For main website, e.g., phase diagram CaO - Al2O3. Graphics and associated structures are divided into two groups, “stable” and “unstable”. It would be useful to have three groups: “stable”, “viable”, and unstable. The viable group could include stable + structures that are more than ~0.03 eV/atom above the convex hull. Perhaps the threshold can be defined by the user. This would be useful. As an example, see the phase diagram on https://en.wikipedia.org/wiki/Calcium_aluminates.
This is definitely something we struggle with. The most fundamental issue is that no one really knows how to define viable as this seems to change from system to system, and when we least expect it someone comes up with a new crazy way to synthesize materials people previously thought were not possible.
You’ve defined an energy cut-off and while that works well in many cases, there are situations where low-energy polymorphs are dynamically unstable, IE their elastic tensor has one or more unstable modes, which suggests they could never be synthesized . Similarly there are known chemical systems such as the nitrides where the stability window can reach into the 100’s of meV/Atom.
Here is a good read on one of our methods that demonstrates how dynamic viability is. If you can come up with a sure-fire way to figure this out, publish it, and we’ll implement it. 
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