#### Transcript Present-day high-intensity and high-resolution neutron

Present-day high-intensity and high-resolution neutron diffraction and neutron scattering under high pressure (introductory lecture) Anatoly M. Balagurov, Frank Laboratory of Neutron Physics, Dubna, Russia 1. Introduction 2. General questions of neutron scattering 2.1. Neutron elastic scattering as Fourier transformation 2.2. Neutron interactions and modes of experiments 2.3. Neutrons vs. x-Rays & Synchrotron light 3. Neutron spectrometers: new capabilities 3.1. Steady state and pulsed neutron sources 3.2. λ = const vs. “white” beam 4. Neutron scattering under high pressure 4.1. High pressure: cells and range 5. Examples of studies (powder diffraction) 6. Prospects of neutron scattering under high pressure Sapphire anvil high pressure cell for neutron scattering experiments. Рmax ≈ 7 GPa (48 mm, h=164 mm) 1 Neutron scattering for structure and dynamics We want to know where atoms (molecules) are situated and how they interact! Inelastic neutron scattering ↓ Atomic (molecular) dynamics (motion) ↓ Atomic (molecular) interactions Elastic scattering (diffraction) ↓ Atomic (molecular) positions ↓ Structure (shape, configuration) Energy transfer (meV) 12.4 24.8 37.2 49.6 62.0 74.4 86.8 99.2 111.6 124.0 300 Eu 280 Ni(OH)2 Eu 260 Mg(OH)2 240 → GDOS (a.u.) 220 → A1g Eg 200 Eu+Eg 180 Eg A2u 160 140 a 120 Eu 100 60 H O b Eg A1g Eg 80 Ni c Eu Acoustic modes 40 20 A2u 0 100 200 300 400 500 600 700 800 900 1000 -1 Energy transfer (cm ) Crystal structure of Sr3YCo4O10.5 Lattice dynamics of Ni-hydroxide, Ni(OH)2 2 How neutrons interact with matter Scattering Inelastic Atomic and magnetic dynamics, diffuse motion Nuclear Crystal structure at atomic, nano-levels Absorption Elastic Neutron imaging Incoherent Coherent Magnetic Magnetic structure at atomic, nano-levels Elastic and inelastic neutron scattering Momentum transfer Energy transfer (Е0 ≈ 0.025 eV) Always takes place to atom, ΔЕ/Е0 ~ 1, “inelastic” to collective mode, ΔЕ/Е0 ~ 1, “inelastic” to crystal, ΔЕ/Е0 ~ 10-24 (ΔE = 0) “elastic scattering” Ei = Ef |ki| = |kf| 4 Neutron scattering at ILL, Grenoble 3 Axis (4.5) HR - TOF (7) Nuclear Physics (5) Powders – Liquids (3) SAS - Reflectometry (4) Single Crystals (3) Proposals: 59% elastic scattering, 35% inelastic scattering, 6% nuclear physics. 5 Neutron space and time domain S(Q, ω) ~ ∫∫ei(Qr – ωt) G(r, t)drdt (L. van Hove, 1954 г.) Scattering law ↕ Fourier transform Correlation function l ~ 2π/Q, τ ~ 2π/ω For elastic scattering: ΔQ = (10-3 – 50) Å-1 Δl = (0.1 – 6·103) Å Elastic scattering as Fourier transform of a structure Intensity of scattered waves I(q) ~ |f(q)|2 Amplitude of a wave function I(q) ~ ∫ eiqr G(r)dr f(q) ~ ∫ eiqr b(r)dr G(r) ~ ∫ e-iqr I(q)dq b(r) ~ ∫ e-iqr f(q)dq Pair correlation function Scattering-length density G(r) = ∫ b(u) b(u + r) du b(r) / G(r) - object f(q) / I(q) - image Real space Reciprocal space 7 Cross-section: Fourier synthesis of HgBa2CuO4+δ structure Cu 0 ≤ x = y ≤ 1, 0 ≤ z ≤ 0.5 Cu Hg O1 Ba O1 O1 Cu Ba Hg O3 O2 Hg O3 HgBa2CuO4+δ structure: the О3 position is partially filled, n(O3) = δ = 0.12. [010] O3 Difference synthesis. Cross-section: 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, z=0 [100] 8 Diffraction limit b(r) ~ e-iqr f(q)dq 0 Q b(r) ~ e-iqr f(q)dq, Q = qmax 0 lс ≈ 2π/Q ≥ λmin/2 – diffraction limit As a rule: for diffraction for SANS In practice: for interatomic distances for lattice parameters for radius of gyration λmin ≈ 1 Å, i.e. lc ≈ 0.5 Ǻ, Q ≈ 0.5 Å-1, i.e. lc ≈ 20 Ǻ. σ ~ 0.002 Å, σ ~ 0.0001 Å, σ ~ 0.2 Å. Diffraction limit is overcome owing to: - periodicity of a structure, - parametric description of an object. 9 Important peculiarities of thermal neutron interaction with matter 1) b (coherent scattering length) does not depend on (thermal factors) 2) no regularity in b dependence on atomic number light atoms in presence of heavy atoms: H-O, Mn-O, U-H, … neighbours discrimination: O-N, Co-Fe, … ) 3) no regularity in b dependence on nuclear mass (isotope contrasting) bH = 0.37 bFe-56 = 1.01 bD = 0.67 bFe-57 = 0.23 4) b can be < 0 (“zero” matrix without coherent scattering from container) 5) strong magnetic scattering (magnetic structure) 6) small absorption (high penetration) Neutron sources for condensed matter studies I. Continuous neutron sources W = 10 – 100 MW Const in time VVR-M, Russia IR-8, Russia, ILL, France LLB, France BENSC, Germany FRM II, Germany BNC, Hungary NPI, Czechia NIST, USA ORNL, USA … SINQ, Switzerland II. Pulsed neutron sources Short pulse II-a. SPS W = 0.01 – 1 MW Pulsed in time Δt0 ≈ (15 – 100) μs ISIS, UK LANSCE, USA SNS, USA KENS, Japan J-SNS, Japan Long pulse II-b. LPS W = 2 – 5 MW Pulsed in time Δt0 ≈ (300 – 1000) μs IBR-2M, Russia ESS, Europe LANSCE (new) ??? 11 Steady state reactor / Pulsed neutron source I() 1 "White" (Maxwellian) distribution 0.1 max min 0.01 0.001 0 1 2 3 , Å 4 5 6 Monochromatic incident beam: Polychromatic incident beam: λ = const ≈ 1.4 Å, Δλ/λ ≈ 0.01, Source: W = (10 – 100) MW = const, λmin ≤ λ ≤ λmax, Δλ ≈ 5 Ǻ, Source: W = (0.01 – 2) MW, pulsed, Scan over time of flight (TOF), Scan over scattering angle, Wide angle range is needed. Fixed angle geometry – higher pressure is possible. 12 TOF diffractometer at LPS or CNS type source Neutron pulse after fast chopper Δt0 ≈ (20 – 50) μs Fermi chopper with 2 slit packages 21.79 m 22.5 m 23.5 m 29.9 m 6 Disc choppers 49.6 m 73.4 m Δd/d ≈ 0.001 for back scattering Magnet (25 T) EXED instrument at BENSC 13 Neutron diffractometer: the most important parameters for structural studies • Flux at the sample position • Resolution • Solid angle of detector • d-spacing interval • Background level • … 14 Intensity / Counting rate I ≈ Φ0 · S · (Ω/4π) · δ [n/s] Φ0 – integrated neutron flux at a sample S – effective sample cross-section Ω – solid angle of detector system ~ 107 n/cm2/s 1 cm2 → 1 mm2 ~ 1 sr δ – probability of scattering ~ 0.1 → 0.01 I ≈ 105 n/s → 102 n/s D20, ILL: DN-2, IBR-2: GEM, ISIS: Ω ≈ 1 sr Ω ≈ 1 sr Ω ≈ 4 sr It is not so important how many neutrons strike a sample; much more important how many scattered neutrons we can collect. 15 Neutron detectors. New generation. GEM at ISIS, UK DRACULA at ILL, France TOF diffractometer ZnS/6Li detector, Ωdet ≈ 3.86 sr λ = const diffractometer Linear-wire, 3He PSD, Ωdet ≥ 1 sr 16 Resolution of λ=const and TOF powder diffractometers 0.01 TOF_Resolut-3 d/d 0.008 HRPT 0.006 0.004 0.002 HRFD HRPD 0 0 1 2 3 4 5 6 7 8 d, Å HRPT: λ = const diffractometer at SINQ neutron source (SINQ, PSI). Resolution functions of: HRFD (RTOF, IBR-2), HRPD (TOF, ISIS), HRPT (λ = const, SINQ). 17 NAC standard (Na2Al2Ca3F14) on TOF and λ0 diffractometers λ = const diffractometer Time-of-Flight diffractometer nac-6000-2_4 HRFD NAC nac-hrpt-2_4 Intensity Normalized intensity HRPT NAC, =1.886 Å 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 d, Å HRFD (IBR-2): 2θ0 = 152, wavelength range = 1.2 – 7.2 Å. 2.4 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 d, Å HRPT (SINQ): λ0 = 1.886 Å, range of scattering angles = 10 - 165. 18 High-pressure cells for neutron scattering Piston-cylinder cell Single-crystal anvil cell Pmax = 7 GPa (sapphire) Pmax = 30 GPa (diamond) T = 0.1 – 300 K Vs = 0.5 – 5 mm3 Paris – Edinburgh press Pmax = 1 GPa Pmax = 3 GPa (with support) T = 2 – 300 K Vs = 100 – 500 mm3 Pmax = 10 GPa (WC) Pmax = 30 GPa (diamond) T = 90 – 1000 K Vs = 30 – 100 mm3 Single crystal anvil cells 1200 Интенсивность, усл. ед. Geometry of the diffraction experiment with single crystal anvil cell. kC 10 K 290 K 5 ГПа 2.3 ГПа 800 k2/3 0 ГПа 3 400 4 5 k2/3 6 5 ГПа 0 ГПа 0 1 2 3 4 5 6 d, (Å) Single crystal anvil cells are used at: - DISC, Kurchatov Institute (1983) - DN-12, FLNP, JINR (1994) - G6.1 “Micro”, LLB (1995) - GEM, ISIS (2002) -… DN-12 diffractometer, IBR-2 reactor. Neutron diffraction patterns of La0.33Ca0.67MnO3 at P = 0 and 5 GPa and T = 290 and 10 K (insert). Sample volume is around 2 mm3. Exposure time is 24 h. At high pressure and low temperature a complex AFM state is observed. HP cell at the DN-12 diffractometer, IBR-2 reactor, Dubna Sapphire anvil cell 3He ring detector Close-cycle refrigerator 21 “Kurchatov-LLB” single crystal anvil cells of Igor Goncharenko Neutron Scattering at High Pressures I October 5 – 7, 1994, Dubna, Russia. Igor Goncharenko 02.06.1965 – 04.11.2007 (diving accident in the Red Sea) Compact “Kurchatov-LLB” high-pressure cells for low-temperature neutron diffraction "Igor Goncharenko: a pioneer in high-pressure neutron diffraction“ High Pressure Research (2008) Diffractometer G6.1 MICRO at the LLB (Saclay) GdAs measured at T = 1.4 K and P = 8.5, 30, 43 GPa with G6.1. PRB 64 (2001). Focusing system and Kurchatov – LLB pressure cell on specialized high-pressure G6.1 with sapphire or diamond anvil cells allows neutron diffraction experiments at: pressures as high as 50 GPa, temperatures down to 0.1 K, applied magnetic fields up to 7.5 T. diffractometer G6.1 (LLB, Saclay) I.N. Goncharenko (2004) “Neutron diffraction experiments in diamond and sapphire anvil cells” High Press. Res. 24, 193 “Toroid” or “Paris – Edinburgh” cell HRPT, SINQ: NiO P = 0 – 9.5 GPa T = 300 K λ = 1.5 Ǻ Vs = 100 mm3 t = 4 hours nuclear magnetic Cd Steel Toroid cells are used at: - POLARIS (PEARL), ISIS (1992) - HIPD, LANSCE (1994) - DN-12, FLNP, JINR (2002) - HRPT, SINQ (2005) - ... “Toroid type high-pressure device: history and prospects” L.G. Khvostantsev et al., High Pressure Research (2004) WC BN TiZr Sample Toroid (Paris – Edinburgh) cell with radial collimator at HRPT (SINQ, PSI) Sample Cryostat walls, etc 2θ Radial collimator Detector Mesoscopic phase separation in complex magnetic oxides and giant oxygen isotope effect Charge-localized AFM insulating matrix Metallic state FM-M clusters (La0.25Pr0.75)0.7Ca0.3MnO3 Insulating state Metal – Insulator percolation phase transition (Nd,Tb)0.55Sr0.45MnO3 with 16O and 18O isotopes at HRPT 150 150 PD-O16 FM + AFM 100 AFM 50 40 0 0.45 5.9 GPa FM + AFM 0 0.4 (Nd,Tb)0.55Sr0.45Mn18O Normalized intensity FM TC & TN, K AFM FM + AFM TC & TN, K Re1-xSrxMn18O 100 50 nts-18_1-6 PD-O16 Re1-xSrxMn16O 60 80 100 120 Scattering angle, deg. 0.5 0.4 0.45 x 0.5 x Phase diagram for Re1-xSrxMnO3 NTS-16-18_Vol with 16O and 18O isotopes Vc, Å3 225 220 Cell volume of (Nd,Tb)0.55Sr0.45MnO3 with 16O and 18O isotopes as the function of external pressure 18 16 O O 215 0 1 2 3 4 P, GPa 5 6 7 8 Neutron diffraction patterns of (Nd,Tb)0.55Sr0.45MnO3, measured at P = 0 и 5.9 GPa (T = 290 K) with VX Paris– Edinburgh press at HRPT (SINQ, PSI) with λ = 1.886 Ǻ Pulsed reactors in Frank Lab of Neutron Physics, Dubna 1961 – 1968 IBR-1 (1 – 6 kW) Fuel PuO2 Power: 1969 – 1980 - average IBR-30 (15 kW) - pulsed 2 MW 1500 MW Frequency 1981 – 1983 IBR-2 (100 – 1000 kW) 1984 – 2006 IBR-2 (1500 – 2000 kW) 2007 – 2010 IBR-2 reconstruction 2010 – 2030 IBR-2M (2000 kW) 5 s-1 Pulse width 350 μs Active core and movable reflector Neutron spectrometers on the IBR-2M reactor (JINR, Dubna) Diffraction (6): HRFD, DN-2, SKAT, EPSILON, FSD, DN-6 (30 GPa, 0.1 mm3) SANS (2): YuMO, SANS-C Reflectometry (3): REMUR, REFLEX, GRAINS Inelastic scattering (2): NERA, DIN 13 spectrometers (5 new) 29 DN-6 – diffractometer for micro-samples Chopper Neutron guide Actual state: Sample Ring-shape detectors Resolution: optimal for high-pressure studies Intensity: one of the best in the world Pressure: up to 7 GPa with sapphire anvils Will be: Intensity: 25 times better than now Pressure: 30 - 40 GPa with diamond or mussonite anvils Ring-shape multi-element ZnS(Ag)/6LiF detector 1. Cold source 2. Detector array 3. Neutron guide 30 Neutron powder diffraction. Where are we going on? Proposals for the third generation pulsed neutron sources (1990) Realized: Structure complexity 100 parameters 50 Scattering Law total pattern decomposition yes Speed: reversible t 5 s (2 – 5) s irreversible ts 10 s (0.5 – 10) s ultimate ts 0.005 s 0.003 s d-range: 0.3 dhkl 30 Å 0.2 – 60 Å Small sample size: Vs 1 mm3 0.1 mm3 Highest pressure: 10 GPa >30 GPa Third generation pulsed neutron sources: SNS (USA), J-PARC (Japan), IBR-2M (Russia), ESS (Europe), … 31 Lecture is finished. Any questions? May I ask you? Yes, sure. I did not understand when it would be possible to realize neutron scattering experiments at 1000 GPa. I am sorry, but it is not a question, it is a statement. 32