Neutron Instruments I & II ESS Instruments Division
Neutron Instruments I & II Overview of source characteristics Bragg s Law Elastic scattering: diffractometers Continuous sources Pulsed sources Inelastic scattering: spectrometers Continuous sources Pulsed sources Transmitted beam: imaging Fundamental physics
Neutrons vs Light light neutrons λ < μm < nm E > ev > mev n 1 4 0.9997 1.0001 θ c 90 1 Φ/ΔΩ 10 19 p/cm 2 /ster/s (60W lightbulb) 10 14 n/cm 2 /ster/s (60MW reactor) P left-right up-down spin 1 ½ interaction electromagnetic strong force, magnetic charge 0 0
Neutron Moderators ILL ISIS 2.5m 1m
Source brightnesses Peak brightness: ILL ~ 1-10 x ISIS Time-integrated: ILL ~ 100-1000 x ISIS Lightbulb ~ 100,000 x ILL
log(intensity) Pulsed-source time structures cold neutrons 10 1 0.1 ISIS- TS1 SNS ISIS- TS2 ILL 0 20 40 60 80 100 120 time (ms)
Pulsed-source time structure.4.2 1 Intensity λ=1å.8.6.4.2 0.2 λ=2å λ=5å time (μs) 0 100 200 300 0 10 20 30 40 A
Distribution by Guides
Neutron transport by total internal reflection ~ 100m at present sources Distribution by Guides
Reflecting Surfaces incident θ n=1 n <1 reflected refracted critical angle of total reflection θ c cos θ n' cos θ c c 1 n' 1 n N λ 2 2π θ b 2 c n' 2 θ c λ Nb/ π for natural Ni, θ c = λ[å] 0.1
Neutron Supermirrors
Neutron Supermirrors
Neutron Supermirrors
Neutron Supermirrors
An Fe/Si multilayer
Neutron transport by total internal reflection ~ 100m at present sources Distribution by Guides
Focusing guide ~ 100 samples < 1 cm 2 cm 2
Bragg s Law
Bragg s Law
Bragg s Law
Bragg s Law 2d sin
Bragg s Law 2d sin 2θ
Diffraction: Bragg s Law 2d sin k i Q θ 2 d θ k f Q
Diffraction: Bragg s Law θ k i f k Q θ f i f i k k Q Q k k k i θ Q k f θ d Q 2
Diffraction: Bragg s Law f i f i k k Q Q k k k i θ Q k f θ 2 sin 2 sin 2 k d k Q k k k f i d Q 2
Diffractometers Measure structure (d-spacings) Assume k i =k f Measure k i or k f : Bragg diffraction Time-of-flight Velocity selection Samples: Crystals Powders Liquids Large molecules or structures Surfaces
Powder diffractometers Measure crystal structure Large single crystals rarely available Polycryst al Q 2 d 2d sin
Time-of-flight method distance detector sample h / mv [Å] 3.956 /v [m/ms] time
and for The POWTEX project is funded by the BMBF. Time-of-flight method
Time-of-flight method
Crystal Monochromators Graphite 002 Copper 200 Germanium 333 Copper 200 Silicon 111 Graphite 002 d-spacing 1.089 Å 1.807 Å 3.135 Å 3.355 Å
Monochromator Focusing A θ A B θ B Q 4 sin /
Powder Diffraction at a Cts Source 2d sin
Powder Diffraction at a Cts Source 2d sin
Powder Diffraction Determining the structure Rietveld refinement Measuring strain Engineering applications
Diffuse Scattering Q 2 d
Resolution in diffraction d 2 sin d 2 2 d d 2 Q Q d d 0.2% Q Q d d 2%
Mosaic-crystal Monochromators 2 d sin <hkl> cot fwhm < 10-4 Perfect crystal fwhm > 0.1 cot B Mosaic crystal
Time-of-flight Resolution d distance 2 sin d 2 2 d d 2 h mv [Å] 4 v[m/ms] 4 t[ms] L[m] L 4 t[ms] 3 B Data 1 L[m] 2.5 2 1.5 1 0.5 0-0.5 Δt -1-5 0 5 10 15 20 A time
Time-of-flight Resolution distance To improve resolution, increase the length: long guides move to a different moderator L B 3 Data 1 2.5 2 1.5 1 0.5 0-0.5 Δt -1-5 0 5 10 15 20 A time
Single-Crystal Diffraction Availability of large (~mm 3 ) crystal No loss of information from powder average Direct and unambiguous structural determination Complex structures
Cts-Source Single-Crystal Diffractometer
Laue Diffraction White-beam method No prior knowledge of k i or k f (110 (310 ) λ(310) ) Peak position depends only on angle of crystal plane, (120 ) not on d-spacing λ(110) Good for crystal orientation, and looking for odd reflections λ(120)
Laue Diffraction
Single-Crystal with TOF TOF determination of k i, k f Large solid-angle coverage Lower flux than Laue method
Small-Angle Scattering
Small-Angle Scattering Probing the longest length scales available to neutrons Monochromator Δλ/λ Sample Detector 10 d 2d sin 2 sin 8 Collimator I - 2θ Q I + 6 4 d 2 λ d 2θ 4-20 Å 5-3000 Å 0.1-20 I - +I + I - -I +
Small-angle scattering Access to smallest angles: remove direct beam Good collimation required
Small-angle scattering Access to smallest angles: remove direct beam Good collimation required Soller collimator Pin-holes separated by distance 5 cm < 30 m 5 cm > 0.1
Continuous-source SANS Δλ/λ 10%
Continuous-source SANS d 2 sin 2 d d 2 2 10 2 Direct beam spot ~ 10% of detector I size - Δθ/θ>10% I + 8 6 4 Δλ/λ 10% 2 I - +I + I - -I +
Log Reflectometry Reflection from surfaces and interfaces in out Specular: θ in =θ out Off-specular: θ in θ out Depth profile of the scattering-length density
Specular reflectometry Monochromatic λ fixed θ θ scan through θ Time-of-flight scan through λ θ θ θ fixed
Specular reflectometry 2 m Horizontal sample geometry all samples (including liquids) Vertical sample geometry solid samples, e.g. magnetic straightforward to vary θ straightforward to build
Off-specular reflectometry Replace single detector with position-sensitive detector Measure in-plane correlations
Neutron Instruments I: Summary Neutron sources Very weak: neutrons are precious Pulsed and continuous Instrument components & concepts Time-of-flight method Guides Monochromators Elastic scattering: diffractometers Powder diffractometers: single-peak, Laue, TOF SANS Reflectometers: specular & off-specular Oxford, 2/9/09 Ken
Neutron Instruments I & II Overview of source characteristics Bragg s Law Elastic scattering: diffractometers Continuous sources Pulsed sources Inelastic scattering: spectrometers Continuous sources Pulsed sources Transmitted beam: imaging Fundamental physics
Neutron Spectroscopy Excitations: vibrations and other movements Structural knowledge is prerequisite Measure diffraction first k i k f Measure k i and k f : Bragg diffraction Time-of-flight Resonant absorption Larmor precession Methods Fix k i and scan k f direct geometry Fix k f and scan k i indirect geometry Energy scales: < μev > ev
Scattering triangle onservation of energy & momentum r r Initial: E i,h Final: E f,h k i E i E f h r r r k f Q k i k f r Q Momentum transfer r k i r k f Q 2 k i 2 k f 2 2 k i k f cos 2 Energy transfer h h 2 2m n 2 k i k f 2 Accessible kinematic range given by scattering triangle Q ki 2θ kf
Chopper Spectrometers
Chopper Spectrometers distance Direct geometry: fix k i by chopper phasing scan through k f by time-of-flight detector sample chopper Pulsed Source 0 time
Chopper Spectrometers distance detector sample chopper 2 Continuous Source chopper 1 0 time
Crystal-Monochromator Chop. Spec. distance detector sample chopper monochromator Continuous Source 0 time
Choppers Fermi Disk choppers choppers f < 600 f < 300 Hz Hz Δt > 1μs Δt > 10μs
Chopper Spectrometers General-purpose spectrometers Energy ranges from 1 mev to 1 ev covered Huge position-sensitive detector arrays Single crystals
Detectors 3 He gas tubes n + 3 He 3 H + 1 H + 0.764 MeV >1mm resolution High efficiency Low gamma-sensitivity 3 He supply problem Scintillators n + 6 Li 4 He + 3 H + 4.79 MeV <1mm resolution Medium efficiency Some gamma-sensitivity Magnetic-field sensitivity
Energy transfer Direct-geometry kinematics ki 2θ E i 2 0 2 180 o Q kf 0 hq 2 2m n E i E f 2 E i E f cos 2 0 Momentum transfer Q
Alternative to direct geometry distance Indirect geometry: fix k f scan through k i by time-of-flight detector analyser sample 0 time
Energy transfer Indirect-geometry kinematics hq 2 2m n E i E f 2 E i E f cos 2 0 Q ki 2θ kf E f 2 0 2 180 o 0 Momentum transfer Q
ev spectroscopy Use resonant absorption to define k f. TOF defines k i. 1) Measure with absorber in and out. Count neutrons. Take difference 2) Measure with absorber in. Count gammas. 238 U
Chemical spectroscopy TOSCA@ISIS Density-ofstates measurements
High Resolution 1: Backscattering 2d sin d d cot cot cos sin 2 0 Use single crystals in as close to backscattering as possible to define k f. Scan through k i with as good energy resolution.
Pulsed-Source Backscattering detectors High k i resolution: long instrument on sharp moderator analyser crystals exact backscattering near-backscattering
Backscattering
Continuous-Source Backscattering
Continuous-Source Backscattering Fix k f by backscattering analysers Scan k i by Doppler-shifting backscattering monochromator Energy resolution < 1μeV Energy range ~ ± 15 μev
High Resolution 2: Neutron Spin Echo High energy resolution < 1 μev Larmor precessions encode energy transfer B 0 B 1 P z -flipper L 0 L 1
Triple-axis Spectrometers Only at continuous sources Very flexible Measures a single point Q in -E space at a time Scans: Q Constant : Scan E at constant k i or k f Q Constant E: Scan in any direction
TAS with Multiplexing IN20 flat-cone multi-analyser Top view Side view sample 31 channels 75º angular range k f = 3 Å -1 k f = 1.5 Å -1
Imaging: Neutron Radiography Neutro ns X- rays
Fundamental Physics
Neutron Instruments 2: Summary Instruments for measuring excitations Energy scales : < μev > ev Instrument components & concepts Direct and indirect geometry Choppers Detectors Inelastic scattering: spectrometers Chopper spectrometers ev spectroscopy Chemical spectroscopy Backscattering Spin-echo Triple-axis spectrometers Imaging & Fundamental physics