Hack The SGTE Casebook

Thermodynamics at Work
2. Auflage 2008
ISBN: 978-1-84569-395-4
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 488 Seiten

Reihe: Woodhead Publishing Series in Metals and Surface Engineering

The Scientific Group Thermodata Europe (SGTE) is a consortium of European and North American research groups developing thermodynamic databases and software to model the thermodynamic properties of metals and other materials. Understanding these properties is critical to improving the processing of metals and their performance in such areas as resistance to high-temperature corrosion.This substantially revised new edition explores both the theoretical background to thermodynamic modelling and its wide range of practical applications. These applications include the analysis of hot salt and other types of high-temperature corrosion, understanding the loss of corrosion resistance in stainless and other types of steel, the processing of steels, as well as the use of thermodynamics to improve the functionality of materials for microelectronics and lighting applications, and in the analysis of nuclear safety issues. New case studies also illustrate applications to kinetically-controlled processes such as the solidification and heat treatment of alloys as well as the production of silicon and titanium oxide pigment.The SGTE casebook is a valuable reference for those manufacturing steels and other materials, those using materials in high-temperature applications such as the power industry and in other areas such as microelectronics and lighting. - This updated and revised edition explores theoretical background to thermodynamic modelling - Practical applications are provided, including types of high-temperature corrosion - Valuable reference for the power and microelectronics industry

Autoren/Hrsg.

Hack, K.

Leseproben

I.1 Basic thermochemical relationships
Klaus Hack Publisher Summary
This chapter discusses the basic thermochemical relationships. Since the publication of Gibbs’ last paper in the series, “On the equilibrium of heterogeneous substances,” in 1878, all the terms necessary to describe chemical equilibrium have been defined. The chemical potential had been introduced and the relation governing the different types of phase diagram and the Gibbs–Duhem equation had been derived. Electrochemistry can only be treated if the electrical work term is explicitly included. The entire database derived under the conditions is a Gibbs energy, rather than a Helmholtz, enthalpy, or internal energy database. Problems with constant temperature and volume have to be treated in an indirect way, which is no problem for the computer. Using the Maxwell relations, one can easily derive a diagrammatic scheme to relate the Gibbs energy in its natural variables with the other state functions and their natural variables, such as the Helmholtz energy, the enthalpy, and the internal energy. I.1.1 Introduction
Since the publication of Gibbs last paper [878Gib] in the series ‘On the equilibrium of heterogeneous substances’ in 1878, all terms necessary to describe (chemical) equilibrium are defined. The chemical potential had been introduced, and the relation governing the different types of phase diagram (the Gibbs–Duhem equation) had been derived. Furthermore the different work terms in what we now rightly call Gibbs fundamental equation had been discussed far beyond the contribution of chemical or electrical work and included already, e.g. the contribution of surface tension or the gravitational potential. Gibbs also stated clearly that it is only the relative magnitude of each of these terms that permits omission for practical purposes; in principle, all possible contributions are always present. Most problems dealt with in equilibrium thermochemistry are those with constant temperature and pressure and where the other work terms, except for the chemical contribution, are usually omitted. Electrochemistry, of course, can only be treated if the electrical work term is also explicitly included. It is important to keep this in mind since the entire database derived under these conditions is a Gibbs energy, rather than a Helmholtz, enthalpy or internal energy database. Problems with constant temperature and volume, for example, have thus to be treated in an indirect way, which is, of course, no problem for the computer. Using the Maxwell relations, one can easily derive a diagrammatic scheme (Fig. I.1.1) to relate the Gibbs energy in its natural variables (G(T, P)) with the other state functions and their natural variables, i.e. the Helmholtz energy F(T, V), the enthalpy H(S, P) and the internal energy U(S, V).
I.1.1 Diagram representing the Maxwell relations. The arrows in the scheme indicate the signs of the derivatives that one has to take of the respective state function with respect to the chosen natural variable, e.g. (?G/?P)T = V or (?G/?T)P = - S. It will suffice here to say that a complete change from one state function to another can be obtained by application of a mathematical procedure, called the Legendre transformation [71Hit]. Such transformations have also been introduced by Gibbs himself. Equilibrium is established if the potential function of the system for the conditions chosen has reached an extremum; in the case of the Gibbs energy as a function of T, P, the mole numbers, etc., it is a minimum as expressed by the following equations:  = min or dG = 0 and d2G > 0 (I.1.1) (I.1.1) G        =–S dT +V dP + ?µi dni+?zjFFj dnj… (I.1.2) (I.1.2) with total entropy S, temperature T, total volume V, pressure P, chemical potential µ, molecular number n, charge number z, Faraday constant F and electric potential F. From Equations (I.1.1) and (I.1.2), two different routes for a quantitative approach to equilibrium are possible. These are described in the following two sections. I.1.2 Thermochemistry of stoichiometric reactions
The historical route, established experimentally before Gibbs, is the method of stoichiometric reactions. For isothermal and isobaric conditions, disregarding electrical and other work terms in a system, one obtains G=?µi dni (I.1.3) (I.1.3) The mass balance of a stoichiometric reaction can generally be written as viBi=0 (I.1.4) (I.1.4) with v being positive for products and negative for reactants. Thus the changes dni of the absolute mole numbers ni of the substances Bi are defined by the change d? in the extent of reaction ? and the stoichiometric coefficients vi of the mass balance equation, and Equation (I.1.4) becomes: ni=vi d? (I.1.5) (I.1.5) After splitting the chemical potential µ into the reference potential µ° and the activity contribution RT ln a (R = general gas constant) =µ°+RT ln a (I.1.6) (I.1.6) one obtains the well-known law of mass action expressed in the equation for equilibrium: G°=?viµi°=-RT In (?aivi)=-RT In K (I.1.7) (I.1.7) This equation permits the derivation of most informative relations between the activities of the products and reactants: i=func (aj,T) with j?i (I.1.8) (I.1.8) It should be noted that the temperature dependence of this relationship is contained solely in the Gibbs functions of the pure substances (µi° = Gi°(T)) that are involved in the reaction. However, in practice, one is usually interested in a relationship between concentrations rather than activities. The derivation of such a relation based on a stoichiometric reaction approach is perfectly feasible but is subject to two pitfalls, one mathematical, the other a chemical. Firstly, the use of numerical methods cannot be avoided except in the simple case of ideal homogeneous systems, e.g. gas equilibria. In general, one has to deal with transcendental equations and even in the simple case an auxiliary equation for the total pressure of the system has to be employed. It is, in other words, not a question of straight linear algebra. Secondly, and much more importantly, all the independent reactions in a system must be known before starting the calculation. In other words, one must either make assumptions on the complete set of independent reactions in the system or analyse these experimentally before a reasonable calculation can be carried out. Such assumptions can easily lead to simplifications with very striking differences in the results, e.g. in a phase diagram. Figure I.1.2 and Fig. I.1.3 show phase stability diagrams for Ni in sulphur- and oxygen-containing atmospheres with additions of H2O(g). This is a typical case for the application of stoichiometric reactions in the derivation of an equilibrium diagram. In Fig. I.1.2, only O2 and SO2 are considered to be important gas species, thus leading to the well-known straight line phase boundaries, whereas Fig. I.1.3(a) and Fig. I.1.3(b) show the influence of the entire equilibrated gas phase with a fixed potential of H2O.
I.1.2 Phase stability diagram for Ni as a function of the partial pressure of O2 and SO2 at 873 K. Use of this diagram could give a misleading impression of the dependence of coexistence lines on log 02 at high and low oxygen potentials (cf. Fig. I.1.3).
I.1.3 Phase stability diagrams for Ni as a function of log 102 and log S pimi, where pi is the partial pressure of each species containing S and mi is the stoichiometry number of S in species i at 873 K for two different pressures of 2O:(a)pH2O=10-5bar; b)pH2O=1bar. Comparison of Fig. I.1.2 and Fig. I.1.3(a) shows that, for some conditions, low H2O and oxygen pressures between 10-20 and 10-4, the results are in good agreement, but outside the appropriate...