Molybdenum (Mo) and its alloys comprise an important group of metals used typica

Question

Molybdenum (Mo) and its alloys comprise an important group of metals used typically for applications requiring high corrosion resistance, chemical resistance and thermal resistance. The figure below shows the X-ray diffraction pattern of a sample of molybdenum metal measured at room temperature using an X-ray powder diffractometer equipped with monochromatic Cu-Ka radiation (wavelength of 0.1542 nm). The pattern shows the first three diffraction peaks of the metal and the (hkl) indices of the peaks in the pattern have been identified ("indexed"). The diffraction angle (2theta°) and relative intergrated diffraction intensities (Irel) of the peaks (as determined by the XRD software) are given in the figure.

a Assuming that the metal is cubic, explain whether it is likely to be to be primitive cubic, BCC, or FCC based on consideration of the (hkl) indices indicated in the diffraction pattern.

b  For the crystal structure determined in Part a), calculate the interplanar spacing for each set of (hkl) planes and determine the lattice parameter and density of the metal (use Mo atomic weight = 95.94). Compare the calculated density with a published value (state source).

c  For the crystal structure determined in Part a), derive an expression for the structure factor of the metal and used it to confirm the (hkl) peaks that appear in the pattern and explain why other peaks such as (001), (111) are absent.

d  Use the structure factor derived in Part c) and other relevant data to calculate the intensity of the peaks. Compare your calculated intensities with those stated in the measured pattern and explain any significant similarities/differences between the calculated and measured intensities.

20000 (110) Peak 200Irel 200rel (110) 40.58 100 (200) 58.76 14 211)7.72 25 15000 10000 (211) 5000 (200) 0 20 30 4050 60 7080 20 (degree)

Explanation / Answer

ANSWERS:

a) Assuming that metal is cubic and by the (hkl) indices as obtained from the X-Ray diffraction, the crystal structure indicates a FCC crystal structure, for which a = 4.95

b) Based on the hkl indices given

the interplanar spacing for each set is calculated as follows,

1/(d110 )2 = [ { (12) + (12) + (02) } /a2 ]

Similarily for the The other two indices

1/(d200 )2 = [ { (22) + (02) + (02) } /a2 ]

1/(d211 )2 = [ { (22) + (12) + (12) } /a2 ]

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