An alloy is cooled from a temperature at which its equilibrium structure is a single phase...

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An alloy is cooled from a temperature at which its equilibrium structure is a single phase a to a temperature at which two phases, a and ß are in equilibrium. The ß phase nucleates heterogeneously at grain boundaries in form of lens-shaped precipitates. a) Assuming a strain free nucleation, derive an expression for the critical radius of ß nuclei and also show that the critical free energy for heterogeneous nucleation is less than that for homogeneous nucleation. In your derivation you may assume the following: Volume of precipitates=³(2+ cose) (1 - cose)² Surface area of the precipitate= 4r² (1-cose) Where r is the radius of a spherical cap and is the contact angle between the nucleus and [16 marks] the grain boundary. b) Briefly describe how the effect of volumetric strain can be incorporated into the above model. An alloy is cooled from a temperature at which its equilibrium structure is a single phase a to a temperature at which two phases, a and ß are in equilibrium. The ß phase nucleates heterogeneously at grain boundaries in form of lens-shaped precipitates. a) Assuming a strain free nucleation, derive an expression for the critical radius of ß nuclei and also show that the critical free energy for heterogeneous nucleation is less than that for homogeneous nucleation. In your derivation you may assume the following: Volume of precipitates=³(2+ cose) (1 - cose)² Surface area of the precipitate= 4r² (1-cose) Where r is the radius of a spherical cap and is the contact angle between the nucleus and [16 marks] the grain boundary. b) Briefly describe how the effect of volumetric strain can be incorporated into the above model.

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Answer A B i To incorporate volumetric strain into a mo... View the full answer