15 length 0 40 divergence ALPHA theta min 10 theta max 140 AT 0 0 0 RELATIVE PREVIOUS Example 2 Linear top and radial bottom collimator instances controlled with an ALPHA instrument parameter 10 Collection SEN Collimator Radial collimator yr A alii All al N i li m AH FA v LX Z Sf NC Z EZ z m 0 6 x m Figure 7 Linear left and radial right collimator components geometry from the Example 2 The collimator slits have a width w and a length L 5 2 3 Choppers One common way to select a neutron energy is to select its speed when passing in between two moving apertures separated by a distance d Let us consider a neutron that passes the initial slit it will only pass the second slit if this latter is opened after a time delay At which is related with the ne
68. tric in angle in order to double the simulation statistics However with a graphite monochromator selecting 1 4 neutrons the transmitted beam from the monochromator intersects the symmetric detector area on the left side of Figure 16 generating an intense parasitic peak A way to remove this artefact is to get rid of the transmitted beam by means of a McStas grammar feature which enables to customize the behaviour of component instances using the EXTEND keyword This latter is applied after the monochromator instance 24 Collection SFN RRR RRR ERR KEK che e ke ke che e ke che e KK KKK ce ke KK RK KER KR KR KK KERR KKK KKK KKK KK KKK KKK KKK KKK KR RK k k k k k k k KR KKK EK KK KEK ckck KK k k k k k k Instrument powder diffractometer instr Description A powder diffractometer with powder sample radial collimator and large detector Parameters lambda Angs neutron wavelength selected by the crystal monochromator DM Angs Monochromator d spacing default is Graphite material Angs powder structure file lazy fullprof crystallographica ALPHA arc min collimator divergence One arc minute is a degree KKK ERK KR KER KR RK KEK KK RK KR KK KKK ce ke KK e ck KK RK KR KK KKK KKK KKK KKK KK KKK KKK k k k KKK KR k k k k k k k k k k k k k k ck k k ck ckckck ck kck ck KKK DEFINE INSTRUMENT powder diffractometer lambda 1 4 DM 3 355 ALPHA 10 string material Na2Ca3Al2Fl4 laz DECLARE double theta
69. utron speed v d At Such a condition may be obtained with two disks rotating with a frequency f in turns per second Hz with the second disk shifted by a phase angle 0 27 At f with respect to the first We then determine the neutron wavelength A selected by the two disk choppers as pc _ 3956 __ 3956 Phra Ans 5 f H4 i Vos 4m fundi The selected wavelength band of the pulse which is ideally triangular will get narrower as the rotation frequency increases and the transmitted intensity decreases The time window selected by the choppers is At 2 7 f In order to avoid multiple order transmissions that is phase angles that are shifted by 27 n with n 1 additional disks are usually required resulting in systems with often more than 4 rotating disks Simulating a disk chopper system consists in positioning at least two DiskChopper components The steady state components listed in Table 2 do not define the initial neutron event time t the same way for continuous time is set to t 0 and pulsed sources time f spans over the pulses In order to adapt the DiskChopper instance to these sources components the instrument description should specify the first DiskChopper parameter IsFirst flag for steady state sources and leave it to sFirst 0 on pulsed sources as shown in Example 3 and Figures 8a and 8b The last component is a time of flight monitor which determines itself the better suited time window JDN 18 11 RR
70. w percent around the central transmitted wavelength 5 2 4 Velocity selectors A chopper like mechanical device is obtained with velocity selectors which are used to select neutrons by transmitting only a given energy They consist in a rotating drum main axis usually parallel to the neutron beam axis with its circumference covered with radial twisted blades as shown in Figure 10a For neutrons not to be absorbed they have to pass any of the entry windows remain in the selected channel in between the absorbing twisted blades angle while propagating length d and exit the rotating drum frequency f RRR kk k k ke k k ek che e ke ke che e ke KR KKK KKK KR KK RK KK RK KR KK KER KR KKK KK KK KKK KKK KKK KR KKK KKK k k k KR k k KK k k k KKK ERK KEK ckck ck ck k k k k k k Instrument velocity selector instr Description A velocity selector example From D118ILL selector EADS Astrium Parameters lambda Angs neutron wavelength selected by the velocity selector phi deg velocity selector twist angle d vs m velocity selector rotating drum length RRR KR RK RRR RRR KK RK KK RRR ke ke KK KK KR KK RK KR KKK RRR KR RR RK RK KK RK KK KR KKK KKK KR KKK KKK RRR ckck ck ckckck ck ckck ck k k ck k k ck k k k kk k ck k ck k DEFINE INSTRUMENT velocity selector lambda 4 phi 48 3 d_vs 0 25 TRACE COMPONENT Source Source simple dist 1 radius 0 03 xw 0 03 yh 0 05 Lambda0 1ambda dLambda lambda 0 15 AT 0
71. when passing a surface in the facility model by means of the PTRAC card and the Virtual mncp input McStas component can read these files and send the neutron events into an instrument description thus replacing the usual source component Such an advanced source model contains all the neutron parameter correlations such as any anisotropy from the geometry whereas the default McStas source components see section 5 1 are approximated by homogeneous event sources However the neutron event files generated by e g MCNP or TRIPOLI are usually very large and contain a finite number of particles which then limits the achievable accuracy from a McStas simulation 8 2 Obtaining dynamical structure factors As we have seen in section 5 3 a large set of material structures may be obtained from crystallographic databases However no similar knowledge base exists regarding material dynamics We propose here two procedures in order to obtain such data in order to simulate inelastic scattering contributions in isotropic materials see section 5 3 2 8 2 1 From experiments 4 di Figure 25 From experimental data to dynamical and structural information Many samples have been measured with neutron scattering spectroscopy instruments since 50 years Some of these results have been published and in some cases the original data files are still available In this case a thorough data JDN 18 33 analysis will provide the dynamical st

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