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A tilt boundary along the xy-plane can be envisaged to consist of a series of parallel edge
dislocations, all with the same Burgers vector b with a length of 0.23 nm. The boundary has
dimensions of x = 30 ¦Ìm by y = 15 ¦Ìm. The tilt angle ・is 6o around an axis in the x direction.
A) What is the direction of the dislocation lines (x, y or z)?

B) What is the distance between dislocations in the boundary, both in meters and in number
of atomic distances?
C) Calculate the dislocation density ¦Ñ・(defined as dislocation line length per unit of volume)
in a volume x ¡Á y ¡Á z = 30 ¦Ìm ¡Á 15 ¦Ìm ¡Á 1 ¦Ìm enclosing the grain boundary.
D) In the case of a random distribution of dislocations the dislocation energy per unit of
volume is given by Ed = ½¦Ìb2¦Ñ, with ¦Ì the shear modulus (160 GPa). Discuss the relation
between this dislocation energy and the interfacial energy ¦Ã.
E) Calculate Ed from the dislocation density found in question c)
F) Give the equation expressing the relation between the dislocation energy Ed and the
interfacial energy ¦Ã. What is the resulting value of ¦Ã?
G) The value for the interfacial energy calculated along the line in the previous questions is
higher than the actual value of the interfacial energy. Explain why.

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