Microstructure From Processing: Evaluation and Modelling Diffusional growth: Lecture 5 Martin Strangwood, Phase Transformations and Microstructural Modelling, School of Metallurgy and Materials

Growth Following nucleation (at g.b.s, dislocations, vacancies) then continued transformation requires growth Growth is usually accompanied by further nucleation until exhaustion of the available active nucleation sites Thus, after the initial line on the TTT/CCT diagram, both nucleation and growth need to be considered

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

Diffusional growth Diffusional growth can result in a change in composition between the parent and product phases and proceeds at a rate governed by atomic diffusion in the parent or product phases In dealing with diffusional growth then a number of simplifying assumptions usually hold The symmetry of most crystal lattices means that, apart from diffusion along grain boundaries and dislocations (pipe diffusion) diffusion is isotropic and geometrical factors can be simply used to convert from 1-D to 2- or 3-D The diffusion of atomic species in one phase is much faster than in the other so that the rate is governed by diffusion in that phase only, e.g. diffusivity in bcc is 100 times larger than that in fcc

Diffusional growth Interfacial equilibrium is assumed (especially at low undercoolings) so that the compositions on either side of the interface can be determined from phase diagrams / thermodynamic modelling From these compositions, the composition gradients driving diffusion in the two phases can be estimated

1-D planar growth Considering a plain carbon steel quenched from the single phase austenite field into the two-phase (  ) phase field will cause extensive and rapid g.b. nucleation so that g.b. decoration can be assumed with further growth being by 1-D movement of the  interface normal to itself Wt % C C0C0 T Austenite   CC CC

1-D diffusional growth Prior austenite grain boundary Ferrite Untransformed austenite Movement of  interface by C redistribution in 

Profile along growth direction C level Distance from grain boundary Grain boundary Ferrite Austenite C0C0 CC CC Equal areas

Interfacial advance C level Distance from grain boundary Grain boundary Ferrite Austenite C0C0 CC CC xx

Carbon redistribution For advance of a unit area of interface by a small distance,  x, in a time,  t, then carbon is rejected into austenite from the newly formed ferrite Carbon rejected is: Carbon diffusion in austenite in this time is: D is diffusivity of carbon in austenite at the formation temperature and is the variable composition gradient in austenite

Conservation of mass The two terms for carbon movement must be equal so that: This can be solved numerically, but the Zener approximation gives a very good fit

Zener approximation C level Distance from grain boundary Grain boundary Ferrite Austenite C0C0 CC CC Equal areas x L

Zener approximation The Zener approximation gives a constant composition gradient of: The growth rate is then: Equating the rectangular and triangular areas gives:

Temperature dependence The separate variations of composition and diffusion terms give another maximum in rate with undercooling (similar to but at a different temperature to that for nucleation) T Equilibrium transformation temperature

Time dependence 1-D diffusional growth is parabolic (x  √t) which would become  t 3/2 for 3-D growth x t This holds until soft then hard impingement C0C0 CC  interfaces

Alloying Element Effects For an Fe-C-Mn steel, at equilibrium, both C and Mn partition between ferrite and austenite What would be the effects of Nb, Cr and Mo?

Partition-local equilibrium For P-LE growth is controlled by Mn (substitutional) diffusion and so proceeds slowly, this allows carbon to redistribute and so there is a small composition gradient for this in austenite At lower temperatures (higher driving forces) growth rates try to be higher resulting in NP-LE - here Mn equilibrium is maintained by a ‘spike’ at the interface, but with no difference in the Mn level in ferrite and austenite (alloying element ‘frozen’ in) The faster growth of NP-LE means that a profile exists for C in austenite, which now controls growth rate

ParaE As undercooling increases further the ‘spike’ cannot be maintained and paraequilibrium growth occurs This occurs for Widmanstätten ferrite and bainite and is partly why substitutional alloying elements have a smaller effect on the ‘C’curves for these transformations

Widmanstätten ferrite growth The plate shape of Widmanstätten ferrite gives point diffusion at the tip rather than 1-D diffusional (as for g.b.allotriomorphic ferrite)    

Transition in ferrite form The point diffusion for growth of Widmanstätten ferrite gives x  t so that there is a transition from allotriomorphic to Widmanstätten ferrite as the ferrite grows from the grain boundary x t g.b. Allotriomorphic ferrite Widmanstätten ferrite

Pearlite nucleation For eutectoid composition, quenched steels or the presence of prior austenite grain boundaries either ferrite or cementite may form first The choice of the phase depends on local conditions, but would be followed by lateral, alternating nucleation events (often get around 2 – 3 pearlite colonies per austenite grain) γγ  C γγ α  γγ α C θ

Continued growth Once sufficient alternating plates have nucleated (or impingement occurs) then growth into the remaining austenite can occur by C redistribution ahead of the austenite / ferrite and austenite / cementite interfaces Growth of pearlite occurs by carbon re-distribution from ahead of a ferrite plate to ahead of a cementite lath Cementite (high C) Ferrite (low C) Austenite (bulk C) C diffusion through austenite at the interface λ ΔCΔC

Composition gradient Diffusional growth will depend on the composition gradient, i.e. ΔC and λ Both of these depend on the growth temperature

Pearlite growth rate Diffusional growth rate is given by: v is interface velocity; k is a constant, D C γ is diffusivity of C in austenite At each temperature there is a minimum spacing (at which growth stops) as the driving force is completely used in providing interfacial energy – observed growth rates occur at approximately twice the minimum spacing

Properties ΔG increases as ΔT increases and ΔG α ΔT Hence, interfacial area can increase α ΔT Strength increases as transformation temperature decreases Experimentally find that λ α 1/ΔT

Patented wire Very high strength levels can be achieved if further refinement can be achieved by deformation Eutectoid composition wire is quenched to 450 – 500 °C in a molten Pb bath This is patented or piano wire with yield stress up to 4.8 GPa The wire is drawn as the austenite transforms to pearlite resulting in refinement of the lamellar structure