CPMG: A sensitivity enhanced magic-angle spinning sideband separation experiment for disordered solids

Journal of Magnetic Resonance 221 (2012) 103–109

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MATPASS/CPMG: A sensitivity enhanced magic-angle spinning sideband separation experiment for disordered solids Ivan Hung a, Trenton Edwards b, Sabyasachi Sen b, Zhehong Gan a,⇑ a b

Center of Interdisciplinary Magnetic Resonance, National High Magnetic Field Laboratory, 1800 East Paul Dirac Drive, Tallahassee, FL 32310, USA Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616, USA

a r t i c l e

i n f o

Article history: Received 6 April 2012 Revised 17 May 2012 Available online 29 May 2012 Keywords: Chemical shift anisotropy (CSA) Magic-angle turning (MAT) Phase-adjusted spinning sidebands (PASS) CPMG Magic-angle spinning (MAS) GeSe4 glass 77 Se

a b s t r a c t A Carr–Purcell Meiboom–Gill (CPMG) sensitivity-enhanced spinning sideband separation experiment is presented. The experiment combines the idea of magic-angle turning and phase-adjusted sideband separation (MATPASS), allowing for isotropic/anisotropic chemical shift separation of disordered solids with line widths far greater than the magic-angle spinning frequency. The use of CPMG enhances the sensitivity of the wide-line spectra by an order of magnitude via multiple-echo acquisition. The MATPASS/CPMG protocol involves acquisition of time-domain data using a MAT/CPMG pulse sequence followed by f1 p shearing during data processing to arrive at the PASS representation. Such a protocol has 2 higher sensitivity than the conventional PASS method because all CPMG echo signals are used for the final PASS spectrum. Application of this method is demonstrated using a GeSe4 glass sample with both 77Se isotropic line widths and chemical shift anisotropy that far exceed the spinning frequency. The sideband separation allows for the measurement of chemical shift anisotropy of the disordered solids. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction

suppression (TOSS) experiment uses a sequence of specifically timed

p-pulses such that the intensities of all ssbs cancel to yield a specResolution and sensitivity are of paramount importance to NMR spectroscopy. For powdered samples, orientation-dependent spin interactions and the distribution of isotropic chemical and quadrupolar shifts in amorphous and disordered systems are usually the dominant sources of line broadening, rather than T2 relaxation. Magic-angle spinning (MAS) can effectively average out second-rank anisotropic broadenings like chemical shift anisotropy (CSA) and significantly reduce higher-rank broadenings like second-order quadrupolar broadening. However, a complete averaging of CSA requires the sample spinning frequency to be greater than the breadth of the anisotropy. For insufficiently fast sample spinning, modulation from the anisotropic interaction gives rise to spinning sidebands (ssbs) that can degrade spectral resolution. In extreme cases with isotropic line widths larger than practically achievable spinning frequencies, MAS alone would not result in any resolution enhancement over static samples due to the overlap among neighboring ssbs. The issue of spinning sidebands, especially at high magnetic fields, has been one of the main driving forces behind the development of fast magic-angle spinners, but the higher speeds usually come at the cost of reduced rotor size and sample volume. At the same time, various pulse sequence methods have been developed, to tackle the ssbs problem from a different angle. The total sideband ⇑ Corresponding author. Fax: +1 850 644 1366. E-mail address: [email protected] (Z. Gan). 1090-7807/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2012.05.013

trum with only the center-band peaks for a powder sample [1]. TOSS works well when only one or two pairs of ssbs are present, otherwise significant loss of signal intensity is observed. The phase-adjusted spinning sidebands (PASS) experiment separates ssbs into a 2D spectrum by their sideband order, from which a quantitative ssb-free isotropic projection can be reconstructed even with spinning frequencies much lower than the anisotropy [2,3]. The separated ssbs also allow for determination of CSA parameters from the intensity of ssb manifolds. As an alternative to continuous sample spinning, the magic-angle hopping (MAH) experiment [4] uses three 120° discrete sample hops about the magic-angle to completely average out CSA. This innovative method yields isotropic spectra along an indirect dimension without any ssbs. However, its application has been limited by the mechanically-demanding hopping system and the signal loss from the three projection-storage periods of the 2D experiment. The first limitation can be overcome with slow continuous spinning or, so-called magic-angle turning (MAT) [5]. By using three evolution segments, each separated in time by 1/3 of a rotor period, isotropic spectra such as those from MAH can be obtained regardless of how slow the sample spinning is. In the case of faster spinning with 1/mr > T2, the signal loss from the three projection-storage periods can be avoided using the 5-p MAT pulse sequence [6]. A comparison of 5-p MAT with the 5-p version of the PASS pulse sequence reveals striking similarities. Both sequences use five p-pulses spread over one rotor period (sr), and have the same

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phase cycling schemes and coherence transfer pathways. The two experiments differ only in their pulse timings. It was realized recently that the two experiments, which have developed and evolved independently, are closely related to each other [7]. MAT and PASS respectively encode only the isotropic and anisotropic parts of the chemical shift in t1. Hence, the data resulting from the two experiments are related merely by a time shift in t2 signal acquisition. A combined MATPASS experiment can take the advantage of less t1increments and straightforward data processing from PASS and easy implementation from MAT to separate the isotropic and anisotropic parts of the CSA [7]. This revelation also lead to the implementation of the efficient PASS method with the projection-type MAT experiment. The exclusive use of short projection pulses can cover a bandwidth of up to 1 MHz, as demonstrated recently by the 7Li and 31P isotropic spectra of paramagnetic lithium-ion battery materials at high magnetic fields [8]. This contribution aims to enhance the sensitivity of MAT and PASS experiments using Carr–Purcell Meiboom–Gill (CPMG) multiple-echo acquisition [9,10]. The combined experiments will be particularly useful for disordered solids with large isotropic line widths and CSA, and long T2 relaxation times. For examples, glasses with high-Z nuclei, such as 77Se [11,12], 125Te [13] and 207Pb [14,15] often exhibit isotropic line widths and CSA, which may each span over hundreds of kHz; beyond the fastest MAS rates currently available (vide infra). The CPMG sequence can generate over a hundred echoes and increase the sensitivity of MAT and PASS experiments by 1–2 orders of magnitude. The concatenation of CPMG with MAT has already been introduced and demonstrated [16–18], but not yet with the PASS experiment which can significantly reduce the required number of t1 increments, and simplify the data processing and spectral representation. However, adding CPMG to PASS is faced with a particular problem that can be described briefly here using coherence transfer pathways. For the PASS experiment, there are two coherence pathways which alternate between p = +1 M 1 due to the p-pulses. The timing of the PASS pulse sequence is designed for the pathway ending with p = 1 for signal detection. The other pathway, that ends with p = +1 (referred to here as the ‘mirror’ pathway), does not contribute to the signal. However, when CPMG is applied, the mirror pathway is re-introduced into the detected signal by the refocusing pulses and contributes to half of the CPMG echo signal. A complication hence arises because the mirror pathway does not satisfy the PASS condition. Thus, half of the CPMG echoes cannot be used for the final PASS spectrum. In the following, a brief theory is presented describing the PASS and MAT experiments, as well as the aforementioned problem with the mirror pathway. The theory will show that this problem does not occur with the MAT experiment and all CPMG multiple-echo signals from both pathways can be used. Considering that PASS and MAT data are related only by a time shift in t2, a so-called MATPASS/CPMG protocol is proposed. This protocol involves acquisition of MAT/CPMG data with t1 evolution spanning only one rotor period, followed by a t1-proportional first-order phase correction applied during f2 data processing, which effectively transforms the MAT data into a PASS representation. The p MATPASS/CPMG protocol yields spectra that have 2 higher signalto-noise ratios (S/N) than the PASS/CPMG experiment because all CPMG echoes are used for the final PASS spectrum. The sensitivity enhanced sideband separation experiment is demonstrated with a sample of GeSe4 glass to obtain isotropic chemical shift spectra and sideband manifolds for CSA measurement.

2. Experimental The GeSe4 glass sample was synthesized in a 10 g batch by melting mixtures of the constituent elements Ge and Se with P99.995% purity (metals basis) in an evacuated (106 Torr)

and flame sealed fused silica ampoule (8 mm ID, 11 mm OD) at 1200 K for 24 h in a rocking furnace. The ampoule was quenched in water and subsequently annealed for 1 h at 433 K. A 19.6 T (830 MHz) narrow bore magnet equipped with a Bruker DRX console was used to acquire 77Se NMR spectra at 158.8 MHz. A single-resonance home-built probe using a 4.0 mm Samoson MAS stator was used for all measurements with 10 kHz MAS frequency, 125 kHz rf field, p/2- and p-pulses of 2.0 and 4.0 ls and a 60 s recycle delay. Hypercomplex t1 acquisition of 2D spectra was achieved by applying the method of States et al. [19] to the CPMG phases u6 and uR. For each 2D experiment, 16 hypercomplex t1 points were acquired, with 96 transients per point and 64 CPMG echoes per transient, in 51 h. Spectra were externally referenced to neat (CH3)2Se at 23 °C by setting the 77Se resonance of a saturated H2SeO3 aqueous solution to diso = 1282 ppm [20]. 3. Results and discussion 3.1. The MAT and PASS experiments The MAT and PASS experiments manipulate the t1 evolution using p-pulses to alternate between the p = +1 and 1 coherence orders, ending with p = 1 for signal detection. The timings of the pulses are designed to encode only the isotropic portion xiso for MAT, or the MAS-modulated anisotropic portion xCSA(t) of the chemical shift for PASS,

xðtÞ ¼ xiso þ xCSA ðtÞ; xCSA ðtÞ ¼

X

xm expðimxr tÞ:

ð1Þ

m¼1;2

For the MAT experiment, the pulse sequence in Fig. 1a shows that the three p = +1 segments have equal lengths and are 120° apart in term of rotor position. The sum of three such evolution segments averages out the l = 2 rank CSA. The CSA evolution for the three p = 1 segments also satisfy this MAT condition. Therefore, only the isotropic part of the chemical shift (xiso) contributes to t1 evolution. The time increment of the three pulses that follow the blue trajectories in Fig. 1a yields a net difference equal to t1 in the durations between the p = +1 and 1 segments. Considering that xiso is not modulated by sample rotation, the t1 evolution then encodes only the isotropic chemical shift by xisot1. Thus, the 2D MAT signal can be expressed as,

   Z t2 expðixiso t 1 Þ exp ixiso t 2  i xCSA ðtÞdt 0 X sk expðixiso t 1 Þ expðixiso t2 þ ikxr t2 Þ ¼

sMAT ðt1 ; t 2 Þ ¼

k

ð2Þ Here h i denotes a powder average. The time evolution from the CSA is periodic giving rise to spinning sidebands with intensity sk in f2 where k is the spinning sideband order.

/CSA ðt 2 Þ ¼

Z

t2

xCSA ðtÞdt; hexp½i/CSA ðt2 Þi ¼

0

X sk expðikxr t2 Þ

ð3Þ

k

On the contrary, the PASS experiment is designed to select the CSA during t1. The timing of the p-pulses is designed to satisfy two conditions. The first condition ensures a null isotropic shift evolution by making the total durations of the p = +1 and 1 evolution segments equal, n X ð1Þnþq ðhqþ1  hq Þ ¼ 0

ð4Þ

q¼0

Here hq = xr  tq (q = 1 to n) describes the pulse timings in terms of rotor position, while h0 and hn+1 denote the beginning and end of

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(a)

t1/6

+t1

(b)

+t1

0 −t1

0

b·τr

φ1

c

d

c

φ2 φ1

d

c

φ2 φ1

d

φ2

φ1

+1 −1

p=0

b·τr

p=0

−b·τr

0

a·τr

φ2

φ1

φ2

φ1

−b·τr

0

a·τr

(c) b·τr

b·τr c

d

c

φ2 φ1

φ1 −b·τr

d

φ2 φ1

c

φ2

+1 −1

b·τr

b·τr

M

b·τr

d

φ2

0

a·τr

φR

φ6 (a + 2b)τr

φR

φ6 (a + 4b)τr

Fig. 1. Pulse sequences and coherence transfer diagrams for the (a) MAT, (b) PASS and (c) MAT/CPMG experiments. Half- and full-length bars represent p/2- and p-pulses, respectively. MAT pulse sequence parameters: c = (a  sr  t1)/6, d = (asr + t1)/6, DW1 = sr/(2NP1) where a – 3n is an positive integer and NP1 is the number of t1 increments. The PASS inter-pulse delays follow non-linear patterns as described in Ref. [3]. In (c), the CPMG pulses are rotor synchronized with a cycle time of 4b  sr (b is a positive integer). The insertion of b  sr before the MAT allows for rotor synchronized whole-echo acquisition in the middle of the CPMG window. Cogwheel phase cycling [22,23] minimizes the cycle length necessary to select the desired coherence transfer pathways (solid-black line  echo, dashed-red line  anti-echo) with u1 = 0, u2 = k2p/12, uR = k  p, k = 0, 1, . . ., 11 for both MAT and PASS and u6 = p/2, uR = 0 for CPMG. Hypercomplex MAT/CPMG data is acquired by applying the method of States et al. [19] on u6 and uR. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

the t1 evolution period. The second PASS condition makes the net evolution during t1 equivalent to a continuous CSA evolution prior to t2 acquisition,

Z n X ½ð1Þnþq

hqþ1 =xr

xCSA ðtÞdt ¼

hq =xr

q¼0

Z

hnþ1 =xr

xCSA ðtÞdt

ð5Þ

ðhnþ1 =xr Þt 1

This condition leads to a set of non-linear equations when the coefficients of xm are equated after insertion of Eq. (1) into Eq. (5), n X ð1Þnþq ½expðimhqþ1 Þ  expðimhq Þ q¼0

¼ expðimhnþ1 Þ  exp½imðhnþ1  xr t 1 Þ

ð6Þ

For second-rank CSA, there are a total of five equations available with m = ±1, ±2 plus Eq. (4). If the total evolution time is fixed to one rotor period (sr), i.e., h0 = 0 and hn+1 = 2p, then the five equations require a minimum of 5 p-pulses to satisfy the PASS condition. Solutions can indeed be found as depicted in Fig. 1b. The PASS conditions lead to the following expression for the signal

  Z sPASS ðt 1 ;t 2 Þ¼ exp i

0

t

¼





xCSA ðtÞdt exp ixiso t2 i

1 X sk expðikxr t1 Þexpðixiso t2 þikxr t 2 Þ

Z

t2

xCSA ðtÞdt



0

ment combines advantages from both experiments: the few t1 increments (spanning only one rotor period sr) and straightforward data processing of PASS, and the convenient linear inter-pulse delays of MAT. It also has been shown that MAT averages rf offset effects in the first-order, leading to lesser artifacts than PASS [24]. Due to the t1-dependent delay of sad, the MATPASS experiment is no longer of ‘constant-time’ and may be subject to relaxation effects for samples with short T2s. The constant-time was a main consideration when the PASS experiment was originally designed under slow MAS conditions. The total MATPASS evolution time spans less then a rotor period. With increasing MAS frequencies, the rotor period gets shorter in comparison with T2, reducing the relaxation effects. Significant deleterious effects due to T2 relaxation have not been observed so far under fast MAS condition, even for paramagnetic samples with very short T2s [8]. The signals for samples with large inhomogeneous broadening are characterized by short T 2 relaxation times, allowing full echo acquisition within the CPMG window (2bsr) with little truncation. For full echo signals, the time shift in t2 required to turn MAT to PASS can be carried out during data processing by applying a t1proportional first-order phase correction in the mixed time-frequency domain (t1, f2) as shown in Fig. 2c and d.

sPASS ðt1 ; f2 Þ ¼ sMAT ðt 1 ; f2 Þ expði2p  f2 t 1 Þ

ð9Þ

k

ð7Þ The result shows that if the t1 evolution spans exactly one rotor period sr, then a Fourier transform in t1 separates the ssbs according to their order. This is the essence of the PASS experiment. More detailed theory of various PASS schemes and solutions can be found in the literature [3,21] and will not be described further here. 3.2. The MATPASS principle The MAT and PASS signals in Eqs. (2) and (7) show only a difference in the selection during t1 of either the isotropic shift (MAT) or the CSA (PASS), respectively. The two signals are related through a shift of the t2 acquisition by a time t1 (i.e., t2 ? t2  t1),

sPASS ðt 1 ; t2 Þ ¼ sMAT ðt1 ; t 2  t 1 Þ

ð8Þ

Thus, a delay of acquisition sad by t1 can change MAT time-domain data into PASS data (Fig. 2a and b). The resulting MATPASS experi-

This phase correction is, of course, analogous to the t1-proportional delay of signal acquisition, since the two operations are related by Fourier transformation. It should be noted that such a procedure can by applied only for full echo signals without causing artifacts. Fig. 2 shows the relation between MAT and PASS during various stages of the 2D data processing. The GeSe4 glass sample used here represents a special case, where the distribution in isotropic shifts is large enough to cause the signal intensity to decay almost completely at relatively short t1 delays (Fig. 2a). Hence, the spectra in both the MAT and PASS representations (Fig. 2e and f) show no sign of truncation although t1 values span only one rotor period. Fig. s1 of the Supplementary Information shows a similar comparison for a half-integer quadrupolar nuclide, 71Ga. In that case, the secondorder quadrupolar interaction contains anisotropic terms of rank up to l = 4, which requires five evolution segments for MAT [25], and more terms (m = ±1, ±2, ±3, ±4) to solve the PASS equations [26,27]. The MAT and PASS experiments for quadrupolar nuclei are essentially the same as for spin-1/2 nuclei, except for their

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PASS

MAT +t1

(a)

+t1 −t1 delayed acquisition

0

0

s(t1,t2)

−t1

(b)

s(t1,t2)

−t1

t2

t2

FT(t2) +t1

FT(t2)

(c) t1-proportional first-order phase correction

0

s(t1,f2)

−t1 1000

500

+t1

(d)

0

s(t1,f2)

−t1

f2 /ppm

1000

FT(t1) f1 /νr −4

f1 /νr −4 f1 shear transform

0

1000

500

f2 /ppm

FT(t1)

(e)

+4 MAT representation

500

(f )

0 +4 PASS representation

s(f1,f2) f2 /ppm

f1 /νr −4

1000

500

s(f1,f2) f2 /ppm

f2 shear transform

(g)

0 +4 isotropic representation 1000

500

s(f1,f2) f2 /ppm

Fig. 2. MAT and PASS data in the (a and b) time domain, (c and d) mixed time-frequency domain and (e and f) frequency domain during the various stages of data processing. (g) Isotropic representation showing isotropic and anisotropic chemical shifts along the f2 and f1 axes, respectively.

use of nine p-pulses instead of five. The main purpose of referring to the 71Ga results is to show the advantages of the PASS representation when the isotropic shift evolution in t1 exceeds one rotor period, which is expected to be a more typical case. With t1 evolution spanning only one rotor period, the MAT representation shows severe truncation artifacts in f1 (Fig. s1). These artifacts completely disappear in the PASS representation. The t1 increments for the PASS representation are only required to span one rotor period regardless of how long the signal lasts in t1. In PASS spectra, the f2 axis represents both the isotropic and anisotropic chemical shift. An additional shearing along f2 can be applied to separate the isotropic (f1) and the anisotropic (f2) part of the chemical shift along the two axes. Fig. 2g shows such a spectrum of GeSe4 glass sample in the isotropic representation. The isotropic representation is particularly useful for spectral analysis of

the full 2D spectrum because of the complete isolation between the isotropic and anisotropic parts of the chemical shift. 3.3. MATPASS/CPMG The CPMG pulse sequence can be appended to the MAT and PASS sequences, as shown in Fig. 1c, to repeatedly refocus signal decay from inhomogeneous broadening, T 2 . The refocusing generates a train of echoes of identical signals with an intensity decay characteristic of T2 relaxation, which can be summed for sensitivity enhancement. When CPMG is applied with the MAT or PASS experiments, only the component of the phase-modulated signal parallel to the refocusing pulse phase is retained. The orthogonal component dephases rapidly due to rf field inhomogeneity and is usually cancelled out by alternation of the refocusing pulse phase. To fully

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recover the phase information encoded during the t1 evolution, it is necessary to acquire both components separately by applying a 90° phase shift to the refocusing pulses and receiver, as in the method of States et al. [19]. The parallel and orthogonal components are denoted here as cosine (C) and sine (S), respectively. For the MAT experiment, the two components of the signal from Eq. (2) can be expressed as

   Z t2 cosðxiso t 1 Þ exp ixiso t2  i xCSA ðtÞdt 0    Z t2 ¼ sinðxiso t 1 Þ exp ixiso t 2  i xCSA ðtÞdt

MAT

PASS

(a) echo

(c) echo

C MAT ¼ SMAT

ð10Þ

f1 /νr (b) anti-echo −4

(d) anti-echo

0

In the context of coherence transfer pathways, the two components are simply the sum and difference of the signals from the two ‘mirror’ image pathways. Phase-modulated data can be reconstructed for each of the mirror pathways individually to form the so-called echo (E) and anti-echo (AE) signals,

  Z t2 E ¼C  iS ¼ exp ixiso t1  ixiso t 2  i xCSA ðtÞdt 0    Z t2 MAT MAT MAT ¼C þ iS ¼ exp þixiso t1  ixiso t 2  i xCSA ðtÞdt AE 0

ð11Þ Note that in the case of MAT, the anti-echo signal is related to the echo signal by a reversal of t1, or the f1 axis. Hence, both the echo and anti-echo signals can be time-shifted (or f1-sheared) accordingly to obtain two symmetrical PASS spectra, as shown in Fig. 3a and b, which can be added together after inversion with respect to the f1 = 0 axis. The procedure described above separating echo and anti-echo then co-adding them is for explanation purpose and comparison with the PASS experiment. In reality, the amplitude modulated 2D data is processed following the conventional method of States et al. [19]. A large first-order phase correction needs be applied along f2 for the whole echo signal. In contrast, when CPMG is appended to PASS, the cosine and sine components of the signal from Eq. (7) are

C PASS

 Z ¼ cos

SPASS ¼



sin

Z



 Z xCSA ðtÞdt exp ixiso t2  i

0

+4 1000



MAT

MAT

MAT

0

t 1



0



xCSA ðtÞdt exp ixiso t2  i

Z

t2

xCSA ðtÞdt

0 t2

xCSA ðtÞdt



500

f2 /ppm

Fig. 3. 77Se 2D PASS spectra of GeSe4 glass obtained from the echo and anti-echo signals of MAT/CPMG (a and b) and PASS/CPMG (c and d) pulse sequences. For MAT, the echo and anti-echo spectra are mirror images (with respect to f1 = 0) of each other. For PASS, the anti-echo spectrum is distorted because the signal in Eq. (13) does not satisfy the PASS equations exactly.

(a) MAS

νr

(b) isotropic projection

f1 /νr

480

420

(c)

−3



0

t 1

ð12Þ

0

and the corresponding echo and anti-echo signals become EPASS ¼ C PASS  iS AE

PASS

¼C

PASS

PASS

þ iS

 ¼

PASS

 Z exp ixiso t 2  i

 ¼



exp ixiso t 2 þ i

t2

xCSA ðtÞdt



t1

Z

0

t1

xCSA ðtÞdt  i

Z

t2

xCSA ðtÞdt



+3

0

ð13Þ PASS

The echo signal E is identical to Eq. (7) for the PASS experiment with the corresponding spectrum shown in Fig. 3c, but the antiecho signal AEPASS describes a non-functional combination of t1 and t2 CSA evolution. In other words, the anti-echo signal does not satisfy the PASS condition and gives a distorted mirror image (Fig. 3d) of the correct PASS spectrum (Fig. 3c). Thus, only half of the CPMG echo train can be used for the final PASS spectrum, leadp ing to a 1/ 2 loss in sensitivity. Since MAT and PASS are closely related to each other (Eq. (8)) and can be inter-converted during either signal acquisition or data processing, this signal loss can be avoided by acquiring data in MAT/CPMG format and then converting them into the PASS representation via data processing, as dep scribed in the previous section, to avoid the 1/ 2 loss. This is the main idea of this work.

1200

600

0 f2 /ppm

Fig. 4. (a) 1D 77Se MAS/CPMG spectrum, (b) isotropic f2-sheared sum-projection and (c) 2D MATPASS/CPMG spectrum of a GeSe4 glass sample. Top and bottom traces were obtained, respectively, with and without summation of the CPMG echoes prior to data processing. The inset shows an expansion of the baseline region of the isotropic spectrum in spikelet format.

3.4. Summed-echo vs. spikelet spectra The CPMG pulse sequence generates a train of echoes that can be summed for sensitivity enhancement. Yet, a popular way of processing CPMG data is by direct Fourier transformation of the echo train. The periodic echo signal yields ‘spikelet’ spectra similar to

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(a) E(t1 = 0, t2)

(b)

AE(t1 = 0, t2)

0

1.5

t2 /ms

3.0

(c) E

480

420

AE

480

420

(d)

1200

600

0 f2 /ppm

Fig. 5. (a) Echo (E) and (b) anti-echo (AE) 77Se time domain signals for a GeSe4 glass sample obtained using the PASS/CPMG pulse sequence. Isotropic f2-sheared spectra from the (c) echo and (d) anti-echo signals. Insets show expansions of the baseline regions of (c) and (d), demonstrating the appearance of half-interval peaks from the time domain echo-modulations.

spinning sidebands. The concentration of intensities into sharp peaks effectively enhances the sensitivity. However, it should be noted that the spikelets are always centered with respect to the carrier frequency and are spaced by the inverse of the echo window time, therefore the individual spikelet positions contain no spectroscopic information [28]. Fig. 4a shows the 77Se MAS/CPMG NMR spectra of a GeSe4 glass sample presented both in echo-sum (top traces) and spikelet (bottom traces) formats, which provide essentially the same information [18,29]. Fig. 4b and c also shows the 2D MATPASS/CPMG spectra and their isotropic projections in both formats without any problems or artifacts. The result demonstrates the usefulness of sideband separation with a GeSe4 glass sample for which the 1D MAS spectrum exhibits a broad pattern 160 kHz in breadth without sufficient features to fully discern the number of Se sites (Fig. 4a). The 2D spectrum (Fig. 4c) shows that the broad signal is actually composed of numerous ssbs which overlap each other substantially. A shear in f2 can be performed to align all the sidebands, which can be summed up to obtain an isotropic projection equivalent to that obtained with infinite spinning speed. The projection shows primarily two resonances with line widths of approximately 32 and 46 kHz, respectively, both far exceeding the 10 kHz MAS rate employed (Fig. 4b). Importantly, the isotropic projection from summing all the ssbs retains the quantitative nature of NMR spectra, while the separated ssbs allows extraction of CSA information at each isotropic frequency. Both of which are useful for structural characterization of amorphous samples, as has been shown using 207Pb PASS NMR for a series of lead-containing glass samples [14,15]. In-depth analysis of the 77Se NMR spectra for GeSe4 and other GexSe100x samples will be presented elsewhere.

For the PASS/CPMG experiment, the spikelet format presents a particular problem, as illustrated in Fig. 5. The problem originates from the fact that only the echo-signal gives rise to the correct PASS spectrum. The time-domain signals in Fig. 5a and b shows the typical CPMG echo modulation for the echo and anti-echo pathways when they are separated. The echo signal has more intensity in odd echoes (Fig. 5a), while the anti-echo signal has more intensity in even echoes (Fig. 5b). The modulation quickly decays as the echoes progress because the effect of non-ideal ppulses accumulates. The modulation does not have any effect on the spectra if the echoes are summed. However, in the frequency spikelet format, the echo modulation introduces additional spikelets at ‘half-intervals’ (Fig. 5c and d, insets) because of the echo modulation of every two CPMG cycles. These half-interval spikelets have opposite signs in the echo and anti-echo spectra and are broader because of the fast decay of the echo modulation. In principle, summing the spikelet spectra from the echo and anti-echo signals cancels the half-interval spikelets. However, in the case of the PASS/CPMG experiment, the spectra from the anti-echo signal are distorted and only the echo signal gives rise to correct PASS spectra. This is evidenced by the isotropic projection from the anti-echo signal (Fig. 5d), which shows a large discrepancy compared to the expected isotropic projection in Fig. 4b in addition to the inverted half-interval spikelets. Thus, in addition to the 1/ p 2 loss, the PASS/CPMG experiment exhibits half-interval spikelets when presented in spikelet format due to exclusion of the anti-echo pathway. 4. Conclusion It has been shown that the proposed MATPASS/CPMG sideband separation experiment is useful for disordered systems such as GeSe glasses, which have large CSA and isotropic line widths beyond available MAS frequencies. These glass systems tend to have long T2 relaxation times such that a large number of echoes can be acquired using CPMG for sensitivity gain. The MATPASS/CPMG protocol allows for efficient acquisition of 2D isotropic vs. anisotropic spectra. The method has the advantages of few t1 increments, simple data processing and clear data presentation. In particular, the signal loss of PASS/CPMG is avoided and all signals from multiple-echo acquisition can be used, yielding maximum sensitivity gain. This protocol can also be extended to the projection-type MAT experiment (see Supplementary Information) by trading some signal loss from the projection/storage periods with a broader excitation bandwidth for samples with even larger anisotropy or at higher magnetic fields. Acknowledgments We would like to thank Prof. Philip J. Grandinetti and Dr. Krishna K. Dey for bringing our attention to PASS/CPMG. This work was supported by the National High Magnetic Field Laboratory through National Science Foundation Cooperative Agreement (DMR0084173) and by the State of Florida. S. Sen and T. Edwards were supported by the National Science Foundation grant DMR1104869. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jmr.2012.05.013. References [1] W.T. Dixon, Spinning-sideband-free NMR-spectra, J. Magn. Reson. 44 (1981) 220–223.

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