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Frequency-stepped acquisition in nuclear magnetic resonance spectroscopy under magic angle spinning
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10.1063/1.4795001
/content/aip/journal/jcp/138/11/10.1063/1.4795001
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/11/10.1063/1.4795001
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Figures

Image of FIG. 1.
FIG. 1.

Simulations illustrating the method of frequency stepping under static conditions. The reference spectrum is shown in (a). Frequency stepping was performed using a spin-echo pulse sequence of the form 90°(y) − τ − 180°(x) − τ, with EXORCYCLE 45 applied to the second pulse, in which the RF field of the pulses was 200 kHz, and τ was 50 μs. The eleven sub-spectra shown in (b) were simulated with the RF carrier frequency being varied from −1000 to +1000 kHz in steps of 200 kHz, and were summed to give the sum-spectrum in (c). The intensity of the sum spectrum is scaled by a factor of 1.30 due to the overlap between the sub-spectra of the neighbouring steps. The arrows on the spectrum in (c) indicate the positions of the carrier frequency for each experiment; those labelled (i)–(n) correspond to the experiments in which part of the resonance was excited. The degree of excitation as a function of (αPL, βPL) is shown for each with a spherical intensity plot. Each point on the surface of the sphere corresponds to the orientation of a particular crystallite with Euler angles (αPL, βPL), and the axis labels (x, y, z) are the spatial Cartesian coordinates corresponding to these Euler angles, and do not refer to the axis of the magnetization. The colour of each point on the surface gives the size of the x-magnetization that is generated for each orientation (the y-magnetization is zero in all cases). Below is the plot indicating the total excitation for the sum of all the spheres (i)–(n). The shift tensor parameters are: ω0δiso/2π = 0, ω0Δδ/2π = +500 kHz, and η = 0.3.

Image of FIG. 2.
FIG. 2.

Illustration of the effect of γPR averaging on conventional and single-sideband-selective excitation MAS spectra. In (a) are shown six simulated single-crystallite spectra acquired after non-selective excitation. The spectra correspond to a particular carousel in which γPR ranges in steps of 60° from 0° to 300°. Below is shown the spectrum of the whole carousel acquired with γPR averaging in which all the sidebands have the same phase (labelled “average”). The corresponding spectra recorded after selective excitation of the centreband (highlighted with the grey, dashed line) are shown in (b). In this case, the result of averaging over γPR, as shown in the spectrum labelled “average,” is that only the irradiated sideband is observed, with the intensities of the others summing to zero. The SA is 160 kHz, with an asymmetry parameter of 0.85, and (αPR, βPR) = (0°, 20°). The rate of MAS is 60 kHz. Selective excitation of the centreband was achieved with a 2 kHz pulse of duration 250 μs (nominal flip angle 180°) which was optimized to give the maximum transverse magnetization. The average over γPR was computed with 200 γPR angles.

Image of FIG. 3.
FIG. 3.

Simulation of single-sideband-selective frequency stepping. Shown in (a) are the 32 sub-spectra that were simulated using a single excitation pulse of length 125 μs for three nominal flip angles of 90°, 50°, and 10°. The nominal flip angle was varied by scaling the RF field, which took the values 2.00, 1.11, and 0.22 kHz, respectively. The spectra formed by summing the sub-spectra are shown in (b) with the reference spectrum that was simulated with non-selective excitation. The differences between the reference and sum spectra are illustrated in (c) which shows the difference spectra (sum spectrum−scaled reference spectrum) for each case. Note that the vertical scale in these three plots is expanded by a factor of 8. The orientational variation of excitation efficiency is shown by the sphere plots below each difference spectrum in (d). Each point on the surface of the sphere corresponds to the orientation of a particular carousel with Euler angles (αPR, βPR), and the axis labels (x, y, z) are the spatial Cartesian coordinates corresponding to these Euler angles, and do not refer to the axis of the magnetization. The colour of each point on the surface gives the size of the x-magnetization that is generated overall for each carousel of this orientation on summing the sub-spectra (the y-magnetization is zero in all cases). The calculated expectation values of were normalized by dividing by the greatest value of the scaling factor F c, the values of which are given below each sphere. The normalized expectation values were then summed to give the total percentage excitation obtained with each of the three flip angles. For comparison analytical value of the maximum scaling factor (θ in radians) is also given. The shift tensor parameters are: ω0δiso/2π = 0, ω0Δδ/2π = +500 kHz, and η = 0.3, and the MAS frequency was ωr/2π = 60 kHz.

Image of FIG. 4.
FIG. 4.

Simulations illustrating the method of frequency stepping under ultra-fast MAS conditions. The reference spectrum is shown in (a). Frequency stepping was performed using a spin-echo pulse sequence of the form 90°(y) − τ − 180°(x) − τ, with EXORCYCLE applied to the second pulse, in which the RF field of the pulses was 200 kHz, and τ was 48.75 μs (so that the sum of τ and half the 180° pulse length was three rotor periods.) The eleven sub-spectra shown in (b) were simulated with the RF carrier frequency being varied from −900 to +900 kHz in steps of 180 kHz (every three sidebands), and were summed to give the sum-spectrum in (c). The intensity of the sum spectrum is scaled by a factor of 1.45 due to the overlap between the sub-spectra of the neighbouring steps. The arrows on the spectrum in (c) indicate the positions of the carrier frequency for each experiment; those labelled (i)–(n) correspond to the experiments in which part of the resonance was excited. The differences between the reference and sum spectra are illustrated in (d) which shows the difference spectrum (sum spectrum−scaled reference spectrum). Note that the vertical scale in this plot is expanded by a factor of 8. The degree of excitation as a function of (αPL, βPL) is shown for each with a spherical intensity plot, which shows the x-magnetization generated for each orientation (the y-magnetization was zero for all cases). Below is the plot indicating the total excitation for the sum of all the spheres (i)–(n). The shift tensor parameters are: ω0δiso/2π = 0, ω0Δδ/2π = +500 kHz, and η = 0.3, and ωr/2π = 60 kHz.

Image of FIG. 5.
FIG. 5.

Comparison of conventional and frequency-stepped 7Li NMR spectra of LiMnPO4. All spectra were acquired at a Larmor frequency of −388.9 MHz and 60 kHz MAS. Shown in (a) are 29 sub-spectra that were acquired with a 50 μs single-sideband-selective pulse of constant amplitude of 5 kHz RF field. The carrier frequency was stepped by 60 kHz so that each sideband was irradiated in turn. The corresponding sum spectrum is shown in (b). Frequency stepping was also carried out with a spin-echo sequence at 200 kHz RF field, and 15.42 μs spin echo delay, in which the carrier frequency was stepped by 180 kHz (every three sidebands) relative to the centreband. The sub-spectra are shown in (d), with the position of the carrier indicated by a grey arrow, which were summed to give the spectrum in (e). Also shown for comparison is the reference spectrum in (c) that was acquired with a double-adiabatic-echo using tanh/tan adiabatic pulses of length 50 μs and 5 MHz sweep width. The RF field for all the pulses for the reference spectrum was 400 kHz.

Image of FIG. 6.
FIG. 6.

Comparison of conventional and frequency-stepped 31P NMR spectra of LiMnPO4. All spectra were acquired at a Larmor frequency of −202.5 MHz and 60 kHz MAS. Shown in (a) are 11 sub-spectra that were acquired with a 25 μs single-sideband-selective pulse of constant amplitude of 10 kHz RF field. The carrier frequency was stepped by 60 kHz so that each sideband was irradiated in turn. The corresponding sum spectrum is shown in (b). The reference spectrum, which is shown in (c), was acquired with a double-adiabatic-echo using tanh/tan adiabatic pulses of length 50 μs and 5 MHz sweep width. The RF field for all the pulses for the reference spectrum was 360 kHz.

Image of FIG. 7.
FIG. 7.

Comparison of conventional and frequency-stepped 1H NMR spectra of TbCsDPM. All spectra were acquired at a Larmor frequency of −500.1 MHz and 60 kHz MAS. Shown in (a) are 13 sub-spectra that were acquired with a spin-echo sequence at 200 kHz RF field, and 15.42 μs spin-echo delay. The carrier frequency was stepped by 180 kHz (every three sidebands) relative to the centreband, with the position being indicated by a grey arrow in each sub-spectrum. The corresponding sum spectrum is shown in (b). The reference spectrum, which is shown in (c), was acquired with a double-adiabatic-echo using tanh/tan adiabatic pulses of length 50 μs and 5 MHz sweep width. The RF field for all the pulses for the reference spectrum was 500 kHz.

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/content/aip/journal/jcp/138/11/10.1063/1.4795001
2013-03-20
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Frequency-stepped acquisition in nuclear magnetic resonance spectroscopy under magic angle spinning
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/11/10.1063/1.4795001
10.1063/1.4795001
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