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Cubic and Orthorhombic Crystals

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Show that the general direction [ hkl ] in a cubic crystal is normal to the planes with Miller indices (hkl). Is the same true in general for an orthorhombic crystal?

Show that the spacing d of the (hkl) set of planes in a cubic crystal with lattice parameter a is:

d = (a)/(h^2 + k^2 +l^2)^(1/2)

What is the generalization of this formula for an orthorhombic crystal?

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Solution Preview

To get a through understanding the problem, an introduction to Miller indices and a note on "how to construct the Miller indices planes" are given. I have used x, y and z as the points of interception of the miller indices planes to the x ,y, and z axis. The vectors along the x,y and z coordinates are represented by a,b,c in ...

Solution Summary

This solution provides an introduction to Miller indices and the construction of Miller indices planes. From the point of interception of the miller indices planes to the x ,y, and z axis, the miller indices planes are described. The derivation is performed based on the method of directional cosines, and by Weiss Zone Law. The full solution is provided in an attached Word document.