Phase transformations, time-temperature-transformation

A discontinuous transformation generally occurs by the concurrent nucleation and growth of the new phase (i.e., by the nucleation of new particles and the growth of previously nucleated ones). In this chapter we present an analysis of the resulting overall rate of transformation. Time-temperature-transformation diagrams, which display the degree of overall transformation as a function of time and temperature, are introduced and interpreted in terms of a nucleation and growth model. 

A molten metal alloy would normally be expected to crystallize into one or several phases. To form an amorphous, ie, glassy metal alloy from the Hquid state means that the crystallization step must be avoided during solidification. This can be understood by considering a time—temperature—transformation (TTT) diagram (Eig. 2). Nucleating phases require an iacubation time to assemble atoms through a statistical process iato the correct crystal stmcture... 

Eig. 15. Time—temperature transformation ia a thin-phase change layer during recording/reading/erasiug (3,105). C = Crystalline phase A = amorphous phase = melting temperature = glass-transition temperature RT = room temperature. 

Characteristics and implementation of the treatments depend on the expected results and on the properties of the material considered a variety of processes are employed. In ferrous alloys, in steels, a eutectoid transformation plays a prominent role, and aspects described by time-temperature-transformation diagrams and martensite formation are of relevant interest. See a short presentation of these points in 5.10.4.5. Titanium alloys are an example of the formation of structures in which two phases may be present in comparable quantities. A few remarks about a and (3 Ti alloys and the relevant heat treatments have been made in 5.6.4.1.1. More generally, for the various metals, the existence of different crystal forms, their transformation temperatures, and the extension of solid-solution ranges with other metals are preliminary points in the definition of convenient heat treatments and of their effects. In the evaluation and planning of the treatments, due consideration must be given to the heating and/or cooling rate and to the diffusion processes (in pure metals and in alloys). 

For a number of applications, particularly those associated with conditions of continuous cooling or heating, equilibrium is clearly never approached and calculations must be modified to take kinetic factors into account. For example, solidification rarely occurs via equilibrium, amorphous phases are formed by a variety of non-equilibrium processing routes and in solid-state transformations in low-alloy steels much work is done to understand time-temperature-transformation diagrams which are non-equilibrium in nature. The next chapter shows how CALPHAD methods can be extended to such cases. 

The WLF equation holds over the temperature range from Tg to about + 100 K. The constants in Eq. (5.76) are related to the free volume. This is a procedure analogous to the one we used to generate time-temperature-transformation (TTT) diagrams for metallic phase transformations in Section 3.1.2.2. 

Fig. 1.12. Water-glycerine phase diagram. On the left hand side the dependence of the phase transformation time on the ice temperature is shown At-140 °C amorphous ice transforms into cubic ice in 10 min (Figure 8 from [1.98])...

Gelation, vitrification and phase-separation transitions in curing systems are very well described in the work of GilUiam (1986) via the use of time-temperature-transformation diagrams. 

Figure 2.9. A time-temperature-transformation (TTT) diagram for a phase-separating thermoset/ thermoplastic blend system. Reprinted from Figure 12 from (Kim et al., 1993). Copyright (1993), with permission from Elsevier.

At this point, the fundamental question, posed at the outset of this section, namely. How fast must a melt be cooled to avoid the formation of a detectable volume fraction of the crystallized phase can be addressed somewhat more quantitatively. The first step entails the construction of a time-temperature-transformation (TTT) curve for a given system. Such a curve defines the time required, at any temperature, for a given volume fraction to crystallize. Here the procedure, not unlike that used to solve Worked Example 9.2, is generalized. 

The nearly two dozen phase diagrams shown below present the reader with examples of some important types of single and multicomponent systems, especially for ceramics and metal alloys. This makes it possible to draw attention to certain features like the kinetic aspects of phase transitions (see Figure 22, which presents a time-temperature-transformation, or TTT, diagram for the precipitation of a-phase particles from the [5-phase in a Ti-Mo alloy Reference 1, pp. 358-360). The general references listed below and the references to individual figures contain phase diagrams for many additional systems. 

Experimental time-temperature-transformation (TXT) diagram for Ti-Mo. Xhe start and finish times of the isothermal precipitation reaction vary with temperature as a result of the temperature dependence of the nucleation and growth processes. Precipitation is complete, at any temperature, when the equilibrium fraction of a is established in accordance with the lever rule. Xhe solid horizontal line represents the athermal (or nonthermally activated) martensitic transformation that occurs when the p phase is quenched. 

An analysis of crystallisation rates is conveniently performed in terms of the so-called time-temperature-transformation (TTT) curves, which relate the time taken to crystallise a given fraction of the undercooled liquid or the supersaturated solution to the temperature. Experimentally, the crystallisation rates are measured by quenching the liquid phase to some predetermined temperature T and measuring the time taken for the solid to crystallise at that temperature, either by monitoring the latent heat of crystallisation or by microscopic observation. The volume fraction 4>(T) that crystallises out in time 1 is given by one form of the Avrami equation ... 

Fig. 10 Thermodynamic and kinetic basis for solute depletion in the case of a binary alloy consisting of solvent A and solute B. (a) Binary equilibrium phase diagram with complete miscibility in the liquid state, partial miscibility in the solid state given by existence of a terminal solid solution. Cs is the composition along the solvus line. is the overall composition of the alloy, (b) Time-temperature-transformation diagram for precipitation of in an a matrix for the alloy shown in (a) with overall composition,...

Fig. 11 Schematic of time-temperature-transformation diagram for alloy indicated in Fig. 10 indicating regions of both heterogeneous and homogeneous precipitation of the p phase in a a matrix.

Eno] Enomoto, M., Maruyama, N., Wu, K.M., Tarui, T., Alloying Element Accumulation at Ferrite/Austenite Boundaries Below the Time-Temperature-Transformation Diagram Bay in an Fe-C-Mo Alloy , Mater. Sci. Eng. A, 343, 151-157 (2003) (Calculation, Experimental, Kinetics, Phase Diagram, Phase Relations, 27)... 

The kinetics of solid-state phase fiansformations are often summarized in time-temperature-transformation (TTT) diagrams. Figure 6.30 illustrates the consuiiction of a TTT diagram using the fiansformation kinetics for the system in Figures 6.26 and 6.28. The TTT diagram shows the time required to achieve certain amounts of transformation as a function of the temperature of the transformation. 

---