At pressures a million times those experienced on earth. Still an advance, of course.
I'm not raging at ttsda. It is an advance. Of sorts. But not nearly as much as the headline suggests.
Basically, low temperature superconductors (e.g. niobium titanium) are liquid helium cooled.
High temperature superconductors (e.g. YBCO, BSCCO) are everything else, but generally liquid nitrogen cooled.
In the scientific community, High-Tc superconductors typically refer to Type II superconductors, eg cuprates. And the “High-Tc” term means above temperatures relative to the usual elemental superconductor Tc’s, eg about 20K or so.
Materials that can superconduct above 77K are especially sought after since they can be cooled with only liquid nitrogen, much cheaper and abundant than liquid helium.
Even if we could compress anything other than a spec of this stuff, it would still require massive amounts of PV work to achieve the P required.
> The effort to manufacture synthetic diamond provided substantial motivation for the development of high-pressure methods. Today, however, synthetic diamonds are grown using a low-pressure technique called chemical-vapour deposition. Optimistically, it might eventually be possible to use similar low-pressure methods to produce metastable superconducting compounds that are initially discovered at high pressure.
So, no, everybody cares about high temperature superconducors, because the higher the temperature, the strongest magnet you can build out of them.
But yah, you can bathe a much more complicated "circuit" in liquid nitrogen a lot easier than compressing it with diamond anvils. Though no commercial superconducting computers have emerged, cmos is just too cost effective currently, and the known examples are still in the 4K range.
But you have to put energy in to compress it, energy that is lost (since you're compressing it isothermally). Since we're talking about 1E6 atm, any appreciable volume would require insane amounts of E to compress.
How much energy it is depends on the volume change as you compress. If your material is completely incompressible, there is no volume change, no work done as the pressure rises, and therefore no energy stored.
In practice, for a material of bulk modulus K by definition you have
-K dV/V = dP.
V = V_0/exp(P/K)
The work done while compressing is the integral of -PdV, which per that first differential equation we can rewrite as the integral of P * V/K * dP (we want to integrate dP because we know what the limits are: it's going from 1atm, or 1e-4 GPa, to 1e6 atm = 1e2 GPa).
Plugging in our expression for V we get the integral, from 1e-4 to 100, of P/K * V_0/exp(P/K) dP. The integral there is:
K * V_0 * (-P/K - 1) * exp(-P/K)
K * V_0 * ((-100/K - 1) * exp(-100/K) + 1)
OK, so let's try an actual material and actual volume. Steel has a bulk modulus of 160 GPa according to <https://en.wikipedia.org/wiki/Bulk_modulus#Selected_values>. So for steel we have:
160 * V_0 * ((-100/160 - 1) * exp(-100/160) + 1) =
160 * V_0 * 0.13 =
21 * V_0
21e9 N/m^2 * 1e-6 m^3 = 2.1e4 J
If your material is more compressible, the numbers are higher, as long as it's not too compressible (in which case it just collapses into a tiny volume quickly and not much more work gets done after that). If we take K = 50 (a typical number for glass from that table), you get:
50 * V_0 * ((-100/50 - 1)*exp(-100/50) + 1) =
50 * V_0 * 0.6 =
30 * V_0
Again, all this assumes pressure-invariant bulk modulus, which seems moderately unlikely when you are dealing with pressures that are on the order of the size of the bulk modulus or even larger, as here.
As the article points out, diamonds naturally form in a high-pressure environment but are stable at standard atmosphere and temperature.
Although I suppose there aren't any theoretical obstructions to indefinitely maintaining low temperatures either.
lanthanum hydride @ 250K at > 1 million atm.
It's still very impressive though.