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

Physical and mechanical properties of polycrystalline materials are determined both by the properties and orientation of individual grains and grain boundaries. Function of mutual misorientation should be considered for description of orientation relations between the crystals. Since the mutual misorientation of two grains can be specified by misorientation angle (α) and misorientation axis (l), or by the Euler angles (φ, θ and ψ), then the mutual misorientation texture can be examined either in the crystallographic angle-axis space or in the Euler space. The mutual orientation of two adjacent crystals is described as a rotation of one crystal, relative to the other, on an angle  around the crystallographic axis (l), common to both grains, using the rotation matrix R = A₂^–1·A₁ (A₂ and A₁ are the crystals' orientation matrix). As a result of the crystal lattice symmetry, the misorientation of crystals can be physically described by equivalent misorientation, using the matrix R = R·C_i^–1, where C_i are the rotation elements of crystal symmetry. The orientation distribution function for α-zirconium is calculated from the pole figures 0002 and 100. For the purpose of determination of distribution function of the mutual misorientation of crystals, several sections of the orientation distribution function were taken in 5^о increments by the parameter j. Several points, corresponding to the maximum and distribution wings, were selected for each section. The data on the distribution function of the mutual misorientation of crystals for -zirconium in the Euler space and in the “angle α – axis l” space are presented. They show that mutual misorientation does not fill the entire space, so it is possible to obtain the mutual misorientation texture in rolled polycrystalline α-zirconium.

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