high resolution methods for quadrupolar nuclei - ir-rmn.fr
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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
Solid-state MAS spectra of half-integer spin nuclei
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 ]
Solid-state MAS spectra of half-integer spin nuclei
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
High-resolution NMR of quadrupolar nuclei
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
High-resolution NMR of quadrupolar nuclei
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
Multiple quantum MAS (MQMAS)
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
Multiple quantum MAS (MQMAS)
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
Multiple quantum MAS (MQMAS)
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
Satellite transition MAS (STMAS)
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
Satellite transition MAS (STMAS)
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)
Satellite transition MAS (STMAS)
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
High-resolution NMR of quadrupolar nuclei
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
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
Very large quadrupolar coupling
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
Very large quadrupolar coupling
Very large quadrupolar coupling
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
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