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Temperature-Dependent Phase Transitions of ZrO₂
The temperature-induced phase transition from monoclinic to tetragonal ZrO₂ is predicted from first principles calculations using a quasi-harmonic approach for the vibrational enthalpy and entropy. The computed transition temperature is within 15% of the experimental value. Relative trends due to vacancies, alloying elements, and mechanical stress can be expected to have a higher accuracy. The present results show the importance of thermal expansion, which is here also obtained from first principles.
At low temperatures, the most stable phase of ZrO₂ is a monoclinic form, which occurs naturally as the mineral Baddeleyite. At a temperature of 1478 K and ambient pressure, a tetragonal structure becomes thermodynamically stable. At 2650 K the tetragonal structure changes into a cubic calcium fluoride structure. The mineral name zirconia is used for both the tetragonal and the cubic structures. ZrO₂ melts at 2983 K.
The present first-principles calculations correctly predict the monoclinic phase of ZrO₂ to be more stable at low temperatures with the tetragonal phase becoming more favorable at high temperatures. The computed transition temperature is 1700 K compared with an experimental value of 1478 K. This deviation of 15% is a respectable result given the subtle nature of temperature-induced phase transitions.
The graph below plots the difference in the free energy of the low-temperature monoclinic and the high- temperature tetragonal phases of zirconia. The solid red line includes effects of thermal expansion. The results shown as dashed line use the computed lattice parameters at T=0 K.
The ability to predict temperature-dependent phase transitions with a first-principles method opens the door for systematic studies of the effect of vacancies, dopants, and external strains on the transition temperature providing useful materials property data as well as insight into the role and mechanism of vacancies, doping, and mechanical load. Relative trends such as stress-induced changes are likely to be more accurately described than the absolute value of a transition temperature.
MedeA®modules used for this application
The present calculations were performed with the MedeA®platform using the following integrated modules of the MedeA®software environment
- Standard MedeA®framework including crystal structure builders and geometric analysis tools as well as JobServer and TaskServers
- InfoMaticA with structural databases (ICSD, Pearson, Pauling) – in this case each of these databases contains the various phases of ZrO2
- VASP 4.6 and its graphical user interface as integrated in MedeA
- Phonon as integrated in MedeA®