## Phase Transformations in Metals

It follows that some of the parent phase volume disappears. * Transformation reaches completion if growth is allowed to proceed until the equilibrium fraction is attained. Two types of Nucleation 1 . Homogeneous: nuclei of the new phase form uniformly throughout the parent phase. 2. Heterogeneous: nuclei form preferentially at structural Inhomogeneous, such as container surfaces, grain boundaries, insoluble impurities, dislocations, etc. Homogeneous nucleation: solidification of a pure material, assume nuclei of solid phase form in the interior of the liquid phase.

There are two contributions to the total free energy change GAG that accompany a solidification transformation 1 . The volume free energy Agave – which Is the difference In free energy between the solid and liquid phases. Agave will be negative if the temperature is below the equilibrium solidification temperature. The magnitude of its contribution is the product of Agave and the volume of the spherical nucleolus (4/3 aorta ) 2. Surface free energy y: energy comes from the formation of the solid-liquid phase boundary during the solidification transformation. s positive; the magnitude of this contribution is the product of y and the surface area of the nucleus (nor) * the total free energy change GAG is equal to the sum of these two contributions: GAG=4/3 aorta GAG_v+nary * In a physical sense, this means that as a solid particle begins to form as atoms In the liquid cluster together, its GAG first increases. If this cluster (embryo) reaches a size equal to the critical radius, then growth will continue with the accompaniment of a decrease in LEG. An embryo with a radius greater than is called a nucleus.

A critical free energy occurs at r*, the maximum of the curve, which corresponds to the activation energy needed for the formation of a stable nucleus. Critical radius of a stable solid particle nucleus: ) Activation free energy required for the formation of a stable nucleus: ) This volume free energy change is the driving force for the solidification transformation, its magnitude is a function of temperature. At the equilibrium solidification temperature (or melting temperature) Tm, Agave is O, and with decreasing temp it becomes increasingly more negative.

Agave 1 OFF is a donation to temperature: A The r* and decrease as temperature decreases meaning, nucleation occurs more readily at temperatures below Tm The number of stable nuclei n*(having r>r*) is a function of temperature as well: 1 ) changes in T have a greater effect on than on the denominator. As T is lowered below Tm the exponential term decreases such that the magnitude of n* increases *another important temperature dependent step in nucleation: the clustering of atoms during short range diffusion during the formation of nuclei. The influence of temp on the rate of diffusion: high temp increases effusion.

Diffusion is related to the frequency at which atoms from the liquid attach themselves to the solid nucleolus, VT. Thus, low temp results in a reduction in VT. The nucleation rate N is the product of n* and VT Heterogeneous nucleation has a lower activation energy than homogeneous because the surface free energy is reduced when nuclei form on the surface of preexisting surfaces. Growth occurs by long range diffusion consequently, the growth rate G is determined by the rate of diffusion, and its temperature dependence is the same as he diffusion coefficient (recall chapters that diffusion increases as temperature increases).

The rate of transformation and the time required for the transformation to reach 50% completion (to. 5) are inversely proportional to one another. This explains several physical phenomena 1 . The size of the new phase partials will depend on transformation temp. So, transformations at temps near Tm correspond to low nucleation and high growth rates, few nuclei form that grow rapidly. The resulting macrostructure is will consist of few and large phase particles (e. G. Coarse grains) transformations at low temps*nucleation rates high and growth rate is slow-?resulting in many small particles (e. . , fine grains) 2. Noncombustible phrase structures can be produced by rapidly cooling the material where the rate is extremely low. Kinetics Phase transformations do not occur instantly because obstacles slow the course of the reaction and make it dependent on time. The time dependence of the transformation rate is termed the kinetics of a transformation and is an important consideration in the heat treatment of materials. *to determine reaction rate: assure the fraction of reaction that has occurred as a function of time while the temperature is held constant. How is degree of transformation measured? *microscopic examination * measurement of some physical property that is distinctive of the new phase *Data are plotted as the fraction of transformed material vs. the logarithm of time; an S shaped curve *For solid state transformation that display S shape kinetic behavior, the fraction transformation y is a function of time t as follows: F the Bavaria equation where k and n are time-independent constants for the particular reaction. He rate of transformation r is taken as the reciprocal of time required for the transformation to proceed halfway to completion, to. 5, or: /t_O. 5 * Temperature is one controllable variable in the heat treatment process that may have a profound effect on the kinetics and thus the rate to a transformation * For most reactions, rate increases with temperature according to Where R= gas constant, T= absolute temp, A= a temperature independent constant, Q= activation energy for the particular reaction.

Most phase transformations require some finite time to go to completion, and the ate is important in the relationship between heat treatment and the development of macrostructure * for solid systems the rate is so slow that true equilibrium structures are rarely achieved, equilibrium is maintained only if heating and cooling are carried out at SLOW unpractical rates. *for other than equilibrium cooling Superimposing: cooling to below a phase transition temperature without the occurrence of the transformation Superannuating: heating to above a phase transition temperature without the occurrence of the transformation

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