Determining Miller Indices of High Index Planes

[beaverdam]

Hi,

can anyone explain how miller indices can be determined for high index planes?
For example, why is it that

(544) = (S)-[ 9(111) x (100) ]

I tried to figure it out but i could no find a pattern

Thx in advance

 

[Modey3]

3-component Miller Indices are defined in terms of cubic unit cells. Go back to the definition of a Miller Index. For (544) = (S)-[ 9(111) x (100) ], I cannot answer because I don't know what S is.

modey3

 

[charng]

Hi there,

Miller indices are used to describe the orientation of crystal planes in a crystal lattice. They are determined by taking the reciprocal of the intercepts of the plane on the crystal axes. In the case of high index planes, the intercepts may not be obvious and require some additional calculations.

In the equation you provided, (544) is the Miller index for a high index plane, and it is derived from the formula (hkl) = (S)-[ n(abc) x (uvw) ], where S is the smallest integer that makes all indices positive, n is the order of the plane, and (abc) and (uvw) are the normal vectors of the plane and the axes of the crystal, respectively.

In this case, (111) and (100) are the normal vectors of the plane and the crystal axes, respectively. By taking the cross product of these vectors, we get a vector that is perpendicular to both and represents the direction of the plane. This vector is then multiplied by the order of the plane, which in this case is 9, to account for the fact that it is a high index plane. Finally, the smallest integer S is chosen to make all indices positive, which in this case is 1.

I hope this explanation helps to clarify the process of determining Miller indices for high index planes. It may seem complex, but with practice, it becomes easier to identify patterns and apply the formula.