The Trouble With T1s

“If you go to a social gathering and announce that you are an expert in relaxation, you could receive responses ranging from curious stares to hearty approvals, neither of which are probably justified.”

– Eiichi Fukushima and Stephen B.W. Roeder, Experimental Pulse NMR: A Nuts and Bolts Approach

The past few weeks of my research has largely been concerned with scandium oxide, Sc2O3. Using both the 7.4 Tesla low-field magnet (about 148,000 times greater than the earth’s magnetic field), and the 17.6 Telsa high-field magnet (350,000 times the earth’s magnetic field) we have attempted to produce detailed frequency spectra describing the compound’s scandium nuclei. (For the uninitiated, an NMR frequency spectrum is a graphical depiction of how the scandium atoms respond to applied magnetic fields. From that information, information about scandium’s location in the crystal, its bond lengths, and other details of scandium oxide’s molecular structure can be extracted.) However, there are two obstacles standing in our way.

First, it is incredibly difficult to determine the accuracy of an experimentally-generated spectrum without having some idea of what the spectrum should look like. Essentially, we are putting together a jigsaw puzzle without looking at picture on the front of the box. Thankfully, there are several tools that can be used to solve this problem. EXPRESS, a computer program created by Dr. Robert L. Vold and Dr. Gina Hoatson, the professors who run William and Mary’s NMR lab, can be used to generate simulations of experimental spectra. By using known information about scandium oxide, such as its quadrupole coupling constant and its asymmetry parameter, EXPRESS can predict the shape of experimental frequency spectra. Metaphorically speaking, the program looks at the shapes and colors of several puzzle pieces, and uses that information of predict what the finished jigsaw puzzle should look like. EXPRESS’ experimental spectra provide a basis of comparison for our measured spectra, allowing us to gauge the accuracy and reproducibility of own experimental results.

The second problem with our research comes from an unlikely source: relaxation. While most students (myself included), believe that relaxation is a necessary tool in the maintenance of sanity, it can prove most problematic during NMR experiments. As described previously, NMR measures the response of nuclei to applied magnetic pulses. When atomic nuclei are hit by a magnetic pulse, they are forced into a higher energy quantum state. Eventually, however, the nuclei return to their equilibrium state, inducing a voltage in an NMR probe coil in the process. This induced voltage is digitized and graphically represented as a free induction decay plot (FID), which is then mathematically converted into a frequency-versus amplitude plot using a Fourier transformation.  (For a better explanation of the process, check this post.) The nuclei’s return to equilibrium, known as “spin-lattice relaxation,” does not happen instantaneously. Instead, the restoration process is exponential, and is governed by a time constant T1. T1 is the time needed for the magnetization vector to return to 63% (or, for the more mathematically inclined, 1-1/e) of its equilibrium state. In order to ensure accurate data, many NMR scans of a sample are taken, with a delay of several T1s in between each scan. The trouble with scandium oxide is that it has a very large T1 value. While many compounds, such as PSW (a piezoelectric compound composed to lead, scandium, and tungsten used to calibrate and test our experiments) have T1 values on the order of several milliseconds (10-3 seconds), scandium oxide has a T1 value between ten and fifteen seconds. As a result, it takes a very long time to complete scandium oxide experiments: while a detailed PSW experiment can be performed in several minutes, a comparable experiment on scandium oxide takes approximately a day. There is no easy way to solve this problem without sacrificing the accuracy of our spectra; as a result, we have been running lengthy experiments overnight and over the weekend. Once these lengthy scans are complete, we will hopefully be performing more complex, multi-pulse experiments, which should shed more light on scandium oxide’s structure and electronic environment.


  1. William Adams says:

    That’s always one of the problems with experimental research. Everything takes longer than it should. So far how have the spectra results you’ve found matched up with the spectrum predicted by EXPRESS?

  2. twmilbourne says:

    The experimental spectra seem to match up nicely with the simulations, with a few interesting exceptions. More on that later.

  3. Ethan Winter says:

    This sounds interesting. Does scandium oxide form a piezoelectric crystal or is this more of a proof-of-concept experiment? What factors determine the T1 value for a crystal structure, and why is it so widely variable? How many scans are done in a typical NMR sample? From my use of NMR spectra in organic chemistry, I was under the impression that only a few scans were necessary. You mentioned how the simulations vary slightly from the actual results. Could this be an artifact of having the scans spread out over such a long period of time?

  4. twmilbourne says:

    There have been a lot of experiments on scandium oxide, so we are able to easily check our results with published literature. Once we can use our experimental procedures to replicate results for scandium oxide, we can begin using them on other, less researched compounds.

    A compound’s T1 value actually is dependent on the substance’s crystal structure. In order for the sample’s to return to equilibrium from the excited state, there must be some means for it to dissipate energy. This energy is usually dissipated into the crystal lattice, usually via molecular motion or atomic interactions. A crystal’s T1 value is thus dependent on how readily its lattice can accept dissipated energy.

    The number of scans needed in an experiment depends from sample to sample. In general, each type of nuclei responds to applied pulses with a certain efficiency – that is, they have a certainty sensitivity to applied fields. A greater sensitivity means a better response to radio-frequency pulses, which in turn means fewer scans are needed. The phase of the sample is also a consideration. For example, when working with a liquid samples, very few scans are needed: the constant molecular motion of liquids averages out any anisotropic signals, allowing for much clearer signal to noise. When working with solid samples, however, more scans are needed to account for their rigid molecular structure. Additionally, the number of scans needed will also depend on the relative amount of nuclei per volume in a particular sample. When there are more nuclei in a sample, the sample has a greater response to the radio-frequency pulse simply because there are more nuclei that can respond. Depending on the time frame of the experiment and it’s T1 value, we will perform several hundred to several thousands scans on a solid sample.

  5. twmilbourne says:

    It seems I forgot to answer your last question in the previous comment. The variations between the simulations and the actual results is not likely the result of the scans being spread over long periods of time. In general, the spectrometer and associated electronics are very stable – the results generally do not shift over time. The discrepancy is more likely the result of differences between the assumed conditions of the simulations and the actual experimental conditions (timings, pulse powers, etc.).