high resolution methods for quadrupolar nuclei - ir-rmn.fr

Franck Fayon

CEMHTI – CNRS

Conditions Extrêmes et Matériaux : Haute Température et Irradiation

Extreme Conditions and Materials : High Temperature and Irradiation

Orléans, France

NMR of quadrupolar nuclei

Half-integer spin quadrupolar nuclei (I>1/2)

82 NMR-active isotopes with I > 1/2

I = 1

Deuterium

Lithium-6

Nitrogen-14

I = 3/2Lithium-7

Boron-11

Sodium-23

Chlorine-35

Potassium-39

Gallium-71

Rubidium-87

I = 5/2Oxygen-17

Magnesium-25

Aluminium-27

….

I = 7/2Scandium-45

Vanadium-51

Cobalt-59

….

I = 9/2Niobium-93

Indium-115

….

I = 1/2

Quadrupolar I > 1/2

I = 3

Boron-10

Integer spin nuclei Half-integer spin nuclei

27Al (I=5/2) in A9B2

B0 = 17.6 T

νR = 15 kHz

23Na (I=3/2) in Na3PO4

B0 = 9.4.0 T

νR = 24 kHz

-1500 (kHz)-1000-500050010001500

113In (I=9/2) in InF3

B0 = 17.6 T

νR = 35 kHz

Solid-state MAS spectra of half-integer spin nuclei

Central Transition

27Al (I=5/2) in A9B2

B0 = 17.6 T

νR = 15 kHz

Satellite Transitions

• First order quadupolar

• Spinning sideband manifolds

• Second order quadrupolar

• Second-order broadening of each ssb

• (m,-m) ↔ No first order quadupolar

• One intense peak (for each site)

• Second order quadrupolar

• Second-order broadening & shift


B0 effects (27Al in A9B2)

Second order shift (A) and width (C) goes with ωQ²/ω0 (Hz) (component B is removed by MAS)

9.4 T

11.7 T

14.1 T

17.6 T

Z. Gan, Gor’kov, T. Cross, A. Samoson, D. Massiot, JACS 2002,124, 5634.

27Al in A9B2 (MAS )

Getting a spectrum with narrow lines with “conventional” magnetic fields (4.7 - 17.6 T)

��∝

��

��[ A + B� ��β �� β ]


Spin I = 3/2

P� cos β =�

��3cos�β-1)

P� cosβ = �

��35cos�β-30 cos�β+3)

Second-rank

anisotropic

2nd-order isotropic

quadrupolar shift

Fourth-rank

anisotropic

A = −I I 1 − 3 − 9m�m− 1�

30

( ) ( )∑=

+−>−< +−+=

2

1

,201,2

)21(θcos

n

tninQmm

reACm

Pφω

βαννν

First order HQ << Hz

( ) ( )∑∑=

+−

=>−< ++=

4

1

)2(

4,2,0

)2(,01, θcos

n

tnin

l

lll

ImmmreAPBC

φωνν

Second order HQ < Hz

��∝

��

��[ A + B� ��β �� β ]

Magic Angle Spinning of quadrupolar nuclei

MAS 54.74°0° = static

P4(cosβ)

P2(cosβ)

β

1

-0.5

90°

B0

30.56°

90°

70.12°

0°=static

MAS

No spinning angle allows to remove simultaneously

first- and second-order broadenings

P� cosβ =�

��3cos�β-1)

P� cosβ = �

��35cos�β-30 cos�β+3)

��∝

��

��[ A + B� ��β �� β ]

0

High-resolution NMR of quadrupolar nuclei

DOR: DOuble Rotation!

removed if βR = 54.74 ° removed if βR = 30.56 ° or 70.12 °

Spinning rate

∼ 5-6 kHz

Spinning rate

∼ 1-2 kHz

MAS 54.74°0° = static

P4(cosβ)

P2(cosβ)

β

1

-0.5

90°

B0

��∝

��

��[ A + B� ��β �� β ]

0

Samoson, Lippmaa, Pines, Mol. Phys., 65, 1013 (1988)

30.56 ° 70.12 °

DOuble Rotation (DOR)

27Al in Y3Al5O12 (7.0 T)

2 Al sites

D. Massiot - CEMHTI

27Al in CaAl2O4 (7.0 T)

6 Al sites

Samoson et al., Mol. Phys., 65, 1013 (1988)

Spinning rate

∼ 5-6 kHz

Spinning rate

∼ 1.0- 1.6 kHz

DOuble Rotation (DOR)

Alderman, Iuga, Pike, Dupree et al, Phys. Chem. Chem. Phys., 2013,15, 8208-8221

11B in Borates (20.0 T)

Spinning rate

∼ 5-6 kHz

Spinning rate

∼ 1.0- 1.6 kHz

CsB9O14 CsB5O8 CsB3O5

Na2Cs2B10O17 K2B4O7 BaB4O7

δISO

PQ

• DOR remains technically challenging

• Limited spinning frequency & sample volume reduced

• Limited number of operating probes (Warwick group)

and applications

Using echo for quadrupolar nuclei

coherencepathway

0

-1

+1

pulsesequence

t1

H prop. Iz

t2

H prop. -Iz

π/2 π

EchoTopt1 = t2

π pulse refocuses all interactions linear in Iz, hence top of the echo is free of H evolution (Chemical Shift, Heteronuclear J, Quadrupolar 2nd)

� Can we reverse the sign of the quadrupolar interaction, and not the chemical shift?

The echo idea

Excitation of quadrupolar nuclei

HZ HRF HD HCSHQ HJ

Central Transition I=3/2 (on resonance excitation)

pulse duration (µs)

Inte

nsité (

a.u

.)

-1.00

-0.50

0.00

0.50

1.00

0.00 5.00 10.00 15.00 20.00

νQ>> ν1

(I+1/2)ν1.

νQ<< ν1

ν1

νQ~ ν1

νQ<<ν1 non selective regime (liquid like) sine behavior of the whole system of transitions.

Solid Quadrupolar Echo π/2(x) - τ - π/2 (y) - acqu

νQ~ν1 intermediate regime, non pure sine behavior, excitation of multiple quanta.

νQ>> ν1 selective regime, “fictitious spin ½” with a nutation frequency of (I+1/2)ν1.

Hahn-Echo - π/2 - τ - π - acqu


Dynamic Angle Spinning (DAS)

Correlation between spectra at β1 and β2

is linear and free of quadrupolar evolution

Mirror images at different angles

Echo with time evolutions at different angles

Dynamic Angle Spinning (DAS)

Detection at Magic Angle

17O DAS in SiO2 Coesite17O DAS in SiO2 Coesite

P.J. Grandinetti et al. J. Phys Chem B 1995

Baltisberger et al. JACS 1992

P.J. Grandinetti et al. J. Magn. Reson. 1993

87Rb DAS in RbNO387Rb DAS in RbNO3

• DAS remains technically challenging

• T1 relaxation during hopping time, limited spinning frequency

• Limited number of operating probes (Grandinetti group)

3 resolved 87Rb sites 5 resolved 17O sites


Multiple quantum MAS (MQMAS) Satellite transition MAS (STMAS)

Scaling the quadrupolar evolution with the coherence order

Scaling the quadrupolar evolution with the external transitions

0

-3

+3

3Q 1Q

t1 t2

-1

+1

0

t1 t2

ST CT

L. Frydman, JACS 1995. Z. Gan, JACS 2000.

L. Frydman, JACS 1995.

Multiple quantum MAS (MQMAS)

Scaling the quadrupolar evolution with the coherence order

87Rb 3QMAS of RbNO3 (9.4 T)

Quadrupolar parameters and CS of all 87Rb sites


Most used MQMAS pulse sequences

MQMAS Shifted Echo

Massiot, Grandinetti et al., Solid-State NMR 1996

• Pure absorption lineshape

• S/N x 21/2 (without relaxation)

• T2 relaxation

MQMAS Z-filter

• Symmetric

coherence

pathways

Amoureux, Fernandez et al., JMR 1996

π/2


Massiot JMR A, 122, 240-244 (1996)

27Al Sillimanite

Unsynchronized

27Al Sillimanite

Unsynchronized

27Al Sillimanite

Synchronized

27Al Sillimanite

Synchronized

Rotor-synchronized 3Q evolution

• Sensitivity

• Easier lineshape simulation


Most used MQMAS pulse sequences

MQMAS Shifted Echo

Massiot, Grandinetti et al., Solid-State NMR 1996

• Pure absorption lineshape

• S/N x 21/2 (without relaxation)

• T2 relaxation

MQMAS Z-filter

• Symmetric

coherence

pathways

Amoureux, Fernandez et al., JMR 1996

π/2

νQ>> ν1

(I+1/2)ν1.

νQ~ ν10Q → 3Q 3Q → 1Q

Amoureux, Fernandez et al., Chem. Phys. Lett. 1996

Satellite transition MAS (STMAS)

Scaling the quadrupolar evolution with the external transitions

Z. Gan, JACS 2000.

Sat Central

Sat Central

I = 3/2

CT infinite spinning rate

ST infinite spinning rate

I = 5/2

CT infinite spinning rate

<3/2 ; 1/2 > ST infinite spinning rate

Trot.

STMAS shifted echo pulse sequence


CTST2

ST1

CT

27Al I= 5/2

FT + shear

STMAS ratio

27Al aluminium acetylacetonate

Ashbrook & Wimperis, J. Magn. Reson. 2002

Most used STMAS pulse sequence


11B DQF STMAS of Na2B4O7

Quadrupolar parameters of all 11B sites

Deviation from ideal lineshapes

Excitation effects

Double quantum filtered (DQF) STMAS

Kwak and Gan, J Magn. Reson. 2003

Remove CT-CT correlation

Remove ST2-CT correlation (I = 5/2)


Highly sensitive to Magic Angle accuracy

(ppm)-12-8-404

-2

0

2

4

6

(ppm)-12-8-404

2

4

6

8

(ppm)-12-8-404

2

4

6

8

(ppm)-12-8-404

V. Sarou-Kanian CEMHTI-CNRS

Exact MAS (θ - θMAS) = 0

(θ - θMAS) = 0Off MAS

First order quadupolar effects on ST

pulse

sequence

coherence

pathway

0

-3

+33Q 1Q

t1 t2

MQ-MAS(Frydman 95)

DAS(Llor&Virlet, Pines 88)

0

-1

+1

t1 t2hop

θ1 θ2

angle

-1

+1

0

t1 t2

Sat Central

STMAS(Gan 2000)

� technically challenging

� hop time is long (~30ms),

diluted spin systems

� Valid for large couplings

CT as a fictituous spin ½

� 17O, 87Rb, 11B (diluted), 71Ga

� easy to implement,

many excitation schemes

(nutation, RIACT, amp.

modulation, freq. sweep...)

� suitable for abundant nuclei

� Intermediate couplings :

needs high rf powers ?

� 27Al, 23Na, 17O, 87Rb, 11B, 71Ga

� accurate MAS angle (1/100°)

and spinning rate

� suitable for abundant nuclei

� Intermediate to large couplings

� 27Al, 23Na, 17O, 45Sc, 93Nb


Magnitude of the quadrupolar interaction

For high symmetry CQ = 0

CQ increases as symmetry decreases

The EFG is caused by distribution of charges in the system

(the coordinating atoms to a first approximation)

CQ = (eQVzz)/h

eQ

nucleus Q (mb)

H-2 2.860(15)

Li-7 -40.1

Al-27 146.6(10)

Ga-69

Ga-71

171 (2)

107 (1)

Exact CQ depends on eQ

-1000-750-500-25002505007501000(ppm)

7.0 T - Static

7.0 T - MAS 15kHz-150-100-50050100150

(ppm)

17.6 T - MAS 15kHz

diso = 128.7 ppm

CQ = 15.37 MHz

ηQ = 0.63

diso = 108.0 ppm

CQ = 23.37 MHz

ηQ = 0.00

Alba et al., J. Phys. Chem. C 114 12125- (2010)

Low Field + Slow Spinning = very complex set of spinning sidebands.

� Increase Speed� Increase Field

� Turn to static (non spinning) echo experiment� Fictious spin-½

45Sc in Sc2O3

Very large quadrupolar coupling


-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.8

δiso CQ ηQ ∆csa %(ppm) (MHz) - (ppm)

-----------------------------------------

250 116 0.15 -70 28

0 86 0.80 -70 46

50 66 0.05 0 11

400 55 0.40 0 15

frequency (MHz)

139La in La2Si2O7 at 20.0 T

-2.0-1.8-1.6-1.4-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.21.41.6

intensity x3

frequency (MHz)

Massiot, D. et al., Solid State Nuclear Magnetic Resonance 4, 241-248, (1995).

Central Transition-selective Static experiment

• Fictious spin ½ regime (νRF << νQ)

• Hahn echo

• Bandwidth limited by CT-selective π pulse length

→ Variable Offset Cumulative Spectrum


Broadband excitation WURST

0

10

20

30

0 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06

amplitude

0

100

200

300

400

0 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06

phase

Time (ms)

Time (ms)

Kupče and Freeman, J.Magn.Reson. A117 246–256 (1995)

O’Dell, Solid State Nycl. Magn. Reson. 55-56 28-41 (2013)

Bhattacharyya & Frydman J. Chem. Phys.127 194503 (2007)

(The first application of WURST (chirp) pulses for the excitation of central

transitions of quadrupolar nuclei, and a discussion of frequency dispersed echoes).

generates a frequency sweep

� broadband excitation

generates a frequency sweep

� broadband excitation

(ppm)-1000-500050010001500

(kHz)-80-60-40-20020406080

WURST-80 pulse shape (ppm)-1000-500050010001500

(kHz)-80-60-40-20020406080

� Variable Offset Cumulatice Spectra (VOCS)

� Frequency Sweep

VOCS

(5 x 12h)

WURST-QCPMG

(1 x 12h)

(ppm)-1000-500050010001500

(kHz)-80-60-40-20020406080



Sensitivity enhancement DFS/RAPT & CPMG

Larsen et al. J. Phys. Chem. A 101 8597–8606 (1997) O’Dell & Schurko, Chem. Phys. Lett. 464 97-102 2008; Rossini et al., J. Magn. Reson. (2010)

87Rb NMR spectra of RbClO487Rb NMR spectra of RbClO4

87Rb NMR spectra of Rb2SO487Rb NMR spectra of Rb2SO4

high resolution methods for quadrupolar nuclei - ir-rmn.fr

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