Commentary: energy barrier model for W_s

H. K. D. H. Bhadeshia, 29-04-2026

A recent publication: Wang, Dai, Sun, Sun, Chen, van der Zwaag, Liu, Sun, Scripta Materialia 280 (2026) 117352. Published during April 2026.

The paper contains errors, previously described during January 2026, and forwarded to Professor Dai:

The equation used for solid-solution strengthening of austenite is wrong [Appendix, reference 1].
The perceived level of resistance to interface motion is mythical [p. 9, reference 1]. The growth rate is explained easily with this set to zero [Fig. 10, reference 1]
The authors have incorrectly decoupled the lengthening and thickening motions [p. 10, reference 1]. The shape is constrained by the deformation accompanying transformation. This is the viable explanation for the elegant thin-plate morphology.
The interfacial energy per unit area is taken as 0.23 J m⁻² but the parameters used for the "barrier" lead to 2.3 J m⁻² [p. 13, reference 1].
Molybdenum diffusion is invoked without credible justification.

Conceptual errors

The method is about a start-temperature. However, the plates are assumed to materialise without nucleation.
The thickening and lengthening of Widmanstätten ferrite are treated independently. These processes are coupled through the fact that the lattice change is generated by a coordinated motion of atoms [2, 3, 4]. The shape deformation is there for all to see:
Observation: Growth of Widmanstätten ferrite in steel
An elementary observation is that thickening does not continue once the plate has reached a hard obstacle.
If lengthening and thickening of plates are uncoupled, the aspect ratio of plates would not be as observed. And of course, the lengthening rate would no longer be constant, given the bizarre assumption that the carbon enrichment all along the sides of the plate would be zero.
Reliance on carbon diffusion means the method cannot address α_W in interstitial-free steels.
What is concise about the method? Here is a ten-second, physically correct way to estimate the W_S temperature.
Both in this paper and in their earlier work, the strain energy of a displacive transformation is equated to the driving force necessary for the dislocation structure of the α/γ interface to drive past obstacles in the austenite. However, this would be dissipated as heat, just as in ordinary plastic deformation. The strain energy due to the shape deformation is stored elastically inside the steel [5] and must be accounted for accordingly.