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Fraction transformed in isothermal process – Avrami analysis

. Fraction transformed in isothermal process – Avrami analysis. Consider    transformation How do we determine the volume (or area) fraction transformed?. How do you deal with the overlap?.

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Fraction transformed in isothermal process – Avrami analysis

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  1. Fraction transformed in isothermal process – Avrami analysis Consider    transformation How do we determine the volume (or area) fraction transformed? How do you deal with the overlap? Mathematical device : extended volume fraction Xex  volume fraction transformed disregarding overlap.

  2. Avrami equation The actual volume fraction grows in a relative amount to the unconsumed fraction, at the same rate the extended volume fraction does.: or Unconsumed fraction Integrate Expand : dilute overlap of two overlap of three

  3. Case (1) constant number of heterogeneous nuclei present from the beginning. concentration: N growth rate of crystals : v x t Application to nucleation & growth : ( Johnson - Mehl) Plot of ln t vs ln[-ln(1-x)] should have slope of 3.

  4. so Plot of ln t vs ln[-ln(1-x)]  slope of 4 These plots are called Johnson- Mehl –Arami plots (JMA plots) Case (2) Assume a constant nucleation rate I, # of nuclei formed between t’ and t’ + dt’ ; concentration, N = I dt’ and at some later time ( t > t’ ) the “radius” of transformed phase is v (t – t’)

  5. 329K power DSC isothermals X 328K 328K 327K 325K 324K 326K 329K 1 327K 326K 325K 1/2 324K 20 40 60 80 100 0 Time (min) Time Case study : Devitrification of Au65Cu12Si9Ge14 glass C. Thompson et. al., Acta Met., 31, 1883 (1983) Calorimetry results Fraction transformed

  6. ln (1-t) JMA plot (327K) ln [-ln(1-x)] ln [-ln(1-x)] slope = 4 ln (t) must be introduced N = Iss(t -) Slope = 4.0

  7. Time-Temperature-Transformation Curves TTT curves” are a way of plotting transformation kinetics on a plot of temperature vs. time. A point on a curve tells the extent of transformation in a sample that is transformed isothermally at that temperature. A TTT diagram shows curves that connect points of equal volume fraction transformed. l+ β l T l+ α α β α+β B A xB →

  8. Time-Temperature-Transformation Curves Curves on a TTT diagram have a characteristic “C” shape that is easily understood using phase transformations concepts. The temperature at which the transformation kinetics are fastest is called the “nose” (•) of the TTT diagram A TTT diagram shows curves that connect points of equal volume fraction transformed.

  9. x log t Construction of TTT diagrams from Avrami Curves decreasing T 50% transformed T1 T4 T4 trans start: 0 transformed 50% transformed T1 100% transformed Temp log time

  10. Construction of TTT diagrams from Avrami Curves Fe-C phase diagram

  11. Fe-C phase diagram: Perlite

  12. Fe-C TTT diagram example

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