Grain Boundary - Describing A Boundary

Describing A Boundary

A boundary can be described by the orientation of the boundary to the two grains and the 3-D rotation required to bring the grains into coincidence. Thus a boundary has 5 macroscopic degrees of freedom. However, it is common to describe a boundary only as the orientation relationship of the neighbouring grains. Generally, the convenience of ignoring the boundary plane orientation, which is very difficult to determine, outweighs the reduced information. The relative orientation of the two grains is described using the rotation matrix:

R = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}

Using this system the rotation angle θ is:

while the direction of the rotation axis is:

The nature of the crystallography involved limits the misorientation of the boundary. A completely random polycrystal, with no texture, thus has a characteristic distribution of boundary misorientations (see figure). However, such cases are rare and most materials will deviate from this ideal to a greater or lesser degree.

Read more about this topic:  Grain Boundary

Famous quotes containing the words describing a, describing and/or boundary:

    “I am not describing a distant utopia, but the kind of education which must be the great urgent work of our time. By the end of this decade, unless the work is well along, our opportunity will have slipped by.”
    —Lyndon Baines Johnson (1908–1973)

    “I am not describing a distant utopia, but the kind of education which must be the great urgent work of our time. By the end of this decade, unless the work is well along, our opportunity will have slipped by.”
    —Lyndon Baines Johnson (1908–1973)

    “It appeared that he had once represented his tribe at Augusta, and also once at Washington, where he had met some Western chiefs. He had been consulted at Augusta, and gave advice, which he said was followed, respecting the eastern boundary of Maine, as determined by highlands and streams, at the time of the difficulties on that side. He was employed with the surveyors on the line. Also he called on Daniel Webster in Boston, at the time of his Bunker Hill oration.”
    —Henry David Thoreau (1817–1862)