Fabrication and/or Selection of a Single Crystal Ionic Conductor

I want to fabricate or buy single crystal ionic conductors for usage as solid state electrolytes in batteries testing. However, I am having trouble finding anyone that can sell appropriate materials.


From my understanding, lanthanium series elements typically have good ionic conductivities. Thus, it seems like Strontium Lanthanum aluminum oxide (SrLaAlO4) or lanthanum aluminum oxide-strontium aluminum tantalum oxide (LSAT) which are both sold in single crystal form, may be suitable. However, I'm having trouble determining if they are compatible with the lithium ion.


Meanwhile, I know that I have seen SiO2 and Al2O3 used as barriers in battery electrodes, and it's possible that single crystals of either of these may be possible to use. However, just because it is a barrier doesn't necessarily render it a solid state electrolyte. Meanwhile, it appears alpha-Al2O3 has previously been used as a [separator](https://repository.asu.edu/attachments/172759/content/Sharma_asu_0010N_16205.pdf), I'm unsure if this is truly because the alpha-Al2O3 can transport the lithium versus the pores of the material transporting the lithium. When trying to discover which was the case, I found [this paper](http://pubs.acs.org/doi/abs/10.1021/jz401231e) discusses the transport mechanism of lithium in Al2O3, but I am unsure if this applied to alpha-Al2O3.


Lastly, I can also find MgAl2O4 single crystals, which appear to be good ionic conductors of lithium but only if doped with lithium. However, I do not know a way to create single crystal LiMgAl2O4, starting with MgAl2O4 single crystal.
Does there exist a suitable single crystal material which can be easily fabricated or bought for my purposes?


