“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.