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6.E: Defects in Solid State Lattices (Exercises)

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  • Crystal Defects and Solids


    All diagrams must be hand drawn, no photocopies or computer images will be accepted.

    1. Give a brief description for each of these terms:

      Point defects

      • Frenkel defect
      • Schottky defect
      Line defects
      • Edge dislocation
      • Screw dislocation

      Nonstoichiometric compounds

    2. Stoichiometric titanium (II) oxide and magnesium oxides have densities of 4.93 and 3.58 g cm-3 respectively. X-ray diffraction studies have shown that both have the NaCl structure, with unit cell edges of 416.2 and 421.2 pm respectively. Assume that the presence of vacancies does not affect the cell edge lengths. Estimate the percentage of vacancies in these solids.
    3. Explain the Pilling-Bedworth principle regarding the protective behaviour of oxide films of metal (Swaddle: p103-104). From the following densities (d), evaluate the molar volumes (Vo = molar mass/d) of the metals and of the oxides. Suggest which oxides forms protective layers?
      Metal  d(metal)   Oxide   d(oxide)   Vo(metal)  Vo(oxide)  Protective?
      -----  --------   -----   --------   ---------  ---------  ----------
        Be     1.85      BeO     3.01
        Ca     1.54      CaO    3.25-3.38
        Al     2.70     Al2O3    3.97
        Fe     7.86      FeO     5.7
                        Fe2O3    5.24
                        Fe3O4    5.18
        Ti     4.50     TiO2     4.26
      FeO, wuestite; Fe2O3, hematite; Fe3O4, magnetite;
      TiO2, rutile.
      What advantages and disadvantages do Al and Ti have in their application as material for tableware? This is an open ended question, and give a common-sense type discussion.
    4. It has been proposed that the oxidation of iron by dry air at ambient temperature proceeds according to the inverse logarithmic rate law, which may be written as

      y-1 = c - k ln t,

      where y is the thickness of the oxide layer at time t.

      Observation made on the oxidation of a sample found that

      y = 1.6 nm after 1 day
      y = 3.5 nm after 1 year

      Estimate c and k. What are the thickness of the oxide layer at t = 5, 10, and 20 years?

      What effect does moisture have on the oxidation of iron?