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Anatoly M. Balagurov, Frank Laboratory of Neutron Physics, Dubna, Russia

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## Anatoly M. Balagurov, Frank Laboratory of Neutron Physics, Dubna, Russia

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**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 anvilhigh -pressure cell for neutron scattering experiments. Рmax≈ 7 GPa (48 mm, h=164 mm)**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) → → Lattice dynamics of Ni-hydroxide, Ni(OH)2 Crystal structure of Sr3YCo4O10.5 2 2**How neutrons interact with matter**Scattering Absorption Elastic Inelastic Neutron imaging Atomic and magnetic dynamics, diffuse motion Incoherent Coherent Nuclear Magnetic Crystal structure at atomic, nano-levels 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|**Neutron scattering at ILL, Grenoble**Nuclear Physics (5) SAS - Reflectometry (4) 3 Axis (4.5) Single Crystals (3) HR - TOF (7) Powders – Liquids (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**I(q) ~ |f(q)|2 Intensity of scattered waves Amplitude of a wave function I(q) ~∫ eiqr G(r)dr f(q) ~∫ eiqr b(r)dr b(r) ~∫ e-iqrf(q)dq G(r) ~∫ e-iqrI(q)dq Scattering-length density Pair correlation function 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:**0 ≤x = y ≤ 1, 0 ≤ z ≤ 0.5 Fourier synthesis of HgBa2CuO4+δ structure Cu Hg Cu O1 Ba O1 O3 O1 Hg Cu Ba O2 Difference synthesis. Cross-section: 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, z = 0 Hg O3 O3 HgBa2CuO4+δstructure: the О3 positionis partially filled,n(O3) = δ= 0.12. 8**Diffraction limit**b(r) ~e-iqrf(q)dq b(r) ~e-iqrf(q)dq,Q = qmax lс ≈ 2π/Q≥ λmin/2 –diffraction limit As a rule:for diffraction λmin ≈ 1 Å, i.e.lc ≈ 0.5 Ǻ, forSANSQ ≈ 0.5 Å-1, i.e. lc ≈ 20 Ǻ. In practice:for interatomic distances σ~ 0.002 Å, for lattice parametersσ~ 0.0001 Å, for radius of gyration σ~ 0.2 Å. Diffraction limit is overcomeowing 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) bcan 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 II. Pulsed neutron sources W = 10 – 100 MW Const in time Short pulse Long pulse II-a. SPS II-b. LPS 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 W = 0.01 – 1 MW Pulsed in time Δt0≈ (15 – 100) μs W = 2 – 5 MW Pulsed in time Δt0≈ (300 – 1000) μs ISIS, UK LANSCE, USA SNS, USA KENS, Japan J-SNS, Japan IBR-2M, Russia ESS, Europe LANSCE (new) ??? 11**Steady state reactor / Pulsed neutron source**Monochromatic incident beam: λ = const ≈ 1.4 Å, Δλ/λ ≈ 0.01, Source: W = (10 – 100) MW = const, Scan over scattering angle, Wide angle range is needed. Polychromatic incident beam: λmin ≤ λ≤λmax, Δλ ≈ 5 Ǻ, Source: W = (0.01 – 2) MW, pulsed, Scan over time of flight (TOF), Fixed angle geometry – higher pressure is possible. 12**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 Magnet (25 T) TOF diffractometer at LPS or CNS type source Neutron pulse after fast chopper Δt0≈ (20 – 50) μs EXED instrument at BENSC Δd/d≈ 0.001 for back scattering**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 ~ 107 n/cm2/s S – effective sample cross-section 1 cm2 → 1 mm2 Ω – solid angle of detector system~ 1 sr δ – probability of scattering ~ 0.1 → 0.01 I ≈ 105n/s → 102 n/s It is not so important how many neutrons strike a sample; much more important how many scattered neutrons we can collect. D20, ILL: Ω ≈ 1 sr DN-2, IBR-2: Ω ≈ 1 sr GEM, ISIS: Ω ≈ 4 sr 15**Neutron detectors. New generation.**DRACULA at ILL, France GEM at ISIS, UK λ = const diffractometer Linear-wire, 3He PSD, Ωdet ≥ 1 sr TOF diffractometer ZnS/6Li detector, Ωdet ≈ 3.86 sr 16**Resolution of λ=const and TOF powder diffractometers**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**Time-of-Flight diffractometer λ = const diffractometer HRFD (IBR-2): 2θ0 = 152, wavelength range = 1.2 – 7.2 Å. HRPT (SINQ):λ0 = 1.886 Å, range of scattering angles = 10 - 165. 18 18**High-pressure cells for neutron scattering**Piston-cylinder cell Single-crystal anvil cell Paris – Edinburgh press Pmax = 1 GPa Pmax = 3 GPa (with support) T = 2 – 300 K Vs = 100 – 500 mm3 Pmax = 7 GPa (sapphire) Pmax = 30 GPa (diamond) T = 0.1 – 300 K Vs = 0.5 – 5 mm3 Pmax = 10 GPa (WC) Pmax = 30 GPa (diamond) T = 90 – 1000 K Vs = 30 – 100 mm3**Single crystal anvil cells**Geometry of the diffraction experiment with single crystal anvil cell. • 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**3He ring detector Close-cycle refrigerator Sapphire anvil cell 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 = 1.4K and P = 8.5, 30, 43 GPa with G6.1. PRB 64 (2001). 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. Focusing system andKurchatov – LLB pressure cellonspecialized high-pressure 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 Cd Steel magnetic WC • Toroid cells are used at: • POLARIS (PEARL), ISIS (1992) • HIPD, LANSCE (1994) • DN-12, FLNP, JINR (2002) • HRPT, SINQ (2005) • ... TiZr BN Sample “Toroid type high-pressure device: history and prospects” L.G. Khvostantsev et al., High Pressure Research (2004)**Sample**Cryostat walls, etc 2θ Radial collimator Detector Toroid (Paris – Edinburgh) cell with radial collimator atHRPT (SINQ, PSI)**Mesoscopic phase separation in complex magnetic oxides and**giant oxygen isotope effect Charge-localized AFM insulating matrix (La0.25Pr0.75)0.7Ca0.3MnO3 FM-M clusters Insulating state Metallic state Metal – Insulator percolation phase transition**(Nd,Tb)0.55Sr0.45MnO3 with 16O and 18O isotopes atHRPT**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 Phase diagram for Re1-xSrxMnO3 with 16O and 18O isotopes Cell volume of (Nd,Tb)0.55Sr0.45MnO3 with 16O and 18O isotopes as the function of external pressure**Pulsed reactors in Frank Lab of Neutron Physics, Dubna**Fuel PuO2 Power: - average 2 MW - pulsed 1500 MW Frequency 5 s-1 Pulse width 350 μs 1961 – 1968 IBR-1 (1 – 6 kW) 1969 – 1980 IBR-30 (15 kW) 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) 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)**DN-6 – diffractometer for micro-samples**Chopper Neutron guide Sample Actual state: Ring-shape detectors Ring-shape multi-element ZnS(Ag)/6LiF detector Resolution: optimal for high-pressure studies Intensity: one of the best in the world Pressure: up to 7 GPa with sapphire anvils • Cold source • Detector array • Neutron guide Will be: Intensity: 25 times better than now Pressure: 30 - 40 GPa with diamond or mussoniteanvils**Neutron powder diffraction. Where are we going on?**Proposals for the third generation pulsed neutron sources (1990) Realized: • 50 • yes • (2 – 5)s • (0.5 – 10) s • 0.003 s • 0.2– 60 Å • 0.1 mm3 >30 GPa • Structure complexity 100 parameters • Scattering Law total pattern decomposition • Speed: reversible t 5 s irreversible ts 10 s ultimate ts 0.005 s • d-range: 0.3 dhkl 30 Å • Small sample size: Vs 1 mm3 • Highest pressure: 10 GPa Third generation pulsed neutron sources: SNS (USA), J-PARC (Japan), IBR-2M (Russia), ESS (Europe), …**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 astatement.