A material composed of only one crystal is called a single crystal, a material which consists of two crystals is called
a bi-crystal, while a material composed of many grains is referred to as being polycrystalline. We described
a low angle, tilt grain boundary as being one which was composed of a series of edge dislocations spaced along the
plane of intersection between the two grains (crystals). In this exercise, you will investigate the relationship between
the magnitude of the tilt angle between the two grains, and the spacing between the edge dislocations along the
grain boundary. In the Picture file, you will find a slide with pairs of grains which have been tilted by 2°, 4°, or 6° from one another. Each square represents a cubic unit
cell and the axis of rotation is vertical, out of the page.
(a) For each pair of grains, move the grains so that they just overlap at the top of the drawing. You do NOT
need to perform any additional rotation of the grains. Print a copy of your slide for this step.
(b) A darker grey region should form in your image where the two crystal overlap. For each pair of grains,
remove unit cells from the left grain to eliminate the regions of overlap between the two crystals. It is Ok
to have some white regions between the two grains as the atoms adjacent to the white area will shift their
atomic positions to better accommodate the void. In general there will be much more open volume along
the grain boundary than in the unaffected region of the grain. Print a copy of your slide for this step.
(c) For each grain boundary, indicate the location of the edge dislocations with a ï symbol.
(d) For each grain boundary, determine the spacing between edge dislocations, D, in terms of the lattice
parameter, a. Print a copy of your slide for steps (c) and (d).
(e) Circle the correct answer that completes the sentence below.
The spacing between edge dislocations, D, _______________ the tilt angle of the grain boundary.
(i) is independent of
(ii) is inversely proportional to
(iii) has a linear relationship with
(iv) has a quadratic relationship with
(f) Circle the correct answer that completes the sentence below.
A tilt grain boundary is one where the axis of rotation of the grains is _____________ the plane of the grain
boundary.
(i) parallel to
(ii) perpendicular to
(iii) is canted out of the plane by an angle ï¹ 90ï° from
(g) On your drawing of the 2ï° tilt boundary, draw a Burgerâs circuit around a perfect region of the crystal AND
around an edge dislocation. Clearly mark the start and end positions of your Burgerâs circuit AND identify
the Burgerâs vector, B as the vector pointing from the end to the start of the Burgerâs circuit. Print a copy
of your slide for this step.
Note: Twist grain boundaries are related to screw dislocations in a similar manner, but the pictures are much
more difficult to draw.
The right grain in each pair is an image, and it is the bottom object in the stack. The left grain has unit cells which are grouped but you can still manipulate/erase individual unit cells. It might be a bit tedious to erase many unit cells.
