National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow, Russia:

T. P. Khramtsova, Post-Graduate Student
V. I. Skrytnyy, Senior Researcher, e-mail: VISkrytnyj@mephi.ru
V. N. Yaltsev, Assistant Professor

Consideration of orientation distribution function makes it possible to investigate the orientation-dependent properties of polycrystalline materials. However, it is necessary to know the mutual disorientations of neighboring grains to describe such properties as grain-boundary diffusion, grain-boundary migration and slipping along the grain boundaries. Application of disorientation matrices allows to construct a disorientation distribution function both in angle-axis crystallographic space and in Euler space. This method was applied for rolled polycrystalline α-zirconium. In particular, mutual disorientations do not fill the whole space, which leads to the possibility of appearance of mutual disorientations, texture in rolled polycrystalline α-zirconium. The physicomechanical properties of polycrystalline materials are determined both by the properties and orientation of individual grains and grain boundaries. For the purpose of description of orientation relationships between the crystals, it is necessary to consider the orientation distribution function. Since the mutual disorientation of two grains can be specified by rotation angle (α), rotation axis (l), or by Euler angles (φ, θ and ψ), then mutual disorientations, texture can be considered either in angle-axis crystallographic space or in Euler space. Mutual disorientation of two neighboring crystals is described as the turn of a crystal relative to another one by the disorientation matrix R = A₂^–1·A₁ (where A₂ and A₁ are orientation matrices of crystals). Because of the crystal lattice symmetry, disorientation can be described by physically equivalent turns with matrices R_i = RC_i^–1, where Ci is the turning element of the crystal symmetry. The data about mutual disorientation distribution function of crystals for α-zirconium are presented both in Euler space and in “angle α – axis l” space.

This work was carried out within the Centre “Nuclear Systems and Materials” with the state support of the Program of Improvement of the Competitiveness of National Research Nuclear University MEPhI (agreement with the Ministry of Education and Science of the Russian Federation (August 27, 2013; No. 02.а03.21.0005)).

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