Introduction to Triple Axis Neutron Spectroscopy

Transcription

1 Introduction to Triple Axis Neutron Spectroscopy Bruce D Gaulin McMaster University The triple axis spectrometer Constant-Q and constant E Practical concerns Resolution and Spurions

2 Neutron interactions with Properties of the neutron Mass m n =1.675 x10-27 kg Charge 0 Neutrons interact with Nucleus matter Spin-1/2, magnetic moment µ n = µ N Crystal structure/excitations (eg. Phonons) Unpaired electrons via dipole scattering Magnetic structure and excitations Nuclear scattering Magnetic dipole scattering NXS School 2

3 Brockhouse and Shull Share 1994 Nobel Prize in Physics Most recent Nobel Prize awarded to a scientist working in Canada

4 The Basic Experiment: (θ, φ) Incident Beam: monochromatic white pink Scattered Beam: Resolve its energy Don t resolve its energy Filter its energy

5 Brockhouse s Triple Axis Spectrometer k i = 2 π/ λ i k f = 2 π/ λ f

6 Momentum Transfer: Q = k i k f Q -k f k i Energy Transfer: k f δe = h 2 /2m (k i2 k f2 )

7 Mapping Momentum Energy (Q-E) space Origin of reciprocal space; Remains fixed for any sample rotation 2 π/ a 2 π/ a

8 Bragg diffraction: Constructive Interference Q = Reciprocal Lattice Vector Elastic scattering: k i = k f k f k i -k f Q

9 Bragg diffraction: a Constructive Interference Q = Reciprocal Lattice Vector k f k i Q -k f 2 π/ a Elastic scattering: k i = k f

10 Elementary Excitations in Solids Lattice Vibrations (Phonons) Spin Fluctuations (Magnons) Energy vs Momentum Forces which bind atoms together in solids

11 Bragg s Law: nλ= 2d sin(θ)

12 Bragg s Law: nλ= 2d sin(θ)

13 Two Axis Spectrometer: 3-axis with analyser removed Powder diffractometer Small angle diffractometer Reflectometers Diffractometersoften employ working assumption that all scattering is elastic.

14 Soller Slits: Collimators Define beam direction to +/- 0.5, 0.75 etc. degrees

15 Filters: Remove λ/nfrom incident or scattered beam, or both

16 Single crystal monochromators: Bragg reflection and harmonic contamination nλ= 2d sin(θ) Get: λ, λ/2, λ/3, etc.

17 Pyrolitic graphite filter: E = 14.7 mev λ= 2.37 A v= 1.6 km/s 2 xv= 3.2 km/s 3 xv= 4.8 km/s

18 Constant k f Constant k i Two different ways of performing constant-q scans

19 Mapping Momentum Energy (Q-E) space Origin of reciprocal space; Remains fixed for any sample rotation 2 π/ a 2 π/ a

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22 Spurions Bragg incoherent Bragg Eg. k i 2k f ħω= 41.1 mev E f = 13.7 mev E i= 54.8 mev 4E f = 54.8 mev Incoherent elastic scattering visible from analyzer λ/2 incoherent Bragg Bragg Neutron Counts/1000s (350,4) (mhz,s/n) (150,2) (90,1) (40,0.3) Energy Transfer (mev) Sample 2θin Bragg condition for k f -k f Even for inelastic config, weak incoherent from mono May 31, 2009 NXS School 22

23 Elementary Excitations in Solids Lattice Vibrations (Phonons) Spin Fluctuations (Magnons) Energy vs Momentum Forces which bind atoms together in solids

24 Constant Q, Constant E 3-axis technique allow us to Put Q-Energy space on a grid, And scan through as we wish Map out elementary excitations In Q-energy space (dispersion Surface)

25 Phonons Normal modes in periodic crystal wavevector 1 u(l,t) = NM ε j ( q)exp( iq l)ˆ B ( qj,t) jq Energy of phonon depends on q and polarization FCC structure Longitudinal Transverse mode Lynn, et al., Phys. Rev. B 8, 3493 (1973). NXS School FCC Brillouin zone 25

26 Phonon intensities ( ) 2 ( ) S 1+ ( Q,ω)= 1 2 u Q ε 2 j q 2NM e Q q jq ω j Structure (polarization) factor ( 1+ n( ω) )δ Q q τ ( ( ) ( )δ ω ω j q Phonon Energy Long Trans 0 1/2 q, [ξ00] NXS School 26 Guthoffet al., Phys. Rev. B47, 2563 (1993).

27 More complicated structures Acoustic phonon Woods, et al., Phys. Rev. 131, 1025 (1963). Optical phonon Chaplot, et al., Phys. Rev. B 52, 7230(1995). NXS School La 2 CuO 4 27

28 Detectors Gas Detectors n+ 3 He 3 H + p MeV Ionization of gas e - drift to high voltage anode High efficiency Beam monitors Low efficiency detectors for measuring beam flux NXS School 28

29 Resolution Resolution ellipsoid Beam divergences Collimations/distances Crystal mosaics/sizes/angles Resolution convolutions I(Q 0,ω 0 ) = S(Q 0,ω 0 ) R(Q Q 0,ω ω 0 )dqdω NXS School 29

30 Resolution focusing Optimizing peak intensity Match slope of resolution to dispersion May 31, 2009 NXS School 30

31 References General neutron scattering G. Squires, Intro to theory of thermal neutron scattering, Dover, S. Lovesey, Theory of neutron scattering from condensed matter, Oxford, R. Pynn, Polarized neutron scattering Moon, Koehler, Riste, Phys. Rev 181, 920 (1969). Triple-axis techniques Shirane, Shapiro, Tranquada, Neutron scattering with a triple-axis spectrometer, Cambridge, Time-of-flight techniques B. Fultz, NXS School 31

32 Constant k f : k f, θ A do not change; therefore analyser efficiency is constant k, i, θ M do change, but monitor detector normalizes to incident neutron flux Monitor detector (low) efficiency goes like ~ 1/v ~ 1/k i

33 Monochromators Selects the incident wavevector θ Q(hkl) = 2π d(hkl) = 2k i sinθ Q(hkl) Reflectivity focusing high-order contamination eg. λ/2 PG(004) Mono d(hkl) uses PG(002) General Be(002) High k i Si(111) No λ/2 l

34 Guides Transport beam over long distances Background reduction Total external reflection Ni coated glass Ni/Ti multilayers(supermirror) NXS School 34

35 Samples Samples need to be BIG ~ gram or cc Counting times are long (mins/pt) Sample rotation Sample tilt HB3-HFIR IN14-ILL Co-aligned CaFe 2 As 2 crystals May 31, 2009 NXS School 35