Nucleation of recrystallization

This paper reviews the mechanisms of nucleation during recrystallization of cold deformed, single phase polycrystalline metals including metals with large particles. The classic nucleation theories and conceptions are shortly summarized, while the main focus is on our results from recent 3D studies of nucleation. The novel results are related to the classic nucleation ideas and agreement/disagreement as well as new suggestions are discussed. More specifically the paper covers recovery leading to intragranular nucleation, bulge nucleation (which is often referred to as strain induced boundary migration), and particle stimulated nucleation. Also, effects of clustered nucleation, crystallographic orientation relationships and residual stress are considered. Finally future studies are suggested, which we consider key to advancing the understanding of nucleation during recrystallization.


Introduction
Primary recrystallization always originates from nuclei.A nucleus is defined by being almost free of defects and having the ability to grow in a deformed matrix upon further annealing.Embryos are volume elements in the deformed matrix, which may develop to become nuclei.The nature of nucleation is still heavily debated: Where exactly will nuclei develop in the deformed matrix material?With which crystallographic orientation?Are there still parameters which are critical, such as residual strain, but not yet included in the understanding of nucleation?
In the very first reports, recrystallization was referred to as "crystallization" and the deformed matrix was considered to be amorphous [1][2][3].Even though it was soon after realized that this was not the case [4], the most classic (re)crystallization theory was based on thermodynamics [5].The first nucleation model assumed random condensation by a group of vapor atoms coming together to form an embryo.If such an embryo is too small, the enhanced vapor pressure at its surface will cause it to re-evaporate.Only if it has a size larger than a critical radius, the embryo becomes a variable nucleus [6].In solid state transformations, such as recrystallization, self-diffusion replaces the motion of vapor atoms [7], but the basic conception of a critical radius for a nucleus remains valid.
To facilitate the transition from an embryo to a nucleus, which can grow rapidly, highly mobile boundaries (or boundary segments) surrounding the embryo, and the nucleus, are required.Although parameters such as driving pressure, annealing temperature, boundary type (e.g.tilt or twist), as well as impurities and solutes are known to affect the boundary migration rates [8,9], it is well accepted that high angle boundaries in general moves faster than low angle ones [10,11].It is thus critical for a nucleus to be at least partly surrounded by a high angle boundary.
Even in the early, very excellent, studies of nucleation referred to above, it is apparent that progress in understanding depended vitally on progress in development of experimental techniques [12].Inspired by this, the aim of the present paper is to review examples of our nucleation results obtained by recently developed 3D characterization techniques, and relate them to the classic theories.The 3D characterization techniques to be considered here, are all, except one example, based on synchrotron Xray diffraction.These synchrotron X-ray diffraction methodologies offer a spatial resolution of 1 μm or better, an angular resolution better than 0.01° and a strain resolution of 10 -4 .These techniques are thus very well suited for in-depth studies of recrystallization.For a broader, in-depth discussions of nucleation in general, the reader is referred to other reviews, for example [13,14].Although annealing twinning is a commonly observed mechanism leading to recrystallizing grains with new crystallographic orientations relative to the matrix, this mechanism will not be reviewed in the present paper.
Finally, we propose experiments which have become, or soon will become, possible due to the continued development of non-destructive X-ray diffraction techniques.These experiments, we expect to be of critical importance, if the goal is one day to become able to predict nucleation -i.e. to answer the questions outlined above.

Intragranular nucleation
The microstructures of cold deformed samples are highly heterogeneous [15].Preferred nucleation sites are expected to be volumes in the deformed microstructures with local maxima in stored energy, having a significant lattice curvature.In the interior of grains, such sites include deformation induced dislocation boundaries [16], transition bands [17] or microbands, deformation twin intersections [18], shear bands [19] and cube bands [20].In regard to intragranular nucleation mechanisms, subgrain boundary migration [21] and subgrain coalescence [22,23] may be dominating.Both are typical recovery mechanisms, and it is generally agreed upon that the subgrain boundary migration is dominating the microstructural evolution during recovery [24].However, when it comes to nucleation, coalescence satisfies the criteria for providing a nucleus of the critical size, and with a higher misorientation across its boundaries than those in the matrix, while subgrain boundary migration do not.Coalescence has thus been suggested as an active intragranular nucleation mechanism [25], yet it has been stated that subgrain coalescence needs further work before it can be considered definitely established as a general phenomenon [26].
In recent work, a synchrotron X-ray microdiffraction methodology, namely differential aperture Xray microscopy (DAXM) was used to investigate the microstructural evolution in 3D in the bulk interior of a 12% cold rolled pure aluminum sample during recovery annealing [27].The work confirmed that subgrain boundary migration is active, preferentially removing small subgrains.However, also clear evidence of subgrain coalescence was observed [27].Furthermore, the work suggested interactions between subgrain boundary migration and coalescence, such that the migration leads to extraction of dislocations from neighboring boundaries, thereby stimulating the coalescence [27].Thus a combination of these two recovery mechanisms may lead to intragranular embryos of nucleation.
Concerning the assumption of high stored energies present at the nucleation site, recent investigations have supported this.In a 3D DAXM investigation of nucleation in a 12% cold rolled aluminum sample, further deformed locally by a hardness indent, nucleation was observed to happen near the hardness indent at sites in the deformed matrix with high stored energies -at least locally as compared to the neighboring volumes [28].This is shown in figure 1.The figure, however, also reveals that there are many regions with high stored energy, which do not stimulate nucleation.It thus appears that local high stored energy, is a necessary, but not sufficient criteria for nucleation.
A similar conclusion was reached in [29].In that work, the nucleation sites within a 40% cold rolled aluminum tricrystal was studied.The nuclei were found to form not at the maximum stored energy, but rather at local smaller maxima in stored energy associated with deformation microstructures subdivided by sharp bands of large misorientations (see figure 2).Based on the data, a new criterion for nucleation was proposed, which incorporate the anisotropy in the orientation distribution [29].

Bulge nucleation (strain induced boundary migration)
This nucleation mechanism was originally suggested by Bailey and Hirsch [30].It considers the situation of a significant difference in stored energy per unit volume ΔE between two original grains in the deformed matrix.If this difference is large enough, the boundary will tend to bulge out in the directions of the higher stored energy, creating a local bulge (see figure 3).Critical parameters are the specific grain boundary energy γ, the surface area A and the volume V of the bulge as well as ΔE.The bulge will grow when ∆ >    ⁄ for all the values of L and α (see figure 3) that the bulge will experience during its formation and growth [6].This is actually equivalent to the critical embryo idea in the original nucleation theory by Volmer [5].
Figure 3. Sketch showing bulge nucleation in 3D at a grain boundary.
The above described mechanism is similar to the strain induced boundary migration (SIBM) idea proposed by Beck and Sperry [31]; only the scales and thus the magnitude of the required ΔE are different.This may be why many papers report SIBM as an efficient nucleation mechanism.
There are many examples in literature showing nuclei, which may have been formed by bulge nucleation on original grain boundary planes or along triple junction lines.A particular beautiful example is reproduced in figure 4. The alignment of these nuclei was found by careful serial sectioning [32] and thus confirmed in 3D.To the best of our knowledge, such neat measurements have not yet been followed up using the modern non-destructive 3D experimental methodologies, which would indeed ease this kind of 3D imaging compared to the tedious serial sectioning.
An interesting aspect of this nucleation mechanism, as well as of the coalescence mechanism discussed in section 2.1, is that the material inside the bulge, or in the coalesced subgrain, is not expected to be a perfect single crystal, as the original dislocations cannot annihilate nor terminate inside the embryo.The presence of very low angle dislocation boundaries inside nuclei, as a kind of reminiscence of the original cell/subgrain structure, has recently been proven by dark field X-ray microscopy (DFXRM) for AA1050 cold rolled 50% and annealed at 325 °C for 50 min [33].
Even though bulge nucleation is a well-documented nucleation mechanism, it has not been explained why bulges only occur at certain places, and not everywhere on these 'active' original grain boundaries or triple junctions.Maybe, it requires some additional microstructural specifics to be fulfilled for the neighbouring deformation microstructures, possibly similar to those suggested above for intragranular nucleation (see Section 2.1). Figure 4. Optical micrograph showing a cluster of nuclei on a grain edge (i.e.triple junction line) in zonerefined Al with 0.008% Cu rolled at 0 °C to 40% reduction in thickness.Reproduced from [32].

Particle stimulated nucleation
It is very well-accepted that large second-phase particles provide nucleation sites [34][35][36], if they fulfil two criteria: i) a region with significant lattice rotation around the particle must be formed during plastic deformation and ii) the driving force must be sufficient for the embryos to grow to reach the critical size.The latter criterion leads to the definition of the critical particle size above which particle stimulated embryos/nuclei can grow with rc(particle)> 2 γ/E.As the stored energy, E, is a function of strain, the critical particle size also depends on strain -the larger the strain, the smaller is the critical particle size [34].
Experimentally, particle stimulated nucleation (PSN) has been observed and the mechanism deduced based on microscopy, where many nuclei have been observed next to the large second phase particles [e.g.[34][35][36][37].It is however a real challenge to quantify PSN based on such 2D observations: even nuclei which are seen far away from particles may be formed by PSN, but the particles are below the inspected surface or had been grinded away during sample preparation, and are thus not seen in 2D.How severe this challenge is, depend, as discussed in [38], on many parameters including size/volume fraction of nuclei and particles, spatial distributions and shapes.It is thus actually very impressive that the 'fathers' of PSN managed to discover this important nucleation mechanism from 2D characterizations.Reproduced from [41].

Clustered nucleation
All the three fundamental nucleation mechanisms; intragranular, bulge and particle stimulated nucleation, are likely to stimulate nuclei which are not uniformly/randomly distributed in space.Rather, clustered nucleation is in most cases dominating.This obviously affects their evolution potentials, as the growth will stop locally when and where impingement with neighbouring nuclei/grains occur.Implications hereof, is for example discussed for PSN in [36].A consequence of clustered nucleation is that the fundamental assumption in the classic KJMA recrystallization kinetics models [43][44][45] is not fulfilled and more advanced models have to be used.For this, we recommend to use the microstructural path methodology (MPM) developed by Vandermeer and coworkers [e.g.[46][47][48].An overview over the suite of MPM models is given in this set of REX&GG conference papers [49].

Crystallographic orientation relationships
The texture is almost always observed to change during recrystallization.It is thus interesting to note that all the classic well-documented nucleation mechanisms, discussed above, lead to nuclei with crystallographic orientations identical to or only very slightly misoriented from the 'parent' orientations at the nucleation sites.As large lattice rotations are created near large particles, nuclei forming there, are often reported to have random or spread rolling orientations, e.g.[36].However, recrystallization textures are almost never random.
To quantify orientation relationships by 2D investigations are largely impossible, because it is not known what is below or above (grinded away) the inspected plane.An additional issue, is the 'lost evidence problem' [50], stating that when a nucleus is observed in a static 2D (or 3D) investigation, it is not known, what was there, at that site, before nucleation.Only few 4D (3D plus time) nucleation studies have been performed.The most recent ones [28,51], confirm that nuclei develop from embryos already present in the deformation microstructure, with orientations identical to those there.This is illustrated in figure 6.It should be noted that the blue voxels in the embryonic volume contain boundary segments with misorientations of 0.23°, suggesting that subgrain coalescence may have occurred prior to nucleation. Figure 6.Sections through the 3D volume in the deformed and annealed state near a nucleus of the sample shown in figure 1.The successive sections are 1.5 μm apart along the rolling direction.The nucleus is shown in blue and all other voxels are colored according to the misorientation angle to the nucleus orientation.The white and black lines show misorientations in the range 2-15° and above 15°, respectively.The 3 voxels, marked by an arrow in the deformed state, have the same orientations as the nucleus.Reproduced from [28].
So what can explain the typically very significant change in texture during recrystallization?If all the nuclei have parent orientations, neither oriented nucleation nor oriented growth [52] can explain a recrystallization texture with new strong components different from those in the deformation texture.A particular concern in this respect, is the strong cube recrystallization texture seen in many pure high stacking fault energy fcc metals.Intragranular nucleation within cube oriented bands [20,53] is so far the only nucleation mechanism suggested to explain this.
To overcome the experimental limitations in studying nucleation related orientation relationships by 2D methodologies of typical polycrystalline materials, nucleation in deformed single crystals and in columnar grained samples have been studied instead.Both types of studies have consistently revealed nuclei with new orientations, i.e. orientations different from those in the deformed matrix [54][55][56][57][58]. Also non-destructive 4D X-ray characterizations have shown nuclei with orientations which were not recorded to be present in the deformed sample -in volumes larger than the spatial resolution, which is typically around a few µm.(The angular resolution of these techniques are below fractions of a degree, so no uncertainty is related to quantifications of orientations before and after annealing).In these 2D, 3D and 4D works, some preferred orientation relationships between nuclei and matrix have been suggested [54,57,58], but a clear defining nucleation mechanism leading to new orientations has yet to be deduced.

Residual stress effects
So far we have discussed recrystallization driven by externally imposed strains.However 'self stress' as it was called [7], has been shown sufficient to drive recrystallization (after the deformation was completed), in some cases.This was observed in graphite [59], and in some ordering alloys, e.g.Co-Pt [60] and Cu-Au [61].The driving force was argued to come from short-range internal strains due to interaction between micro-domains.
The 3D X-ray diffraction techniques offer determination of local residual strains [62], besides of course crystallographic orientations.It is with these techniques rather straight-forward to map the distribution of the local residual strains for the recrystallizing grains, from which clear diffraction peaks are observed.It is much more challenging to do for the deformed microstructure.For recrystallizing grains, such measurements have revealed the surprising result that substantial residual strains can be present [63,64].When converted to stress, even values near the yield stress are observed at early stages of recrystallization.It is thus clear that future nucleation studies have to include considerations of the distribution of local residual stresses; different deformed grains should be characterized as they exhibit different residual strains [65] and nucleation potentials [66].Local residual strains may well be a missing link in our understanding of recrystallization.

Outlook
In our view, nucleation is the most complex part of recrystallization to study experimentally, and the least well understood scientifically.The novel non-destructive 3D microstructural characterization techniques offer a new 'take' on experimental nucleation studies with good potentials for advancing the understanding of the topic.Key investigations may include:  In-situ (or ex-situ) studies of intragranular recovery in typical polycrystalline samples leading to pinpointing embryos which subsequently develop into nuclei that are able to grow.It would be of particular interest to test i) if the suggested combined subgrain boundary migration and subgrain coalescence mechanism is of critical importance and ii) if an additional term related to the spatial distribution of deformation induced dislocation boundaries is of relevance when the aim is to pinpoint which high stored energy sites are developing into nuclei. In-situ (or ex-situ) studies of nucleation at original grain boundaries/triple junction lines and at large second-phase particles, with the aim of quantifying which boundaries/particles are the most active, and where along a given boundary nuclei may form as well as why. Simple 3D mapping of many nuclei within a reasonably large sample volume to clearly reveal linear or planar clustering of nuclei formed by bulge nucleation and particle stimulated nucleation. Combined characterization of the spatial distribution of local residual strains and crystallographic orientations within the deformed microstructure, followed by in-situ (or ex-situ) annealing leading to nucleation, to clarify the role of residual strains in stimulating nucleation.
These four experiments will all benefit from faster measurements and finer spatial resolution, enabling proper characterization of large volumes as well as highly strained microstructures.The large volume is needed to ensure a high chance of nucleation happening within the characterized volume, and the finer spatial resolution is to ensure characterization of orientations and residual strains in even small dislocation filled local volume elements (<1 µm).Thereby, it will also be possible to substantiate if nuclei with new orientation may develop, and if 'yes', then where, why and how.
All of this with the long term goals of full 4D verification of the classic nucleation mechanisms, maybe refining them by adding extra terms/conditions and possibly deducing new nucleation mechanisms needed for example to explain the commonly observed substantial texture change during recrystallization.

Figure 1 .
Figure 1.Distribution of stored energy in the deformed state of a 12% cold rolled aluminum sample, further deformed locally by a hardness indent.(a) a 3D map of the stored energy (magnitude indicated by the color legend).The crosses mark the positions of the identified embryonic volumes.(b,c,d and e) show sections near the indentation tip: (b) 8.5 μm above, (c) 4.3 μm above, (d) at exactly at, and (e) 3.2 μm below the tip.Reproduced from [28].

Figure 2 .
Figure 2. Annealing microstructure in a region close to the triple point, in the TD-ND plane, within a 40% cold rolled aluminum tricrystal.(a) ECC image, where the grain boundaries are highlighted in red.Nuclei are observed only in crystal A. (b) EBSD orientation map (Rodrigues vector map) within the region indicated on (a).Reproduced from [29].

Figure 5 .
Figure 5. (a) Inverse pole figure (IPF) map of the partly recrystallized microstructure of 75% cold rolled AA5182 acquired from Laue micro-diffraction.(b) Visualization of CT data of the same sample containing the volume seen in (a).The yellow dashed rectangle indicates the surface area approximately corresponding to the sample surface in (a).The planes showed on the surfaces of both data sets are ∼10 µm below the sample surface.Reproduced from[41].