As I alluded to in a recent entry, NMR has been vital to science in recent decades - it's used in characterizing chemicals, cells, people, textiles - just about anything people have managed to figure out how to get into a strong enough field.
Like many organosilicon compounds, tetramethylsilane has a very low "chemical shift" - this is where its usefulness comes in - TMS has a shift of exactly zero, so you can use it as an internal reference.
A lot of people dislike TMS because it's just another thing you have to get rid of. Fortunately, it's barely a liquid - it boils just above room temperature, so evaporating the NMR solvent will remove the TMS. Usually though, you can just use the trace nondeuterated NMR solvent (e.g.,, CHCl3 for deuterated chloroform, or CDCl3).
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TMS has a shift of exactly zero, so you can use it as an internal reference.
TMS is defined as the reference for proton zero chemical shift. FT-NMRs use a deuterium lock from the deuterated solvent - put no TMS in FT-NMR samples!
Would it be too annoying if I asked what "chemical shift" means?
I'll also sign on to John Baez's question above, and raise you a "why define TMS's shift as zero"?
Dr Baez: Chemical schift = scale used in NMR spectroscopy, to measure the position of resonance signals (of the same kind of nuclei) in ppm of the operating frequency.
All nuclei of the same type resonate around the same frequency, depending on the strenght of the magnetic field, but because of the shielding by electrons (=chemical bonds)their signals can be resolved even though they are pretty close one to another.
The typical schift scale used in chemistry is measured in ppm units of the instrument operating frequency. The relative location of signals in ppm units is independent of the instrument used.
[More powerful instruments with giant magnets operate at higher frequencies so you can have beautiful spectra with less sample due to better sensitivity (signal/noise ratio)and get much better signal resolution (the signals are further apart and multiplets are less complicated) but the spectra in ppm values recorded on one instrument can be directly compared to spectra from another instrument with a different operating frequency - if the experimental conditions (like solvent, temperature) are reproduced
As the spectra signals are often reported in the literature with precision down to 0.001 ppm, the chem schift scale zero needs to be referenced to something - for better reproducibility of the values. So tetramethyl silane was accepted as an universal standard for 1H spectra, and declared as the zero point, chemical shift = 0 ppm because the signal is conveniently downfield from other typical 1H signals so most other 1H signals in the spectra will likely show up between +0.5 and +15 ppm. (There are organometallic compounds and funky bridgehead aromatic compounds that have hydrogens that show at lower values than tetramethyl silane, in negative ppm region).
Tetramethyl silane is not essential for NMR spectroscopy - often a residual signal from a deuterated solvent used to dissolve the sample is used, to set a reference point of the scale - the numbers are tabelated - and this method gives a pretty good agreement with tetramethyl silane reference signal, for a routine work.