Strange logic, you want to adjust the calculated parameters of the model so that the transition m-t in ZrO2 takes place at practically certain dopant concentrations, considering that in this way you prove that the transition takes place precisely at this concentration.

Are you sure that this model will work in case of Sc, or you adjust the parameters also?

No, dear Vadim Sergeevich. You misunderstood me. The fact is that, according to some recent experimental work, monoclinic zirconia after doping with more than 3 mol% Y2O3 takes on a tetragonal phase. However, according to my calculations, this does not happen. Therefore, I turn to experts and specialists about how to correctly relax the system so that everything works?

I think maybe I'm doing the calculations wrong or somewhere I don't take into account some parameter.

Dear Nematov,

Admittedly you are not offering enough pieces of information to help you.

1) How did you simulate your system? How big the unit cell and other parameters to dope the system? Did you use any model for the doping?

2) How did you relax the system?

3) Did you try to do the reverse? Namely, if you start from the tetragonal or cubic phases, do you get energies that are lower than the corresponding monoclinic phase at the same doping concentration? (This indirectly proves if you could detect the transition.) What happens if you try to increase/decrease the doping level for the two structure?

It is possible that the relaxation mechanism in Vasp are not able to produce the transition. Remember that the search for the optimised structures looks mostly for "local" minima and thus you might end up stuck in one of those rather than reaching a better minimum with a structural transition.

From the experimental point of view, the transition might also be triggered by a certain amount of impurities and defects that might render the structural change simpler.

I hope this helps,

Roberto

In the scientific field, the transformations from alfa to beta or gama are made by pressure and temperature and mostly the transformation is the form of a crystal .

Thank you very much for your comments dear Roberto.

1. When modeling, I relaxed the system throughout all degrees of freedom (ISIF=3 - internal coordinates, shape and volume). To do this, I created a 2x2x2 supercell consisting of 96 atoms, and then replaced the corresponding number of yttrium atoms with zirconium, taking into account the oxygen vacancy.

2. We relaxed the system at ISIF=3 by

structural optimization within LDA.

INCAR file parameters are shown below:

SYSTEM = 123

PREC = Accurate

ALGO=NORMAL

LREAL = Auto

ENCUT = 425

NELMIN = 6

ISPIN = 2

LWAVE = .T.

LCHARG = .T.

ISMEAR = 0

SIGMA = 0.05

EDIFFG = -0.005

NSW=400

IBRION = 2

ISIF = 3

ISTART = 0

ICHARG = 2

EDIFF=1.0E-05

3.No. I haven't tried this before opposite. Nothing will happen when the doping concentration is increased. It's just that the volume and lattice parameters change, and there will be no distortion until the new phase.

My third question was aiming at understanding if DFT can predict the phase change. If you construct a structure with the structure of the experiments and compare the energies of the doped structures, what do you get? If VASP finds that the energy of the doped monoclinic is smaller than the energy of the doped tetragonal then there is no hope to see any structural change.

On the other hand, if VASP puts the energy according to the experiment, it is possible to find a way to observe the phase transition. However, it still might be difficult as the structural change might be far in coordinate space.

Another point you might need to consider: Are the two structures commensurate? You said you build up a structure with 96 atoms. And then doped it. Does the tetragonal phase reconstruct to give you a certain supercell (not necessarily 2x2x2) with 96 atoms?

I hope this helps,

Roberto

Thank you very much for your answer dear Roberto!.

Regarding your third question, I want to note that yes, using DFT calculations, it is possible to detect phase transitions of materials under the influence of temperature, pressure and alloying.

Regarding your question and sentence " If you construct a structure with the structure of the experiments and compare the energies of the doped structures, what do you get? " then I have not tried this yet, since I am new to DFT and VASP calculations, but I try to do it as much as possible, if I can, of course.

YES, if you create a 2x2x4 supercell from a tetragonal phase, then the number of atoms will be 96.

The ZrO2-Y2O3 system has been studied for many years and by many scientists (see, for example, a short review http://journals.ioffe.ru/articles/viewPDF/47849). It is difficult to expect "discoveries" here. Especially related to changing the m-t transition boundary (by the way, it depends on temperature; this diagram is easy to find on the Internet; see, for example, in https://pandia.ru/text/80/246/47322-8.php). It is essential that in reality, especially at low temperatures, it is very difficult for the system to achieve equilibrium, and, as is often the case in technology, a metastable, "supercooled" composition is used. The limit is about 7 wt. %, indicated in many works, refers to a technologically stable material, and 2.8 wt. % - to the "equilibrium" diagram (and then near RT ...). Although these are fundamentally different values. Moreover, industrial designs require not only special mechanical, but also, for example, electrical properties.

See also https://diss.unn.ru/files/2019/940/diss-Sidorova-940.pdf or even http://www.issp.ac.ru/lsds/pdf/StepanovaMaster.pdf (all literature - in Russian).

As for computer simulation, my doubts remain. After all, you model a crystal lattice, but compare it with a material (the properties of which are determined not only and not so much by the crystal structure ...).