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Material Science

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Exercise 1 (15 points)

Bismuth telluride, especially the Bi2Te3 compound, is a well investigated material, also because it has favourable thermoelectric properties. This means that a heat gradient, applied across the material, via the Seebeck effect generates an electric current. This is of interest for directly generating electrical power from (waste) heat. We first consider an alloy with a Te concentration of 70 at.% being cooled down from 700°C; see figure below.

a. At what temperature does the first (tiny amount of) solid form? Give the composition (value) of this solid. (2 pt)

b. At what temperature does the last liquid drop disappear upon cooling? Give the composition (value) of this liquid. (2 pt)

c. Compute (based on the lever rule) the fractions of phases present at 430 °C and 150 °C. (4 pt)

d. Explain, using a schematic drawing, what the microstructure of this alloy looks like when an

alloy containing 90 at.% Te is cooled down to 150 °C. Describe the qualitative difference with

a 70 at.% Te cooled sample. (3 pt)

e. Do you expect the samples in d) to be more or less brittle than a 64 at.% (pure Bi2Te3) sample?

Why? (2 pt)

f. Why does the heating need to be performed even slower than the cooling to obtain the

behaviour predicted by the phase diagram, e.g. for our 70 at.% alloy (consisting of Bi2Te3+Te) when it is reheated to 700 °C? (2 pt)

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Exercise 2 (14 points)

We have a bicycle wheel containing 32 spokes (Dutch: spaken). Each spoke has a diameter of 1 mm and a length of 30 cm. The spokes are made out of steel with a yield strength of 500 MPa, a Young’s modulus of 200 GPa and a Poisson ratio of 0.26. Consider a spoke under (uniaxial) tensile loading along its length direction. A safety factor of 2 has to be used. Assume that the spokes behave according to linear elasticity.

a. What is the maximum load (in kg’s) that can be exerted on a spoke? (2 pt)

b. What will be the strain in the spoke (in the direction of loading)? (2 pt)

c. How much will the diameter of the spoke change (increase or decrease)? (2 pt)

d. Describe what will happen when a load would be exerted on the spoke that is greater than the

yield strength (explain what happens on macro scale and on atomic scale).(3 pt)

e. Cold work can be used to harden the spokes. Explain what cold work is and whether hardening

the steel spokes is favourable or not. ( 2pt)

f. Spokes cannot be made of a ceramic material, but a ball bearing (Dutch: kogellager) with

ceramic balls can be superior to one with metallic balls. Explain why ceramic materials can be used (for the balls) in ball bearings and not in spokes and why ball bearing with ceramic balls can be superior to metallic balls (provide at least 2 factors). (3 pt)

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