Thermodynamics crystal structure

It may be desirable to predict which crystal structure is most stable in order to predict the products formed under thermodynamic conditions. This is a very difficult task. As of yet, no completely automated way to try all possible crystal structures formed from a particular collection of elements (analogous to a molecular conformation search) has been devised. Even if such an effort were attempted, the amount of computer power necessary would be enormous. Such studies usually test a collection of likely structures, which is by no means infal-... 

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. 

In order to answer these questions as directly as possible we begin by looking at diffusive and displacive transformations in pure iron (once we understand how pure iron transforms we will have no problem in generalising to iron-carbon alloys). Now, as we saw in Chapter 2, iron has different crystal structures at different temperatures. Below 914°C the stable structure is b.c.c., but above 914°C it is f.c.c. If f.c.c. iron is cooled below 914°C the structure becomes thermodynamically unstable, and it tries to change back to b.c.c. This f.c.c. b.c.c. transformation usually takes place by a diffusive mechanism. But in exceptional conditions it can occur by a displacive mechanism instead. To understand how iron can transform displacively we must first look at the details of how it transforms by diffusion. 

At the beginning of the century, nobody knew that a small proportion of atoms in a crystal are routinely missing, even less that this was not a mailer of accident but of thermodynamic equilibrium. The recognition in the 1920s that such vacancies had to exist in equilibrium was due to a school of statistical thermodynamicians such as the Russian Frenkel and the Germans Jost, Wagner and Schollky. That, moreover, as we know now, is only one kind of point defect an atom removed for whatever reason from its lattice site can be inserted into a small gap in the crystal structure, and then it becomes an interstitial . Moreover, in insulating crystals a point defect is apt to be associated with a local excess or deficiency of electrons. 

Crystal structure, crystal defects and chemical reactions. Most chemical reactions of interest to materials scientists involve at least one reactant in the solid state examples inelude surfaee oxidation, internal oxidation, the photographie process, electrochemieal reaetions in the solid state. All of these are critieally dependent on crystal defects, point defects in particular, and the thermodynamics of these point defeets, especially in ionic compounds, are far more complex than they are in single-component metals. I have spaee only for a superficial overview. 

Conversely, when A-alkyl tryptophan methyl esters were condensed with aldehydes, the trans diastereomers were observed as the major products." X-ray-crystal structures of 1,2,3-trisubstituted tetrahydro-P-carbolines revealed that the Cl substituent preferentially adopted a pseudo-axial position, forcing the C3 substituent into a pseudo-equatorial orientation to give the kinetically and thermodynamically preferred trans isomer." As the steric size of the Cl and N2 substituents increased, the selectivity for the trans isomer became greater. A-alkyl-L-tryptophan methyl ester 42 was condensed with various aliphatic aldehydes in the presence of trifluoroacetic acid to give predominantly the trans isomers. ... 

Evans considers that corrosion may be regarded as a branch of chemical thermodynamics or kinetics, as the outcome of electron affinities of metals and non-metals, as short-circuited electrochemical cells, or as the demolition of the crystal structure of a metal. 

The formation of the combination of defects may be described as a chemical reaction and thermodynamic equilibrium conditions may be applied. The chemical notations of Kroger-Vink, Schottky, and defect structure elements (DSEs) are used [3, 11]. The chemical reactions have to balance the chemical species, lattice sites, and charges. An unoccupied lattice site is considered to be a chemical species (V) it is quite common that specific crystal structures are only found in the presence of a certain number of vacancies [12]. The Kroger-Vink notation makes use of the chemical element followed by the lattice site of this element as subscript and the charge relative to the ideal undisturbed lattice as superscript. An example is the formation of interstitial metal M ions and metal M ion vacancies, e.g., in silver halides ... 

A number of other thermodynamic properties of adamantane and diamantane in different phases are reported by Kabo et al. [5]. They include (1) standard molar thermodynamic functions for adamantane in the ideal gas state as calculated by statistical thermodynamics methods and (2) temperature dependence of the heat capacities of adamantane in the condensed state between 340 and 600 K as measured by a scanning calorimeter and reported here in Fig. 8. According to this figure, liquid adamantane converts to a solid plastic with simple cubic crystal structure upon freezing. After further cooling it moves into another solid state, an fee crystalline phase. 

Vaterite is thermodynamically most unstable in the three crystal structures. Vaterite, however, is expected to be used in various purposes, because it has some features such as high specific surface area, high solubility, high dispersion, and small specific gravity compared with the other two crystal systems. Spherical vaterite crystals have already been reported in the presence of divalent cations [33], a surfactant [bis(2-ethylhexyl)sodium sulfate (AOT)] [32], poly(styrene-sulfonate) [34], poly(vinylalcohol) [13], and double-hydrophilic block copolymers [31]. The control of the particle size of spherical vaterite should be important for application as pigments, fillers and dentifrice. 

Oxidative addition of H2 and Ph3SiH to IrBr(CO)(chiraphos), where chiraphos 2,S, 3,S -bis (diphenylphosphino)butane, leads to stable kinetic (115a,115b), followed by thermodynamic (116a,116b) diastereomers as shown in reaction Scheme 15.2 3 The crystal structure of cis-[IrH2(chiraphos)2]BF4 has been reported.204... 

The free energy perturbation calculations on mutation of the central statine residue of pepstatin to its dehydroxy and other derivatives were carried out using the window method. The crystal structure reported by Suguna et al.l4 l5was used for these calculations. In most simulations, the mutations were achieved either in 101 or 51 windows with 0.4 ps of equilibration and 0.4 ps of data collection at each window. The calculation for each mutation was repeated in water to determine the difference in the free energies of solvation and to complete the thermodynamic cycle. 

The same requirement extends to the minerals considered in the calculation. Minerals in nature occur as solid solutions in which elements substitute for one another in the mineral s crystal structure, but thermodynamic datasets generally contain data for pure minerals of fixed composition. A special danger arises in considering the chemistry of trace metals. In nature, these would be likely to occur as ions substituted into the framework of common minerals or sorbed onto mineral or organic surfaces, but the chemical model would consider only the possibility that the species occur as dissolved species or as the minerals of these elements that are seldom observed in nature. 

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