In Cuprous Oxide Cu2O(111) lattice when oxygen atoms from upper three surfaces are removed there two types of sites are generated- vacancy and interstitial site. How can I identify which one is vacancy and which one is interstitial?
No direct answer!
Because when disorder comes, both descriptions are one and the same
If Cu2O has one oxygen removed, it needs to leave as neutral atom. So, we have two copper(I) ions, one empty place where there used to be oxide ions and two electrons.
Now, It can be possible that, the negative electrons remain attached to the oxygen vacancy. At that spot, formerly sat oxide ion, being surrounded by more cation than anion as before, and electrostatically stabilized.
But the vacancy can be ionized, letting the electrons lose in the cuprous oxide matrix.
What about the remaining copper(i) ions? Do they want to leave their site?
Close to them, when there was an oxide, and even two electrons, there was electrostatic attraction to stabilize. Once there is a 'surface vacancy' with no charge, they are more free to ream into lattice, roll on top surface and go even inside bulk of lattice. These extra ions might tuck hard into interstices of cuprous oxide.
Now, think like this - would you call a formerly lattice site occupied by an anion that have been open to surface, but now empty of even electrons, a vacant lattice site, or an empty vacuum spot adjacent to lattice? choose and suit yourself. But of course, if that site is filled up by an oxide from inside, the place just this new oxide ion left is indeed a vacancy
And what about former spots of cuprous cations exposed to surface? do you treat those vacancies of lattice points, or vacant lattice spaces near laattice, where new atoms are likely not to come. The dislodged cations can roll onto surface, get tucked into other sweet spots on surface. Those new-spots on surface would be your new lattice points, and to compete the charge neutrality, you need to imagine a vacant lattice site as well, where the oxygen never came. If those unruly cupous cations get inside bulk, they are interstitials!
So in short, whether you see as two cuprous cations at lattice site and a vacant site where oxygen were supposed to come (1 oxygen vacancy); or two cuprous cation coming from somewhere else trying to tuck themselves here and there (2 copper (i) interstitials), both points to the very same thing.
BTW, do you consider whole of empty part of 3D space filled with one oxide vacancy for two cuprous vacancies? ponder and you'd get the whole point.
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