硅酸盐学报

氧化锆四方到单斜相变的原子弛豫机制

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孙雨萌 ¹ , 罗文东 ² , 张思岩 ³ , 孙鲁超 ⁴ , 王杰民 ⁴ , 王京阳 ⁴

硅酸盐学报 | 研究论文 2026,54(3): 1052-1062

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硅酸盐学报 |研究论文 2026 , 54 (3) : 1052 -1062

氧化锆四方到单斜相变的原子弛豫机制

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孙雨萌¹, 罗文东², 张思岩³, 孙鲁超⁴, 王杰民⁴, 王京阳⁴

作者信息

^1．沈阳化工大学，沈阳 110142

^2．中国航空制造技术研究院，北京 100024

^3．辽宁材料实验室燃氢防护技术研究所，沈阳 110167

^4．中国科学院金属研究所，沈阳 110016

通讯作者:

罗文东（1989—），男，硕士，高级工程师

王杰民（1984—），男，博士，副研究员。

作者简介:

孙雨萌（2000—），女，硕士研究生。

Atomic Relaxation Mechanisms on Tetragonal-to-Monoclinic Phase Transitions in Zirconia

Yumeng SUN¹, Wendong LUO², Siyan ZHANG³, Luchao SUN⁴, Jiemin WANG⁴, Jingyang WANG⁴

Affiliations

^1.Shenyang University of Chemical Technology, Shenyang 110142, China

^2.Manufacturing Technology Institute, Aviation Industry Corporation of China, Beijing 100024, China

^3.Hydrogen fuel protection Technology Institute, Liaoning Academy of Materials, Shenyang 110167, China

^4.Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China

Corresponding Author:

LUO Wendong (1989-), male, Senior Engineer. E-mail: lwd524057@163.com

WANG Jiemin (1984-), male, Associate Professor. E-mail: jieminwang@imr.ac.cn

SUN Yumeng (2000-), female, Master candidate. E-mail: 2191982605@qq.com

出版时间: 2026-03-20 doi: 10.14062/j.issn.0454-5648.20250175

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摘要

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抑制氧化锆在高温时从四方相到单斜相的相变过程是其作为热障涂层等高温结构材料领域应用的核心需求。目前，实验上广泛采用掺杂的方法实现这一目标，但是对于抑制相变的动力学原理尚不清楚。基于第一性原理计算和过渡态搜索的方法，系统研究了氧化锆从四方相向单斜相转变的可能路径和不同相变路径对应的能垒和原子弛豫机制。计算结果表明，单斜相中3配位和4配位氧原子混合的结构比四方相全4配位氧原子结构具有更高的平均键合强度，是其低温下热力学稳定的根源。四方相向单斜相转变有2条路径：第1条路径以原子面切变方式一步转变为单斜相，对应能垒低（2.4 meV/f.u.）、动力学阻力小；第2条路径以一个亚稳相过渡，经历配位数改变和不同配位氧原子空间分布重构2步完成，相变过程最高能垒达27.03 meV/f.u.。不同配位氧原子空间分布重构对应的能垒远大于配位数改变的能垒，是阻碍四方相向单斜相转变的重要动力学机制。

关键词

氧化锆 / 相变 / 第一性原理

Abstract

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Introduction

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.

Methods

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).

Result and discussion

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.

Conclusions

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.

Key words

zirconia / phase transition / first-principles

引用本文

孙雨萌, 罗文东, 张思岩, 孙鲁超, 王杰民, 王京阳. 氧化锆四方到单斜相变的原子弛豫机制. 硅酸盐学报, 2026 , 54 (3) : 1052 -1062 . DOI: 10.14062/j.issn.0454-5648.20250175

Yumeng SUN, Wendong LUO, Siyan ZHANG, Luchao SUN, Jiemin WANG, Jingyang WANG. Atomic Relaxation Mechanisms on Tetragonal-to-Monoclinic Phase Transitions in Zirconia[J]. Journal of the Chinese Ceramic Society, 2026 , 54 (3) : 1052 -1062 . DOI: 10.14062/j.issn.0454-5648.20250175

基金

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中国科学院C类先导专项(XDC0160203)
中国航发集团产学研合作项目(HFZL2023CXY022)

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2026年第54卷第3期

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文章信息

doi: 10.14062/j.issn.0454-5648.20250175

接收时间：2025-03-13
首发时间：2026-10-27
出版时间：2026-03-20

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收稿日期：2025-03-13
修回日期：2025-04-02

基金

中国科学院C类先导专项(XDC0160203)

中国航发集团产学研合作项目(HFZL2023CXY022)

作者信息

^1．沈阳化工大学，沈阳 110142

^2．中国航空制造技术研究院，北京 100024

^3．辽宁材料实验室燃氢防护技术研究所，沈阳 110167

^4．中国科学院金属研究所，沈阳 110016

通讯作者:

罗文东（1989—），男，硕士，高级工程师

王杰民（1984—），男，博士，副研究员。

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https://castjournals.cast.org.cn/joweb/gsyxb/CN/10.14062/j.issn.0454-5648.20250175

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2种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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