Part 5: Magnet Shimming

The art of shimming an nmr magnet is often made unnecessarily difficult by the belief that the process is too complex for a straightforward approach. While the room-temperature shims (RTS) provided on all superconducting NMR systems today do contain many interactions, a logical approach to shimming is nevertheless the best way to optimize the magnetic field. If you know which shims are interacting, then you can devise a system which eliminates many uncertainties from the shimming operation. Also, there is no substitute for experience when it comes to shimming. As I tell all new users, learning to shim the magnet is like learning to ride a bicycle ... you can be told how to do it but there is simply no substitute for actually doing it!

More than likely you will never have to go through the complete shimming procedure given below, rather you will probably only have to adjust the Z 1 and Z2 shims. Less frequently the Z3 and Z 4 shims will need adjustment. Nonetheless it is instructive to see what the whole procedure is. Also, the figure at the end of this article shows the lineshapes corresponding to maladjusted shims ... very useful for knowing which shims are out of adjustment. Also useful, is the technique of adjusting the shims while looking at a real-time display of the lineshapes in your spectrum. How to do this is discussed below.

The shims on most NMR magnets are designed to approximate the spherical-harmonic functions given in Table 1. These functions are orthogonal (independent) over any sphere centered at the origin. Some possible causes for shim interactions are a) the sample is not spherical b) the sample is not centered at the origin c) the real shims are imperfectly described by their model functions and d) the probe does not excite and measure the NMR signal in all regions of the sample equally.

Table 1

                                             Shim                                    Function

                                              Z0                                          1

                                               Z1                                         Z

                                               Z2                                   2Z 2-(X2+Y 2)

                                               Z3                                   Z[2Z 2-3(X2+Y 2)]

                                               Z4                           8Z 2[Z2-3(X 2+Y2) + 3(X 2 +Y2)2

                                               Z5                          48Z 3[Z2-5(X 2+Y2)] + 90Z(X 2 +Y2)2

                                               X                                              X

                                               Y                                              Y

                                               ZX                                           ZX

                                               ZY                                           ZY

                                               XY                                           XY

                                               X2-Y2                                  X 2 - Y 2

                                               Z2X                                  X[4Z 2 -(X2+Y2)]

                                               Z2Y                                  Y[4Z 2 -(X2+Y2)]

                                               ZXY                                         ZXY

                                               Z(X2-Y2)                              Z(X 2 - Y 2)

                                               X3                                         X(X 2 - 3Y2)

                                               Y3                                         Y(3X 2 - Y2)

General shimming instructions

All of the instructions in this article are directed towards maximizing the lock signal. Another criterion for evaluating the homogeneity, such as the total area of the FID or a real-time fourier transform ( see the end of this article for more information on this technique ) of the spectrum could be used. Final shim adjustments should be made while the system is locked on the desired sample. Start with the lock level adjusted to 80% of its maximum value, in other words the lock signal is 80% of the way up the lock window. Be absolutely sure that the phase of the lock system is adjusted properly. If the lock signal becomes too large (or too small) then readjust the the lock level to 75-80% using the lock gain and start the current step of the procedure over again. In all of the shimming procedures, continue adjusting the shims in the same direction until you see a 20 unit decrease in the lock level, and then back up until you reach the maximum lock level. If you do not do this, then you will often fail to find the true maximum.

All of the following procedures are designed to minimize the complications introdued by the shim interactions. However, you will observe that, when the resolution becomes better, the shims can be adjusted directly without recourese to these procedures. In other words, when the shims have been adjusted close to their proper values, they will drive directly to those values.

It is important to decouple the spinning and nonspinning shims by alternating between spinning and nonspinning during the shimming process. During all shimming operations, adjust Z2 - Z5 only while the sample is spinning, Z1 should usually be adjusted while the sample is spinning, but it can also be adjusted whil the sample is not spinning as described in the procedures.

Spinning shims

Spin the sample at 20-30 Hz whenever you are adjusting the spinning shims.

Z1 and Z2

Adjust Z1 to obtain a maximum reading on the lock level display. Move Z2 in the negative direction to decrease the meter reading 20 units. Reoptimize Z1. If this maximum is greater than the previous maximum, then change the Z2 setting enough to lower the lock level 20 units and reoptimize Z1. Continue this process until the best combination of Z1 and Z2 is found. Continue past what you think is the maximum to be sure that you have really found it.

If the first new setting of Z2 in the procedure above leads to a decrease in the lock level after you reoptimize Z1, then move Z 2 in the positive direction until the lock level decreases 20 units and reoptimize Z1. Follow the procedure above, except continue to change Z2 in the positive direction until the best combination of Z 1 and Z2 is found.

Z3

Move Z3 in the negative direction to decrease the lock meter reading 30 units. Optimize Z1. If this new maximum is greater than the previous maximum, then move Z3 in the negative direction until the lock level decreases 30 units and reoptimize Z1. Continue this process until you find the best combination of Z1 and Z3 .

If moving Z3 in the negative direction produces a decrease in the lock level after you optimize Z1, then move Z3 in the positive direction until the lock level decreases 30 units. Repeat the procedure above, except move Z3 in the positive direction until you find the best combination of Z1 and Z3.

After you find the best combination of Z1 and Z3 , repeat the procedure for Z1 and Z2. If this yields a better maximum, then repeat the Z3 procedure. Repeat this entire cycle until you observe no further gain in the lock level.

Z4

Move Z4 in the negative direction to decrease the lock level 40 units. Optimize Z2, and then optimize Z1. If this yields a better lock level than existed at the start of the process, then continue in this direction until you find the best setting for Z4 . If this process yields a lower lock level, then move Z4 in the positive direction, and repeat the process above until you find the best Z 4 setting.

It is sometimes necessary to interactively adjust Z3 and Z 4. To do this, move Z4 in one direction, maximize the lock sevel with Z3, and the maximize the lock level with Z1 . continue this process until you find the best setting for Z4 . Make sure that when Z4 is moved, the change is large enough to decrease the lock level at least 40 units. Neglecting to make large enough changes in Z4 followed by remaximizing the locke level with the orther Z controls is the most frequent reason for failing to obtain the best Z 4 setting.

Z5

Move Z5 in one direction to decrease the lock level 40 units. Maximize the lock level with Z3, and then maximize the locke level with Z1. If this lock level is greater than the original maximum, then move Z5 some more in the same direction and repeat the process. If the lock level is less, then move Z5 in the opposite direction and repeat the process. Continue this procedure until you find the best Z5 setting. There is often a broad range of Z 5 settings in which the lock level remains about the same. Find the setting at each end of this range, where the remaximized lock level definitely decreases, and set Z5 in the middle of this range.

Non-spinning Shims

When you are adjusting the nonspinning shims, adjust the lock level to 80% of maximum with the lock gain and do not spin the sample.

X and ZX

Move ZX in one direction to decrease the lock level 20 units. Maximize the lock level with X and then with Z1. If thes new lock level is better than the original lock level, then continue the procedure by adjusting ZX in the same direction. If the new lock level is lower, then move ZX in the opposite direction. Continue the procedure until you find the best settings for X and ZX.

It is necessary to adjust Z1 when adjusting ZX becuase of the Z 1 impurity in the ZX shime. If you change Z1 significantly in this process, then spin the sample and reoptimize Z1 and Z2 before proceeding. This is necessary to decouple the ZX and Z1 shims as much as possible; otherwise the process becomes complicated.

Y and ZY

The procedure for adjustin Y and ZY is analgous to that for adjusting X and ZX.

XY and X2-Y2

Maximize the lock level with XY and then with X2-Y2 . Repeat the process until you find the best settings. Then repeat the procedure for X and ZX and the procedure for Y and ZY. Continue this entire cycle until no further improvements can be made.

Z2X

With the sample not spinning, move Z2X in one direction to lower the lock level 40 units. Maximize the lock level by adjusting ZX, Z 1 and X in that order. If this new lock level is better than the previous locke level, then continue adjusting Z2X in the same direction. If the new locke level is lower, then adjust Z2X in the other direction. If you make a significant change in Z1, then spin the sample and remaximize the lock level by adjusting Z1 and Z2. If you make a significant change in Z2X , then spin the sample and follow the procedure for adjusting Z3 again. A significant change in Z 2X usually leads to a change in Z3.

Z2Y

The procedure for adjustin Z2Y is analogous to that for adjusting Z2X. Substitute Z2Y, ZY and Y for Z2 X, ZX and X in that procedure.

ZXY

Move ZXY in one direction to lower the lock level 10 units. Carry out the procedure for adjusting XY and X2-Y2. If the new lock level is larger than the original lock level then continue in the same direction with ZXY. If it is smaller then adjust ZXY in the opposite direction.

Z(X2-Y2)

Move Z(X2-Y2) in one direction to lower the lock level 10 units and then follow the procedure for adjustin XY and X2 -Y2. If the new locke level is higher than the original lock level then continue in the same direction with Z(X2-Y2 ) until you find the best setting. If the lock level is lower then try the other direction.

X3

Move X3 in one direction to lower the lock level 10 units. Remaximize the lock level with X and Y. If the lock level is greater than the original lock level then continue adjusting X3 in the same direction. If it is less then try the other direction.

Y3

The procedure for adjustin Y3 is analgous to that for adjusting X 3.

Maladjustment Symptoms

You can often tell which shim is out of adjustment by examing the lineshape. A symmetrical lineshape distortion is always produced by an odd-order shim. This can be seen by examining the equations in the table. Likewise, an asymmetrical lineshape distortion is produced by an even-order shim. These types of distortions are shown in the following figure. the higher the order of the gradient which is causing the distortion the farther down the peak the distortion occurs.

The nonspinning shims which produce one cycle of field gradient per revolution of the sample produce the first order spinning sidebands. The nonspinning shims which produce two cycles of field gradient per revolution give rise to the second order spinning sidebands. The third order, nonspinning shims produce both spinning sidebands and low order humps. Z2X and Z 2Y sometimes produce a situation in which adjusting Z3 changes the spectrum from one with no spinning sidebands and a low order hump to one with no low order hump and large spinning sidebands. The other third order, nonspinning shims usually produce only low order humps.

Real-Time Lineshape Monitoring

Lineshapes can be monitored in real time during shimming on the AMX 300 spectrometer. The spectrometer issues a pulse, receives the signal and transforms it into a frequency domain spectrum and phase corrects it continuously in 'gs mode'. In order to phase correct there must already be phase correction constants for the current sample in memory. This means that in order to do this, one must first acquire a spectrum as usual, transform it and manually phase correct it. Then, after switching to the acquisition screen, the spectrometer is put into setup mode by typing 'gs'. The acquired fid will be continuously displayed by default but this can be changed to the transformed spectrum by clicking the middle mouse button while the mouse cursor is over the button containing 'F' and 'S' (standing for fid and spectrum respectively). This will change the display to the continuously updated transformed/phase corrected spectrum. A bug in the program initially displays the real and imaginary data but clicking on any button (the vertical zoom for example) will change this to real only display. You can now shim while looking at the effect of the changes on the spectral lineshapes ... very useful.