Select and answer 5 of the following 8 questions. All questions carry 20 points. If you answer more than five questions, your score will be obtained by summing the best five. The exam is closed-book. Useful formulae and material properties are provided on the attached sheet.

  1. Dilithium is an element with an atomic mass of 300. Dilithium forms crystals which have a bcc structure. If the effective atomic radius of dilithium is 2nm, what is the density of a dilithium crystal (in kg/m3)? At 900 K, dilithium undergoes a phase change to an fcc structure. What is the percentage change in volume associated with this transformation?

  2. A positively charged sodium ion is brought from infinity to a distance x from a negatively charged chlorine ion. Sketch two graphs, one of force vs x, showing the force required to bring the ion from infinity to a distance x, the second of energy vs x, showing the potential energy that the sodium ion possesses while at the distance x Explain the shapes of the two graphs. You need not give exact values on the two axes, but give an order-of-magnitude figure for the scales used -- e.g., is the x-axis labelled in metres, millimetres or microns? How would the graphs differ for

    1. two copper atoms
    2. two helium atoms?

    Consider a cubic salt crystal, 1 cm on a side. What compressive force would be required to change the length of one side by a micron? (Density of salt = 2000 kg/m3; sodium and chlorine are both monovalent.)

    1. What is the linear density in the [100] direction for a bcc crystal?
    2. What is the planar density of the (110) plane for an fcc crystal?
    3. In what line do the (110) and (101) planes intersect?
    4. Suppose an fcc crystal of copper has 1 impurity atom [of tin] for every 10,000 atoms of copper. How many tin atoms will there be in a square metre of the (110) plane of the crystal? (Density of copper = 8600 kg/m3.)

  4. Distinguish between a Schottky and a Frenkel defect.

    The number of vacancies in a material is given by the equation

    Nv= N exp(-Qv/kT)

    where N is the total number of lattice sites, Qv is the activation energy, and k is Boltzmann's constant. Use this formula to work out the number of vacancies in a cubic metre of iron at 900 K, given that there is one vacancy per 1,000,000 atoms at 600 K. (Atomic weight of iron = 56 amu, density of iron = 7800 kg/m3.)

  5. Distinguish carefully between the mass-average and the number-average molecular weights of a polymer. Which of these two numbers will be greater?

    A sample of 10 gms of polyethylene (C2H4)n is analysed, and found to contain 1 gm of molecules having lengths 50-150, 2 gms of molecules having lengths 150-250, 3 gms of molecules with lengths 250-350, and four gms with lengths in the range 350-450. Calculate the mass-average and number-average molecular weights, the average degree of polymerisation, and the polydispersity index.

  6. Copy Figure 1, and mark on it

    1. the solidus line
    2. the liquidus line
    3. the solvus line
    4. a eutectic point

    Suppose a sample having the composition A is cooled from 1000 K to room temperature. Sketch a graph of the variation in the sample's temperature with time, explaining any interesting features. Do the same for a sample of composition B.

    Referring to Figure 1, consider the cooling of a sample having the composition C. Explain the phenomenon of segregation, supporting your explanation with quantitative figures for the composition of the first and last solids to precipitate out. What consequences does segregation have for the bulk properties of the material? How could it be prevented? Are there ever conditions under which you would want segregation to occur?

    Still referring to the sample of composition C, what fraction of the final solid is made up of the alpha phase?

  7. Figure 2 is an enlargement of a photograph of 10 mm2 of the etched surface of a metal. Calculate the ASTM grain-size number for this metal. Calculate also the mean chord length, pL.

    Alloys can be prepared either by precipitation or eutectoid decomposition . What differences are there between these two processes? The rate at which each process takes place depends on temperature. Sketch a graph showing the dependance of precipitation or decomposition rate on temperature and explain its shape.

  8. Sketch the stress-strain curve for a ductile metal. Mark on the graph, or show how you would use the graph to calculate:
    1. the ultimate tensile strength
    2. the yield strength
    3. Young's modulus of elasticity
    4. the toughness of the material
    5. the resilience of the material

    Describe the differences, at microscopic and macroscopic levels, between

    1. ductile fracture
    2. brittle fracture
    3. fracture resulting from fatigue.

    1. Describe, giving full electrochemical equations, the process of galvanic corrosion.
    2. Describe, giving full electrochemical equations, the process of crevice corrosion, which occurs when different regions of the surface of a material are exposed to different concentrations of exposed oxygen.

Useful Formulae

Avogadro's number: 6 * 1023 atoms/gram-mole

Boltzmann's constant: 8.12 * 10-5 eV/atom.K

Planck's constant: 6.63 * 10-34J-s

1 eV = 1.602 * 10-19 J

Some bond energies: C--C: 368 kJ/gram-mole; C=C: 719 kJ/gram-mole

Electrostatic attraction:

F = q1q2 /(4 pi epsilon0 x2)

where

1 / (4 pi epsilon0) = 9 * 109 farads/metre

TSR = sigmaf k/ (E alphal)