1. Microstructure From Processing: Evaluation and Modelling Nucleation: Lecture 4 Martin Strangwood, Phase Transformations and Microstructural Modelling, School of Metallurgy and Materials

2. Multiple phases?  Phase identification requires composition and crystal structure with quantification for simulation  OM will identify phases given sufficient contrast – good for quantification, but not composition  XRD – phase identification, but no composition – needs more than 5 % by volume  SEM – crystallography (EBSD) and composition (EDS / WDS) – quantifiable with enough images  TEM – crystallography and composition, but difficult to quantify  EM sensors – phase balance in steels

3. Multiple phases?  How to distinguish bainite and martensite in complex phase (CP) steels?  Precipitate fractions in Al-based alloys?

4. What is needed for a new phase?  In 2-phase region then atoms need to cluster in the structure of the product (or daughter) phase  Classical theory of nucleation considers this to arise from random fluctuations (as atoms vibrate) forming ‘embryos’  Many embryos re-dissolve – nucleation occurs when the embryos become stable and grow

5. Driving Force Classical nucleation involves the formation of a critically-sized embryo Quenching from a single phase to a two-phase region makes the parent phase unstable w.r.t. the product and provides a driving force T1T1 T2T2  at T 1  at T 1 G Wt % C

6. Driving Force T1T1 T2T2  at T 1  at T 2  at T 1 and T 2 GG G Wt % C

7. Homogeneous nucleation (solid-state)  Energy sources –Creation of volume V of new phase with free energy change  G v (from common tangent –Creation of an interface of area A with energy per unit area  –Misfit strain energy  G s due to imperfect match between matrix phase and precipitate in material volume V

8. Energy Balance Initially (at small cluster sizes) the proportion of interfacial atoms is high compared with bulk so that ΔG is +ive As size increases then volume terms become dominant leading to –ive ΔG r GG 0  G* + atom Interface energy  r 2 Volume energy  r 3

9.  Other analyses for coherent and incoherent precipitates all show strain energy linearly proportional to precipitate (inclusion) volume  For a spherical transformed phase Homogeneous nucleation

10. Nucleation rate For the behaviour above the nucleation rate (no. of nuclei per unit volume per unit time) depends on the number of critically-sized embryos For homogenous nucleation the no. of critically-sized embryos per unit volume is the fraction of nucleation sites (atoms per unit volume) have the critical energy This is given by the Arrhenius relationship

11. Critical stage In order to form a stable nucleus a critically-sized embryo must acquire a further atom to exceed the critical size (radius) so that further growth is accompanied by a decrease in free energy r GG 0  G* + atom Interface energy  r 2 Volume energy  r 3

12. Nucleus size? How many atoms are there in a critically-sized embryo?

13. Nucleation rate For the behaviour above the nucleation rate (no. of nuclei per unit volume per unit time) depends on the number of critically-sized embryos and the rate at which they acquire further atoms

14. Interfacial diffusion The rate at which embryos acquire atoms and convert to nuclei is given by the diffusional flux across the interface The nucleation rate is then:

15. Temperature dependence I v varies with temperature as: IvIv T Equilibrium transformation temperature Increasing driving force and proportion of critically-sized embryos Reducing diffusion rates

16. Heterogeneous nucleation  Defects exist in real, polycrystalline materials –Excess vacancies, dislocations, grain boundaries, stacking faults, inclusions, free surfaces –All the above increase the free energy of the material  Creation of a nucleus may result in destruction of a defect releasing some free energy (  G d ) thereby reducing the free energy barrier

17. Other nucleation sites Situations involving heterogeneous nucleation involve smaller nucleation barriers (  G*) but also a smaller number of atoms associated with nucleation sites (C 1 ) High Low

18. Grain boundary nucleation  Balancing forces Original α⁄α grain boundary  Last term describes energy released by destruction of part of the grain boundary  Heterogeneous nucleation analogous to inoculation / mould effects in casting

19. C 1 for grain boundaries For spherical grain, radius r, grain volume is: Grain boundary area is: Grain boundary width, w, is 2 - 3 atoms so that, for one grain, the width is w/2 giving a relative volume of : C 1 is then just:

20. C 1 and  G* het - dislocations  G* het is related to  G* by interfacial and strain energies of the defects which can be incorporated into a multiplying factor S(  ) C 1 depends on no. of atoms associated with defects, i.e. number of atoms along line of dislocations or across grain boundaries Compression Tension Dislocation density is length of dislocation per unit volume so that fraction of atoms with higher energy is C 0 x area of strain fields x dislocation density

21. G.b. precipitation Initial nucleation at triple points Prior austenite grain structure Nucleation on grain edges Growth along grain boundaries from triple point- nucleated particles Growth into bulk from fully decorated grain boundary