Some problems around the application of XRD powder

1. XRD Spectroscopy Training Sheet
(Dr. Chris UP Feb.2016)
Necessary formulas:
(1)
(2) Write the Miller Indices :
(3) Write the names for this cubic crystal cells:
How many atoms does the unit cell contain ?
Calculate the distance between the
110 planes in W metal – the unit cell
is cubic, edge length = 0.316 nm
Draw the 110 plane.
Cu-Kα λ = 0.154 nm

2. (4) BCC Fe placed in an x-ray diffractometer using x-ray with λ = 0.1541 nm.
Diffraction from {110} planes was obtained at 2θ = 44.704 deg. Calculate lattice
constant a.
(5) An element that has either BCC or FCC structure shows diffraction peaks at
following 2θ angles: 40, 58, 73, 86.8, 100.4 and 114.7.
Wavelength of x-ray λ = 0.154
a. BCC or FCC?
b. determine the lattice constant a.
(6) A reaction between Zn(OAc)2 and NaOH gives a product with IR and XRD
Compared to XRD of ZnO:

3. Infos
IR spectrum of sodium hydroxide

4. Answers

5. 5 bcc or fcc lattice?
For bcc, the first peak should come from 110, for fcc from 111.
The second peak comes in both cases from 200.
Which is consistent with the 2 formulas ?
d(40) = 0.154/sin 20 = 0.45 nm
 Lattice constant a = 0.45 v = 0.636 nm for (110)
or a= = 0.45 √(3) = 0.779 nm for (111)
 Next peak at 58: d(200) = 0.154/sin 29 = 0.318 nm
lattice constant a = 0.318 √(4) = 0.635 nm
Therefore the data fit with BCC structure !