> you don't need a big science lab like CERN to do useful experiments

Did anyone really ever claim that?

No, but that's still pretty cool to hear (even though everything else to conduct the experiment was probably a bit pricier if not just as pricey)

While your first statement is true, in this specific case, you actually need a "big science lab":

* lasers used to heat up the sample (at least a few 10k$), * the actual X-ray source (i.e. a synchrotron, which costs hundreds of millions to build and millions annually to run, albeit for thousands of experiments a year), * surrounding instruments (such as X-ray detector for diffraction and spectrometer+camera for temperature measurements) * people who actually makes things work

This kind of experiment is far from being cheap technically speaking. However, access to beamtime at such state-run X-ray facilities (CERN job's is not to produce X-rays) is often free of charge, at least for academia (or as long as you publish your results). You "only" have to apply for beamtime.

And how cheaply can you create a environment of "1.4 million atmospheres of pressure, and over 4,000 °C"?

A diamond anvil makes both of those on the tips of the diamond (briefly)

Diamond anvil cells produce the pressure, however, here, the temperature is created by lasers. If you are careful enough (and reasonable enough), your diamond anvil cell can last forever, as long as you don't break the diamonds you can reuse the same cell for another sample or another run.

The pressure usually requires a pressure driver to push the diamonds towards each other (some kind of very precise gas pump) which runs of of electricity.

The temperature however evolves rapidly: the sample is heated via laser (usually pulsed to observe dynamics but can also be considered continuous, i.e. above millisecond time scale).