1 / 6

Miller Indices & Steriographic Projection

Miller Indices & Steriographic Projection. The Miller indices can be determined from the steriographic projection by measuring the angles relative to known crystallographic directions and applying the law-of-cosines. (Figure 2-39 Cullity).

Download Presentation

Miller Indices & Steriographic Projection

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Miller Indices & Steriographic Projection The Miller indices can be determined from the steriographic projection by measuring the angles relative to known crystallographic directions and applying the law-of-cosines. (Figure 2-39 Cullity) For r, s, and t to represent the angles between the normal of a plane and the a1, a2, and a3 axes respectively, then: Where a, b, and c are the unit cell dimensions, and a/h, b/k, and c/l are the plane intercepts with the axes. The inner planar spacing, d, is equal to the distance between the origin and the plane (along a direction normal to the plane).

  2. Vector Operations Dot product: Cross product: b a a Volume:

  3. Reciprocal Lattice Unit cell: a1, a2, a3 Reciprocal lattice unit cell: b1, b2, b3 defined by: b3 B P C a3 a2 A O a1

  4. Reciprocal Lattice Like the real-space lattice, the reciprocal space lattice also has a translation vector, Hhkl: Where the length of Hhkl is equal to the reciprocal of the spacing of the (hkl) planes Consider planes of a zone (i.e..: 2D reciprocal lattice). Next overhead and (Figures A1-4, and A1-5 Cullity)

  5. Zone Axis Planes could be translated so as not to intersect at a common point.

  6. C (hkl) dhkl H N B O f A Reciprocal Lattice (Zone Axis) Zone axis = ua1 + va2 + wa3

More Related