Uses of Nuclear Magnetic Resonance (NMR) in Metal Hydrides and - - PowerPoint PPT Presentation

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

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Uses of Nuclear Magnetic Resonance (NMR) in Metal Hydrides and Deuterides  Lots of good spins in the sea: 1H, 2D, 11B, 27Al, 45Sc . . .  Lots of applications to measure:  rates of motion, by spin relaxation  slow motions, by T1D  metallic-electronic properties, by Knight shift and Korringa T1  diffusion, by pulsed field gradients

 local structure, using magic-angle spinning (MAS-NMR)

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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 ωhop ~ ∆ωRL  Maximum in 1/T1 when ωhop = ω1 (=γB1)  Maximum in 1/T1 for ωhop = ω0 (=γB0)  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.

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H Motion in LaNi5H6

 0 ~ ½ x 109 s-1 ( 0/2π = 85 MHz)  serve T1 minimum (max of 1/T1) near room-T  Clearly, hop of H is very fast in this very useful battery material.

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Skripov, T1 in Laves-phase hydrides

 low-T peak in 1/T1 is motion between 6 nearby sites; localized motion  high-T peak is long- range diffusive motion

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T1 useful for slower motions

 1/T1 max for hop ~ 1  1/T1 max for hop ~ 0  1 << 0, so T1 probes slower motions  Clearly motions faster in amorphous >LT >HT

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T1D, to probe the slowest motions

Consider a system with only H nuclear spins. t = fixed at T2, typ. 8 μsec Vary τ, amplitude of Jeener echo varies Ae¯ τ/T

1D

 1st 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 T1D.  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.

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Dipole order

 Spin alignment (with B0 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 10-13s (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: T1D = τhop, the time for nearly every spin to have jumped at least

• nce.

1/T1D = (1/τhop) 2 (1-p), more exactly.  T1D = τhop has maximum possible sensitivity to motion.

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T1D to detect H hopping in MgH2

 At 400 °C, T1D = 2.5 msec  So hop = 400 s-1 at 400 °C  Way too small to narrow the line (need hop = 105 s-1)

 At lower T, T1D

• 1 dominated

by spin flips (T1

• 1) of

inabundant 25Mg spins

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Skripov’s studies of BH4 reorientations in LiBH4, Mg(BH4)2

 Skripov et al. fit T1

• 1 vs 1/T using 1, 2, or 3 reorientation motions, often each

with a distribution of activation energies, reflecting local disorder.

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The Relaxation Map

 We assume attempt freq ~ 1013 s-1  At max of 1/T1, hop = 109 s-1  At max of 1/ T1 hop = 2x105 s-1  At onset of narrowing, hop = 105 s-1  For slow motions, hop = 1/T1D  Very large scale  Very powerful

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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/T1K = Const • K2 • T

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Diffusion, measured by Pulsed Field Gradient (PFG)

 Measures long-range diffusive displacement, directly!  Echo amplitude falls ~ A exp (-γ2G2Dδ2τ)  Can use very large gradients, to measure small D  Large externally-imposed G needed to dominate internal gradient  Note: Gint ~ B0χ/size χ = susceptibility, size = radius of particles See C.P. Slichter, Principles of Magnetic Resonance and M. Levitt, Spin Dynamics

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Diffusion in ZrHx

 Eact is larger as x → 2.

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Magic-Angle Spinning (MAS) NMR

 Spin sample rapidly (2-60 kHz) about angle tilted to B0 by 54.7°.  Any spin interaction varying as 3cos2θ-1 time averages to zero, under MAS. dipole-dipole, susceptibility effects (1st-order), quadrupole effects  H-H dipole broadening in MHx 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 2D lines in MDx.

 Also removes quadrupole interactions and susceptibility effects.  Result – broad lines become narrow, can reveal/distinguish resonances of different sites.

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YD2+x; Work of Natalie L. Adolphi

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ZrNiDx

 Two 2D resonances seen, 1:1  “Known” structure has all D

• n equivalent sites

 “Known” structure is wrong  Adolphi and Bowman

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Local Structure and Chemistry by MAS-NMR

 by Son-Jong Hwang et al.  shows species generated by de- hydriding LiBH4  partly explains why re-hydriding is so difficult  found Li2B12H12 as intermediate – a low energy “trap,” difficult to go beyond

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Hydride-Gas Exchange as an Effective Relaxation Path

 In gas-phase, T1 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 T1 in gas) T1 apparent = τ exchange

 Can measure rate of hydride-gas

exchange events

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Relaxation in Pd-deuteride, surrounded by D2 gas

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