## Friday, January 22, 2010

### Pulse Power Expressed in Hz

On several occasions I have been asked what it means when a power level for a pulse is expressed in frequency units (e.g. "The proton decoupling power was 75 kHz"). The frequency here is the precession frequency about the magnetic field due to the pulse in the rotating frame of reference and NOT the frequency within the pulse itself. The power level expressed in Hz is simply the reciprocal of the time required for a magnetization vector to travel 360° (one cycle) under the influence of the pulse (i.e. the reciprocal of the 360° pulse duration). The algebra is as follows where the power level in Hz is expressed with respect to the 90° pulse rather than the 360° pulse.

#### 9 comments:

Anonymous said...

Hello Glen,

Does this apply to quadrupolar nuclei? Or is that in the reference solution? Literature often states Omega(rf) between 50-100 kHz for a quadrupolar sample, but it isn't clear to me what that actually means.
Thanks.

Glenn Facey said...

Anonymous,
omega(rf) usually means (2*pi)*nu(rf). This value is usually obtained by measuring a 90 degree pulse but whether that pulse is for a reference solution or whether it is for the central transition of a solid sample should be specified in the experimental details.

Glenn

Bernie O'Hare said...

No, it doesn't matter if nucleus is spin 1/2 or greater. The excitation profile is the reciprocal of the pulse width regardless of the spin number. Hope this helps.

Bernie O'Hare said...

I'm sorry, I meant excitation bandwidth, not excitation profile in the above comment.

Anonymous said...

Hi,

I have heard that in order to determine the rf in samples with I>1/2 that one must measure 90 deg time in a solution and multiply that by the ratio of Q factors (Q(solution)/Q(sample)). Is this even remotely true? Thanks.

Jeff

Glenn Facey said...

Hi Jeff,

When the pulse power expressed in Hz is much greater than the quadrupolar frequency then the pulses are non selective (i.e. they excite all transitions). This is true in solution, where the quadrupolar interaction is averaged and in the solid state for quadrupolar nuclei in sites of cubic symmetry. When the pulse power is much lower than the quadrupolar frequency then the pulses are selective to the m=1/2 - m=-1/2 transition. In such cases a 90 degree pulse for the central transition is shorter than the 90 degree pulse in solution (or for a cubic solid). See this post.

http://u-of-o-nmr-facility.blogspot.com/2008/11/90-degree-pulses-for-i-n2-nuclei-in.html

Glenn

Anonymous said...

Hi,

Thanks. What if the rf and quadrupolar frequency are similar? How do you the conditions you mention change?

Jeff

Glenn Facey said...

Jeff,

When the quadrupolar frequency is comparable to the amplitude of the rf (expressed in Hz), things get much more complicated. I suggest you read the following section from Melinda Duer's book.

Melinda J. Duer, "Introduction to Solid State NMR Spectroscopy" chapter 5 pp 249-252.

Glenn

Anonymous said...

thank you for answering this question!! i'm just learning CP, after doing ss nmr for years-- and I understood it on the theoretical level, but some of the practical nuts and bolts aspects I don't know -- like this! and it was too basic for any text to explain it, but also so basic as to make it embarrassing for me to ask someone! ( I know, I know, bad policy, no stupid q's, etc etc, but I am happy to have found the answer w/o having to ask :)