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These problems are available from the WATTLE site:

problem 1: Forensics case study

As a forensic materials expert – you have been asked to recognize a metallic powder found on the clothing of someone suspected of fabricating an incendiary device used in an armed robbery.

The suspect suggests that the powder is tungsten – which he employs a lot in his line of work. The police believe that the powder is part of a chromium/silver/nickel mixture frequently used in such devices. Armed with the given information from an X-ray powder diffraction analysis – what can you conclude?

Using Cu kα radiation of 0.1542nm, three large diffraction peaks were observed at 44.4°, 64.6° and 81.7°.

problem 2: Metal density

Titanium (element number 22) has an HCP unit cell for which the ratio of lattice parameters at a specific elevated temperature is c/a = 1.633. If the radius of the Ti atom is 0.1445nm

a) Find out the unit cell volume.          
b) Compute the density of titanium.

problem 3: Crystallographic transformation

On cooling from the molten state, titanium solidifies to a BCC lattice structure. Though, on cooling to below 880°C, a change takes place whereby the crystal structure transforms into an HCP structure. Supposing the number of atoms remains constant and that the lattice parameters are as shown below, compute the volume change related with this transformation.

For the BCC lattice: a = 3.32Å
For the HCP lattice: a = 2.956 Å and c = 4.683 Å

Titanium is a generally used metal in engineering structures. Describe why your findings above must be cause for concern if these engineering structures are to be employed at high temperatures.

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