Chap28 solutions

Physical Chemistry

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28 Processes at solid surfaces Solutions to exercises Discussion questions E28.1(b) The motion of one section of a crystal past another (a dislocation) results in steps and terraces. See Figures 28.2 and 28.3 of the text. A special kind of dislocation is the screw dislocation shown in Fig. 28.3. Imagine a cut in the crystal, with the atoms to the left of the cut pushed up through a distance of one unit cell. The surface defect formed by a screw dislocation is a step, possibly with kinks, where growth can occur. The incoming particles lie in ranks on the ramp, and successive ranks reform the step at an angle to its initial position. As deposition continues the step rotates around the screw axis, and is not eliminated. Growth may therefore continue indefinitely. Several layers of deposition may occur, and the edges of the spirals might be cliffs several atoms high (Fig. 28.4). Propagating spiral edges can also give rise to flat terraces (Fig. 28.5). Terraces are formed if growth occurs simultaneously at neighbouring left- and right-handed screw dislocations (Fig. 28.6). Successive tables of atoms may form as counter-rotating defects collide on successive circuits, and the terraces formed may then fill up by further deposition at their edges to give flat crystal planes. E28.2(b) Consult the appropriate sections of the textbook (listed below) for the advantages and limitations of each technique. AFM: 28.2(h) and Box 28.1; FIM: 28.5(c); LEED: 28.2(g); MBRS: 28.6(c); MBS: 28.2(i); SAM: 28.2(e); SEM: 28.2(h); and STM: 28.2(h). E28.3(b) In the Langmuir–Hinshelwood mechanism of surface catalysed reactions, the reaction takes place by encounters between molecular fragments and atoms already adsorbed on the surface. We therefore expect the rate law to be second-order in the extent of surface coverage: A + B P ν = A θ B Insertion of the appropriate isotherms for A and B then gives the reaction rate in terms of the partial pressures of the reactants. For example, if A and B follow Langmuir isotherms (eqn 28.5), and adsorb without dissociation, then it follows that the rate law is ν = kK A K B p A p B ( 1 + K A p A + K B p B ) 2 The parameters K in the isotherms and the rate constant k are all temperature dependent, so the overall temperature dependence of the rate may be strongly non-Arrhenius (in the sense that the reaction rate is unlikely to be proportional to exp ( E a /RT ) . In the Eley-Rideal mechanism (ER mechanism) of a surface-catalysed reaction, a gas-phase molecule collides with another molecule already adsorbed on the surface. The rate of formation of product is expected to be proportional to the partial pressure, p B of the non-adsorbed gas B and the extent of surface coverage, θ A , of the adsorbed gas A. It follows that the rate law should be A + B P ν = kp A θ B The rate constant, k , might be much larger than for the uncatalysed gas-phase reaction because the reaction on the surface has a low activation energy and the adsorption itself is often not activated.
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