Process parameters time history, temperature

There are two hypothetical limiting cases of interest. In one, an infinitely slow cooling rate maintains thermodynamic equilibrium to the ideal glass, and the equilibrium formalism is applicable. In the other a fluid in equilibrium (at its fictive temperature) is quenched infinitely fast to a temperature low enough so that no molecular transport occurs. In this case, what were dynamic fluctuations in time becomes static fluctuations in space. The most elementary treatment of this glass is then as a thermodynamic system with one additional parameter, the fictive temperature. In an actual experiment, of course, relaxations take place and the state of the system is dependent upon its entire thermal history and requires many parameters for its definition. Detailed discussion of the use of irreversible thermodynamics for the study of relaxation processes in liquids and glasses is contained in reviews by Davies (1956, 1960). 

In order to monitor the mechanical properties in relation to the microstructure, the knowledge of the precipitation state at the end of a thermo-mechanical treatment is of prime importance. In this purpose, Arcelor develops models that allow for the prediction of the influence of the process parameters on the state of precipitation. The model Multipreci, developed at IRSID is one of them. It (Hedicts the precipitation kinetics of mono- and di-atomic particles in ferrite and austenite as a function of the time-temperature history. It is based on the classical theories for diffusive phase transformation and treats simultaneously the nucleation, growth and ripening phenomena. The state of precipitation that is predicted includes the particle size distribution, their number and volume fraction. From these values, the effect of the precipitates on the mechanical properties can be calculated. 

The main characteristics of the green mixture used to control the CS process include mean reactant particle sizes, size distribution of the reactant particles reactant stoichiometry, j, initial density, po size of the sample, D initial temperature, Tq dilution, b, that is, fraction of the inert diluent in the initial mixture and reactant or inert gas pressure, p. In general, the combustion front propagation velocity, U, and the temperature-time profile of the synthesis process, T(t), depend on all of these parameters. The most commonly used characteristic of the temperature history is the maximum combustion temperature, T -In the case of negligible heat losses and complete conversion of reactants, this temperature equals the thermodynamically determined adiabatic temperature (see also Section V,A). However, heat losses can be significant and the reaction may be incomplete. In these cases, the maximum combustion temperature also depends on the experimental parameters noted earlier. 

In addition to the free volume [36,37] and coupling [43] models, the Gibbs-Adams-DiMarzo [39-42], (GAD), entropy model and the Tool-Narayanaswamy-Moynihan [44—47], (TNM), model are used to analyze the history and time-dependent phenomena displayed by glassy supercooled liquids. Havlicek, Ilavsky, and Hrouz have successfully applied the GAD model to fit the concentration dependence of the viscoelastic response of amorphous polymers and the normal depression of Tg by dilution [100]. They have also used the model to describe the compositional variation of the viscoelastic shift factors and Tg of random Copolymers [101]. With Vojta they have calculated the model molecular parameters for 15 different polymers [102]. They furthermore fitted the effect of pressure on kinetic processes with this thermodynamic model [103]. Scherer has also applied the GAD model to the kinetics of structural relaxation of glasses [104], The GAD model is based on the decrease of the crHiformational entropy of polymeric chains with a decrease in temperature. How or why it applies to nonpolymeric systems remains a question. 

It is recognized here that 7, as well as density n, thickness h and temperature T, may vary with time t. Since the thickness and temperature are normally controlled parameters in a relaxation process, the histories h t) and T(t) can be assumed to be known for many circumstances. However, n t) is an internal variable that cannot be controlled. The density evolves during a relaxation process in a way that has not yet been captured in a concise and generally applicable representation. This evolution includes contributions resulting from nucleation, multiplication, annihilation and blocking. For most purposes, it is probably adequate to postulate that n(t) evolves according to a rate equation of the form... 

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