A physical quantity used to predict the variant selection tendency of phase transition processes - phase transition orientation difference

The nucleation of solid-state phase transitions in polycrystalline metallic materials preferentially occurs at grain boundaries, and the parent phase and the child phase generally have a fixed orientation relationship. Therefore, the structure of the parent phase grain boundaries has a direct impact on the variant orientation, microstructure morphology, and properties. The in-phase grain boundaries alone require five degrees of freedom to be defined geometrically, and their complexity makes it difficult to describe them precisely. If the phase transition process is involved, it becomes even more complicated. Therefore, the reverse design of material structure through interface control still needs theoretical and conceptual innovation.

During his tenure in the high-temperature titanium alloy research team of the former Institute of Metal Research, Chinese Academy of Sciences, Researcher Zhao Zibo proposed a new physical quantity for describing the crystal orientation relationship of the parent Phase grains - Phase Transformation Misorientation (θp). This physical quantity is defined as: the minimum Angle at which the parent phase grains rotate to produce any sub-phase with the adjacent grains. Its mathematical expression is:

Among them, G₁ and G₂ respectively represent the orientation matrices of two adjacent parent phase grains; T is the phase transformation matrix, representing all potential parent phase orientations that may produce subphases during the phase transformation process of grain G₁. R represents the phase transition orientation difference rotation matrix. Considering the crystal symmetry, its expression is:

Si represents the symmetry operation matrix of the parent phase grains, and i indicates the number of symmetry operation matrices. For example, in the cubic crystal system,i =24. Therefore, the minimum rotation Angle can be obtained through the rotation matrix Ri as:

In the formula, tr(R) represents the trace of the phase transition orientation difference rotation matrix.

Based on the definition and the experimental results in titanium alloys, the study confirmed that the phase transition orientation difference can more directly reflect the free energy changes of the subphase variants at the grain boundaries after phase transition, and effectively evaluate the tendency of the grain boundaries to select subphase variants. The article also discusses the synergistic effect of phase transition orientation difference and grain boundary planes in variant selection prediction, and analyzes the influence of cooling rate on phase transition orientation difference in evaluating variant selection tendency. The introduction of phase transition orientation differences is conducive to deepening the understanding of the physical essence of the solid-state phase transition process at grain boundaries. The research results are presented as "An orientation relationship between parent grains and its application to variant selection of transformed α in. titanium alloys was published online in the journal Metallurgical and Material Transactions A. Given the innovation and systematicness of this work, the article was recommended by the chief editor as a free and open-source article.

Orientation difference, which is used to describe the orientation relationship of crystals, is also frequently employed in materials science for the analysis and research of microstructure evolution, recrystallization processes, and grain boundary structures, etc. Similar to the orientation difference between two grains, as a fundamental physical quantity used to describe the orientation relationship between grains with the same crystal structure, phase transformation orientation difference shows extensive application potential. This concept not only helps to deeply reveal the solid-state phase transformation mechanism in polycrystalline metallic materials, but also provides an important theoretical basis for optimizing the grain boundary design of the parent phase and directivity regulating the microstructure morphology and texture after phase transformation, thereby promoting theoretical innovation and practical application of grain boundary engineering.

The first author of the paper is Liu Yuanhong, a master's graduate from the Institute of Metal Research, Chinese Academy of Sciences. The corresponding authors are Researcher Zhao Zibo and Researcher Wang Qingjiang. Engineer Yang Jiuxu provided important experimental verification data and participated in the concept demonstration. Researcher Liu Jianrong guided the experimental design, and Researcher Yang Rui guided the concept deepening. Teacher Liu Yujing from Yuhua Research Institute provided crucial guidance in aspects such as conceptual argumentation and optimization of paper structure.

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