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Applications of Nuclear Magnetic Resonance to Metal Hydrogen Materials

Part I: Basic Principles & General Applications

Robert C. Bowman, Jr. and Son-Jong Hwang

California Institute of TechnologyPasadena, CA

Summer School LecturesMH2008

23 June 2008

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Outline

Part I: Basic Principles & General Applications-Introduction to Hydrogen Storage Materials-Nuclear Magnetic Resonance (NMR) Concepts & Terminology

• The basics of NMR• Solid State NMR fundamentals (Low Resolution)• Dynamics via nuclear relaxation times – diffusion

phenomenon-ReferencesPart II: High Resolution (HR) Solid State NMR-Principles & methods of multinuclear spectroscopy (MAS, CP, MQ)-HR-NMR Studies of MHx materials – phase compositions, etc.-Summary & Conclusions-References

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Sorption Methods for Hydrogen Storage(Mostly reversible reactions, compact, mass issues)

•ABsorption (chemisorption) – metal hydride family•ADsorption (physisorption) – zeolites, carbons, etc.

[Images from J. Miller, Chromatography: Concepts and Contrasts (Wiley, NY, 1987)]

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Family tree of hydriding alloys and complexes [1,2].(TM = transition metal)

Elements

Alloys Complexes

Solid Solutions

Intermetallic Compounds Other TM Non-TM Other

AB 5 AB 2 AB A 2B

Other AB 3, A 2B 7A 2B 17, etc.

Multiphase Amorphous Nanocrystalline Quasicrystalline

Alanates Other

Misc. Polyhydrides

“Stable” Metastable

Borohydrides

AxByOz, etc.

Nitrides/Imides

[1] G. Sandrock, J. of Alloys and Compounds, 293-295, 877 (1999).[2] R.C. Bowman, Jr. and G. Sandrock: “Metal Hydrides for Energy Storage and Conversion Applications”, ANS/ENS 2003 Winter Meeting, New Orleans, LA, Nov. 19, 2003

Extreme range of physical & chemical properties (nearly are all solids!)

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PART I

General Background of NMR Spectroscopy and its Applications to Solids

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What’s NMR?

Nuclear Magnetic Resonance (NMR) spectroscopy is based upon splitting of nuclear spin (I) energy levels in an external magnetic field (Bo), where transitions between levels are induced via radiofrequency (rf) radiation at the Larmor frequency νI

(2π) νI = γIBo

I = 1/2

Each non-zero spin I has an unique magnetogyric ratio γI

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Types & Properties of NMR Active NucleiNo NMR for I = 0 nuclei (i.e., 4He, 12C, 28Si, etc.)

NMR active nuclei for M-H StudiesI = 1/2: 1H, 3H*, 13C, 15N, 29Si, etc.I = 1: 2H, 6Li, 14NI = 3/2: 7Li, 11B, 23Na, etc.I = 5/2: 25Mg, 27Al, etc.I = 7/2: 45Sc, 51V, etc.

Figures from Rob Schurko’s Introductory Solid State NMR Notes (http://mutuslab.cs.uwindsor.ca/schurko/ssnmr/ssnmr_schurko.pdf)

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Foundation of Pulse FT-NMR Spectroscopy

Schematic of Fourier transformation of FID in time domain to NMR spectrum in frequency domain.

Schematic view of 3 stages in a simple NMR Experiment:A. Magnetic moment precesses around principal axis of applied Zeeman field Bo.B. Sample irradiated at Larmor frequency with plane-polarized rf radiation generating magnetic field B1 causing net magnetization M to incline. A π/2 pulse orients M perpendicular to Bo.C. As the spin system coherently precesses in the transverse plane, a voltage is induced in a rf coil to be detected as the FID (Free Induction Decay) signal.

Figures from K. J. D. MacKenzie and M. E. Smith, Multinuclear Solid-State NMR of Inorganic Materials (Pergamon, Amsterdam, 2002).

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Basic NMR Spin Echo Experiment

Basic pulse sequence (π/2-τ- π) forming a Spin-Echo with effect on the spin packets.

*

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Schematic Description of FT-NMR Spectrometers

Bruker DSX 500 solids NMR spectrometer (Bo = 11.7 T) in the Caltech Solid State NMR Facility

• A number of solution and solids NMR probes available.• Capability of variable Temperature Exp. (-100 o C ~ +150 o C).

[Bruker 4 mm triple resonance CP-MAS probe.]

Schematic of High Field superconducting magnet

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Overview of Nuclear Spin Interactions in Solids

Notation: I = NMR resonant spin and S = Non-resonant spin(s)

1: Zeeman interaction of nuclear spins2: Direct dipolar spin interaction3: Indirect spin-spin coupling (J-coupling), nuclear-electron spin coupling (paramagnetic), coupling of nuclear spins with molecular electric field gradients (quadrupolar interaction)4: Direct spin-lattice interactions3-5: Indirect spin-lattice interaction via electrons3-6: Chemical shielding and polarization of nuclear spins by electrons4-7: Coupling of nuclear spins to sound fields

Bo = Zeeman external magnetic field

B1 = rf magnetic field (NMR pulses)

Figure & next few charts adapted from: http://mutuslab.cs.uwindsor.ca/schurko/ssnmr/ssnmr_schurko.pdf

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Nuclear Spins Couple to External Magnetic Fields via Interaction Tensors:

All NMR interactions are anisotropic - their three dimensional nature can be described by second-rank Cartesian tensors, which are 3 × 3 matrices.

Dipolar Interactions

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Chemical Shielding in NMR of Solids

Methods for reducing dipolar broadening and CSA effects to yield high resolution spectra from solids where peaks are narrowed to only σiso will be given in Part II

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Solid State NMR of Quadrupolar Nuclei

I = 5/2 Spectra for CQ(A) > CQ(B)

Methods for extracting information from NMR of quadrupolar nuclei will be covered in Part II

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Examples of General NMR Studies for some representative Metal Hydrides

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NMR for Crystal Structure & H-Site LocationsNMR spectra can be used to determine the location(s) of protons within the host crystal structure as well as detect different phases (i.e., H2 gas in the solid or metal particles in the hydride).

•Second Moments are extracted from the time domain signal G(t) where the rigid-lattice dipolar interactions are used.

•NMR is not as powerful to solve crystal structures as neutron diffraction for deuterides but sometimes an advantage when samples are nanocrystalline or “amorphous” as dipolar terms rapidly decay with spin separations (~1/r6) .•Most examples involve protons with one or two locations in rather simple structures.

M2D = (3/5)CII∑n(1/rmn)6 + (4/15)CIS∑n'(1/rmn')6

Sometimes there can be complications!

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Variable Temperature Proton Spectra for YH3

Reference: G. Majer, et al., Phys. Rev. B 70, 134111 (2004)

This splitting is anomalous! Not predicted for protons in the known P63cm structure for YH3 – should be just a single peak from dipolar interactions in rigid lattice.

Dipolar M2d for YH3 in rigid lattice limit (T < 310 K)

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Reliable Rigid Lattice 1H Line Shape Measurements“Magic-Echo” method will give proton spectra without distortions due to very large dipolar interactions seen in many MHx coming from instrumental recovery limitations.

S. K. Brady, et al., Phys. Rev. B 72 (2005) 214111

Correct proton Line Shape using Magic Echo peak

Line Shape distorted by a 5.0 µs shift of Magic Echo

Line Shape distorted by a 11.6 µs shift of Magic Echo gives an erroneous “doublet” spectra as found from a FID signal with similar dead time

M2 (E) = 17.5 Oe2

M2 (D) = 18.3 Oe2

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Many Factors Influence MHx Absorption/Desorption Kinetics•Heat transfer (bed design)•H2 gas permeability in powder•Surface Reactivity/Activation

–Native oxide layers (barrier)–Selective oxidation (AB2, AB5)–Poisoning (CO, SO2, etc.)–Surface area/decrepitation–Permeable layers (Pd, fluorides)

•Diffusion processes–Grain boundaries/microfractures–Bulk diffusion (Dbulk) in metal/hydride phases

1.E-17

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1 1.5 2 2.5 3 3.5 41000/T (K-1)

Diff

usio

n C

oeffi

cien

t (cm

2 /s)

MgH2 Mg2NiH4

PdH0.7 LaH2.00

LaH2.92 LaNi5H6.0

ZrH1.58 a-Zr3RhH3.5

ZrV2H5.0 b-TiH0.70

TiFeH1.0 D = 10-8 cm2/s

Bulk Diffusion Constants in MHx

Horizontal Dash Line Indicates:DBulk = 1.67 x 10-8 cm2/s

= d2/6t = (10 µm)2/6(10 s)Condition when D rarely limits reaction rates in activated MHx

[Bowman & Fultz, MRB27 (2002) 688.]

Note: While researchers can change/improve many kinetic parameters, but usually do NOT improve the intrinsic diffusion constants except by raising operating temperature!

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Direct Diffusion Constant Measurements via NMRWhen D(T) > 10-12 m2/s, it can be directly measured without using any models

G. Majer, et al., Phys. Rev. B 57 (1998) 13599.

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• Correlation time, τc:

1/T2 = K * M2 * τc

• Mean residence time, τ = 1/ωΗ:

τc = τ / 2

• Activation energy (Arrhenius), EA:

1/ τ = (1/τo)exp(-EA/kT)

T1, T2 depend on τC and M2(M2 = mean-squared dipolar interaction)

τO-1 = attempt frequency

NMR Relaxation Times & Diffusion (Very General - Focus on Hydrogen)

Pulsed NMR Sequences:T1 Spin-Lattice: from 180º-τ-90º and (90º-t)n-τ-90ºT2 Spin-Spin: from free induction decays (T2*), 2-pulse echoes (T2'), and

Carr-Purcell-Meiboom-Gill (CPMG) echo trains (T2m) .T1ρ Rotating-Frame: from CW (not chopped) spin-locking.T1D Dipolar: (T1 of dipolar-ordered state, essentially T1 in zero field)

Diffusion Coefficient:

D(T) = f<l2>/(6 τ)

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Temperature Dependence of NMR Relaxation Rates for an Arrhenius Diffusion Process

T1d = Dipolar (i.e., protons)T1e = Conduction electrons (metals)T1p = Paramagnetic species

Idealized BPP Model

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Examples: LaNi5H6.0 & LaNi4.8Sn0.2H5.8

Diffusion in LaNi5Hx involves superposition of localized hops within subset of protons in the mid-plane region of the Ni(3) layer as well as long range motion that cause deviation from the Arrhenius relation for the proton relaxation times.

G. Majer, et al., Phys. Rev. B 57 (1998) 13599.

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Proton Relaxation Times in LaNi5H6.8

In LaNi5Hx magnetic precipitates (presumably Ni) distort field uniformity and keep T2* of FID very short (~10 µs). The T2 data is from two-pulse spin echoes. The T1 data are from 53.14 MHz (upper) and 21.25 MHz (lower).

[M. P. Mendenhall, et al., “Rate of Hydrogen Motion in Ni-Substituted LaNi5Hx from NMR”, J. Alloys Compounds 446–447 (2007) 495–498.

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Guide to Interpreting NMR ResultsωH ≡ rate of H hopping motion

• Motional averaging of local dipolar fields is evident as increase of T2 with temperature.At onset,

ωH ~ 105 s-1 (approx. the low-T linewidth).

• At T1ρ minimum,ωH ~ 5 × 105 s-1 (about 1.6 γB1).

• At T1 minimum at 21 MHz,ωH ~ 2 × 108 s-1 (about 1.6 γB0).

• T1D is approx the mean time between hops,T1D ~ 1/ωH, a strong-collision result.

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Measuring Very Slow Motion – T1D

•Dipolar order = spins oriented along local dipolar field.

•Dipolar field varies from site-to-site, almost 100%.

•If spin jumps to neighbor site, it is no longer oriented along the local dipolar field.

•Signal decays ~exp(-τ/T1D) and T1D ≅ 1/ωH.

•Measured T1D detects motions when D(T) is in range ~10-15 – 10-11 cm2/s, which is much slower (i.e., 3-6 orders of magnitude) than other relaxation times.

J. Jeener and P. Broekaert, Phys. Rev. 157 (1967) 232-240.

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Proton NMR Studies of Diffusion in the Mg-Sc-H

System Illustrates Effect of Structure

Conradi, et al. [J. Alloys Compounds 446–447 (2007) 499–503] have measured H hopping rate ωH using various proton relaxation times for Mg65Sc35Pd2.4H220 and compared to MgH2, ScH2, and LaNi5Hx.•Hydrogen diffusion in MgH2 could only be detected using T1D times

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Proton Hopping TimesComparing ωH give increasing mobility in the sequence: MgH2, ScH2, MgScHx, and LaNi5H6.8

Fits are ωH = 1013 s-1 exp(-Ea/kT)

Data points are from T1 and T1ρ minima, onset of increase of T2, and T1D (ωH = 1/T1D).

Ea (eV)LaNi5H6.8 0.29

Mg65Sc35H220 0.52ScH2 0.63MgH2 1.45

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Summary & Conclusions for Part I

Solid State NMR is a powerful & versatile method to assess numerous properties of hydrogen storage materials

Multi-nuclear spectroscopy (hydrogen isotopes & host species)•Monitor phase compositions and transformation from spectra and relaxation times.

•Local structure & site occupancy from dipolar interactions of “rigid lattice” spectra

Diffusion behavior over large dynamic range•Direct measurement (D > 10-12 m2/s) via Pulsed Field Gradients

•Several types of relaxation times are available to cover wide range of rates; however, quantitative analyses are difficult for complex materials with multiple diffusion processes and/or complicated structures.

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Reviews on Mostly Conventional Solid State NMR Studies of Metal Hydrides

R. M. Cotts, “Nuclear Magnetic Resonance on Metal-Hydrogen Systems” in Hydrogen in Metals I –Basic Properties, edited by G. Alefeld and J. Völkl, Topics in Appl. Phys. Vol. 28 (Springer, Berlin, 1978) pp. 227-265.

R. C. Bowman, Jr., “Hydrogen Mobility at High Concentrations” in Metal Hydrides, edited by G. Bambakidis (Plenum, New York, 1981) pp. 109-144.

R. C. Bowman, Jr., “NMR Studies of the Hydrides of Disordered and Amorphous Alloys” in Hydrogen in Disordered and Amorphous Solids, edited by G. Bambakidis and R. C. Bowman, Jr. (Plenum, New York, 1986) pp. 237-264.

D. Richter, R. Hempelmann, and R. C. Bowman, Jr., “Dynamics of Hydrogen in InternetallicHydrides” in Hydrogen in Intermetallic Compounds II – Surface and Dynamic Properties, Applications, edited by L. Schlapbach, Topics in Appl. Phys. Vol 67 (Springer-Verlag, Berlin, 1992) pp. 97-163.

R. G. Barnes, “Nuclear Magnetic Resonance in Metal Hydrogen Systems” in Hydrogen in Metals III – Properties and Applications, edited by H. Wipf, Topics in Appl. Phys. Vol. 73 (Springer, Berlin, 1997) pp. 93-151.

R. Hempelmann and A. Skripov, “Hydrogen Motion in Metals” in Hydrogen-Transfer Reactions, edited by R. L. Schowen, J. P. Klinmann, J. T. Hynes, and H. H. Limbach (Wiley-VCH, Weinheim, 2007) pp. 787-829.