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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.

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Question Bank - Bravais Lattice, Miller indices, Bragg's Law

See the attached file.

1. We know that face centered lattice in cubic and orthorhombic (FCC & FCO) system are listed in Bravais lattice system but face centered tetragonal (FCT) is not listed, why?
2. Draw the plane with miller indices (122) in the unit cell of cubic lattice having lattice parameter 'a'. Find its distances from the parallel plane through the origin.
3. Find the miler indices of plane which makes intercept of 2 on a-axis and 3 on b-axis and is parallel to c-axis.
4. Find the miller indices of plan that makes intercepts on a, b and c axis equal to 4 A, 2 A and 3 A in the orthorhombic crystal with a : b : c = 2 : 4 : 3.
5. The Bragg angle for reflection from (110) plane is 20.2 degree. Find the wavelength of X-ray. (lattice parameter of the crystal is 3.15 A).

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