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Spin-locking of half-integer quadrupolar nuclei in nuclear magnetic resonance of solids: Second-order quadrupolar and resonance offset effects
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10.1063/1.3263904
/content/aip/journal/jcp/131/19/10.1063/1.3263904
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/19/10.1063/1.3263904
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Figures

Image of FIG. 1.
FIG. 1.

Spin-locking pulse sequences allowing the observation of (a) and and (b) and coherence transfer. The duration, , and radiofrequency field strength, , of the spin-locking pulse are indicated. In each sequence, the duration and field strength of the preparation pulse are optimized for the excitation of the desired coherence order and in (b) the phase is cycled to select the conversion of the desired nQ coherence order back into observable 1Q coherence.

Image of FIG. 2.
FIG. 2.

Simulated NMR spectra showing the positions of the central-transition 1Q (solid), 3Q (dashed), and 5Q (dotted) spin and line shapes for (a) a single crystallite (with ), (b) a static powder, and (c) a powder under MAS. Simulations were performed with and 375 kHz , and .

Image of FIG. 3.
FIG. 3.

Expectation values of spin spherical tensor operators, , created by rapid dephasing of an initial state (a, b) and (c, d) , as a function of , considering (a, c) the first-order and (b, d) the first- and second-order quadrupolar interactions. Tensors with coherence order (p) 0, 1, 2, and 3 are denoted by black, red, blue, and green lines, while tensors with rank (l) 1, 2, and 3 are denoted by solid, dotted, and dashed lines, respectively. Other parameters include , , , and .

Image of FIG. 4.
FIG. 4.

The norm of the spin density operator created by rapid dephasing of an initial state (a) and (b) , as a function of , shown for either a first-order quadrupolar interaction (solid line) or, additionally, a second-order quadrupolar interaction (dashed line). Other parameters are as in Fig. 3.

Image of FIG. 5.
FIG. 5.

Two-dimensional greyscale plot of the expectation values of (a, c) and (b, d) created by rapid dephasing of a spin initial state (a, b) and (c, d) , under a spin-locking Hamiltonian that includes the first- and second-order quadrupolar interactions, as a function of and . Positive signal intensity is shown in white while negative intensity in red. In each case, a cross section through the two-dimensional plot is shown for (dashed line). For comparison, similar cross sections considering the quadrupolar interaction to first order only (solid line) are also shown. Other parameters are as in Fig. 3.

Image of FIG. 6.
FIG. 6.

(a, b) Expectation values of spin spherical tensor operators, , created by rapid dephasing of an initial state , under a spin-locking Hamiltonian that includes the first- and second-order quadrupolar interactions as a function of , with a resonance offset, , of (a) 7382 Hz and (b) −3164 Hz. Tensors with coherence order 0, 1, 2, and 3 are denoted by black, red, blue, and green lines, while tensors with rank (l) 1, 2, and 3 are denoted by solid, dotted, and dashed lines, respectively. (c) Norm, , of the spin density operator, created by rapid dephasing of an initial state , under a spin-locking Hamiltonian that includes either the first- (solid line) or, additionally, the second-order quadrupolar interaction as a function of with of 0 (dotted line), 7382 Hz (dashed line), and −3164 Hz (long-dashed line). Other parameters are as in Fig. 3.

Image of FIG. 7.
FIG. 7.

Expectation values of spin single-element operators, , created by rapid dephasing of initial states (a) , (b) , and (c) as a function of , for Hamiltonians including first- (solid line) and, additionally, second-order (dashed line) quadrupolar interactions. Expectation values for , 3/2, and 5/2 are denoted by black, red, and blue lines, respectively. Other parameters include , , , and .

Image of FIG. 8.
FIG. 8.

Two-dimensional greyscale plot of the spin expectation values of single-element operators, , created by rapid dephasing of initial states , and , under a spin-locking Hamiltonian that includes the first- and second-order quadrupolar interactions, as a function of and . Other parameters are as in Fig. 7.

Image of FIG. 9.
FIG. 9.

Spin-locking of 3Q coherences with an initial state , simulated for a spin static powder using an exact density matrix approach. [(a)–(c)] 3Q amplitude as a function of the duration, , of a spin-locking pulse with (a) first- and (b, c) first- and second-order quadrupolar Hamiltonians included. In each case , , and . In (a, b), and are varied between 12.5 and 200 kHz. In (c), the offset was either 0 (black line) or chosen to match the 1Q (red line), 3Q (green line), or 3Q/3 (blue line) isotropic shift, with , 750, or 250 Hz, respectively, with a fixed of 25 kHz. (d) Average (over ) spin-locked 3Q amplitude as a function of , with , for either first-order (black line) or, additionally, second-order (red line) quadrupolar interactions.

Image of FIG. 10.
FIG. 10.

Experimental (132.3 MHz) NMR of static powdered . (a) Central-transition and signal intensity as a function of the radiofrequency field strength of the spin-locking pulse with . (b) signal intensity as a function of the duration, , of a spin-locking pulse for a variety of field strengths. In (a), the relative intensity of the 3Q-filtered signal has been scaled by an estimated amount to take into account the efficiency of the reconversion pulse.

Image of FIG. 11.
FIG. 11.

Experimental (132.3 MHz) MAS NMR of powdered . Central-transition (solid line) and (dotted line) signal intensity as a function of the spin-locking duration . The relative intensity of 3Q-filtered signal has been scaled by an estimated amount to take into account the efficiency of the reconversion pulse. Spin-locking is performed with and , corresponding to (black line) and and , corresponding to (red line).

Image of FIG. 12.
FIG. 12.

Expectation values of spin spherical tensor operators, , created by rapid dephasing of an initial state, , under a spin-locking Hamiltonian that includes (a) the first-order and (b) first- and second-order quadrupolar interactions, as a function of the rotor phase . The adiabatic approximation has been assumed. Other parameters include , , , , and . Tensors with coherence order 0, 1, 2, and 3 are denoted by black, red, blue, and green lines, while tensors with rank (l) 1, 2, and 3 are denoted by solid, dotted, and dashed lines, respectively.

Image of FIG. 13.
FIG. 13.

Expectation values of spin single-transition operators (black line), (red line), and (blue line), created by rapid dephasing of an initial state , under a spin-locking Hamiltonian that includes (a) the first-order and (b-d) first and second-order quadrupolar interactions, as a function of the rotor phase , for resonance offsets of (a) 0, (b) 0, (c) 3058 Hz (1Q), and (d) −1163 Hz (3Q/3). The adiabatic approximation has been assumed. Other parameters are as in Fig. 12.

Image of FIG. 14.
FIG. 14.

Expectation values of spin single-transition operators (black line), (red line), and (blue line) operators, as a function of the duration of a spin-locking pulse under MAS conditions, simulated using an exact density matrix approach for a powder, including (a) first- and (b-d) first- and second-order quadrupolar interactions. The initial state was . Resonance offsets, , were (a) 0, (b) 0, (c) 1000 Hz (1Q), and (d) −1000 Hz (3Q/3). Other simulation parameters include , , , , and , corresponding to .

Image of FIG. 15.
FIG. 15.

Expectation value of spin single-transition operator simulated for a powder using an exact density matrix approach, plotted as a function of the duration of a spin-locking pulse with first- (black line) and first- and second-order (red, green, and blue lines) quadrupolar Hamiltonians included. The initial state was . Resonance offsets, , are 0 (black and red lines), −250 Hz (green line), or 250 Hz (blue line). Other simulation parameters include , , , , and , corresponding to .

Image of FIG. 16.
FIG. 16.

Experimental (132.3 MHz) MAS NMR of powdered . (a) signal intensity as a function of (a) the duration, , of the spin-locking pulse and (b) the resonance offset . Other experimental conditions include and . In (a), resonance offsets from the chemical shift of −230 Hz (black line) and (red line) were included, while in (b) .

Image of FIG. 17.
FIG. 17.

Expectation values of single-transition operators (a, c) and (b) operators for (a, b) spin and (c) spin , as a function of the radiofrequency field strength of a spin-locking pulse under MAS conditions, simulated using an exact density matrix approach for a powder. The initial state was . Simulations use either a first-order quadrupolar Hamiltonian only (black line) or both first- and second-order Hamiltonians (red, green, and blue lines). Resonance offsets, , in (a, b) of −250 Hz (1Q) and (3Q/3) are shown by the green and blue lines, respectively. Other simulation parameters include , , , , and . Also shown in (a, c) is the corresponding central-transition nutation rate .

Image of FIG. 18.
FIG. 18.

(a) Experimental (132.3 MHz) MAS NMR of powdered . Central-transition (black lines) and (red lines) signal intensity as a function of the radiofrequency field strength of the spin-locking pulse. Resonance offsets, , of −230 Hz from the chemical shift (on resonance with the 1Q signal) and from the chemical shift (3Q/3) were used, denoted by solid lines and dashed lines, respectively. Other experimental conditions include and . The dip in spin-locking efficiency caused by rotary resonance recoupling of dipolar couplings is highlighted by . (b) Expectation values of spin central-transition (black lines) and (red lines) operators as a function of the radiofrequency field strength of a spin-locking pulse under MAS conditions, simulated using an exact density matrix approach for a powder. The initial state was . Both first- and second-order quadrupolar interactions were included, with resonance offsets of 230 Hz (1Q) and (3Q/3) denoted by solid lines and dashed lines, respectively. Other simulation parameters include , , , , and . Also shown is the corresponding central-transition nutation rate, .

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/content/aip/journal/jcp/131/19/10.1063/1.3263904
2009-11-19
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spin-locking of half-integer quadrupolar nuclei in nuclear magnetic resonance of solids: Second-order quadrupolar and resonance offset effects
http://aip.metastore.ingenta.com/content/aip/journal/jcp/131/19/10.1063/1.3263904
10.1063/1.3263904
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