Growth 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. 

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. 

Discuss the kinetic and thermodynamic factors governing liquid-solid and solid-solid phase transformations. Explain and predict nucleation, growth, and time-temperature-transformation (1 IT) processes in solid-state systems both qualitatively (through diagrams) and quantitatively (through equations). 

For the tin pest reaction, the time exponent, n, is 3 [60]. Using the data in Ref. 52, it is approximated that a 40% volume fraction transforms after 1.5 years at —18°C, which yields a calculated value of K= 5.7 x lO sec when substituted into Eq. (2). It was also noted in Ref. 52 that tin pest was evident after 0.58 years. This results in approximately 2% of the volume transformed based on the previously calculated value of K. These time-temperature transformation reaction kinetics yield the classic S-shaped curves when the volume fraction transformed is plotted against the log of time. On that basis, it would require approximately 8.4x 10 min to transform 50% of a 99.5Sn-0.5Cu alloy. Other measurements of reaction kinetics in pure tin [56] are given in Table 6 which indicates that the time to transform a 50% volume fraction at — 15°C is 72 min. This difference, a factor of 10,000, is due to several parameters alloy additions, surface condition, residual stress, and prior thermal history. This very large difference in reaction rate illustrates the difficulty encountered when a tin-based solder is evaluated for use in microelectronic assemblies. Fig. 14 depicts the effect of temperature on the growth rate of the white-to-gray tin transformation. The maximum growth rate occurs at —40°C and decreases by a factor of 10 as the temperature approaches 0°C [56]. 

Black and Davey (1988) describe a number of the interrelationships and practical aspects of the control of nucleation, crystal growth, and polymorphic transformation of amino acids. The factors described and demonstrated for primary nucleation of L-glutamic acid include temperature, critical nucleus, relationship of interfacial tension to solubility, thermal history, induction time, agitation, and effect of additive. 

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. 

In an amorphous material, the aUoy, when heated to a constant isothermal temperature and maintained there, shows a dsc trace as in Figure 10 (74). This trace is not a characteristic of microcrystalline growth, but rather can be well described by an isothermal nucleation and growth process based on the Johnson-Mehl-Avrami (JMA) transformation theory (75). The transformed volume fraction at time /can be written as... 

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