ME 3701 Chapter : Indexing A Diffraction Pattern For Cubic Materials
Document Summary
Bragg"s law tells us the location of a peak with indices (cid:1)(cid:2)(cid:3) which is related to its interplanar spacing, (cid:4), by the relation. For cubic crystal structures, such as fcc and bcc, the interplanar spacing between two closest parallel planes with the same miller indices can be determined as (cid:1)(cid:2) = 2 (cid:6)(cid:7)(cid:8)(cid:9) sin(cid:13) (cid:14) (cid:6)(cid:7)(cid:8)(cid:9) = Combining these two equations gives (cid:21)(cid:22)(cid:1)(cid:17)(cid:13) = (cid:23) (cid:24)(cid:25) (cid:26)(cid:27)(cid:25)(cid:28)(cid:29) (cid:17) + (cid:19)(cid:17) + (cid:20)(cid:17)(cid:30) = (cid:31) (cid:29) (cid:17) + (cid:19)(cid:17) + (cid:20)(cid:17)(cid:30), (cid:31) = (cid:23) (cid:24)(cid:25) (cid:26)(cid:27)(cid:25)(cid:28) where , (cid:5), and (cid:6) are constants. It can be inferred that (cid:21)(cid:22)(cid:1)(cid:17)(cid:13) is proportional to (cid:17) + (cid:19)(cid:17) + (cid:20)(cid:17) i. e. planes with higher miller indices will diffract at higher values of . For any two different planes, the following can be written: The ratio of (cid:21)(cid:22)(cid:1)(cid:17)(cid:13) values scales with the ratio of (cid:17) + (cid:19)(cid:17) + (cid:20)(cid:17) values. This should yield a list of integers that represent the various values.
