ANALYSIS OF TIME-OF-FLIGHT DIFFRACTOMETER DATA …

1 Version (December 2000) ANALYSIS OF time -OF-FLIGHTDIFFRACTOMETER DATAFROM LIQUID AND AMORPHOUS SAMPLESI ncorporating the SANDALS survival , , , ISIS FacilityRutherford Appleton LaboratoryChilton, Didcot, Oxon OX11 0 QXTel: 01235-445543 (AKS)01235-445680 (WSH)01235-445358 (ACH)01235-556397 (DTB)23 TABLE OF CONTENTSSECTION 1: TIME-OF-FLIGHT The time of flight neutron diffraction Overview of diffraction theorySECTION 2: STEPS IN DATA ANALYSIS OF TOF diffraction Deadtime Normalizing to the incident beam Measuring the neutron cross Attenuation and multiple scattering Furnace Vanadium or standard sample Basic algorithm to determine differential cross Inelasticity (Placzek) Merging the data to form the structure ANALYSIS to pair correlation functionSECTION 3: STRUCTURE IN MOLECULAR LIQUID SYSTEMS BY H/DISOTOPIC SUBSTITUTION NEUTRON SCATTERING Isotopic subsitution neutron An example of a binary molecular mixtureSECTION 4.

2 THE SANDALS SURVIVAL on to the SLS Front End file the SANDALS start a new end a of sample raw data and detector data the (Q) for uncorrected data (SQRAW) SQRAW results in current data from checking Check time , number of microamps and n/p ratio (CHECK_RUNS) Check stability of detectors (PURGE_D) Check detectors for a run (FINGER) Plot of sample temperature (TPLOT) Check counts in each detector (SUMSPEC) : selection of detectors to use in and multiple scattering (CORAL) .MUT .MUT files from transmission monitor Calculation of .MUT data files for To copy and rename existing .MUT To combine .MUT files using Genie CORAL CORAL What output is required for the experiment? Submitting jobs Parameters for vanadium, ti-zr cells and Absorption and scattering cross-sections for samples of more than oneatom type (CROSS) data correction and smoothing (VANSLS) Input and Batch Interactive cross-sections (ANALYSE) ANALYSE input and Running Cylindrical Flat Plate correction (SUBSELF) of S(Q) (MERGE_SLS) of partial structure factors using H/D scattering function (CALCSELF3) of self scattering (SUBSELF3) detector groups (MERGE_SLS) structure factors (PARTIAL) of g(r) routine ANALYSIS on to SANDALS data from archiveSECTION 5: APPENDICESAR esolution of a time -of flight diffractometerBHow to estimate the count rate of a diffractometerCMaximum Entropy methods in neutron scattering.

3 Application to the structure factorproblemDNeutron absorption resonances5 SECTION 1 The time of flight neutron diffraction experimentThere are seven principle components to a TIME-OF-FLIGHT diffraction experiment:1. Production of neutrons in a target2. Slowing down and thermalization of the neutrons in a moderator3. Collimation of the neutrons into a beam4. A sample to scatter the neutrons5. A detector to measure the " diffraction " pattern of the scattered neutrons6. A set of data acquisition electronics (DAE) to accumulate and store the data7. A data ANALYSIS packageNormally the user is involved in providing the sample and performing the data ANALYSIS , therest is provided as part of the neutron of neutrons at a spallation neutron source is achieved by accelerating bunches ofprotons to sufficiently high energies (typically 500-800 MeV) that when they collide with aTARGET nucleus they produce highly excited nuclear states.

4 These states either decayimmediately or after a delay by throwing off nuclear particles such as neutrons, rays,neutrinos etc. The maximum energy of neutrons produced in this way corresponds to theenergy of the impinging proton beam, and if the target is uranium, up to 30 neutrons perproton can be produced. Other non-fissioning targets such as tantalum or tungsten produceabout half the number of neutrons. The so-called "prompt" neutrons are the ones used fortime-of- flight ANALYSIS while the "delayed" neutrons form a low level background in thediffractometer which is independent of time . This background in general must be correctedfor as it can be sample dependent.

5 Normally the delayed fraction is on the order of a fewtenths of a percent of the prompt neutrons, but in cases where an enriched booster target isinstalled, such as at the Argonne National Laboratory in the US, this fraction can be proton beam is pulsed so that a pulse of neutrons less than 1 s wide is produced in thetarget. These neutrons are however not useful as they typically have energies 109 times toohigh for diffraction effects to be seen. These neutrons are therefore slowed down in aMODERATOR that scatters the neutrons many times before they escape. Light atoms such asfound in hydrogenous materials ( methane or water) are used for the moderator since theenergy transferred in a collision is greatest when the two particles have the same mass.

6 Up toa point, the thicker the moderator, the slower the neutrons become, but the process is selflimiting, because as well as slowing the neutrons down, the moderator has the effect ofbroadening the initial very narrow pulse significantly. Moderators are therefore designed tocompromise between the production of slow neutrons and the requirements for reasonablynarrow neutron pulses. In comparison with a nuclear reactor, the spallation target would beregarded as under-moderated. The target-moderator assembly is surrounded by neutronreflecting material, usually beryllium, to enhance the neutron production and pulse and show a typical neutron spectrum from the methane moderator at ISIS,plotted as a function of energy and TIME-OF-FLIGHT respectively.

7 Two regions in the spectrumcan be identified, the epithermal region where the intensity varies as 1/E, or 1/t, respectively,and a Maxwellian "hump" which occurs when the neutrons in the moderator reach atemperature close to that of the moderator. The neutron spectrum is therefore described bytwo functions which are added together using a joining function [2].78 The Maxwellian region is described by the function: max(E) = J (E/T2) exp(-E/T) the slowing down epithermal region is represented by epi(E) = 0 / two functions are combined by means of an empirical switch function, (E): (E) = max(E) + (E) epi(E) (E) = [1 + exp{W1/ E - W2}] these equations J is the integrated Maxwellian intensity, T is the effective temperature ofthe Maxwellian in energy units, 0 is the differential flux at 1eV, A is a leakage parameterand W1,W2 are two parameters which define the switch function.

8 Table lists the values ofthese constants for the methane and ambient moderators at H2 OEpithermal* 0 (at 750 MeV)[1010 n (eVsr100cm2 As)-1] [1010 n (sr100cm2 As)-1] (eV) functionW1 (eV) ISIS moderator constants* The above numbers for the 0 refer to 750 MeV proton energy. The 100cm2 refers tothe area of the moderator normally neutrons emerge from the moderator in all directions and so to be useful for diffractionthey must be COLLIMATED. An essential difference between TOF and reactor diffraction isthat there is no monochromator for the TOF experiment which means the full spectrum ofneutron energies, from 800 MeV downwards, is incident on the sample. It then follows thatmaterials like cadmium and gadolinium which might be used in a reactor situation are uselessin the TOF case, and may even be detrimental because of the high energy s produced byneutron capture in those materials.

9 Instead boron, which has a 1/v capture cross section over awide energy range, is the primary component, with large amounts of iron and hydrogen (the9latter usually in the form of wax or resin) to provide the basic scattering cross section. Sincethe final scattered intensities are small compared to the incident beam intensity, and because itis essential to provide a radiation free environment for people working near thediffractometer, the TOF collimator is a massive construction. At ISIS the collimator plusshielding measures typically square. Figure shows a diagram of the prototypeSANDALS collimator. This collimator is surrounded on all four sides by about of iron,and a further borated wax outside the collimator defines a NEUTRON BEAM at the sample position.

10 This must be sufficientlywell collimated to give adequate angular resolution for the type of experiment beingundertaken, but large enough to give an acceptable count rate. Crystalline powderexperiments generally need high resolution in order to discriminate effectively betweenadjacent Bragg reflections and also to determine the sample contribution to the shape ofindividual reflections. However, because Bragg reflections are so sharp in count rate is rarelya severe constraint, unless special effects are being determined, such as the change instructure as a function of time . In contrast for liquids and amorphous materials the structurefactor consists of a few broad peaks which merge together continuously.