Uses of Nuclear Magnetic Resonance (NMR) in Metal Hydrides and Deuterides. Mark S. Conradi

Transcription

1 Uses of Nuclear Magnetic Resonance (NMR) in Metal Hydrides and Deuterides Mark S. Conradi Washington University Department of Physics St. Louis, MO USA 1

2 Uses of Nuclear Magnetic Resonance (NMR) in Metal Hydrides and Deuterides Lots of good spins in the sea: 1 H, 2 D, 11 B, 27 Al, 45 Sc... Lots of applications to measure: rates of motion, by spin relaxation slow motions, by T 1D metallic-electronic properties, by Knight shift and Korringa T 1 diffusion, by pulsed field gradients local structure, using magic-angle spinning (MAS-NMR) 2

3 Nuclear Spin Relaxation to Measure Rate of Motion As H hop site to site, HH and H-metal dipole interactions are modulated. Gives rise to onset of linenarrowing for ω hop ~ ω RL Maximum in 1/T 1 when ω hop = ω 1 (=γb 1 ) Maximum in 1/T 1 for ω hop = ω 0 (=γb 0 ) Often, activation energy of motion is given by slope of log (relaxation rate) vs. (1/T) In cases of a distribution of motion rates, slopes may be misleading. 3

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5 H Motion in LaNi 5 H 6 0 ~ ½ x 10 9 s -1 ( 0 /2π = 85 MHz) serve T 1 minimum (max of 1/T 1 ) near room-t Clearly, hop of H is very fast in this very useful battery material. 5

6 Skripov, T 1 in Laves-phase hydrides low-t peak in 1/T 1 is motion between 6 nearby sites; localized motion high-t peak is longrange diffusive motion 6

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8 T 1 useful for slower motions 1/T 1 max for hop ~ 1 1/T 1 max for hop ~ 0 1 << 0, so T 1 probes slower motions Clearly motions faster in amorphous >LT >HT 8

9 T 1D, to probe the slowest motions Consider a system with only H nuclear spins. t = fixed at T 2, typ. 8 μsec Vary τ, amplitude of Jeener echo varies Ae τ/t 1D 1 st two pulses create dipole order. This is where spins preferentially point parallel to the local dipolar field they see. During τ, dipole order decays towards zero, with time constant T 1D. Third pulse reads-out the remaining dipole order, making a Jeener echo. Reading: J. Jeener and P. Broekaert, Phys. Rev. 157, p. 232 (1967). Also, C.P. Slichter, Principles of Magnetic Resonance. 9

10 Dipole order Spin alignment (with B 0 or with local dipolar field) is always weak. So local field varies in sign and magnitude from site to site. Suppose initially, spins are preferentially aligned along their local fields. When a spin jumps onto a neighboring site, takes about s (one vibrational half-period). Spin orientation remains same. So, on average, spin is no longer aligned along the local field (local field at new site is different than at old site). Result: T 1D = τ hop, the time for nearly every spin to have jumped at least once. 1/T 1D = (1/τ hop ) 2 (1-p), more exactly. T 1D = τ hop has maximum possible sensitivity to motion. 10

11 T1D to detect H hopping in MgH 2 At 400 C, T 1D = 2.5 msec So hop = 400 s -1 at 400 C Way too small to narrow the line (need hop = 10 5 s -1 ) At lower T, T 1D -1 dominated by spin flips (T 1-1 ) of inabundant 25 Mg spins 11

12 Skripov s studies of BH 4 reorientations in LiBH 4, Mg(BH 4 ) 2 Skripov et al. fit T 1-1 vs 1/T using 1, 2, or 3 reorientation motions, often each with a distribution of activation energies, reflecting local disorder. 12

13 The Relaxation Map We assume attempt freq ~ s -1 At max of 1/T 1, hop = 10 9 s -1 At max of 1/ T 1 hop = 2x10 5 s -1 At onset of narrowing, hop = 10 5 s -1 For slow motions, hop = 1/T 1D Very large scale Very powerful 13

14 If the Hydride is a Metal... Electron spins at top of Fermi sea are unpaired. Coupling to nuclear spins produces Knight shift., K. Like Pauli paramagnetic susceptibility of ordinary metals, K is temperature independent; K (in % or ppm) is independent of field; K = your freq freq of insulators freq of insulator Chemical shift is from orbital motions of electrons. Knight shift is from electron spins. Knight shifts are typically times larger than chemical shift range. Fluctuating part of electron spin nuclear spin interaction causes relaxation Korringa relaxation. 1/T 1K = Const K 2 T 14

15 Diffusion, measured by Pulsed Field Gradient (PFG) Measures long-range diffusive displacement, directly! Echo amplitude falls ~ A exp (-γ 2 G 2 Dδ 2 τ) Can use very large gradients, to measure small D Large externally-imposed G needed to dominate internal gradient Note: G int ~ B 0 χ/size χ = susceptibility, size = radius of particles See C.P. Slichter, Principles of Magnetic Resonance and M. Levitt, Spin Dynamics 15

16 Diffusion in ZrHx E act is larger as x 2. 16

17 Magic-Angle Spinning (MAS) NMR Spin sample rapidly (2-60 khz) about angle tilted to B 0 by Any spin interaction varying as 3cos 2 θ-1 time averages to zero, under MAS. dipole-dipole, susceptibility effects (1 st -order), quadrupole effects H-H dipole broadening in MH x generally too large, except for very fastest MAS (35-60 khz). But D has much smaller nuclear magnetic moment x 20 smaller dipoledipole. Even 4 khz MAS spectacularly narrows 2 D lines in MD x. Also removes quadrupole interactions and susceptibility effects. Result broad lines become narrow, can reveal/distinguish resonances of different sites. 17

18 YD 2+x ; Work of Natalie L. Adolphi 18

19 ZrNiD x Two 2D resonances seen, 1:1 Known structure has all D on equivalent sites Known structure is wrong Adolphi and Bowman 19

20 Local Structure and Chemistry by MAS-NMR by Son-Jong Hwang et al. shows species generated by dehydriding LiBH 4 partly explains why re-hydriding is so difficult found Li 2 B 12 H 12 as intermediate a low energy trap, difficult to go beyond 20

21 Hydride-Gas Exchange as an Effective Relaxation Path In gas-phase, T 1 is very short, 2 ms Spins in hydride can relax, via Korringa and modulation of dipole interactions Or, H or D can exchange with one from gas (fully relaxed recall short T 1 in gas) T 1 apparent = τ exchange Can measure rate of hydride-gas exchange events 21

22 Relaxation in Pd-deuteride, surrounded by D 2 gas 22