A specimen is made of 80 atom % iron and 20 atom % Ni. When sufficient FCC nickel is added to BCC iron, it is possible to produce FCC iron-nickel alloys, which are austenitic. The results of an x-ray diffractometer scan of this specimen with cobalt K? radiation that has a wavelength of 0.1790 nm results in peak intensities at the following angles: 26.1°, 30.56°, 45.99°, 57.49°, and 61.74°.
(a) Is this iron-nickel alloy BCC or FCC?
(b) Determine the lattice parameter using the 26.1? peak.
All of the terms in this equation will be constant for the different peaks except h, k, and l. Thus the sum of the squares of the possible h, k and l values should be in the same sequence as the squares of the square of the sine of the diffraction angles. The squares of the sine of theta are as follows: 0.194, 0.259, 0.517, 0.711, and 0.776. Dividing each of these by 0.194 the sequence is: 1, 1.33, 2.66, 3.66, and 4. If we multiply this sequence by 3 the result is 3, 4, 8, 11, and 12 or the sequence for the FCC structure.
For the FCC structure the possible reflections must be h, k, and l unmixed or
(111), (200), (220), (311), (222)….. For these peaks the values of 2 22 ( ) hkl + + are:
3, 4, 8, 11, 12, 16,…….
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