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Are there any crystals (that exist at standard temperature and pressure) that are theoretically possible, but haven't yet been made?

For example, the predicted requirements for temperature, pressure, materials, etc. for crystallisation to occur are too difficult to achieve.

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    $\begingroup$ You might want to clarify what you mean by "crystals". Are you talking about specific crystal symmetries or space groups (e.g. body-centered-cubic or P422), or are you talking about any chemical substances in crystal form? -- If the latter, a large number of organic molecules (and even proteins!) will crystallize at standard temperature and pressure, and there's a practically unbounded number of them we've yet to produce (let alone crystallize). $\endgroup$
    – R.M.
    Commented May 17, 2019 at 15:04
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    $\begingroup$ This feels like asking if there are any integers we haven't written down yet. $\endgroup$
    – user2357112
    Commented May 17, 2019 at 20:39
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    $\begingroup$ Is the "perfect" crystal at absolute zero with zero absolute entropy theoretically possible? $\endgroup$
    – Eashaan Godbole
    Commented May 19, 2019 at 6:31

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When we are talking about the prediction of materials, it is generally about the structure and corresponding free energy, not the crystallization process. That being said there are a huge number of inorganic materials that predicted to be stable yet no one has synthesized them.

There are computational databases like Materials Project that contain automatically generated (theoretical) structures and their estimated free energy, solubility, magnetic properties, bandgap, stability compared to competing phases, etc.

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    $\begingroup$ As an addition, at much smaller scale than the Materials Project -- so far about 3k entries -- COD's sister, Theoretical Crystallography Open Database, crystallography.net/tcod. $\endgroup$
    – Buttonwood
    Commented May 18, 2019 at 21:38
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Arguably, there are more such crystals than those which have been made. It is just that nobody bothered to write them all down, because hey, what's the point.

A tiny minority of those theoretical crystals haven't been made for the reasons you envisioned, that is, because the conditions of crystallization are hard to achieve. Here by "conditions" we mean pressure because temperatures that are relevant to solid state chemistry can't be much of a problem. Slowly and painstakingly, one by one, these crystals are being dragged into existence. Oganov's discoveries are relatively recent examples. Metallic hydrogen is still waiting for its turn.

A vast majority, however, haven't been made for an entirely different reason: not because the conditions are hard to reach, but because there are no such conditions. If you want to make them, you have to invent some ingenious workaround ways.

You surely heard of graphite and diamond, and of the amount of effort it takes to turn the former into the latter, and that it's been successfully done. Now, what about this guy? fullerene

Diamond does have a place (albeit far away on the phase diagram) where it is stable. Fullerenes don't. I can claim with a good deal of confidence that you won't find the conditions where they are thermodynamically stable, not even in the areas where we haven't reached yet. However, they have been made. Others are still waiting: tetragonal 1 tetragonal 2

(more can be found at https://en.wikipedia.org/wiki/Allotropes_of_carbon)

So it goes.

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