Shimming, Part V
How the sample and probe affect shimming
- End effects (magnetic susceptibility) of the sample.
- Particulate materials in the sample.
- Dissolved materials in the sample.
- Radiation damping.
An often overlooked parameter in the shimming process is the magnetic susceptibility effect caused by the ends of the sample. All solvents have a very high magnetic susceptibility value, and water is higher than most. Unless the sample is infinitely long, the end effects of the solvent can be seen. Usually the NMR operator tries to shim out these effects without fully appreciating their origin. The NMR probe has an rf coil which is used to generate the excitation of the nucleus and to receive its signal. When properly constructed, the NMR probe’s coil generates and receives a signal over a sample volume which is a cylinder with height equal to the height of the coil window. This region is referred to as the “active” region of the probe. An empirical method of determining the active region of the probe’s receiver coil is discussed in the Before You Start To Shim chapter. If the ends of the sample are far removed from the active region, then the magnet field change caused by the ends of the sample and the solvent’s magnetic susceptibility are also far removed from the active area of the probe’s coil. Under this condition, there may be a change in the absolute value of the magnetic field in the active area of the probe’s coil, but it is a constant change best described by the Z0 gradient.
The key question in this discussion is how far is “far enough removed” from the active area of the probe. The answer depends on many variables, a few important ones being the height of the receiver coil, the diameter of the receiver coil and the magnetic susceptibility of the solvent. The larger the diameter of the tube the farther the effect from the solvent ends is detectable. For a 5 mm tube, the effects are easy to measure when the sample extends 1 cm above and below the active region of the probe’s coil. The effects are difficult to measure when the sample extends 2 cm above and below the active region of the coil. This is more sample length than most NMR operators want to use. The shorter the sample used, the more difficult the shimming process will be, but less sample is required. This is another example of the trade-offs always being made when operating an NMR spectrometer.
As a general rule, if the sample length used in the NMR spectrometer’s 5mm probes is going to be longer than 2 cm above and below the active region of the probe’s coil, the sample-to-sample variations of the shim values derived from the end effects of the solvent will be negligible. If the typical sample to be run on the NMR spectrometer is going to be shorter than 1.5 cm above and below the active region of the coil, then the sample length should be tightly controlled and maintained the same for all samples. Then if the sample tube’s position in the spinner is kept the same, a set of shim values can be developed and reused from sample to sample.
When a spectrum of a limited amount of sample is necessary, one can use a micro sample probe or constrain the sample in a spherical micro-cell. A spherical micro-cell works better than a cylindrical micro-cell. This is because the magnetic susceptibility influences on the sample caused by the glass of the micro-cell are only of the Z0 type when the sample is surrounded by a sphere or is part of an infinite cylinder. When the micro-cell is inserted in a 5mm NMR tube, it is usually best to surround the micro-cell by the same solvent as used in the micro-cell such that the ends of the surrounding solvent extend more than 2 cm above and below the coil’s active area.
Since deuterochloroform is a common NMR solvent, another trick which has been used by many NMR laboratories is to take advantage of the fact that Teflon has about the same magnetic susceptibility as chloroform. The sample is then placed between two Teflon plugs. The total length of the sample and Teflon plugs is then maintained to be 2 cm above and below the probe’s active region. This technique also minimizes the effects from the end of the solvent and makes shimming small samples easier.
After much expense and time to obtain precious sample and put it into an NMR tube, many an NMR spectrum has been of much lower quality than necessary because of particulates in the sample. When the NMR sample is examined under a magnifying glass, one can often see little bits of this and that floating around. These particulates often have a very different magnetic susceptibility from the NMR sample. This influence on the magnetic homogeneity over the active volume of the probe cannot be compensated for by shimming since the particulates are moving about while the sample is spinning. These need to be removed by filtering through commercial sample filters or glass wool stuffed into the bottom of a pipette.
As surprising as it sounds, it is not at all uncommon for the particulates to be iron. Holding a small magnet to the side of the NMR sample can cause these iron particles to run to one side of the sample tube, as seen by examining the sample under a magnifying glass. Some samples with iron particles can be examined before putting them into the NMR spectrometer and appear clean. After shimming for a while with unsatisfactory results, the sample can be removed and examined under a magnifying glass and big chunks can be seen. This comes about because the original sample had some very fine iron particles that could not be seen, but which coagulated (stuck together) after being magnetized in the magnet. It is often a good idea to look at the sample under a magnifying glass before expending a lot of time on a sample which seems difficult to shim.
In addition to having macroscopic iron particles in the sample, it is possible to have dissolved paramagnetic material in the sample. This will not be visible to the eye, but can cause dramatic broadening of NMR lines due to paramagnetic relaxation, which is a very efficient mechanism of T2. relaxation. Even dissolved oxygen in the sample will cause broadening, which is why NMR resolution standard samples are always supplied degassed in sealed tubes.
Viscosity is also a cause of broadening of NMR lines because of the reduced correlation times for molecular tumbling. Slower motions are a more efficient mechanism of T2 relaxation.
Another broadening phenomenon which can be observed under some conditions is called “radiation damping”. This phenomenon when used in conjunction with NMR is different from radiation damping when discussed by an electronics engineer. When discussed in relation to NMR, it is an additional relaxation mechanism for the nuclei arising from energy in the NMR sample being coupled into the probe’s coil. Losses in the probe’s circuit then provide a means for removing energy from the nuclei or “relaxing” the nuclear polarization. This relaxation process is proportional to the strength of the nuclear signal, the frequency of the nuclear signal, the sample coil filling factor and the Q of the probe’s tuned circuit at the nuclear frequency. This means that it is most likely to be observed on high field instruments when observing proton in water solutions. The phenomenon can be seen with other samples such as CHCl3 on 500 MHz and 600 MHz systems if the CHCl3 sample is very concentrated ( >5% ).
The presence of radiation damping is easy to detect. Run a spectrum of the sample under conditions where you suspect radiation damping and measure the linewidth of the signal. Then tune the probe way off resonance and run the same spectrum again. You will of course have a reduced signal to noise, but if the line becomes narrower, then radiation damping was present. Since the degree of relaxation the nucleus receives by this mechanism is directly related to the strength of the NMR signal, it is possible that water of a protein sample could be broadened by this process without broadening the protein signals themselves.
Ideally, probes should have little or no influence on the shimming process. However, many probes have one or more characteristics that make them non-ideal. In general, the “better” the probe, the easier the shimming process. Major areas where probes can influence shimming are:
- The materials used in probe construction.
- Size (length and diameter) of the probe coil.
- The RF homogeneity generated by the probe coil.
Each of these areas produces constraints and/or influences on the shimming process. An understanding of these influences and what the NMR operator can and cannot do makes shimming less frustrating.
The basic way probe materials can influence the shimming process is by the magnetic susceptibility of the probe materials. The area of the probe of major concern is the probe’s coil because it is closest to the active region of the probe, the volume of sample which contributes to observed signal. Other parts of the probe can influence the shimming process, but they usually are farther away from the probe’s active region and, because the effects fall off with distance, they have less influence. Because of the distance from the sample, the effect that these probe parts produce is a low order gradient. Low order gradients can cause the shim values of particular gradients to change, but they are usually straightforward to shim. The coil, however, is much closer to the probe’s active region and has a complex geometric arrangement relative to the sample. Any magnetic susceptibility of the probe’s coil changes the magnetic field profile in the active region in a complex manner related to the complex geometric pattern. The NMR operator is then faced with the prospect of trying to correct this influence with the shims.
The influence of the probe coil’s magnetic susceptibility was mentioned in the chapter on Symptoms of Inhomogeneity. Here we will expand on this issue and explore in more depth a simple probe coil often referred to as a single turn Helmholtz or coaxial cavity.
A simplified drawing of this probe design is shown on the left. If the coil material has a magnetic susceptibility, it perturbs the magnetic field producing a gradient whose geometry is related to the geometry of the coil.
If the coil described were made of material with non-zero magnetic susceptibility such as copper, the gradient profile generated along the Z axis through the center of the sample can be calculated and would look like the graph to the left. The vertical axis in this figure represents position along the sample. The heavier horizontal blue lines represent the ends of the coil window.
Gradients are displayed as horizontal deviations from zero at the center. A perfect field would have a profile which is a straight, vertical line at the center of the plot, showing no gradient over the active region of the probe, which is the area between the top and bottom edges of the window. The deviation from ideality of the gradient profile shown would result in a distorted lineshape. Note that the largest gradients are found at the ends of the coil window, where there is a sudden change in magnetic susceptibility.
If it is assumed that only the sample within the window generates signal, the values of Z0 through Z4 gradients best able to correct this coil-induced gradient can be calculated. If we apply these gradients to the induced field to correct them (called shimming), the result is shown on the graph to the left. Notice that there are residual field gradients not correctable with Z0 – Z4.
The corrections applied here (in arbitrary units) were:
- Z0 -77
Most of the distortion is 2nd order.
This is the same field profile as in the previous figure, with the horizontal scale increased to make the distortion more obvious.
This is the lineshape corresponding to the gradient plot above. Even though the gradients have been corrected to the best extent possible using gradients Z0 through Z4, the result is a split line — totally unacceptable.
As can be seen in the graphs, substantial field gradients can be induced by the probe coil if the materials have non-zero magnetic susceptibility. If using such a probe, the NMR operator would adjust these shim gradients to correct the coil-induced gradients. Even after this is done, there are residual gradients that are not correctable by Z0 through Z4. These residual gradients oscillate between a slightly positive and a slightly negative field value. This field would generate the “split field” type of lineshape shown above, where the peaks would either be broader than necessary or split into a doublet. This type of lineshape would result from perfectly compensating for the coil-induced gradients up to 4th order. However, the NMR operator would be very unhappy with the resulting lineshape and might continue to shim, probably concentrating on the even order shims. In general, the operator would probably move Z2 a little one way and Z4 a little the other way and then adjust Z1 for the best lineshape. This process consists of misadjusting the shims to smear out the lineshape so that it is acceptable. This results in shimming symptoms that many operators may have noticed: the resolution gets better while the lineshape distortions get worse. In extreme cases of this phenomenon, the NMR operator observes a very frustrating symptom. When the NMR instrument is shimmed the lines in the spectrum tend to split. About the only cure for such a problem is to de-shim the system to spread out the doublet to a broad singlet or use a different probe.
The actual shimming process to correct for the probe coil’s magnetic susceptibility influence is more complicated from the NMR operator’s point of view. Using the example of the typical single turn Helmholtz coil made from made from a material with magnetic susceptibility one fifth that of pure copper in a perfect magnetic field, the magnetic gradients induced by the probe on the sample would generate a lineshape as shown on the left below. The user would look at this and try to correct the lineshape problem using Z4. Using only pure Z4 the user would get the result shown the figure on the right below.. This generates a lineshape which looks like Z2 needs adjustment.
Effect of non-zero susceptibility on lineshape
Attempt to correct using only Z4
Correcting with pure Z2 would give the result shown on the left below. This again looks like Z4 needs adjustment, but less than at the start shown in step 1. Iterating back and forth between Z2 and Z4 would correct the lineshape with the final result shown at the right below.
Attempt to correct using only Z2
Attempt to correct using Z2 and Z4.
While the result looks like an acceptable lineshape, its low order lineshape, width at half height and peak amplitude are all poorer than what would have been obtained with the same probe and sample in a probe with zero magnetic susceptibility components.
In the absence of magnetic susceptibility problems, as the operator changes the value of Z4, the hump in the base of the lineshape peak moves through the peak and appears on the opposite side. The time when the hump is totally under the peak results in the best resolution. In cases where the probe’s magnetic susceptibility is a problem, the lineshape hump looks like a Z4 problem, but is a magnetic susceptibility problem. The gradients induced in the sample by magnetic susceptibility of the probe coil perturb the sample near the ends of the coil more than in the center of the coil. This creates a gradient profile that looks like Z4. The actual profile is a much more complex function which, in its simplest form, contains Z2, Z4, Z6, Z8 etc. Since most NMR spectrometers do not have these as shimable gradients, the best the operator can do is over-correct the sample near the ends of the coil with Z4 and try to back-correct the sample near the middle of the coil with Z2. In process of doing this, when the small hump starts to move under the peak, the resolution degrades. It is impossible to get the best resolution and no Z4 hump in these cases.
The previous discussion can be simulated using the SAM program to simulate shimming. In doing so, it can be seen that the peak height obtained from a copper coil probe is about 80% that of a zero susceptibility probe. The use of Z6 as well as Z2 and Z4 brings this up to around 90%. More can be gained using Z8. The nice thing about the shimming simulator is that it can produce a known perfect magnet, with perfect non-interacting shims and a probe of known magnetic susceptibility. All these things are usually unknown in the real world.
The susceptibility phenomenon is usually present more in lower frequency probes than high frequency probes. This is because the lower frequency probes usually have more inductance in the probe coil. Therefore, the probe coil has more turns of wire, and therefore larger amounts of the magnetically imperfect material. The lower frequency probes are also more likely to have a separate decoupler coil which also adds more metal to the probe. However, the same PPM of magnetic susceptibility problems perturb high frequency nuclei more in Hertz. For this reason, lineshape problems produced by probe coil magnetic susceptibility are usually observed more with higher frequency probes such as proton. The addition of more probe coils and therefore more materials in reverse probes and dual probes where one of the nuclei is proton is one of the reasons that good lineshape performance in these probes is more difficult.
Today, all NMR probe manufacturers correct the probe coil’s magnetic susceptibility to some degree. It is interesting to note that glass has a much greater magnetic susceptibility than the copper from which coils are commonly made. The insert and sample tube are effectively infinitely long uniform cylinders and, by virtue of this symmetry, generate no field gradients at the sample. When a hole is drilled in the center of an NMR probe insert (as in a CIDNP probe), this symmetry is lost and results in substantially degraded resolution. A cracked insert can also perturb lineshape. In these cases, continued shimming can be of little use. If the user can turn the probe upside down and bits of glass rattle or even fall out, then the cracked insert will make shimming very difficult. When constructing a probe, always make the material in the probe appear as a long cylinder to the sample area. This will ensure the minimum perturbation on lineshape and resolution.
Magnetic Susceptibility Correction
There are several techniques used by probe builders to reduce problems with gradients induced by probe coil materials. One way is to correct the magnetic susceptibility of the probe material. A common way to do this is to use a copper-aluminum sandwich. Good, oxygen-free copper is diamagnetic (negative magnetic susceptibility) and aluminum is paramagnetic (positive magnetic susceptibility). The goal is to make a composite with close to zero magnetic susceptibility by adjusting the amounts of the component materials. Other plating techniques are also commonly used. The difficulty is that the magnetic susceptibility varies greatly with purity and measuring the magnetic susceptibility accurately for these materials is difficult.
Very few techniques can measure magnetic susceptibility at the absolute levels which cause very strong gradients in a probe. A common way is to measure a large amount of the probe coil material in a very strong, very inhomogeneous magnetic field either by a change in weight or a change in deflection when the magnetic field is present and absent. To have the necessary sensitivity, a large sample of the probe coil material is necessary. This presents the additional problem that small point-to-point fluctuations in the magnetic susceptibility within the large sample of material can average to zero. When these materials are used in a probe, point-to-point susceptibility fluctuations can be present all along the probe coil leading to field gradients and lineshape distortions.
Another method is to use the NMR spectrometer itself to measure the materials. This is usually done by placing a piece of the material to be tested at the top of a shimmed NMR system’s probe coil. This will create a lineshape distortion which resembles a solids powder pattern. If the material is diamagnetic, the powder pattern is sloped in one direction and if the material is paramagnetic, the powder pattern is sloped in the opposite direction. If the material has no magnetic susceptibility, there is no lineshape distortion. This technique has the ability to test smaller samples more resembling the probe coil itself and in fact can be used on an actual probe coil. A limitation of the technique is that you need a good lineshape to do the test well. The better a lineshape is to start with, the more sensitive the technique becomes. This technique ends up being a bootstrapping technique where a good probe is used to make better materials, which are used to make better probes which allows one to make better materials…
Another technique to improve the situation of gradients induced by probe coil magnetic susceptibility is to change the shape of the coil window. Depending on several parameters such as the length of the coil and the height and width of the window, the shape of the window can change the type and magnitude of the gradients induced. This improvement in lineshape can be obtained just by changing the window shape even if the materials in the probe coil are not magnetically compensated. In the previous discussion of the single turn Helmholtz coil, the coil window was rectangular in shape. As the bands of copper at the coil ends become small compared to window height, the minimum influence from the coil’s magnetic susceptibility will be observed with this rectangular shape. As the bands of copper at the coil ends become large compared to the coil window height, an ellipsoid window shape becomes better. The best shape depends on the ratio of the height and width of the window as well as the size of the bands at the top and bottom of the coil. The relationship is complex and can be explored in much greater detail with the SAM shimming simulator program.
Another common problem which comes from probe coil magnetic susceptibility arises when the susceptibility at the top and the bottom of the coil are different. In this situation, a high order even gradient, typically Z4, is used to correct the asymmetrical lineshape induced by the probe’s materials. But the amount of correction required for the top region and the bottom region are different. Typically what happens is that, as the asymmetry is improved with the change of Z4, a different asymmetry is produced on the other side of the lineshape. One of these situations can be demonstrated with the SAM shimming simulation program discussed later. With probes of this type the “best” lineshape does not occur at the settings which give best width at half height. This produces a situation where shimming for the best response produces an asymmetrical lineshape. The NMR operator is then forced to use Z4 to produce the best lineshape and the remaining controls to produce the best width at half height. Shimming for the best response with Z4 does produce the best width at half height but not the best lineshape. This is a case that many NMR operators will recognize and makes shimming Z4 very difficult. It is also a case where automatic computer shimming will lead to the “wrong” answer. What is happening is that Z4 is being used to destroy the field in the center of the probe’s active region, but make the field values at the ends of the coil acceptable for lineshape. The NMR operator then tries to make the field in the center of the probe’s active region as good as possible with lower order gradients. Here is an example of a situation where the use of a Z6 or Z8 shim would provide better results.
Size of the Probe Coil
The size of the probe coil, or its length and diameter, can affect the shimming process in three ways. The first way is by the magnetic susceptibility of the probe materials and the induced, non-correctable gradients as was just discussed. As the coil length becomes larger at a constant window width, the NMR lineshape tends to split. This aspect ratio of the coil is very important when shimming probes which have less than perfect magnetic susceptibility compensation for their materials. Having a longer receiver coil is also something many probe manufacturers try to do since longer coils “see” more sample and therefore have greater sensitivity.
If the probe’s materials were perfect, then longer coils and larger diameter coils would still be more difficult to shim, but only because it is always more difficult to make a magnetic field perfect over a larger volume than a smaller volume. The case of longer and larger diameter probes is a situation where a “good” magnet is easier than a “bad” magnet to shim. This also means that wide bore magnets are better than narrow bore magnets at a given sample volume. As the amount of sample decreases relative to the probe materials, the probe materials become more important to the shimming process than good or bad magnets. This is one reason why micro-sample probes are difficult to shim and not commonly used. As probe material compensation becomes better, micro-sample probes will probably become more useful.
RF homogeneity affects many areas of an NMR instrument’s performance, but not usually the shimming process. One notable exception is spinning sidebands (SSB). An SSB is a small peak occurring at the spin rate on one or both sides of the main peak and is present only when spinning the sample. There are three kinds of SSBs listed below. Types 2 and 3 are not improved by shimming. Note their characteristics and avoid trying to improve them by shimming.
1. One kind of SSB is first- and second-order (sometimes more) sidebands which are in phase with, and usually present on both sides of, the main peak. These signal average with the main peak so do not tend to decrease with acquisition of more scans. These arise from off-axis gradients in the magnetic field and can be decreased or eliminated with shimming.
2. Another kind of SSB is a first-order (sometimes second) SSB present on both sides of the main peak and out of phase with the main peak. These will not have the same phase with each scan (not phase coherent) and do not signal average with the main peak. They arise from perturbations in the probe’s tuning from irregularities in the sample tube and wobbling while spinning. As the probe’s tuning is affected, the phase of the NMR signal is affected. Therefore, as the sample spins, the signal is phase modulated. These are not improved by shimming. Improving these requires either much better symmetry while spinning, better sample tubes or balancing the probe’s electrical circuit.
3. Another kind of SSB occurs on one side only at either twice or four times the spin rate. This SSB is in phase with the main peak and signal averages with the main peak. It arises from the RF inhomogeneity of the probe. If the probe has two vertical bands on its coil, the SSB will be the second order (at twice the spin rate). If the probe coil has four vertical bands, the SSB will be a fourth order SSB. Which side of the main peak the offending SSB appears on is determined by the sign of the magnetogyric ratio of the NMR nucleus and its spinning direction. This SSB arises from the sample spinning through areas of stronger and weaker RF pickup by the coil, which takes place near the coil’s bands when RF homogeneity is poor. Larger coils in both length and diameter tend to have lower RF homogeneity. This is not improved by shimming.
Many instrumental approaches to automatic shimming have been used in the past. These include electrical feedback systems which maintain the Zl shim at optimum lock level while running for prolonged periods to the more recent computer methods for shimming. The most common computerized methods on the NMR market today use computer-driven DACs as one input to the shim power supplies and a Simplex computer optimization routine to adjust the shim settings. The Simplex routines do have some requirements. If these requirements are not met, then the results obtained will not be optimum. Some of the parameters to watch are listed below:
- Each shim should have equal control of the homogeneity. This is best done by setting the voltage from the DACs to the shim power supply such that an equal DAC step for each shim produces an equal depression of the lock level.
- The initial step size for the Simplex search should be large enough to include the best value for each shim to be optimized by the Simplex routine.
- The lock phase must be correctly adjusted if the Simplex routine is using the lock signal for measuring homogeneity.
- The waiting period between measurements of homogeneity must be long enough to allow the NMR system time to respond. This is especially true if the lock signal is being used as a measure of homogeneity. The response time for a lock with deuteroacetone as a lock solvent can be several seconds as the homogeneity improves.
- When the FID is used, a steady state must be established and maintained between the rf pulses before the FID can provide a valid measurement of the homogeneity.
- The most sensitive method to adjust the final values for Zl and Z2 is by using the FID as the measurement of homogeneity.
In theory, the Simplex routines should be able to optimize the homogeneity regardless of the shim interactions. However, experience has shown that with second-order shim interactions, Simplex often fails to find the best values. In these cases, slower and less elegant computer routines following a shimming sequence similar to the one described above give better results.
Return to Part I, Introduction
Return to Part II, Basics
Return to Part III, Symptoms of Inhomogeneity
Return to Part IV, The Z1 Profile
Last updated: 01/22/03