[Image above] Atomic perspective of vacancies and vacancy complexes in strontium titanate (SrTiO3). North Carolina State University researchers showed there is a significant difference between barium titanate and strontium titanate defect mechanisms. Credit: Jonathon Baker
“You two look exactly the same!” If identical twins earned a dollar for every time they heard that phrase, they would be millionaires within a year. When it comes to twins, people focus so much on exterior similarities that they commonly forget to look for internal dissimilarities, which can be detrimental when twins seek medical treatment and the doctor assumes their genetic profiles are perfect duplicates of each other (multiple studies showed this is not the case).
Making assumptions based on surface similarities is not limited to fans fawning over Mary-Kate and Ashley Olsen at a meet-and-greet. Scientists make these kinds of assumptions as well when they categorize similar materials to simplify research—assumptions that sometimes result in scientists overlooking stark differences.
One example of this assumption happens in electronics. Barium titanate (BTO) and strontium titanate (STO) are materials central to established electronics technology. They serve both separately and together in an array of products, including thin film and multilayer ceramic capacitors, positive temperature coefficient resistors, and varactors.
Researchers largely believe the dominant metal vacancy in BTO is a B-site vacancy (the position normally filled by a titanium atom is vacant) while STO experiences more vacancies at the A site (the position normally filled by a strontium or barium atom is vacant). Despite this difference, researchers sometimes treat point defects in BTO and STO as analogues, and use models of the mechanisms and defects interchangeably with minor modifications.
If researchers suspect there may be a difference in dominant metal vacancy sites, why do they use almost identical defect models for these two separate materials? In an email, Douglas Irving, university faculty scholar and associate professor of materials science and engineering at North Carolina State University, says there is no easy answer to that question.
“These are pretty complex materials and it can be hard to measure all the relevant properties, including the metal vacancy concentrations,” Irving says. “As such, there is a big challenge in getting all of this data and, because of the similar structure/chemistry, it is a reasonable first order approximation to expect that defects might have some similarities. Nevertheless, subtle property differences may not be captured with a first order approximation.”
While understanding these specifics may not be essential for some applications, applications that involve donor doping—like varactors—exacerbate the difference between the materials’ vacancy defects and make accurate models even more important. In these situations, then, correctly modeling metal vacancies is crucial.
“Although BTO is a simple isovalent modification of STO with [barium] substituting [strontium] on the A sublattice, vacancy behavior differs dramatically between the two systems,” they say in the paper. Using a state-of-the-art hybrid exchange correlation functional to perform density functional theory calculations, the researchers found A-site vacancies dominate in STO (with B-site vacancies only favorable in donor-doped, highly oxidizing conditions), but that BTO experiences different combinations of A-site, B-site, and vB-vO complexes depending on how the material was processed and doped (a vB-vO complex is a vacancy of titanium and oxygen atoms on neighboring sites).
To highlight BTO’s vacancy reliance on processing and doping choices in comparison to STO, the researchers ran simulations where BTO and STO were doped with niobium and iron, two donor dopants commonly used in these systems. Then, they varied processing methods and measured the simulated results. They found while A-site vacancies dominated in STO despite changes in processing method, the ratio of A-site, B-site, and vB-vO complexes changed noticeably in BTO.
In the paper, the researchers say two mechanistic reasons explain these differences in metal vacancy behavior: thermodynamic differences in the accessible processing conditions of the two materials, and energy differences in bonds broken when forming vacancies.
“First, the two materials have slightly different chemical environments for the same processing conditions. Because of this, it requires less energy to lose an A-site atom in STO than BTO for equivalent processing conditions,” they explain. “Second, differences in the electronic energy changes associated with removing cations from each material enhance the favorability of [A-site] in STO, and of [B-site] and the vB-vO complex in BTO.”
While their research addressed some of the BTO-STO debate, Irving explains there is still a lot of work to be done, particularly on dopants that cause the materials to become insulating.
“I would say that the current models in widespread use are suitable for modeling donor impurities like lanthanum and niobium that push the electron concentration high enough to overcome the aforementioned measurement challenges, in both materials,” he says. “However, for dopants in insulating BTO and STO there is a much more subtle balance and because of this there is still work to be done to bring the two defect frameworks together for these cases.”
The paper, published in Journal of Applied Physics, is “Mechanisms governing metal vacancy formation in BaTiO3and SrTiO3” (DOI: 10.1063/1.5044746).