Many times, when ceramics are used for their electronic properties, we use oxides with a crystal structure that has two cation locations in the lattice. Having two cation sites provides more flexibility to tailor which dopants are used. If you're curious to learn more, the most common crystal structure like this is called "perovskite", and there are many perovskites with different compositions used in a broad range of electroceramic applications.

Our research adviser has suggested that we consider the composition $L{a}_{2}Mg{O}_4.$ She suspects that this composition would have a fairly open crystal structure, and she thinks it might be possible to create oxygen vacancies or oxygen interstitials in the lattice depending on how we dope it$.$ The La and Mg cations sit at different locations in the lattice. She wants us to go in the lab and test this idea out by creating some brand new compositions of doped $L{a}_{2}Mg{O}_4.$

Please suggest four dopants we could try. Specifically, suggest a dopant that:

a$)$ would likely sit on the La location and create oxygen vacancies

b$)$ would likely sit on the La location and create oxygen interstitials

c$)$ would likely sit on the Mg location and create oxygen vacancies

d$)$ would likely sit on the Mg location and create oxygen interstitials

In each case, provide a sentence or two explaining how$/$why you chose this dopant and then give the defect chemical reaction for adding this dopant to the $L{a}_{2}Mg{O}_4$ crystal.