Uses of Nuclear Magnetic Resonance (NMR) in Metal Hydrides and Deuterides Mark S. Conradi Washington University Department of Physics St. Louis, MO 63130-4899 USA msc@physics.wustl.edu 1

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

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 line- narrowing 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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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

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 long- range diffusive motion 6

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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

T 1D , to probe the slowest motions Consider a system with only H nuclear spins. t = fixed at T 2 , typ. 8 μ sec 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

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 10 -13 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

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 ) -1 dominated At lower T, T 1D -1 ) of by spin flips (T 1 inabundant 25 Mg spins 11

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

The Relaxation Map We assume attempt freq ~ 10 13 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

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 5-100 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

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

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

Magic-Angle Spinning (MAS) NMR Spin sample rapidly (2-60 kHz) about angle tilted to B 0 by 54.7°. 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 dipole - dipole. 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

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

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

Local Structure and Chemistry by MAS-NMR by Son-Jong Hwang et al. shows species generated by de- hydriding 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

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

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

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