Are there ionic solids that conduct electricity?

We are taught in school that ionic substances don't conduct electricity, and when they do, it is either because they are in a molten state or because they are in solution. I understand these concepts.


Are there any exceptions? By exceptions, I am looking for ionic compounds that may not conduct electricity well, but they conduct electricity better in comparison to other ionic compounds. Additionally, what makes such a compound a better conductor of electricity?




**Yes**. 


Another example is [VO2](https://en.wikipedia.org/wiki/Vanadium%28IV%29_oxide). Over 67 °C its crystal structure changes to rutile with a band gap of ~0.1 eV. Dopants of other substances can reduce the temperature at which it becomes a conductor.


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**Yes, there are.**


Ionic conductivity greatly varies between compounds. For some of them is *much* higher then for others. They are called [**fast ion conductors**](https://en.wikipedia.org/wiki/Fast_ion_conductor), or **superionic conductors**.


Well known example is [silver iodide](https://en.wikipedia.org/wiki/Silver_iodide). While it may be called a "salt", it's probably more covalent then ionic, that is, before it's heated to 146 °C, when its structure changes and Ag ions are "set loose" to conduct electricity. In result conductance rises a few *thousand* times. 


If rubidium iodide is added to $\ce{AgI}$ we can get [rubidium silver iodide](https://en.wikipedia.org/wiki/Rubidium_silver_iodide) which is even better, and is sometimes classified as one of "advanced" superionic conductors. 


Many substances can be superionic in right circumstances, even [water ice](https://chemistry.stackexchange.com/questions/115429/what-would-superionic-water-ice-look-like) can, if temperature and pressure are high enough. 


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