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Materials for engineering, 3rd Edition - (Malestrom)

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Problems<br />

Chapter 1<br />

1. Distinguish between the following types of bonding in solids:<br />

van der Waals bonds<br />

covalent bonds<br />

ionic bonds<br />

metallic bonds.<br />

Name four materials in which each of these types of bonding occur.<br />

2. Show that differentiation of equation [1.4] leads to equation [1.5]. Obtain<br />

an expression <strong>for</strong> the value of ∆G* (Fig. 1.4), which is the activation free<br />

energy <strong>for</strong> the <strong>for</strong>mation of a nucleus of critical size (r c ). By substituting<br />

equation [1.3] into your expression, derive an equation which describes<br />

the dependence of the value of ∆G* upon the degree of supercooling.<br />

Can your derived equations enable you to predict qualitatively the<br />

observed relative grain sizes of metal objects <strong>for</strong>med by casting the molten<br />

metal (a) into a cold metal mould of large wall thickness and (b) into a<br />

preheated sand mould?<br />

Estimate the critical nucleus size and the free energy of <strong>for</strong>mation of<br />

the critical nucleus of solid tin at 473 K given the following data:<br />

Melting point of tin = 505 K<br />

Solid liquid interfacial energy = 0.1 J m –2<br />

Latent heat of solidification = 4 × 10 5 kJ m –3 .<br />

[Answer: 7.9 nm]<br />

3. Discuss the appropriate metallographic techniques <strong>for</strong> the following studies:<br />

(a) determination of the grain size of the sand-cast bronze marine propeller<br />

blade,<br />

(b) determination of the grain size of a mild sheet plate,<br />

(c) examination of a fatigue fracture surface, and<br />

(d) the identification of a precipitated phase in a tempered steel.<br />

4. During the solidification of an alloy, it is assumed that there is complete<br />

mixing in the liquid and no mixing in the solid (i.e. ‘cored’ crystals are<br />

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