The driving force for structural change

When the structure of a metal changes, it is because there is a driving force for the change. When iron goes from b.c.c. to f.c.c. as it is heated, or when a boron dopant diffuses into a silicon semiconductor, or when a powdered superalloy sinters together, it is because each process is pushed along by a driving force. 

We will be looking at kinetics in Chapter 6. But before we can do this we need to know what we mean by driving forces and how we calculate them. In this chapter we show that driving forces can be expressed in terms of simple thermodynamic quantities, and we illustrate this by calculating driving forces for some typical processes like solidification, changes in crystal structure, and precipitate coarsening. 

Flow can we calculate the free work The simplest case is when the free work is produced by the decrease of potential energy, with 

This equation does, of course, assume that all the potential energy is converted into useful work. This is impossible in practice because some work will be done against friction - in wheel bearings, tyres and air resistance - and the free work must really be written as 

What do we do when there are other ways of doing free work As an example, if our car were initially moving downhill with velocity v but ended up stationary at the bottom of the hill, we would have 

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The Si(OOl) Surface. Our analysis begins with perhaps the most studied of such surfaces, namely, the (001) surface. The ideal and reconstructed geometries were presented in fig. 9.10 and are contrasted in more detail in fig. 9.21 where it is noted that the presence of two dangling bonds per surface atom for the ideal bulk termination should provide a strong driving force for structural change. We have already remarked on the analogy between this tendency on the (001) surface and... 

However, the question must always be asked as to whether these processes could have taken place on the primordial Earth in its archaic state. The answer requires considerable fundamental consideration. Strictly speaking, most of the experiments carried out on prebiotic chemistry cannot be carried out under prebiotic conditions , since we do not know exactly what these were. In spite of the large amount of work done, physical parameters such as temperature, composition and pressure of the primeval atmosphere, extent and results of asteroid impacts, the nature of the Earth s surface, the state of the primeval ocean etc. have not so far been established or even extrapolated. It is not even sure that this will be possible in the future. In spite of these difficulties, attempts are being made to define and study the synthetic possibilities, on the basis of the assumed scenario on the primeval Earth. Thus, for example, in the case of the SPREAD process, we can assume that the surface at which the reactions occur could not have been an SH-containing thiosepharose, but a mineral structure of similar activity which could have carried out the necessary functions just as well. The separation of the copy of the matrix could have been driven by a periodic temperature change (e.g., diurnal variation). For his models, H. Kuhn has assumed that similar periodic processes are the driving force for some prebiotic reactions (see Sect. 8.3). 

R = Me because the initial reaction is then more complicated than expressed by equation (85). In dimeric Cr2(NR2)6, steric hindrance prevents chromium(III) from obtaining its preferred octahedral coordination this, the ligand field stabilization in Cr(NR2)4 (tetrahedral, d2), the covalency of the Cr —NR2 bond, and the polymeric structure of involatile Crn(NEt2)2 all contribute to the driving force for reaction (86). The structural changes are represented for R = Et in equation (87). 

Since the radical motions are unlikely to involve changes in bonding, the effects of deuterium in the P positions are almost certainly steric, but the sense of the effect (kH > kD) is opposite the steric isotope effects that are normally observed. Given the standard interpretation of steric isotope effects, which assumes that the transition state survives several periods of normal vibration [98], the present results imply that the smaller size of deuterium reduces the driving force for radical motion. That is, the P methylene group is under more stress in Species A24 than in the transition state leading to the next intermediate structure. 

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