Zirconia is a preferred material for thermal barrier coatings (TBCs) on the surface of super alloys in gas turbines due to its high melting point, low thermal conductivity and suitable thermal expansion coefficient. However, the tetragonal to monoclinic phase transition of pure zirconia in a service temperature range causes volume expansion and coating spalling failure. Y doping (YSZ) is commonly used to suppress this phase transition. With the development of gas turbines, higher requirements put forward for the service temperature and lifetime for TBCs. Sintering densification under long-term application of YSZ can increase the thermal conductivity and elastic modulus, which impairs its thermal insulation and damage tolerance. To address this issue, multi-element co-doping method was used to further improve the performance of YSZ. A doping material selection theory needs to be proposed from the point view of suppressing the tetragonal to monoclinic phase transition due to the large number of candidate dopant elements and complexity of doping composition ratios. Since the thermodynamic driving force for the tetragonal to monoclinic phase transition during cooling always exists, a key to stabilizing the tetragonal phase to room temperature increases the phase transition kinetic resistance. It is thus necessary to analyze the phase transition kinetic process to reveal the critical atomic relaxation mechanism related to high kinetic resistance, and propose theoretical strategies for stabilizing the tetragonal phase of zirconia.

In this study, a software package named VASP was employed for the relevant calculations of density functional theory (DFT). The electron-ion interaction was described by the projected augmented wave (PAW) potential function. The electron exchange-correlation energy was treated by the generalized gradient approximation (GGA). For elements Zr and O, their valence electron configurations were set as 4s², 4p⁶, 5s¹, 4d³ and 2s², 2p⁴, respectively. The cutoff energy of the plane wave basis set was set at 600 eV, and the k-point grid density based on the Monkhorst-Pack method was 4 × 4 × 4. During the structure optimization process, the energy convergence criterion was 1×10^–6 eV, and the force convergence criterion was 1×10^–4 eV/A.

The transition state search for the phase transformation from the tetragonal phase to the monoclinic phase was conducted by the solid-state nudged elastic band (G-SSNEB) algorithm in the VTST toolkit. During the transition state search, 12 images were inserted along the transition path, the maximum force threshold for the structural optimization of each image in the elastic band was set at 0.03 eV/A, and the energy convergence criterion was 1×10^–7 eV. The VTST toolkit was also used to analyze the Bader charge of different structures during the phase transition process.

We employed a software package named LOBSTER to perform orbital decomposition of the electronic structures of tetragonal and monoclinic zirconia phases, and analyzed the chemical bond properties within the crystal via calculating the crystal orbital Hamilton population (COHP).

The average coordination numbers in a monoclinic phase are lower than those in a tetragonal phase. In the monoclinic phase, Zr atoms exhibit a 7-coordinate environment, whereas O atoms display a mixed coordination of 4-coordinated and 3-coordinated states in equal proportions. Conversely, in the tetragonal phase, Zr and O atoms are exclusively 8-coordinated and 4-coordinated, respectively. The crystal structure analysis and COHP characteristics reveal that the Zr—O bonds in the monoclinic phase exhibit shorter average lengths and higher bond strengths, compared to those in the tetragonal phase. In addition, the [OZr] polyhedral in the monoclinic phase displays lower distortion degrees. These factors constitute the thermodynamic driving force for the tetragonal-to-monoclinic (t-m) phase transformation of zirconia during the cooling process. This indicates two pathways for the t-m phase transition via performing the transition state search. The energy barrier in path 1 is only 2.4 meV/f.u.. There is a meta stable orthorhombic phase in path 2, and the energy barriers for tetragonal-to-orthorhombic (t-o) and orthorhombic-to-monoclinic (o-m) phase transitions are 6.33 meV/f.u. and 27.03 meV/f.u., respectively. In path 1, t-ZrO₂ directly transforms into m-ZrO₂ via the sliding of the (010) Zr atomic layer, which is indicative of a martensitic phase transformation. The transition resistance in path 1 is attributed to the breaking of 1/8 Zr—O weak bonds. In the first step of path 2, the phase transition resistance is similar to that in path 1. Specifically, the 1/8 Zr—O weak bonds are broken via increasing the distance between (100) Zr atomic planes without any sliding, leading to an atomic coordination environment in o-ZrO₂ that closely resembles that of m-ZrO₂. In the second step in path 2 (o-m), the sliding of Zr atomic plane (100) leads to the alternative stacking of 3 and 4 coordinated O atoms along the (100) direction, accompanied by a high energy barrier. The high transition resistance is related to the broken of weak Zr—O bonds and the stretch of strong Zr—O bonds and increase of distortion degree of [OZr] polyhedral. It is thus plausible to infer that stabilizing the metastable phase with a coordination environment analogous to that of the monoclinic phase can significantly enhance the kinetic resistance to phase transition. This stabilization can result in the phase transformation necessitating the redistribution of 3- and 4-coordinated O atoms.

The transition state search indicated two t-m phase transition paths. Path 1 involved a one-step direct phase transition with an energy barrier of 2.4 meV/f.u., characterized by the sliding of Zr atomic plane (010), consistent with the shear-dominant characteristic of martensitic phase transitions. The low phase transition resistance could be attributed to the breaking of 1/8 Zr—O weak bonds. Path 2 proceeded in two steps via a metastable orthorhombic phase, with respective energy barriers of 6.33 meV/f.u. and 27.03 meV/f.u.. The high phase transition resistance of path 2 could be attributed to the redistribution of O atoms with different coordination numbers in the second step, which was related to multiple structure changes, including weak bond breaking, strong bond stretching and local distortion degree increasing. Enhancing the stability of low-coordination metastable structures and introducing spatial distribution reconstructions of O atoms with different coordination numbers could serve as a theoretical mechanism for suppressing the tetragonal to monoclinic phase transition.