It perhaps does not make you happy if I simply answer that it is a transformation controlled by energy and preferably uses closed-packed planes and directions. These are the concept of the models K-S and N-W. Unfortunately, these are only models, and frankly speaking I myself havn't ever seen an exact K-S or N-W. The orientation relationships I've found were always somehow in between which found its result in the definition of the so-called Greninger-Trojano orientation relationship. The reason is also very simple. Immediately if the chemical composition is changing the match of the atoms of both structures does not match exactly so that small tilts compensate these differences. Obviously, these deviations still reduce the energy of the crystal so that they are stable. Please note, K-S and N-W only describe directions and planes but do not say anything about the lattice dimensions (or the distances between atoms since finally they have to match, not the crystal lattice points).    

The nucleation of the ferrite plates at the austenite grain boundaries is determined by: the driving force for transformation, the nature of the nucleation grain boundary and the interfacial energy of the  new phase.  What is the major determinate of the ferrite morphology is the growth mechanism of the Widmanstatten ferrite.  This is controlled by the interfacial energy and structures of the plate.  The broad faces of the plates are either coherent or semicoherent and thus provide an interfacial barrier to growth. If thickening of the plate occurs, it does so by a ledge mechanism, growth being produced at the edges of the ledges.  Major growth is confined to the sharp edges of the plate because they are incoherent and there is no barrier to transfer of atoms to the structure of the daughter crystal across the interface, in which the growth kinetics are encouraged by the "edge effect".  It is somewhat discouraging to find that an enormous literature (including some published by the answerer) related to the morphologies of phases produced by diffusional transformations seems to have been forgotten.  What is now being taught in the science of materials?

As for allotriomorphic ferrite (AF) and Widmanstätten ferrite(WF):

(1) Crystallography

AF usually forms near K-S OR with neighboring grain instead of the grain it grows into.

WF forms near K-S OR with the grain it grows into.

(2) Thermodynamic

WF probably forms with lower driving force, one reason is that the interface is of low interfacial energy.

(3)Kinetic aspect

Whether there is partition of alloy elements, that relates to paraequilibrium model and  local equilibrium model (partition LE/negligible partition LE). Sorry, I donot know about the recent progress.

The kinetics of this transformation shows that it is nothing to do with with the conventional nucleation and growth process. That means atomic rearrangements required for the transition from FCC structure of austenite to the super saturated  ferrite having BCT structure should involve short range displacements, which can be easily achieved by the collective shear mechanisms that may be represented by finite deformation matrices that involve invariant planes and direction in 3D-lattice space  as properly mentioned by Gert and others.  However, at the interface of their sharp edges, which involve not only large deformations characterized by hydrostatic_dilations_ in type  but also that have skew symmetric components (rotational) that  are partially relaxed by the generation of the dislocation tangles and even by disclinations. Therefore these domains are completely in the nonequilibrium stationary state conditions, and involve large stored elasto-plastic energies,  which may  be easily triggered by externally applied properly selected stress systems or  by the  thermal  shocks having short duration time (ultrasonic waves).   The sensitivity of MS temperature to the sign of the applied stress system having large hydrostatic parts gives us a clue that the local activation volume; DelV= DelG/DelP  of this quasi-phase transformation plays important role in the kinetics. 

Dear Song,

I suggest that you also read H.K.D.H. Bhadeshia and J.W. Christian on this topic. The alternative explanation for the formation of Widmanstatten ferritic plates is based on a displacive mechanism rather than diffusional. There had been a long lasting debate regarding the nature of this transformation mechanism (also and mostly concentrating on the mechanism of Bainitic transformation) between two camps basically. One was led by the late Prof. Aaronson of Carnegie Melon and the other by Christian, D.V. Edmonds and Bhadeshia of Oxford and Cambridge Universities. In my view, the more convincing arguments were given by those who favoured the displacive mechanism. You should consider two very important experimental observation that orientation relationships exist between the product phase and the parent, and furthermore surface relief is observed in these transformations. Final evaluation and decision will belong to you.

Widmanstatten plates are controlled by diffusional processes, particularly the need to displace carbon from that austenite transforming into ferrite which cannot accept the carbon at concentrations much above the equilibrium amount.  Do the atoms in the austenite displace into ferrite by shear processes?  Perhaps, at an atomistic level and at diffusional kinetics.  After the residual austenite becomes sufficiently enriched it forms pearlite, again by diffusion of carbon in the austenite ahead of the advancing pearlite front, to establish the carbon concentrations of the ferrite and the carbide.  Bolling et al produced pearlite formed at the eutectoid composition by pulling a solid steel bar through a steep temperature gradient at varying rates and produced pearlite of appropriately decreasing lamellar spacing at higher mechanical extension rates, just as if a eutectic structure was being formed. This can be done surely by atomistic jumping at the interface.  Further, the production of surface relief at a "diffusional" transformation can be interpreted by either diffusional jumping or shear mechanisms.  Laird et all have observed surface relief produced by gamma plates forming over weeks of aging in Al-15% Ag alloy (at carefully controlled temperature).  The compositional difference between the solid Al solution and the gamma plate is huge, so there has to be compositional adjustment by diffusional jumping at the interface.  Of course it is also true that the solid solution and the gamma differ in crystal structure, giving rise to the surface relief.

Orientation relationships start off at the nucleation process by the need to overcome the interface energy barrier  to transformation, and that low energy interface is sustained by diffusional barriers to growth, leading to the eventual morphology of the product phase. Laird et all have found by electron microscopy partial dislocations at the semi-coherent interfaces of plate precipitates in Al-Cu, Al-Au and Al-Ag.  Those partial dislocations in all three alloys acted to produce barriers to diffusional growth.  Certainly those in Al-Ag could be interpreted as capable of accomplishing a dsiplacive transformation. 

Thus the evidence is ambiguous.   Both sides in the dispute apparently remain complacent  in their respective positions.

Widmannstaetten patterns have been discovered in iron meteorites and they commonly do not have any carbon (of course there are a few exceptions). In so far I do not really understand the  argumentation with carbon if it also happens without carbon. bcc/fcc orientation relationships also appear e.g. in Co-Al alloys and also they do not have any carbon. Also the above mentioned Al-Cu, Al-Au and Al-Ag systems obviously show transformations described by K-S or N-W. Iron meteorites are also nice examples to demonstrate that phase transformation dos not only happen along the grain boundaries since many of them have austenite crystal dimensions in the scale of meters. The fact that precipitation does not only starts along grain boundaries is certainly not new. I only want point this out for all of them who perhaps follow from the question that this is only related to grain or phase boundaries.  

There is at least one error of fact in Gert's answer, namely, the references contained in the answer above concerning Al-Cu, Al-Au and Al-Cu dealt with alloys at the Al-rich end of the equilibrium diagram, and therefore DO NOT show transformations described by K-S or N-W.  They involve transformations having other orientation relationships but are nevertheless relevant.  Others of Gert's statements cannot be evaluated because insufficient information is provided.  For example, Widmanstaetten patterns occur in many, many systems involving solid solutions and/or interstitial solutions.  We need more information about his meteorites.  No one will dispute that phase transformations occur both at grain boundaries and within grains.  The classification of morphological types concerning precipitates in metallic systems was provided decades ago by Dube and his publications are recommended for study.  Gert is correct that the issue of interest here was stated in terms of grain boundaries, but the answers raised by it in discussion pertain to more general questions about phase transformations both at grain boundaries and within grains.

One problem of discussion on Researchgate is that contributors have widely differing backgrounds and experience and written answers take time that discussers do not have.  I have retired from teaching, I suffer pressure of time, and I am not prepared to go on teaching without pay! 

Dear Campbell,  If this would be a genuine phase transformation taking place in multi components system there should be redistribution of the chemical species through the long range diffusion, and then the degrees of advancement of the transformation for a given time  interval should be depend on the isothermal annealing temperature exponentially,  since the rate is proportional with   A exp(S/R)  exp-H/RT.  Therefore,  Transformation should approach to the completion asymptotically for any given temperature below the certain threshold value, which may depend not only the equilibrium phase diagram but also the constrains on the solid state matrix due to the surface traction and body forces.  In the case of the kinetics of Martensitic transformations not the rate of advancement of transformation but the amount of advancement is temperature dependent quantities. . MS  and MF  temperatures are reality. The rate is almost equal to the propagation of the shear waves (group velocity) in that matrix.  

For me this is not a first order phase transition as described by Landau, where the nucleation and growth can be described by the Fokker-Planck equation.  This may be higher order displacement transition,  which involves cooperative movements of the large numbers of atoms '(not necessarily different species)'  that generate severe hydrostatic deformation on their immediate  environments or matrix!  

Dear Gert, In the case of iron carbon system the end product of this morphological evolution process is not bcc ferrite having carbon atoms in the octahedral sites distributed evenly along the x,y,z  directions but rather show anisotropy  along the major axis of the plates due to the severe stress concentration at the sharp edges or tips. 

Dear Campbell, regarding the meteorites: From my point of view it is quite convincing since the austenite orientation does not change in many iron meteorites, but as function of the Ni concentration coarse but also very fine lamellae, or even plessite which shows transformed crystals down to nonameter size appear. For all of them is valid: there is no grain boundary. In so far (and from my point of view) it classifies them as intergranular Widmannstaetten plates or needles.

Sorry for the misunderstanding of your comment regarding Al-Cu, Al-Au and Al-Cu. I assumed you were still talking about K-S and N-W which was the reason that I used "obviously".

My answer for  the question;  why grain boundaries are prefered for the martensite formation?  Because of the large hydrostatic expansion occurs during martensite formation,  this induces negative  hydrostatic stresses or constrain on the growing martensite, which  can be partially accommodated by the lens or disc shape morphology,  of which  the flat  circular section with wage shape edges grow fast and extends all along the grain boundary with minimum resistance, and the lateral dimension on the other hand is  suppressed by the neighboring grains, and  showing minimum growth rate. 

Gentlemen:  If the questioner specifies Widmanstaetten plates, and questions their formation in terms of growth, he is not specifying a nucleation question.  The plates in question develop from diffusional growth mechanisms, different from the martensite reaction.  Thus the above two answers are irrelevant.

Hello everyone,

I need to apologize for the late reply.

Thank all of you for the valuable answers. I learnt a lot. I really appreciate it.