Hello,
Normally, the lattice constant increases with addition of rare earth doping which is owing to the difference in ionic radii of rare earth ion and Ti4+ ions. However, in my present case, the lattice constant increases for some Ln3+ ion concentration of doping at decreases for others what is the reason of this non-linear variation of the lattice constant.
best regards.
Leonardo Saraiva
Dounia Hamdi
There's no straightforward answer to your question. First, you need to be sure that you have only the lattice phase that interests you, the formation of spurious phases affects lattice constants. Once you have sure, you can look to the electronic effects of doping, and not only the size effect. If you are replacing a 4+ cation with a 3+ cation there'll be more charge defects in your system, which will have different effects. For instance, if your defect concentration is too high, your system will be smaller, since it will attract atoms to each other to compensate for the electronic defect. If you are doping with a lanthanide such as Terbium or Cerium whose oxidation states can be 3+ or 4+, there might be a mixture of oxidation states, and therefore some of the defects will be compensated by the concentration of ions in 4+ state, which will allow you to have a higher lattice constant due to the expansion of the lattice.I suggest you perform a Rietveld refinement of your system and a X-ray photoelectron spectroscopy analysis to estimate the oxidation states of your ions.
Good Luck!
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