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Recently, there's been some talk of potential lab results in an attempt to create pure, solid hydrogen in a stable form, which, if true, would be a first. Much of the excitement seems to be about the fact that this 'metallic hydrogen' is meta-stable, specifically at normal temperatures and pressures. Whether this is true, or the researchers are simply observing some silica from the surface coating on the diamond anvil, remains to be seen.

What is it about an element or material that makes it meta-stable rather than just stable? Is it the shape of its atoms (orderly lattice vs random alignment)? Or an energy state of a material?

I've read these other questions on the recent solid hydrogen report, especially the last one, but I'm not sure whether they address my question about what causes metallic hydrogen, or another material, to be meta-stable in general.

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The stability at constant volume for any system of elements can be described by its potential energy surface. In the cartoon below, the local minimum is a metastable state: it is higher in energy than the global minimum (the stable or ground state), but there is an energy barrier between the two, which is essentially caused by the need to rearrange the atoms in the system, breaking bonds. This is what prevents a metastable state from sponaneously transitioning to the ground state.

enter image description here

This is just an illustration; the real energy surface is a function of all atomic coordinates, and would require a high dimensional graph (3N dimensions for an N-atom system).

I don't think there is a satisfying answer to your question, since it is very much dependent on the system and conditions. Diamond (carbon), for example, is metastable at atmospheric pressure, but is the hardest known substance. This can be explained by the large energy barrier separating the diamond atomic configuration from the graphite (the stable state) atomic configuration, the strong bonds in diamond that remain strong at ambient pressure, the efficient packing of atoms, the hybridised atomic orbitals that give make the carbon atoms tetrahedrally coordinated, and so forth.

Hydrogen is a very different case. There is a very small energy difference between the different atomic configurations, and there are very many possible atomic configuration depending on the temperature and pressure (see for example http://www.nature.com/articles/ncomms8794). Hydrogen has a high zero-point energy, which can also affect the stability of these states, and at finite temperatures, there is also a free energy contribution to consider --- if you give the system some thermal energy, it can be pushed out of one minimum and into another.

Metallic hydrogen gets its exotic properties from the high pressure at which it is formed. The necessary electronic states require high pressure, such that the atoms are squeezed together. For most materials, when the pressure is reduced, and the atomic lattice is allowed to relax (non-constant volume), the electronic state will change, or the atomic structure will change due to vibrational effects (which are large for hydrogen). My suspicion is that if it is metastable, there is a low barrier to the ground state, and it will decompose easily.

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First, as far as I understand, there is no experimental evidence so far that the hydrogen in the recent experiment (https://arxiv.org/abs/1610.01634) is metastable at normal pressure and temperature: they keep the sample at low temperature and high pressure.

What is it about an element or material that makes it meta-stable rather than just stable? Is it the shape of its atoms (orderly lattice vs random alignment)? Or an energy state of a material?

Metastability of some state means that there is another state at the same external parameters that has lower energy (or, to be precise, a lower relevant thermodynamic potential). In this case, the molecular state of hydrogen has lower energy than the metallic hydrogen state at normal temperature and pressure, but the hope is that small deviations from the metallic hydrogen state increase the energy of this state, so the transition to the molecular state will take a lot of time, and we will be able to use the metallic hydrogen state in practice, the same way that we use, say, window glass, which is metastable. From what I read, though, it seems that these hopes are not well-founded.

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