Make a table with five columns. Label the first two columns “hkl” and “ s ”. Usi

Question

Make a table with five columns. Label the first two columns “hkl” and “s”. Using h2 + k2 +l2 = s, generate a series of hkl reflecting planes and their associated “s” values from 1 to 24. Thus, for {100} the first value of s = 1, and for {110} the second value of s = 2, etc. Label the other three columns “primitive cubic”, “body-centered cubic”, and “face-centered cubic”. Use the structure factor rules for these Bravais lattices to write a “yes” in the column for each crystal structure opposite the “s” values for which a diffracted peak is expected to occur.

Explanation / Answer

In Cubic system , the first XRD peak in the diffraction pattern will be due to diffraction from plans with lowest Miller indices.

Conditions for allowed reflection from cubic lattice

1. Primitive - all possible h, k, l values

2. Body centered-

a) reflection is allowed when ( h+ k+ l) is even

b) reflection is not allowed when (h+k+l) is odd

3) face centered

a) reflection is allowed when h, k, l values are either all odd or even

b) reflection is not allowed when h,k, l values are mixed ( odd and even)

hkl s = h2+k2+ll2 primitive cubic BCC FCC 100 1 ? × × 110 2 ? ? × 111 3 ? × ? 200 4 ? ? ? 210 5 ? × × 211 6 ? ? × 220 8 ? ? ? 300,221 9 ? × × 310 10 ? ? × 311 11 ? × ? 222 12 ? ? ? 320 13 ? × × 321 14 ? ? × 400 16 ? ? ? 410,322 17 ? × × 411,330 18 ? ? × 331 19 ? × ? 420 20 ? ? ? 421 21 ? × × 332 22 ? ? × 422 24 ? ? ? 430 25 ? × × 431 26 ? ? ×

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