MATERIALS SCIENCE I (2)

SPH 308: MATERIALS SCIENCE I Instruction:  Section one is COMPULSORY, attempt ANY OTHER TWO questions from section two. Use � = 8.314 J. mol−1 K−1 , ℎ = 6.626 × 10−34 J s, � = 5.67 × 10−8 W m2 K4 , �Hg = 13600 kg/m3 , �� = 9.11 × 10−31 kg, � = 1.6 × 10−19 C, � = 3 × 108 m s−1 , � = 9.80 m s−2 , �A = 6.022 × 1023 atoms mol, �0 = 8.854 × 10−12 C2 /N m2 , � = 1.38 × 10−23 J/K , �Al = 69 GPa, �f = 80 cal g, �Al = 26.98 g/mol, where necessary SECTION ONE: COMPULSORY QUESTION ONE [30 MARKS] a) b) c) State two important quantum-mechanical concepts associated with the Bohr model of the atom. 0.5 mark Briefly state the main differences between ionic, covalent, and metallic bonding. State the Pauli exclusion principle. 1 mark Study Figure 1 below on the three states of water and answer the questions that follow. i. ii. iii. iv. v. vi. vii. d) Figure 1: Phase diagram of the three states of water. State any two crystalline structures of ice. Microscopically, explain why the density of solid ice is 8 % less than liquid water. What are the consequences of strong hydrogen-bonding between water molecules? Why is liquid water referred to as universal solvent? What is a phase diagram? Derive the Lever’s rule. State any three types of interactions taking place in the liquid phase. What causes occurrence of physical differentiation of the denser liquid water phase and the less-dense gas phase? −2 The half-length of cracks in a steel is 2 μm. Taking � = 200 GN m , estimate the brittle 1 mulamaustine@gmail.com 0.5 mark 0.5 mark 1.5 marks 0.5 mark 1.5 marks 1.5 marks 0.25 mark fracture strength at low temperatures, if the true surface energy is 1.5 J m−2 . The actual fracture strength is found to be 1200 MN m−2 . Explain the difference, if any, between this and your result. e) State the three major classes of materials science. f) Explain why the properties of polycrystalline materials are most often isotropic. g) Distinguish between ductility and resilience properties of materials. h) Define piezoelectric material and state any two types of polarization in dielectric materials. i) Upon what three criteria are factors of safety based? j) A specimen of aluminium having a rectangular cross section 10 mm × 12.7 mm is pulled in tension with 35,500 N force, producing only elastic deformation. Calculate the resulting strain. k) Distinguish between spheroidal or nodular graphite and white cast irons. l) Briefly discuss the statement ‘several factors promote the formation of non-crystalline structures’. m) State the compositions of the following non-ferrous metals: Duralumin, Y-alloy and Magnalium. n) Find the fraction of atoms with energy equal to or greater than 1 eV in a solid at room temperature (300 K). o) Explain why hydrogen fluoride (HF) has a higher boiling temperature than hydrogen chloride (HCl) (19.4 vs. –85 °C), even though HF has a lower molecular weight. p) The net potential energy between two adjacent ions, �� , may be represented by � � �� =− + � � � Calculate the bonding energy, �0 , in terms of the parameters A, B, and n. q) r) s) t) What are the degrees of freedom of a system of two components when the number of phases is one, two, three, and so on? Define a superparamagnet and calculate the intrinsic carrier density of silicon if resistivity of pure silicon at room temperature is 3000 Ω m. Distinguish between the following properties of materials: i. Expansivity and conductivity ii. Thermal energy and thermoelectric effects iii. Ferroelectrics and phase rule Give the electron configurations for the following ions: Al3+ and O2− . 2 mulamaustine@gmail.com 2 marks 1.5 marks 0.5 mark 0.5 mark 3 marks 0.75 mark 2 marks 1 mark 1 mark 1.5 marks 0.75 mark 0.25 mark 2 marks 1 mark 2 marks 1.5 marks 1 mark SECTION TWO: ATTEMPT ANY TWO QUESTIONS QUESTION TWO [20 MARKS] a) Define the following mechanical properties of common engineering materials: i. Elasticity ii. Hardness iii. Malleability iv. Toughness v. Creep b) Study Figure 2 below and answer the question that follows. Figure 2: Rectangular block tilting at various positions to illustrate stability and metastability From Figure 2, state the positions with the most stable, unstable and metastable equilibrium. c) Iron tested at –196 °C is brittle. It, however, becomes ductile at this temperature, if a thin layer of silver is diffused along the grain boundaries of iron. Explain this change in behaviour. d) A transformer core is wound with a coil carrying an alternating current at a frequency of 50 Hz . Assuming the magnetization to be uniform throughout the core volume of 0.01 m3 , calculate the hysteresis loss. The hysteresis loop has an area of 60 000 units , when the axes are drawn in units of 10−4 Wb m−2 and 102 A m−1 . e) List down any three semiconductor devices. 3 mulamaustine@gmail.com 5 marks 3 marks 3 marks 6 marks 3 marks QUESTION THREE [20 MARKS] a) Let �(�, �) = � – � + 2 ≤ � (� – 1) + 2 , where �(�, �) is the degrees of freedom (number of independent variables), � is the number of components and � is the number of phases of a system. 1 mark i. Why do we have number 2 in �(�, �)? 3 marks ii. Briefly explain �(�, �). 6 marks iii. Describe �(�, �) for a single-, two- and three-phase systems. b) Study Figure 3 and answer the questions that follow: Figure 3: Lead – Tin phase diagram i. Identify the following phase boundaries from Figure 3: Liquidus I, Liquidus II, Solidus I, Solidus II, Solvus I and Solvus II. ii. What is meant by eutectic temperature and eutectic composition from Figure 3? iii. State the compositions of �� , ��� and ��� from Figure 3. c) Calculate the entropy increase when one mole of ice melts into water at 0 °C. 4 mulamaustine@gmail.com 3 marks 2 marks 3 marks 2 marks QUESTION FOUR [20 MARKS] a) As the concentration of electrons in a semiconductor is changed by changing the impurity level, the conductivity also changes. Show that it passes through a minimum when �� = �� �ℎ /�� and find the minimum value. Here �� is the intrinsic concentration. b) Name two important copper alloys and give their typical compositions. c) Calculate the equilibrium number of vacancies per cubic meter for copper at 1000 ℃. The energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000 ℃) for copper are 63.5 g/mol and 8.4 g/cm3 , respectively. d) Determine the composition, in atom percent, of an alloy that consists of 97 wt. % aluminum and 3 wt. % copper. 8 marks 4 marks 4 marks 4 marks QUESTION FIVE [20 MARKS] a) Silicon has the unique ability to be oxidized into silica, which produces a chemically stable, protective and insulating layer on the surface of the wafer. The production of high quality integrated circuits (ICs) requires an understanding of the basic mechanisms of oxidation and the ability to form in a controlled and repeatable fashion a high quality oxide. State four functions of oxide layer on silicon. b) Cobalt (Co) has the highest exchange energy and the highest Curie temperature of 1400 K. Gadolinium (Gd) with a small exchange energy has a Curie temperature of 289 K. The net magnetic moment of Gd is 7 per atom, as compared to 1.7 per atom in the Co crystal. Which of the two solids, Co and Gd, has the higher saturation magnetization at 0 K, 300 K? c) Calculate the relative dielectric constant of a barium titanate crystal, which, when inserted in a parallel plate condenser of area 10 mm × 10 mm and distance of separation of 2 mm, gives a capacitance of 10−9 F. d) Briefly discuss carburization of steel. 5 mulamaustine@gmail.com 4 marks 6 marks 4 marks 6 marks