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Harry Pfeifer's NMR experiment in 1951 Harry Pfeifer's NMR experiment in 1951 H. Pfeifer: Über den Pendelrückkoppel-empfänger und die Beobachtungen von magnetischen Kernresonanzen, About pendulum feedback receiver and observation of magnetic resonances,

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Harry Pfeifer's NMR experiment in 1951. H. Pfeifer: Über den Pendelrückkoppel-empfänger und die Beobachtungen von magnetischen Kernresonanzen, About pendulum feedback receiver and observation of magnetic resonances, Diplomarbeit, Universität Leipzig, 1952. NMR of quadrupolar nuclei. - PowerPoint PPT Presentation

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Page 1: Harry Pfeifer's NMR experiment in 1951

Harry Pfeifer's NMR experiment in 1951Harry Pfeifer's NMR experiment in 1951Harry Pfeifer's NMR experiment in 1951Harry Pfeifer's NMR experiment in 1951

H. Pfeifer: Über den Pendelrückkoppel-empfänger und die Beobachtungen von magnetischen Kernresonanzen, About pendulum feedback receiver and observation of magnetic resonances, Diplomarbeit, Universität Leipzig, 1952

Page 2: Harry Pfeifer's NMR experiment in 1951

NMR of quadrupolar nucleiNMR of quadrupolar nucleiNMR of quadrupolar nucleiNMR of quadrupolar nuclei

WEB of Science refers to approximately 10 000 papers per year, which concern NMR investigations.

35% of these works refer to 1H, 25% to 13C, 8% to 31P, 8% to 15N, 4% to 29Si and 2% to 19F as one of the nuclei under study. In all these nuclei, we have the nuclear spin I = ½.

If we look at nuclei with a quadruple moment and half-integer spin I > ½, we find the nuclei 27Al in 3% of all the NMR papers and 1% for each of the nuclei 11B, 7Li, 23Na and 51V.

For even numbered spin, only the I = 1 nuclei are frequently encountered: 2H in 4% and 14N and 6Li in 0.5% of all NMR papers.

Page 3: Harry Pfeifer's NMR experiment in 1951

Dieter Freude, Institut für Experimentelle Physik I der Universität Leipzig METU-Center Workshop on Solid State NMR, 30 and 31 October 2007

Solid-state NMRSolid-state NMRof quadrupolar nuclei of quadrupolar nuclei

with half-integer spinwith half-integer spin

Solid-state NMRSolid-state NMRof quadrupolar nuclei of quadrupolar nuclei

with half-integer spinwith half-integer spin

Introduction to quadrupolar line broadening in solid-state NMR spectra of nuclei with half-integer spin

Excitation problems for solid-state NMR

Double-rotation (DOR) and Multiple-quantum solid-state (MQMAS) NMR of quadrupolar nuclei with half-integer spin

Page 4: Harry Pfeifer's NMR experiment in 1951

HistoryHistoryHistoryHistory

Classic techniques: single crystal and broad line NMR

Encanced rf power allows pulse excitation and echo observation in broad line NMR

1980, MAS reduces the powder line broadening of the central transition by 1/4

1984, nutation techniques improve the quadrupolar resolution

SATRAS reduces quadrupolar line broadening for powders

1988, DOR removes line broadening for powders

1988, DAS removes line broadening for powders

1995, MQMAS removes line broadening for powders, less laborious than DOR/DAS

MQMAS techniques are improved in sensitivity and resolution

1998, MQMAS is combined with DOR, Carr-Purcell, cross-pol., REDOR, VAS

2000, STMAS cobines high single-quantum sensitivity wit high resolution

2004, SPAM (soft pulse added mixing) increases sensitivity

Page 5: Harry Pfeifer's NMR experiment in 1951

Zeeman splitting of energy levelsZeeman splitting of energy levelsZeeman splitting of energy levelsZeeman splitting of energy levelsNeglecting quadrupole interaction, we have the pure Zeeman splitting

Em =   m B0

As an example, we consider the Zeeman splitting of a I = 5/2-nucleus:

Double-headed arrows showsingle-quantum up to quintuple-quantum transitions.

m

5/2

5/2

3/21/21/2 3/2

The right-hand side demonstrates level populations, which van be changed, e. g., by double frequency sweep (DFS).

Page 6: Harry Pfeifer's NMR experiment in 1951

Parameters of quadrupole interactionParameters of quadrupole interactionParameters of quadrupole interactionParameters of quadrupole interactionThe quadrupole coupling constant Cqcc is commonly defined as

h

qQeC

2

qcc

For the quadrupole frequency, Q, different definitions exist in the literature. We use

122

3

122

3 qcc2

Q

II

C

hII

qQe

where h denotes Planck's constant. Elements of the traceless tensor of the electric field gradient V are given in the principal axis system. The ZZ-component is VZZ = eq, where e denotes the elementary charge and the value q alone has no physical meaning in SI units. Q is the quadrupole moment. eQ is called the electric quadrupole moment.

where I denotes the nuclear spin. The asymmetry parameter is in the range 0    1. With the convention |VZZ|  |VYY|  |VXX| we obtain

ZZ

YYXX

V

VV

Page 7: Harry Pfeifer's NMR experiment in 1951

Euler's angles andEuler's angles andthe angle-dependent quadrupole frequency the angle-dependent quadrupole frequency ''QQ

Euler's angles andEuler's angles andthe angle-dependent quadrupole frequency the angle-dependent quadrupole frequency ''QQ

A positive rotation to a frame (x, y, z) about the Euler angles includes the rotation about the original z axis, the rotation about the obtained y' axis, and the rotation about the final z" (identical with z''') axis.

x

y

y', y''

x'

x''

z, z'

z'', z'''

x'''

y'''

2cossin

22

1cos3 22

QQ

Page 8: Harry Pfeifer's NMR experiment in 1951

Quadrupole shift of theQuadrupole shift of the Larmor frequency Larmor frequencyQuadrupole shift of theQuadrupole shift of the Larmor frequency Larmor frequency

Assuming resonance offset and chemical shift to be zero, the quadrupole shift is given as m,m' =   L. Conventions m,m+1 and m,m for single-quantum transitions and symmetric transitions, respectively, assign the central transition 1/2,+1/2 to m = 1/2. The first-order quadrupole shift becomes

2

1Q1, mmm

We see that there is no quadrupole shift for the central transition in first-order perturbation theory. Symmetric satellites appear around the central transition.

But for all transitions a second-order quadrupole shift exist. It is for the central transition

CBAII

24

L

2Q

2/1,2/1 coscos4

31

6

static MAS

A 27

8

9

42

3

822 2 cos cos

21

16

7

82

7

4822 2 cos cos

B 15

4

1

22 2

3

422 2 2 cos cos

9

8

1

122

7

2422 2 2 cos cos

C 3

8

1

3

1

42

3

822 2 2 cos cos

5

16

1

82

7

4822 2 cos cos

Note that the second-order quadrupole shift and broadening in powder spectra is proportional to (Q/L)2 , if expressed in ppm.

Page 9: Harry Pfeifer's NMR experiment in 1951

Quadrupolar shift for single crystalsQuadrupolar shift for single crystalsQuadrupolar shift for single crystalsQuadrupolar shift for single crystals

2

1Q1, mmm

+5/2+3/2 +3/2+1/2 +1/2–1/2 –1/2 –3/2 –3/2 –5/2

L

Zeeman

first-order

second-order

,6

131

3

171

30

313191

30

L

2Q

2

L

2Q

1,

fmmII

mmIImm

Page 10: Harry Pfeifer's NMR experiment in 1951

A useful different form of the equationA useful different form of the equationA useful different form of the equationA useful different form of the equationSecond-order quadrupole shift under MAS conditions can be written in a different form as

Table taken from Gan 2001: Ratios of expansion coefficients between satellite (m* - ½ m* + ½) and central transition (m* = 0).

CBAmmII

mmIImm

24

L

2Q

2

L

2Q

1,

coscos6

131

3

171

30

313191

30

2cos48

352cos

8

35

16

105 22A

2cos24

352cos5

12

5

8

45 222 B

2cos48

352cos

8

5

3

1

16

9 222 C

I = 9/2, m* = ±4

rank 0 rank 4

I = 3/2, m* = ±1 2 8/9

I = 5/2, m* = ±1 1/8 7/24

I = 5/2, m* = ±2 7/2 11/6

I = 7/2, m* = ±1 2/5 28/45

I = 7/2, m* = ±2 7/5 23/45

I = 7/2, m* = ±3 -22/5 12/5

I = 9/2, m* = ±1 5/8 55/72

I = 9/2, m* = ±2 1/2 1/18

I = 9/2, m* = ±3 19/8 9/8

5 50/18

rank 0

rank 4

Ratios on the left are the base of MAS satellite (SATRAS) and satellite transition (STMAS) spectroscopy.

Page 11: Harry Pfeifer's NMR experiment in 1951

Quadrupole line shapes for half-integeger spin Quadrupole line shapes for half-integeger spin II > ½ > ½

first-order, cut central transition second-order, central transition onlyfirst-order, cut central transition second-order, central transition only

Quadrupole line shapes for half-integeger spin Quadrupole line shapes for half-integeger spin II > ½ > ½

first-order, cut central transition second-order, central transition onlyfirst-order, cut central transition second-order, central transition only

169 16

9 329 1 0 0 5

6 149 4

21

L

Q2

L161

34

I I

= 0

= 0.5

= 1

MAS static

L

Q

3 2 1 0 -1 -2 -3 3 2 1 0 -1 -2 -3

= 0 = 1

I = 3/2

I = 5/2

I = 7/2

= 0 = 1

I = 3/2

I = 5/2

I = 7/2

Q

L

43

116 L

2Q

L

II

All presented simulated line shapes are slightly Gaussian broadened,

in order to avoid singularities.L is the Larmor frequency.spectral range: Q(2I  1) or 3 Cqcc/ 2I

Page 12: Harry Pfeifer's NMR experiment in 1951

Excitation, a broad line problemExcitation, a broad line problemExcitation, a broad line problemExcitation, a broad line problem

Basic formula for the frequency spectrum of a rectangular pulse with the duration and the carrier frequency 0 with  =   0:

sind2cos

1 2/

2/

ttf

We have a maximum f () = 1 for  = 0 and the first nodes in the frequency spectrum occur at  = 1/. The spectral energy density is proportional to the square of the rf field strength given above. If we define the usable bandwidth of excitation 1/2 in analogy to electronics as full width at half maximum of energy density, we obtain the bandwidth of excitation

886.0

2/1

It should be noted here that also the quality factor of the probe, Q =  / probe, limits the bandwidth of

excitation independently from the applied rf field strength or pulse duration. A superposition of the free induction decay (FID) of the NMR signals (liquid sample excited by a very short pulse) for some equidistant values of the resonance offset (without retuning the probe) shows easily the bandwidth probe of the probe.

Page 13: Harry Pfeifer's NMR experiment in 1951

Excitation profile of a rectangular pulseExcitation profile of a rectangular pulseExcitation profile of a rectangular pulseExcitation profile of a rectangular pulse

5 4 3 2 1 0 1 2 3 4 5

/ MHz

We denote the frequency offset by Positive and negative values of are symmetric with respect to the4 carrier frequency 0 of the spectrometer. The rectangular pulse of the duration has the frequency spectrum (voltage)

The figure describes a pulse duration = 1 µs. The first zero-crossings are shifted by 1 MHz with respect to the carrier frequency.

2/

2/sindcos

2/

2/

ttf

Solid-state NMR spectrometer use pulse durations in the range = 1 10 µs. Respectively, we have single-pulse excitation widths of 886 – 88.6 kHz.

The full width at half maximum of the frequency spectrum correspond to a power decay to half of the maximum value or a voltage decay by 3 dB or by 0.707.

886.0

2/1

Page 14: Harry Pfeifer's NMR experiment in 1951

For example, NOESY and stimulated

echo require 3 pulses. Than we have

n

k

Tkf1

cos212/

2/sin

Tf

cos212/

2/sin

Excitation profile ofExcitation profile of 2n + 1 pulses 2n + 1 pulsesExcitation profile ofExcitation profile of 2n + 1 pulses 2n + 1 pulses

The figure on the left side corresponds to a pulse duration = 1 µs and a symmetric pulse distance of 10 µs. Correspondingly, the first zero-crossings are shifted by 100 kHz with respect to the carrier frequency. The beat minima are shifted by 1 MHz.

5 0 5

/ MHz

0,5 0,1 0 0,1 0,5 / MHz

Page 15: Harry Pfeifer's NMR experiment in 1951

21 subsequent 1-µs-pulses with 10 µs spacing21 subsequent 1-µs-pulses with 10 µs spacing21 subsequent 1-µs-pulses with 10 µs spacing21 subsequent 1-µs-pulses with 10 µs spacing

10

1

cos212/

2/sin

k

Tkf

The central excitation has a fwhm of 4 kHz, whereas we have had 30 kHz for three pulses.

The excitation bandwith of the center band decreases with increasing number of pulses.

0,5 0 0,5

/ MHz

Page 16: Harry Pfeifer's NMR experiment in 1951

21 subsequent 1-µs-pulses with 1 ms spacing21 subsequent 1-µs-pulses with 1 ms spacing21 subsequent 1-µs-pulses with 1 ms spacing21 subsequent 1-µs-pulses with 1 ms spacing

The excitation band width of the center band decreases with increasing number of pulses and increasing pulse distance. Therefore, the excitation profile should be simulated in critical cases.

1 0 1 / kHz

40 Hz

Page 17: Harry Pfeifer's NMR experiment in 1951

Selective excitation, a quadrupole problemSelective excitation, a quadrupole problemSelective excitation, a quadrupole problemSelective excitation, a quadrupole problemThe intensity of the free induction decay G(t = 0) after the pulse with the radio frequency field strength rf and the duration is for nonselective excitation of all transitions m  m + 1

The equation above gives also the relative intensities of all transitions, e. g. 12/30, 9/35 and 4/21 for the central lines in the case of nonselective excitation of the I = 3/2, 5/2 and 7/2 nuclei, respectively. The selective excitation of a single transition can be described by

Comparison of both equations reveals that the maximum observed intensity is reduced by

rf

selectivenon1, sin

1212

1130

III

mmIIG mm

rf

selective1, 11sin

1212

1130

mmIIIII

mmIIG mm

11 mmII , but, the effective nutation frequency is enhanced by the same value.

For the central transition, m = 1/2, we obtain

rfeffrf 2

1

I

This is very important and should be discussed in detail on the table.

Page 18: Harry Pfeifer's NMR experiment in 1951

Highly resolved spectra of quadrupolar nucleiHighly resolved spectra of quadrupolar nucleiHighly resolved spectra of quadrupolar nucleiHighly resolved spectra of quadrupolar nuclei

Resolution of signals having relatively small chemical shift differences

Determination of quadrupole parameters for resolved signals

Improvement of the sensitivity

Simulated line shape of a central transition with an anisotropy factor  = 0.2 and

slight Gaussian broadening;

the static NMR spectrum without MAS,

the MAS NMR spectrum for rot > static linewidth,

the rotation-synchronized MQMAS NMR spectrum.

DOR spectrum looks like MQMAS spectrum, but many spinning side bands appear.

Motivation:

Page 19: Harry Pfeifer's NMR experiment in 1951

MQMAS, the MQMAS, the zz-filter experiment-filter experimentMQMAS, the MQMAS, the zz-filter experiment-filter experiment

,4cos702cos3601812960

1017136

360

3143

2

40,4

240,2

40,0

2

L

22Q

L

222Q

2/,2/

dddpIIp

pIIppp

t

tpp

11

2

2 ,27136

1017136tpIRt

II

pIIpt

Election of coherence pathway is obtained by corresponding phase cycles.

p

5 4 3 2 1 012345

two rectangular pulses + z-filter

t1 t t2

p = 1 is the single-quantum central transition. p = 3 and 5 refer to triple- and quintuple- quantum transitions, respectively. d(4) denote Wiegner's reduced matrices of rank 4.

Averaging of the anisotropic (rank 4) contributions in the echo after the time t2:

The phase development for symmetric single and multiple-quantum transitions is described by

Page 20: Harry Pfeifer's NMR experiment in 1951

Where we go?Where we go? Where we go?Where we go?

The pulse sequence has to be further prolonged, in order to include "cyclops" and to get real and imaginary part of the signal (after Fourier-transform in F2-direction) for the 2D-Fourier-transform in F1-direction.

The transformation (spin density operator) of a coherence of sp at rotation around z-direction by the angle is described by

Now we consider a quintuple-quantum experiment and set the phases of the first and third pulses and the receiver phase to 0°. But the phase of the second pulse is incremented in steps of (360/5)° starting from 0°. After five steps, we have five times accumulated the coherences p = +5 and p = 5, and averaged (to zero) other coherences; unfortunately, except the coherences p = 0 which were also five times accumulated. In order to quench the coherences p = 0, we increment ten times by (360/10)° and use an alternating receiver phases 0° and 180°. The signal for p = 0 is quenched after two scans with alternating receiver phases. After 10 scans we remain with the coherences p = 5 only.

The preparation pulse creates coherences in all orders p 0. Of course, their intensity is drastically decreasing with the number of the order. How can we go a selected pathway?

A radio frequency pulse with the phase transfers at the time t coherences from the order p to the order p+. In the following, tand p- means before pulse, t+ and p+ means after pulse. Then we have

ppFp z iexp

pptPtP pp iexp1

Page 21: Harry Pfeifer's NMR experiment in 1951

Improved coherence transfer and Improved coherence transfer and whole-echo-split-whole-echo-split-tt11 MQMAS techniques MQMAS techniques

Improved coherence transfer and Improved coherence transfer and whole-echo-split-whole-echo-split-tt11 MQMAS techniques MQMAS techniques

3Q MAS 3Q DFS 3Q FAM II

+3 +2 +1

p = 0 1 2 3

131

12t

131

12t

131

12t

131

19t

131

19t

131

19t

2t

2t

2t

For 5QMAS split-t1-factors are 12/37 and

25/37.Echo occurs at Echo occurs at tt 2==. The evolution time . The evolution time tt11 is split is split

between MQ and 1Q coherences. DFS means between MQ and 1Q coherences. DFS means double frequency sweepdouble frequency sweep, FAM denotes , FAM denotes fast fast amplitude modulation.amplitude modulation.

Kentgens introduced 1999 the double frequency sweeps in static, MAS and MQMAS NMR experiments on the basis of an amplitude modulation to the carrier frequency.  

The double frequency sweeps (DFS's) are generated by a programmed time-dependent amplitude modulation of the rf which causes two sidebands that are adiabatically swept from a start frequency to a final frequency during the pulsing.

What is an adiabatic frequency sweep?

Page 22: Harry Pfeifer's NMR experiment in 1951

Adiabatic sweep for Adiabatic sweep for II = 5/2 = 5/2Adiabatic sweep for Adiabatic sweep for II = 5/2 = 5/2

Single crystal, no sample rotation, Q’ = 300 kHz, z-axis of EFG and B0 coincide. The energy (m) is a function of the resonance offset in the rotating system (E = offset m h). In the frequency-stepped adiabatic half-passage (FSAHP) the spin system is far off-resonance at the beginning of the irradiation.

The frequency is then stepped through the region of resonances slowly enough, that the density operator can follow the Hamiltonian. Switching off the rf power at the Larmor frequency creates a single-quantum coherence like a /2 pulse applied to a spin-1/2 system. A full passage would be comparable with a nonselective pulse. The figure inset shows the level repulsion at the crossing of the -1/2 and +1/2 levels. There is an energy gap of h rf between the upper and lower branch

600 400 200 0 400 200 600

0.5

0

0.5

1

resonance offset / kHz

ener

gy

h

/ MH

z

2/3 2/3 2/5 2/5

2/1 2/1

2/1 2/1

m = 1 m = 3 m = 2

Page 23: Harry Pfeifer's NMR experiment in 1951

Optimization of pulse lengthsOptimization of pulse lengthsOptimization of pulse lengthsOptimization of pulse lengths

MQMAS NMR pulse sequences require the adjustment of pulse lengths. It depends on the nuclear spin, on the order of multiple-quantum coherences, on the rotation frequency, on the nutation frequency and on the quadrupole parameters of the species under study.

Pulse optimization by SIMPSON (Bak, Rasmussen, Nielsen) features an excellent agreement with the results of pulse optimization by NMR experiments. Both, SIMPSON optimization and the experiment show that the pulse optimization should focus on those species in the sample which have the largest quadrupole coupling constant. This leads to the lowest distortions of the quantitative character of the spectrum.

Result of a SIMPSON-simulation of the first two pulses of a 3QMAS-split-t1 experiment for one of the 27Al signals in the spectrum of the zeolite AlPO4-14 which has a quadrupole coupling constant of 4.08 MHz.

Page 24: Harry Pfeifer's NMR experiment in 1951

2727Al 3QMAS NMR study of AlPOAl 3QMAS NMR study of AlPO44-14 -14 2727Al 3QMAS NMR study of AlPOAl 3QMAS NMR study of AlPO44-14 -14

40 30 20 10 0

40

30

20

10

0

1/ ppm

2/ ppm

position 1

position 2

position 3

position 5

AlPO4-14, 27Al 3QMAS spectrum (split-t1-whole-echo, DFS pulse) measured at 17.6 T with a rotation frequency of 30 kHz.

The parameters CS, iso = 1.3 ppm, Cqcc = 2.57 MHz, = 0.7 for aluminum nuclei at position 1, CS, iso = 42.9 ppm, Cqcc = 1.74 MHz, = 0.63, for aluminum nuclei at position 2, CS, iso = 43.5 ppm, Cqcc = 4.08 MHz, = 0.82, for aluminum nuclei at position 3, CS, iso = 27.1 ppm, Cqcc = 5.58 MHz, = 0.97, for aluminum nuclei at position 5, CS, iso = 1.3 ppm, Cqcc = 2.57 MHz, = 0.7 were taken from Fernandez et al.

Page 25: Harry Pfeifer's NMR experiment in 1951

1177O 3QMAS NMR O 3QMAS NMR and MAS NMR spectra of zeolite Na-Aand MAS NMR spectra of zeolite Na-A1177O 3QMAS NMR O 3QMAS NMR and MAS NMR spectra of zeolite Na-Aand MAS NMR spectra of zeolite Na-A

Two signals without shoulders are resolved in the isotropic projection of the 3Q MAS spectrum. This corresponds to three different SiOAl bond angles, which can be determined from the X-ray data of the hydrated zeolite Na‑A (Si/Al = 1). But three slices from the 2D spectrum were taken, see right side, since the existence of three sites was proved by the DOR spectrum. The deconvolution of the MAS spectrum (bottom right) uses the quadrupole parameters obtained by a simulation of the three anisotropic slices of the MQ MAS spectrum and gives finally the real intensities of three signals. The sheared 3Q MAS spectrum is presented with anisotropic projection on the top and isotropic projection on the side on the left hand side.

Na-A

2 / ppm

60.0 50.0 40.0 30.0 20.0 10.0

MQMASiso / ppm

64

56

48

40

32

24

01020304050 2 / ppm60

017345168 / ppm

MQMAS iso = 35.9 ppm

= 45.0 ppm

= 46.4 ppm

3

1 2

Page 26: Harry Pfeifer's NMR experiment in 1951

Double rotation (DOR)Double rotation (DOR)Double rotation (DOR)Double rotation (DOR)

Double rotation was introduced by Samoson et al. in 1989. It averages the anisotropic contribution of the second-order quadrupole shift by fast sample spinning around the magic-angle (54.74°) and an angle of 30,56° or 70,12° in addition. This technique is based on an excellent fine mechanic and a computer controlled pneumatic unit.

,271363cos30cos3528

9

4cos702cos3601812960

4

31

90

3

24

40,4

240,2

40,0

2

L

2Q

L

22Q

QanisoQiso2/,2/

II

ddd

IIpppp

  30.56° or 70.12°

145/966

arccos

  = goes to zero for

Page 27: Harry Pfeifer's NMR experiment in 1951

DOR setupDOR setupDOR setupDOR setup

νouter = 12 kHz, νinner = 510 kHz

Iy/Ix has to be adjusted, in order to have J parallel to Z.

2

1

2

1

y

z

Z

L

Jy

2 sin1

Jz (1 +2 cos1)

B0

Page 28: Harry Pfeifer's NMR experiment in 1951

DOR NMR spectra of the zeolite Na-ADOR NMR spectra of the zeolite Na-ADOR NMR spectra of the zeolite Na-ADOR NMR spectra of the zeolite Na-A

Three signals, one peak with shoulder and another well-resolved peak can be found in the DOR spectrum of zeolite Na-A in the field of 17.6 T. This corresponds to three different SiOAl bond angles. Intensities were obtained n a direct fit of the center line of the DOR spectrum under the assumption of equal envelope line shapes for the spinning sidebands of all species. The intensities ratio of ca.1:1:2 for sites O-1, O-2, O-3, respectively, is in good agreement with the relative occurrence of the SiOAl bond angles in the X-ray data.

* ** *

*

20 0204060 /ppm

*

*

***

11.7 T

20 0204060 /ppm

17.6 T

Page 29: Harry Pfeifer's NMR experiment in 1951

MAS, MQMAS or DOR?MAS, MQMAS or DOR?MAS, MQMAS or DOR?MAS, MQMAS or DOR?

Signal-to-noise ratios of AlPO4-14 and andalusite spectra. The ratios of the experimentally obtained spectra were recalculated, in order to base all values to the same acquisition time of 10 h. The acquisition time is the product of repetition time and number of scans for MAS and DOR, whereas for the 2D experiments the number of experiments is included.

The numbers listed in the table show the large differences between the techniques. As example, we have for AlPO4-14 at 9.4 T the values 4740 and 56 for MAS and 5QMAS, respectively. It means that we need the (4740/56)2-fold acquisition time, in order to get an identical signal-to-noise ratio of the 5QMAS DFS spectrum compared to the MAS spectrum. It is well-known that 5QMAS takes the four-fold acquisition time as 3QMAS. The high signal-to-noise ratio of the DOR experiments compared with the 3QMAS techniques is remarkable. From this point of view, the combination of DOR with MAS and simulation of the MAS spectra seems to be the most effective procedure. Particularly for amorphous materials or other samples with a large distribution of isotropic values of the chemical shift, MQMAS experiments should be favored.

MAS DOR 3QMAS DFS 5QMAS DFS

AlPO4-14 at 17.6 T 4222 2791 149 75

AlPO4-14 at 9.4 T 4740 2782 114 56

andalusite at 17.6 T 555 615 197

andalusite at 9.4 T 569 635 129

Page 30: Harry Pfeifer's NMR experiment in 1951

I acknowledge support from

Özlen ErdemHorst Ernst

Johanna KanellopoulosBernd Knorr

Thomas Loeser Dieter Michel

Lutz MoschkowitzUlf Pingel

Ekaterina RomanovaDagmar Prager

Daniel Prochnow Ago Samoson

Denis Schneider

Deutsche ForschungsgemeinschaftMax-Buchner-Stiftung