Grain Nucleation and Growth during Phase Transformations

Grain nucleation and growth are important phenomena in polycrystalline materials like metals and most ceramics. They govern the kinetics of many phase transformations and recrystallisation processes that take place during processing. The final average grain size after the transformation is directly related to the strength of the material. In general a smaller average grain size results into a stronger material. Despite the various transformation models that have been proposed in the last 60 years, the kinetics of these phase transformations are still poorly understood. Most of these models are based upon the Classical Nucleation Theory (CNT) [1] and the law of parabolic grain growth as derived by Zener [2], which describe the behaviour of individual grains in the bulk of the material.

The experimental techniques which have been available to verify these nucleation and growth models are either limited to observations at the surface or the determination of the average grain growth behaviour in the bulk. The development of the 3DXRD microscope at beamline ID11 has created the opportunity to study individual grains in the bulk of a material [3]. These measurements give unique information about the grain nucleation and growth during the phase transformations. Thanks to a combination of fundamental scientific interest and technological importance the phase transformations in steel have been investigated more extensively than in any other material.

Carbon steel consists of iron and carbon (up to 2 wt.%) with small quantities of alloying elements, and exists in three stable crystalline phases: austenite (above 822°C), ferrite (below 822°C), and cementite Fe3C (below 685°C). In the experiments we continuously cooled the steel from 900°C to 600°C in 1 hour. In order to study the time evolution of individual grains during the phase transformations, a relatively small volume of steel is illuminated with a monochromatic beam of hard X-rays (80 keV). A number of individual grains give rise to diffraction spots on a 2D-detector. From the standard diffraction theory it can be shown that the intensity of each spot is proportional to the volume of the grain it originates from. By repeated acquisition of images, the nucleation and growth of the individual grains are studied with a typical time resolution of 10 seconds.

 


Fig. 79: Nucleation as a function of temperature: (a) the total number of valid ferrite reflections; (b) the normalised experimental nucleation rate (bars) compared to the classical nucleation theory (line). The different stages during the phase transformations in steel are schematically drawn at the top of the figure, which shows the three phases: Austenite (), ferrite (), and cementite ().

Our measurements show that the activation energy for grain nucleation is at least two orders of magnitude smaller than that predicted by the CNT (Figure 79). The observed growth curves of the newly formed grains confirm the parabolic growth model, but also show three fundamentally different types of growth. On the level of individual grains we can distinguish four types of grain growth as shown in Figure 80. There are grains that do not interact with neighbouring grains, grains that continue to grow with the same crystallographic orientation into another phase, grains that indirectly interact, and grains that directly interact with neighbouring grains.).

Fig. 80: Particle radius of individual ferrite grains as a function of temperature: (a) no interaction with neighbouring ferrite grains; (b) ferrite grains, which continue to grow with the same crystallographic orientation during the pearlite formation as part of a pearlite colony; (c) ferrite grains that indirectly interact; (d) ferrite grains that directly interact with neighbouring grains. The solid line indicates the classical Zener theory.

We conclude that the current models do not accurately predict the phase transformation kinetics in polycrystalline materials. From a technological perspective these new insights are of importance to the modern materials production process, which relies heavily on grain nucleation and growth models to produce tailor-made materials.

References
[1] J.W. Christian, The Theory of Transformations in Metals and Alloys, Pergamon Press, Oxford, (1981).
[2] C. Zener, J. Appl. Phys. 20, 950-953 (1949).
[3] E.M. Lauridsen, D.J. Jensen, H.F. Poulsen, U. Lienert, Scripta Mater. 43, 561-566 (2000).

Principal Publication and Authors
S.E. Offerman (a), N. H. van Dijk (a), J. Sietsma (a), S. Grigull (b), E.M. Lauridsen (c), L. Margulies (b,c), H.F. Poulsen (c), M.Th. Rekveldt (a) and S. van der Zwaag (a), Science 298, 1003-1005 (2002).
(a) Delft University of Technology (The Netherlands)
(b) ESRF
(d) Center for Fundamental Research: Metal Structures in 4D, Risø National Laboratory, Roskilde (Denmark)