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Abstract
On the basis of a simple geometrical analysis, exact formulae for the average misorientation angle of random tilt boundaries in the structural unit and disclination models are obtained. Two important consequences following from these formulae are considered: the relation between the Burgers vector of grain boundary dislocations and the geometrical parameters of short-period areas composing the random boundary, and an exact expression for the Burgers vector of a dislocation equivalent to a disclination dipole with given strength and structure of the related boundary
