lecture 5 PHASE TRANSFORMATIONS in Metal and Alloys [Autosaved].pptx

Phase Transformation Lecture 1

1. PHASE TRANSFORMATIONS in Metal and Alloys By Dr. Feroz Shah Lecture No.5

2. The Influence of Interfaces on Equilibrium The free energy curves that have been drawn so far have been based on the molar free energies of infinitely large amounts of material of a perfect single crystal Surfaces , grain boundaries and interphase interfaces have been ignored In real situations these and other crystal defects such as dislocations do exist and raise the free energies of the phases Therefore the minimum free energy of an alloy, i.e. the equilibrium state, is not reached until virtually all interfaces and dislocations have been annealed out In practice such a state is unattainable within reasonable periods of time

3. The Influence of Interfaces on Equilibrium Interphase interfaces can become extremely important in the early stages of phase transformations when one phase, , say, can be present as very fine particles in the other phase, , as shown in Fig. 1a If the phase is acted on by a pressure of 1 atm the phase is subjected to an extra pressure due to the curvature of the interface   Figure 1

4. The Influence of Interfaces on equilibrium If is the interfacial energy and the particles are spherical with a radius , is given approximately by: The Gibbs free energy at constant temperature Therefore the curve on the molar free energy-composition diagram in Figure 1b will be raised by an amount: where is the molar volume of the phase  

5. The Influence of Interfaces on equilibrium This free energy increase due to interfacial energy is known as a capillarity effect or the Gibbs‑Thomson effect The concept of a pressure difference is very useful for spherical liquid particles , but it is less convenient in solids Finely dispersed solid phases are often non-spherical Consider an alternative derivation of Equation 1 which can be more easily modified to deal with non-spherical cases

6. The Influence of Interfaces on equilibrium Consider a system containing two particles one with a spherical interface of radius r and the other with a planar interface embedded in an α matrix (Fig. 2) If the molar free energy difference between the two particles is T he transfer of a small quantity of from the large to the small particle will increase the free energy of the system by a small amount is given by   Figure 2

7. The Influence of Interfaces on equilibrium If the surface area of the large particle remains unchanged the increase in free energy will be due to the increase in the interfacial area of the spherical particle Since and The consequence of the Gibbs‑Thomson effect is that the solubility of in is sensitive to the size of the particles  

8. The Influence of Interfaces on equilibrium From the common tangent construction in Figure 1b it can be seen that the concentration of solute B in in equilibrium with across a curved interface is greater than Assuming for simplicity that the α phase is a regular solution and that the β phase is almost pure B, i.e. We can write: Similarly can be obtained by using in place of  

9. The Influence of Interfaces on equilibrium Therefore, For small values of the exponent For typical values it can be written as:  

10. Diffusion Diffusion refers to the net flux of any species, such as ions, atoms, electrons , holes and molecules The magnitude of this flux depends upon the concentration gradient and temperature In materials processing technologies, control over the diffusion of atoms, ions, molecules, or other species is key There are hundreds of applications and technologies that depend on either enhancing or limiting diffusion

11. Diffusion Following are some examples of diffusion dependent processes: Carburization for Surface Hardening of Steels Dopant Diffusion for Semi-conducteur Devices Conductive Ceramics Creation of Plastic Beverage Bottles Oxidation of Aluminum Coatings and Thin Films Thermal Barrier Coatings for Turbine Blades

12. Mechanisms of Diffusion Self-diffusion: In materials containing vacancies, atoms move or “jump” from one lattice position to another If we to introduce a radioactive isotope of gold onto the surface of standard gold After a period of time, the radioactive atoms would move into the standard gold After a period of time, the radioactive atoms would move into the standard gold  

13. Mechanisms of Diffusion Interdiffusion: Diffusion of unlike atoms in materials also occurs Figure 3 Diffusion of different atoms in different directions is known as interdiffusion Consider a nickel sheet bonded to a copper sheet At high temperatures Nickel atoms gradually diffuse into the copper, and copper atoms migrate into the nickel T he nickel and copper atoms eventually are uniformly distributed Figure 3

14. Mechanisms of Diffusion There are two important mechanisms by which atoms or ions can diffuse: Vacancy Diffusion In self-diffusion and diffusion involving substitutional atoms , an atom leaves its lattice site to fill a nearby vacancy (thus creating a new vacancy at the original lattice site ) During diffusion we will have counterflows of atoms and vacancies (Figure 4a) The number of vacancies increases as the temperature increases It influences the extent of both self-diffusion and diffusion of substitutional atoms Figure 4

15. Mechanisms of Diffusion Interstitial Diffusion: When a small interstitial atom or ion is present in the crystal structure, the atom or ion moves from one interstitial site to another (Figure 4b) No vacancies are required for this mechanism As there are many more interstitial sites than vacancies Interstitual diffusion also occurs more easily than vacancy diffusion Interstitial atoms that are relatively smaller can diffuse faster

16. Diffusion and Gibbs free energy Figure 5