Applications of NMR in Materials Physics: Applications of NMR in Materials Physics: From Nano to Bulk MaterialsFrom Nano to Bulk Materials

Yue Wu

Department of Physics and Astronomyand

Curriculum in Applied and Materials SciencesUniversity of North CarolinaChapel Hill, NC 27599-3255

Email: yuewu@physics.unc.edu

Support: NSF, ARO, ONR, NASA, DOE, PRF, and CNSF

Two bottom line questions we face:Two bottom line questions we face:

1. When a funding agency solicits proposals to address a certain problem, what could NMR offer to get you funded?

relevance to technology

2. Could NMR provide unique information and discover new physics?

relevance to science

MoneyMoney

PapersPapers

1952 Physics

1991 Chemistry 2002 Chemistry

Kurt Wüthrich

Paul C. Lauterbur Sir Peter Mansfield

2003 Medicine

Felix BlochEdward Purcell

Richard Ernst

30 MHz

0.68 T

Nobel Prize and NMR

Some Basic Information by NMR• Structures (protein)• Electronic properties (d-wave of high-Tc superconductor)• Dynamics (diffusion)

Necessary conditions to be competitiveSensitivity, resolution, extreme conditions (high and low temperatures, high pressure, etc…), environment control (orientation, optical, vacuum or vapor, etc…)

Outline: a few examples on what we have learned Outline: a few examples on what we have learned with NMR with NMR

Very Important: You have to have interesting, the best, and very well characterized materials.

1. Nanotubes and nanocontainers

2. Bulk metallic glasses

B Zhang, D. Q. Zhao, M. X. Pan, W. H. Wang, A. L. Greer, PRL 94, 205502 (2005)

Intrinsic Electronic Properties:

X.-P. Tang, et. al. Science 288, 492 (2000).13C

Gas Adsorption:A. Kleinhammes et. al.Phys. Rev. B 68, 075418 (2003).

NMR Studies of SWNTsNMR Studies of SWNTs

Lithium Intercalation:B. Gao et al. Chem. Phys. Lett. 307, 153-157 (1999).H. Shimoda et al. Phys. Rev. Lett. 88, 015502 (2002).

Water Adsorption:S.-H. Mao et al.

Uncorrelated electron theory!

Structure Theoretical Prediction1. n1=n2 armchair Truly metallic2. n1 - n2 =3m Very narrow gap3. all others Semiconducting

Electronic Structure of SWNTs

1/3

2/3

InformationInformation

13C

e n e nen 3 5

2en

3( )( )= dipolar interaction

8= ( ) Fermi contact interaction3

( ) [ , ]

n e en

e n

r rr r

I S r

d t idt

μ μ μ μ

π γ γ δ

ρ ρ

= + +

−

=

i i i

i

H H H H

H

H

H

H0

Hloc

Electron spin Nuclear spin

e e Sμ γ= −n n Iμ γ=

FT

rf pulse

rf detection

Sample in coil

gate

LC1

=ω

Nuclear Magnetic ResonanceNuclear Magnetic Resonance

H0

( )

dJ Hdt

Jd Hdt

μ

μ γμ μ γ

= ×

=

= ×

M0

Ref:TMS σ11 σ22 σ33 σiso (ppm) η Benzene 217 141 1 120 0.64Graphite 178 178 0 119 0

C60 220 186 25 143 0.29SWNTs (0.85 nm) 195 160 17 124 0.33SWNTs (1.40 nm) 120

1313C NMR of Pure Carbon NanotubesC NMR of Pure Carbon Nanotubes

H0

Hloc13C

Nuclear SpinNuclear Spin--Lattice RelaxationLattice Relaxation

Thermal equilibrium

Infinite temperature

Thermal equilibrium

0nz n

B

HNMV k T

μμ=

[ ])/exp(1)( 10 TtMtM z −−=

equilibrium

Tn = ∞Te = T

H0

2 2

1

2 1 ( )Bdip F

ave

k A g ETT

π=

Metallic and Semiconducting SWNTsMetallic and Semiconducting SWNTs

βα αα 11 //* )1()( TtTt eetM −− −+=

Ni/Co: 0.6 at% each

SpinSpin--Lattice Relaxation in SWNTsLattice Relaxation in SWNTs

2 2

1

2 1 ( )Bdip F

ave

k A g ETT

π=

Nuclear Spin-Lattice Relaxation

2 2

1

2 1 ( )Bdip F

ave

k A g ETT

π=

23

2 15dip e nA

rγ γ= 78.23 10dipA eV−= ×Ab initio for ppπ:

1 1

1

1 0.00028ave

K sTT

− −= ( ) 0.022 /( )Fg E states eV spin atom= ⋅ ⋅

Prediction for (10,10) tubes: ( ) 0.015 /( )Fg E states eV spin atom= ⋅ ⋅

Lithium BatteryLithium Battery

Graphene sheet Li

High Density Anode Storage Material

B. Gao et al. Chemical Physics Letters 307, 153-157 (1999).

50 mA/g, 800 mAh/g

Molecular AdsorptionMolecular Adsorption

Molecular transport and delivery

Molecular filters, sensors, and toxic molecule removal

sarin methanesulfonylchloride

methyl methacrylate

Fuel cells: hydrogen storage

Lithium IntercalationLithium Intercalation

Cut SWNTs

Uncut SWNTs

T1=12.0s

T1=3.2s

T1=6.0s

13C

H. Shimoda et al. Physical Review Letters 88, 015502 (2002).

H2: 2.96ÅO2: 3.43ÅN2: 3.85ÅHe: 2.57ÅCO2: 3.897ÅCO: 3.59ÅN2O: 3.816ÅXe: 4.31ÅCH4:3.82Å

Gas AdsorptionGas Adsorption

(10,10)

17Å

13.56Å

surface

groove

interstitial

inside

2.6Å

Surface area (N2-B.E.T.):300 m2/g50 tubes/bundleBundle diameter:12 nm

A. Kleinhammes et. al., Phys. Rev. B 68, 075418 (2003).

Gas ExposureGas Exposure

Pump

H2Pressure Gauge

Valve Superconductor

Magnet

Probe

Saddle Coil

Sample holder

System Control

Influence of Gas ExposureInfluence of Gas Exposure

interstitial(10,10)

17Å

13.56Å

surface

groove

inside

2.6Å

H2: 2.96ÅO2: 3.43ÅN2: 3.85ÅHe: 2.57ÅCO2: 3.897ÅCO: 3.59ÅN2O: 3.816ÅXe: 4.31ÅCH4:3.82Å

0.1

1

0 5 10 15 20 25 30 35 40

vacuumH

2 gas

CO2 gas

He gasairO

2 gas

M*(

t)

Recovery time t (s)

13C NMR

Proton Spectrum of CHProton Spectrum of CH44 Adsorbed in Cut SWNTsAdsorbed in Cut SWNTs

Adsorbedmoleculesinside SWNTs

NMR rf coil

Gas molecules

NMR sampletube

-1 104-5000050001 104

Frequency (Hz)

CH4 at 0.044 MPa Cut SWNTs

Methane and Ethane AdsorptionMethane and Ethane Adsorption

-1.5 104-1 104-5000050001 1041.5 104

Frequency (Hz)

C2H

6

CH4

1H at 4.7 Teslacut SWNTs Gas pressure: 0.045 MPa

)/exp(10 13 Tks Bετ −=

meV 330for 108.2 8

=×= −

ετ s

Residence time

Gas

Adsorbed outside

Adsorbed inside

0.01

0.1

1

0 2000 4000 6000Ec

ho H

eigh

t2τ (μs)

T2a

: 125 (μs)

T2b

: 2.8 (ms)

SpinSpin--Spin RelaxationSpin Relaxation

Gas

Adsorbed outside

Adsorbed inside

2

2

0

1

( )

( )

( )

x xx

y yy

zzz

dM MHdt T

dM MH

dt TM MdM H

dt T

γ μ

γ μ

γ μ

= × −

= × −

−= × +

H0 H0 H0 H0

T2 T1rf pulse

-1 104-5000050001 104

Frequency (Hz)

CH4 at 0.044 MPa Cut SWNTs

Spin Lattice RelaxationSpin Lattice Relaxation

0

50

100

150

200

250

300

350

0 1 105 2 105 3 105 4 105 5 105 6 105

T 1 (ms)

Pressure (Pa)

Gas

Adsorbed

ethane

1

1 ( ) ( )

collision collision

gas wall

R gas R wallT

cn n

= +

=+

B0

rLocal field fluctuations

νh

-1 104-5000050001 104

Frequency (Hz)

CH4 at 0.044 MPa Cut SWNTs

0

1

2

3

0 2 105 4 105 6 105 8 105

CH4 gas

Adsorbed CH4 (cut)

Adsorbed CH4 (uncut)

C2H

6 gas

Adsorbed C2H

6 (cut)

Num

ber o

f Mol

ecul

es (m

mol

/g)

Pressure (Pa)

Adsorption IsothermAdsorption Isotherm

Cut SWNTs

Uncut SWNTs

-1 104-5000050001 104

Frequency (Hz)

CH4 at 0.044 MPa Cut SWNTs

Langmuir Adsorption IsothermLangmuir Adsorption Isotherm

bPbPnTPn+

= ∞ 1),(

)/exp( 20

TkETmk

b BdBπν

σ=

kJ/mol 22.7meV 235 ==dEFor methane

kJ/mol 29.2meV 303 ==dEFor ethane

219methane m 106.1 −×=σ 219

ethane m 100.2 −×=σ

-1 104-5000050001 1041.5 104

420 torr CH4, 600 torr O

2

420 torr CH4

Frequency (Hz)

Competitive Adsorption: Methane and OxygenCompetitive Adsorption: Methane and Oxygen

---The adsorption energy of oxygen molecules in carbon nanotubes is very small. ---Why is there then such large oxygen effects on electronic properties?

Question:Could dipole-dipole interactions be tuned in gases/liquids without changing the density?

Yes!

Size and shape effect:

Gases in NanoGases in Nano--ContainersContainers

J. Baugh, et. al. Science 294, 1505 (2001).

Dipolar Interactions of Gas Contained in an EllipsoidDipolar Interactions of Gas Contained in an Ellipsoid

( ) ( )2

23

3cos 11 32

jkd j k jz kz

j k jk

I I I Ir

θγ

<

−= • −∑H

( )223

(cos )3jk

d j k jz kzj k jk

PI I I I

rθ

γ<

= • −∑H

( )2 23

,

(cos ) 1 3cos 1 ( / )2

jk j k

jkV V

P dV dV f b ar V V V

θ= Ω −∫∫

oB

Ωrθ

b

a

Elongated Aligned Nanovoids in HWCVD aElongated Aligned Nanovoids in HWCVD a--Si:HSi:H

0.1

1

10

100

200 400 600 800 1000

858068554530150

time (microseconds)

Echo

hei

ght (

a.u.

) angle (o)

Orientation DependenceOrientation Dependence

)(cos Hz 4602/36.2 22 Ω= PM π

2

3

224

2

3

224

2 21cos3)1)(1(3

1cos31)1(23

rNII

rNIIM

kj jk

jk −−+=

−+= ∑

<

θγθ

γ

V

PabfVNIIM

)(cos2)/(/)1()1(32

2Ω−+

=γ

2a=9.2 nm,2b =3 nm

Estimation of the NanoEstimation of the Nano--Container SizeContainer Size

2 22.36 / 2 460 Hz (cos )M Pπ = Ω

2 3 ( 1) ( 1)/ ( / ) (cos )22

I I N V f b a PM

V

γ + − Ω=

2a

2b

Glass TransitionGlass Transition

Ent

halp

y or

Vol

ume

Temperature

Glass

Crystal

Tg Tm

liquidsolid: glass

solid: crystal10 s

Tc>Tg

---X.-P. Tang, R. Busch, W. L. Johnson, and Y. Wu, Phys. Rev. Letts. 81, 5358 (1998).---X.-P. Tang, U. Geyer, R. Busch, W. L. Johnson, and Y. Wu, Nature 402, 160 (1999).---J. Schroers, Y. Wu, R. Busch, and W. L. Johnson, Acta Materialia 49 (14), 2773 (2001).---L. Li, J. Schroers, and Y. Wu, Phys. Rev. Letts. 91, 265502 (2003).

NMR and Local FieldNMR and Local Field

|-1/2>

|1/2>

0( )n local zE B B Iγ ωΔ = + =

Probability of finding a spin at a given local field

B0

Shift:local field

( ) ( ) ( )i i ir t R t u t= +

The average shift of this peak is not affected by in glassy and liquid systems regardless of its timescale. How about ?

( )iR t( )iu t

3000 2500 2000 1500 1000 500 0

Glass

Shift (ppm)

Liquid

31PPdNiCuP

induced motional narrowing( )iR t

Knight Shift

vibrations

Dynamically Induced ShiftDynamically Induced Shift

0 s 0.1 ps 0.2 ps

T

28 (0)3 F

obs refPauli

Eref

Kν ν π ψ χ

ν−

≡ = Ω

22 ( )Pauli B Fg Eχ μ=

0( ) ( ) ( ( ))i i ir r r R uψ ψ ψ= + − +∑

F

2 20 1 (0)

Ea a uψ = + < >

A crude analysis of explicit T dependence

Volume dependence, , i PauliR χΩ

0( ) ( ) ( ) ( )i i ii neighbors

r r r R uψ ψ ψ=

= + − +∑

F

2 20 1 (0)

Ea a uψ = + < >

28 (0)3 F

PauliE

K π ψ χ= Ω

2 2 2vib ratu u u< >=< > + < > 2

vib Bu k T< >∝

Mode-coupling theory

Above Tc: constantBelow Tc

22 2 11 ( ) /

2rat c c cu u a T T T⎛ ⎞< >= − −⎜ ⎟⎝ ⎠

2ratu< >

Dynamically Induced Shift Dynamically Induced Shift

2 20( ) ( ) ( ) )vib ratK K V a V u b V u= + Δ < > + Δ < >

3131P NMR Spectra of PdP NMR Spectra of Pd4343NiNi1010CuCu2727PP2020

3000 2500 2000 1500 1000 500 0

CrystalGlass

Shift (ppm)

Liquid

RT

1057 K

550 600 650 700 750 800 850 90050

100

150

200

250

Tx=670 K

Tliq=870 K

Hea

t Flo

w (m

J/s)

Temperature (K)

DSC: 20 K/min, Pd43Ni10Cu27P20

Tg=583 K

B2O3 flux

Al2O3spacer

PdNiCuPIsothermal DSC

3000 2000 1000 0Shift (ppm)

1036K

750K

730K

583K

300K

2200 2100 2000 1900 1800 1700 1600Shift (ppm)

1036K

740K

750K

730K

Temperature Dependence of the ShiftTemperature Dependence of the ShiftPd43Ni10Cu27P20

31P

550 600 650 700 750 800 850 90050

100

150

200

250

Tx=670 K

Tliq=870 K

Hea

t Flo

w (m

J/s)

Temperature (K)

DSC: 20 K/min, Pd43Ni10Cu27P20

Tg=583 K

200 400 600 800 1000

1000

1100

1200

160017001800190020002100 Tliq

Shift

(ppm

)

Temperature (K)

Melting point

Tg

Temperature Dependence of the ShiftTemperature Dependence of the Shift

crystal

Tc=660 K to 700 K2

22 /)(211 ⎟

⎠⎞

⎜⎝⎛ −−>=< cccrat TTTauu

ln ln lnln ln lnP T V P

K K K TV V T V

∂ ∂ ∂ ∂⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

200 400 600 800 1000

1000

1100

1200

160017001800190020002100 Tliq

Sh

ift (p

pm)

Temperature (K)

Melting point

Tg

Effect of Thermal ExpansionEffect of Thermal Expansion

I.-R. Lu et al., APL 80, 4534 (2002)

For a volume increase of 6%, the expected increase of the shift is:

2/3 2( ) ( ) (1 / )3

K V V V V V V Vα α+ Δ = + Δ ≈ + Δ2/ / 4%3

K K V VΔ = Δ =

F

221 3 3 2 2 21 e n F B

64 (0) ( )9 E

T g E k Tπ γ γ ψ− =

22 e

1 s 2B n

4

TTK fkγ

π γ=

SpinSpin--Lattice Relaxation: Lattice Relaxation: KorringaKorringa RelationRelation

300 600 9001

2

3

4

5

6

T 1TK2 (1

0-6 K

*s)

Temperature (K)28 (0)

3 FPauli

EK π ψ χ= Ω

28 (0)3 F

obs refPauli

Eref

Kν ν π ψ χ

ν−

≡ = Ω

22 22 2 0

0 20 0

(0) ( )1(0) ( ( )) (0) ( ) shear strain terms2 ( / )

F

F F

E

E E

V t VV t VV V V

ψψ ψ

∂ ⎛ ⎞−= + +⎜ ⎟∂ ⎝ ⎠

compressional strain2

0

0

( ) /BV t V k T

Vβ

⎛ ⎞−≈ Ω⎜ ⎟

⎝ ⎠β: volume compressibility

Qualitative InterpretationQualitative Interpretation

200 400 600 800 1000

1000

1100

1200

160017001800190020002100 Tliq

Shift

(ppm

)

Temperature (K)

Melting point

Tg

Participants in my group: Alfred Kleinhammes, Xiaoping Tang, Jonathan Baugh, Lilong Li, Shenghua Mao, Marcelo Behar

Otto Zhou’s group at UNC-CH

Weihua Wang’s group at the Institute of Physics, CAS.

AcknowledgementAcknowledgement