Abnormal Grain Growth: A Spontaneous Activation of Competing Grain Rotation

Unconventional white‐beam Laue synchrotron X‐ray diffraction is used on fine‐grained, as‐rolled magnesium alloy during an in situ heating experiment. At high temperatures, reflections of single grains are superimposed on the halo stemming from matrix grains. Some unique grain reflections spontaneously move, indicating grain rotations in response to torque expedited at grain boundaries. When a grain boundary spontaneously activates, it can begin to rotate, allowing diffusive mass transport and activating the boundaries of its other neighbors. Now the given grain can freely rotate toward coalescence; however, the multitude of grain boundaries compete in torque orientation and magnitude, resulting in zigzag rotations. After coalescence, the larger grain is still active and continues this scenario of growth, while the majority of the matrix grains remain inactive. The first‐time experimental observation of such erratic grain behavior supplies the missing puzzlestone leading to anomalous grain growth, long postulated in literature. The method of white beam Laue diffraction on fine‐grained polycrystalline materials delivers a novel experimental method to study the erratic behavior of grain reorientation, as requested long ago by the scientific community. Such findings apply to wide ranges of materials undergoing grain growth, creep, and superplasticity, including those in metal engineering, ceramics, and geophysical disciplines.

theory between normal and abnormal growth, the latter stating that abnormal growth only takes place when the size of the growing grain is already large. [4]5][6] Moreover, the present inspections have been enabled through an unconventional and novel experimental approach using the white-beam X-ray Laue diffraction method in bulk transmission mode on a polycrystalline material, which is generally said to be inappropriate in such a situation.In this in situ study, we can distinguish reflection spots for the first time from a single reorienting bulk crystallite over the background of a static halo, diffracted from the matrix grains, delivering the up-to-now lacking simple experimental approach to observe erratic grain rotations in the bulk, in situ, fast, and over a wide range. [3] An In Situ Heating White Beam Laue Experiment on Magnesium Alloy The study has been performed on as-rolled sheet material of magnesium alloy AZ91 with a nominal composition in mass% of Mg-9Al-1Zn, 1.50 mm thickness and an initial grain size of 5-20 μm.White-beam Laue diffraction has been performed at SPring-8 under proposal number 2013B3606 at the beamline BL14B1, which offers 5-150 keV photons in a wavenumber range [7] covering 2.5-76 Å À1 , incident perpendicular to the specimen sheet for transmission measurements.Two PILATUS flat panel detectors of types 300K and 100K have been placed off-centered at %0.25 and 1 m distance, respectively.Detector frames have been recorded continuously at 0.9797 Hz upon a heating ramp of 0.13 K s À1 to 773 K, holding for 1800 s, and subsequent furnace cooling.Both of their videos are available as S1 and S2, Supporting Information.Apart from the beam conditions and detector locations, the present setup is identical to that of a conventional monochromatic diffraction experiment, utilizing the same experimental equipment, heating parameters, and same-batch specimens as published by Liu et al. [8]

Interpretation and Overall Evolution of Diffractograms and Microstructure
Figure 1 represents some typical white-beam Laue diffractograms framed by the 300K detector, with the incoming beam position located at the top center.The halo of a broad diffuse ring represents the powder diffraction distribution convoluted with the very wide wavenumber range of the incident white beam.The salient feature we focus on is the distinct intensity spot stemming from Laue-Bragg interferences of individual crystallites.In fact, such distinguishable crystallite reflections are well expressed through spotty Debye-Scherrer rings in a monochromatic beam diffraction experiment, [7,9] when the number of crystallites in the X-ray-illuminated volume is small and the assumption of random orientation for powder diffraction fails.The temporal evolution of such spots has been exploited to deduce microstructural rearrangements, for example, during thermomechanical processing. [7,10]Actually, the present white-beam Laue patterns can be thought of as a superposition of many concentric monochromatic Debye-Scherrer rings, integrated over the wavenumber distribution.Here, the salient novelty is that, upon grain rotation, the reflections do not move off the Ewald sphere, as the Bragg condition is always fulfilled for some incoming wavevectorthus, the orientation of crystallites can be followed in all two dimensions over a wide range.
The temperature and temporal evolution of the Laue diffractograms are evident in Figure 1.Qualitatively, the diffractogram does not change when heated to 537 K referring to a fine-grained microstructure.This has coarsened to the figure at 586 K, exposing still a relatively high number of spots, which themselves are expressed as little streaks denoting deviatoric strain in the microstructure. [11]Further coarsening occurs at 636 K through 710 K with evolution and reduction of the deviator part.Above, a diffuse halo appears with sparsening spot numbers displayed at 760 K.At the holding temperature of 773 K, the deviatoric strain largely disappears, and the density of spots evolves sluggishly, albeit with fluctuations to be discussed later.Upon the relatively fast cooling, reflection numbers become static as displayed for 714-711 K, increasing tremendously the deviatoric strain.Basically, below 710 K, the diffuse halo disappears and the deviator strain becomes paramount, while in principle, all spots from 711 K can be mapped to those at 335 K, revealing a generic static microstructure with a settlement of stress fields and distortions.
This article focuses on the observation at high temperatures, where we observe grain rotation and grain coalescence; however, a quick interpretation of the overall scenario is given in the following, together with a first analysis, plotting the average intensity per selected solid angle in the main ring, as displayed in Figure 1 (bottom), against temperature.A first significant increase is observed starting at 440 K which we attribute to a primary recovery in subgrains, which render crystals better and thus more reflective.Larger rearrangements occurring from 536 K onward are consistent with earlier reports by Liu et al. [8] where limited grain growth occurs, producing more perfect crystallites that are less in number and experiencing the onset of primary extinction of X-ray diffraction revealed in the decrease of integrated intensity. [12]From about 540 K on, the intermetallic phase Mg 12 Al 17 continuously dissolves and disappears at 636 K, as reported by Liu et al. [8] and in consistency with the Mg-Al phase diagram, [13] exposing lattice distortions to the matrix crystallites partly expressed by the observed deviatoric strain, reducing primary extinction of radiation, and thus increasing overall intensity.After the phase dissolution at 636 K, the system continuously recovers, as seen by the diminishing deviator strain.As we will see in the focus of this article, the system becomes more dynamic, showing fluctuations in grain reorientations, when approaching the eutectic temperature of 710 K. Above, we'll find evidence for molten or partly molten grain boundaries, at which the dynamics become very high, and the intensity follows an exponential decrease with a decay time of 312 s.Upon cooling, the system freezes, and anisotropic thermal lattice expansion leads to large deviator stresses, particularly when the intermetallics reappear with a larger mismatch and strong temperature dependence of thermal expansion, as well as lattice gradients on concentration due to segregation.
Figure 1.Time frames representing selected white-beam Laue diffractograms (upper part, exposure time 1 s), taken in situ from the magnesium alloy AZ91 upon heating plus cooling, as per the temperature profile and selected-area integrated intensity (bottom graph).Upon grain growth, the initial halo distribution of a powder-average white-beam diffraction intensity segregates into diffraction spots that stem from individual crystallites.The temperature and time evolution of the Laue diffractograms reveal significant structural transformations, as indicated in the text.Data taken with the 300K detector; the forward beam is located at the top center of each framethe small white spot.

Observations of Singular Grain Rotation in Zigzag Ways within a Stiff Matrix
While most Laue spots at 773 K look sharp in Figure 1, at least two elongated zigzag lines can be clearly distinguished.These are traces of reflections off one grain, which rotates during the exposure time of 1 s.Indeed, they can be followed over many seconds with grain reorientation angles sweeping up to 10°and 5°s À1 .We emphasize such observations in a sequence of difference images over 12 s and a color-coded time superposition of images over 75 s, as displayed in Figure 2 and 3, respectively.The arrow at Δt = 0 s (Figure 2) points to a little streak off grain I that is still there at Δt = 1 s, meaning grain orientation is stable but fluctuating slightly-otherwise, it would not be detected in the difference plot.At Δt = 2 s, it escapes from its initial orientation, leading to a longer streak, at which the grain rotates about 0.5°s À1 .At Δt = 3 s, the trace spontaneously changes direction, corresponding to an instantaneous change of the crystallite rotation axis.The angular velocity is even increased at Δt = 4 s, while it settles at Δt = 5 s, wobbles a bit at Δt = 6 s, and finally is static, disappearing from the difference map at Δt = 7 s.A reflection from a second grain II starts moving at Δt = 5 s during which it slightly reorients its rotation axis; at Δt = 6 s, the axis spontaneously changes twice, followed by a fast uniaxial rotation maximizing with 1°s À1 at Δt = 9 s, slowing down and eventually fluctuating a little at Δt = 11 s. Figure 2 shows the specific features in the observation of grain rotation; however, the moments of fluctuation at which only minor grain reorientation takes place are neither the beginning nor the end of the grain activity.A sixtimes longer time evolution is compiled in Figure 3, where point A on the left is the measurement of grain I at Δt = 0 s in Figure 2. Point C in Figure 3 corresponds to grain II orientation at Δt = 11 s.At both of these wobbling points, Figure 3 demonstrates that they belong to longer-lasting reorientation streaks, where crystallite reorientation has a rest but still fluctuates, until rotating again much further.For grain I (A), the observed path length is %4°, while it is even larger for grain II, amounting to 10°.The wobbling point A on the aforesaid trace of crystallite I can be recognized at another reflection trace of the same crystallite, also denoted A to the right in Figure 3.It is easily recognized by forming a knob on the trace while the crystallite is fluctuating, together with earlier and later corresponding trace parts.Grain II shows even three reflections traced from B through F, expressing a zigzag line with straights and major kinks.Depending on the rotation axis, those straights can have different lengths, and the kinks deviate at different angles.Nevertheless, the spontaneous change of rotation axis can be well recognized at points C, D, and E, where, at the right trace in Figure 3, D and E degenerate because they would contain the rotation axis.With this in mind, we now recognize the two or three reorientation kinks between point B and C, which we described already along Figure 2. At later times, a long runaway occurs with a kink at F. Such grain rotations are likewise observed below the eutectic temperature in the single-phase field (636-710 K), and their rotation speed scales with temperature.Figure 4 demonstrates a zigzag grain reorientation over 43 s when it enters and leaves the field of view from the top to the bottom, respectively.The temperature during these frames rises from 690 to 695 K, lying well below the eutectic point.Most of the other reflections remain static, stemming from a stable bulk matrix in which only the one observed grain reorients widely in a highly serrated way.Also, the rotational velocity jumps up and down, demonstrating its erratic behavior.Moreover, this moving reflection is among the strongest in these frames, suggesting it stems from a particularly large grain, containing lattice gradients as indicated by a fat lateral breath of the trace.
So far, we've described the grain rotations, but what about the grain growth?Grain coalescence is observed in Figure 5, where reflections from two grains, A and B, become active and wobble around their locations at Δt = 0 s (yellow color in the integrated image).Actually, grain B has been excited before (red color) rotating already toward A. Eventually, both A and B rotate toward each other (Δt = 1 s), meet (Δt = 2 s), merge (Δt = 3 s), rest a while in a wobbling spot until Δt = 5 s, and escape together (Δt = 6 and 7 s).

Underpinning Models Leading to the Interpretation of Activated Grain Rotation and Abnormal Growth
A theory of diffusion-accommodated grain rotation has been developed by Harris et al. [14] for thin films and then expanded by Moldovan et al. [15] to columnar grains, based on the diffusion mediated model by Raj and Ashby on sliding of corrugated grain boundaries under shear. [16]Figure 6 schematically presents a grain embedded in a polycrystalline matrix, which may be exposed to a torque τ due to an asymmetric grain boundary energy [14] to one of its neighbor grains.In order to rotate such a polygonal body by an angle ω embedded in a matrix, material has to be transported from the purple to the green shaded volumes, either by grain boundary or by bulk diffusion.In a further study, Moldovan et al. investigated grain coalescence by grain rotation, [17] which occurs when two neighboring grains align their lattices.In their model, the authors introduce a rotational  mobility M(R) = C/R p to describe the angular velocity ω : ¼ τ MðRÞ, which reduces strongly with increasing grain size R by an exponent p = 4 and 5, respectively, for grain boundary and lattice diffusion.Further, they simulate their scaling behavior by applying simultaneous torque and activity on all grain boundaries.In contrast, our observations of grain rotation demonstrate that, first, only a minority of grains rotate at any given moment.Second, the rotational mobility M is not necessarily small for a very large grain, as represented by a strong Laue-Bragg interference (Figure 4) or even after grain growth by coalescence (Figure 5).
We ascribe those effects to a necessary spontaneous grain boundary activation.Once a single grain boundary has been activated, diffusion channels open and enlarge, activating the other grain boundaries of that same grain under torque, allowing for rotation while the majority of the other grains remain inactivated and thus stable.It is well known that solute segregation at grain boundaries is an effective route to control and inhibit grain growth at high temperatures, including magnesium alloys. [18]egregates have been found in relatively thick films between the bulk grains of as-cast AZ31 alloy [19] and our recent in situ study on the same AZ91 sheet material as employed in this article reported on the dissolution of Al 12 Mg 17 intermetallics, leading to concentration gradients and the interdiffusion of surplus Al from the outer grain perimeters to the center. [8]It is evident that segregation or even intermetallic compounds at grain boundaries must be dissolved before diffusive channels open, allowing for grain rotation.Nakata et al. recently studied the role of grain boundary segregation on microstructure evolution in Mg-Al-Zn alloys by displaying 2 nm-thick segregation layers surrounded by 4 nm-thick depleted regions, which are thermal history dependent. [20]et's consider this Nakata segregated grain boundary, which may still exert a torque on a given grain.At some location, a hole may nucleate in this barrier.Under the torque, the area drives to increase and eventually open a 10 nm-thick diffusion layer channel for the grain rotationthe activation of the grain boundary, say between grain no. ( 1) and the central one in Figure 6.Eventually, the local stresses act on the other boundaries of the central grain, activating them too.Now the central grain is free to rotate, while the other grains of the matrix remain inactive  and static.This is a rare and random process, giving rise to some of the erratic behavior in grain growth.Say the orientation (I) of some lattice plane family in Figure 6 is attracted by the top neighbor grain no.(1) with an orientation (1), starting to rotate to decrease the misorientation angle ω to ultimately result in orientation (II), which would be a continuation of the crystal lattice (1), coalescence would then happen.During the rotation, however, torque of another boundary of the same grain but potentially on a different lattice plane family, say orientation (III), attracted by grain no.(2) when orientation (2) takes over, it results in a spontaneous reorientation.Competition may now be played with the many boundaries of the activated grain, resulting in the erratic zigzag paths observed in Figure 5 and 3. Obviously, such competition will hinder grain coalescence, as the zigzag path is longer than a direct rotation to a crystal lattice-matching condition.
Once a grain has been activated at all its boundaries, it remains so for a long time since relative stable orientations still fluctuate due to competition with their neighbors, as supported by the observation of wobbling grains.It can be regarded as an equal competition between two torque sources fluctuating while acting together against a third, hard reorientation axisand thus not settling down completely.As this wobbling continues, there is a chance that eventually another torque axis becomes largely favorable, making the grain reorient rapidly into an escape.Very nice demonstrations are points A in Figure 3 and the wobbling time between Δt = 3 and 5 s after coalescence in Figure 5.
Moreover, the activated grain status breaks down Moldovan's mobility law, M(R) = C/R p , after which grains of large size R rotate much less by a power of p = 4 in the case of grain boundary diffusion.For doubling the grain volume upon coalescence of two similar grains, the predicted mobility is reduced to 40%; for increasing the volume by an order of magnitude, M scales down to 5%.In contrast, after the coalescence of two similar grains, as shown in Figure 5, the resulting grain remains highly activated, exhibiting erratic behavior and rotating extremely quickly, as seen at Δt = 6 and 7 s.Even for an extraordinary fat grain, as estimated by the strong diffracted intensity in Figure 4, its mobility remains orders of magnitude higher than that of the inactive grains, paving its erratic zigzag way and eating up neighbor grains by coalescence.It is worth noting that the fat grain rotates within the matrix, as evidenced by the fact that such a large grain exposes more facets in its habitus, resulting in more competing rotation axes, as shown by a fine serrated erratic trace in Figure 4. On top of this, the large breath of the fat rotating grain trace denotes a deviator strain gradient across the bulk, indicating that atoms are in motion, underscoring the high activity of that grain.

Grain Rotations and Dislocations
So far, we have considered the Harris-Moldovan model, which accounts for diffusion, specifically grain boundary diffusion.However, we must also explore the role of dislocations.Notably, at high homologous temperatures, crystallites tend to recover, transitioning from diffraction streaks of deviatoric strain to more circular intensity dots upon heating, and vice versa upon cooling, as depicted in Figure 1 between 773 and 714 K.The exponential decrease of average solid-angle intensity above 710 K, observed during heating and holding at 773 K, indicates vanishing lattice gradients due to dislocations in increasingly perfect crystals. [12]Nevertheless, dislocations may play a role in grain rotation.In particular, grain rotation is related to the effect of superplasticity in metals, at which grain boundary sliding occurs not on a linear but on an angular scale.In this way, the above introduced Harris-Moldovan rotational model based on the Raj-Ashby linear model regarding pure grain boundary diffusion corresponds to the Lifshitz grain boundary sliding at low stresses. [21,22]However, at higher local shear stresses, dislocations may nucleate at grain boundaries, accumulate at triple junctions and ledges, and expel dislocation walls and low-angle grain boundaries into the crystallite's bulk, defining the regime of Rachinger sliding. [22,23]Naturally, the predicted diffusion channel opening at the grain boundaries consists of high-vacancy concentrations and amorphous-like regions, allowing to nucleate local dislocations in the vicinity of the grain boundaries.It can be postulated that above the eutectic temperature of 710 K, grain boundaries locally meltrepresenting another expression of a fast diffusion channel. [6]Nevertheless, mass transport must occur to accommodate the corners of the rotating grain.Since the Laue spots at such high temperature are sharp dots, we assume recovery is faster than the introduction of dislocations and subgrain walls.The observation of the streaks in Figure 2 and 3 over the 1 s exposure time stems from the sweeping of the reflection due to rotation, especially because their lateral dimension is sharp, even when the streak suddenly reorients, such as seen at Δt = 6 and 7 s in Figure 3.At fully solid phases and lower temperatures, such as 690-695 K, the reflections show some deviator strain, evident from the lateral width of the moving reflection trace, indicating the abundance of lowangle grain boundaries, that is, subgrains separated by dislocation walls.In conclusion, subgrains may form within large grains at relatively lower temperatures.

Closing the Problem of Abnormal Grain Growth by Spontaneous Activation of Its Boundaries for a Long Time
Overall, the main findings of this study discovered the previously missing puzzle stone of the initiation of abnormal grain growth: First, a favorable grain boundary is spontaneously activated.The driving torque activates all other of its boundaries, and the grain can freely rotate by the Harris-Moldovan model of diffusionmediated shape adaptation within an inactive, stiff matrix.Once two grains merge due to coalescence, this larger one remains active for a long time, causing further erratic rotation and engulfing the surrounding grainswhich is the effect of abnormal grain growth.Such a process is continuous for even much larger grains, in contradiction with previous theories predicting that larger grains stand still.Of course, at some stage the abnormally growing grain will cease to rotate by itself; however, the boundaries of the smaller, surrounding grains will be activated and then will transit to a subsequent model, which leads to the often-observed accumulations of neighboring large grains separated by regions of fine grains. [24]hus, our findings fit well with and explain the requisites for abnormal grain growth previously postulated or observed, which were found partly by incomplete theoretical models or empirical experiments.1) A high degree of texture is advantageous for abnormal grain growth, [4] as underpinning grain rotation is predominantly along a single axis, the crystallographic c-axis leading to faster lattice matching.Indeed, the basal texture of our magnesium alloy AZ91 had a distribution of AE20°around the sheet normal. [8]2) Incipient melting or fluxing at grain boundaries has been reported as a prerequisite for abnormal grain growth, [6] which is well supported by the findings of this article, namely, grain boundary activation in a vast channel below the eutectic temperature (supported by Nakata's findings [20] ) and an accelerated kinetics above, where segregated zones at the grain boundaries transition into such incipient melting, although the equilibrium phase diagram would show a solid.
3) Abnormal grain growth often leads to a clustering or string-like chain of large grains in a bimodal size distribution. [24]his can be understood when a large-grown grain ceases reorientation just by its size effect, while it is still highly activated.In a similar scenario as for the activation of the initial boundary propagating to all other boundaries of the grain under torque, one of the small neighbor grains gets activated by the boundary to the huge grain, then taking over anomalous grain growth by itself.

Importance to Other Systems and Research Communities
Finally, the spontaneous activation of grain boundaries is not only important for grain coalescence, at which grain reorientation necessitates large mass transport through diffusion.Similarly, such findings have an impact on theories of grain boundary sliding, in which the displacement is linear translational rather than rotational, resulting in creep and superplasticity. [22,25]By far, such phenomena are not limited to metals, alloys, or ceramics in an engineering design; moreover, their understanding equally plays a critical role in geology, for example, in the formation and deformation of the Earth's crust as studied on olivine, including both abnormal grain growth and grain boundary sliding [26] or even the creep and superplastic flow of glaciers and ice shields. [27]

Figure 2 .
Figure 2. Difference images of intensities I(t)-I(t -1 s) in the lower-left selected detector area, starting at absolute time t = 4300 s, frame exposure time 1 s, and temperature T = 773 K.These differences show the changes in an image to its previous.Beginning at the orange arrow at Δt = 0 s, a particular reflection of grain I evolves to move due to its grain rotation, while a second one, II, appears at Δt = 5 s.The streaks they trace correspond to the angle they sweep during the 1 s exposure time and can be zigzagged.Maximal grain rotation angular velocities are about 1°s À1 in this figure.Note that the majority of static reflections are not visible in these difference images.

Figure 3 .
Figure 3. Superimposed Laue images of the 300K detector over 75 s, where each rainbow color represents the same time step (see color bar in Figure 4) and static intensity adds up to white.Particular features of grain rotations can be seen on simultaneous reflections from the same crystallite, as pointed out on the traces A and B-F.The middle trace corresponds to the one in Figure 2. The scale bar shows an angular range of %10°Â 1°in azimuthal (h) and polar (v) dimension at the center of the image.The center of the transmitted beam is the dot at the top center of the image.

Figure 4 .
Figure 4. Color-superimposed frames from 3111 to 3154 s of the 100K detector at T % 690-695 K, below the eutectic temperature of the alloy.A strongly reflecting grain traces erratically from the top right to the bottom left.The maximum rotational speed reaches 0.2°s À1 .The scale bar shows an angular range of %0.2°Â 0.2°in horizontal and vertical image dimension.

Figure 5 .
Figure 5. Observation of grain coalescence in frame difference plots.Reflections of two grains A and B are observed to become active (0 s), rotate together (1-2 s), merge (3 s), rest a while (up to 5 s) before the newly coalesced grain quickly rotates away (6-7 s).Temporal colorplot superimposing frames from À6 to 9 s (color bar similar to Figure 4).

Figure 6 .
Figure 6.Sketch of erratic grain rotation upon coalescence.The central grain with initial lattice orientation (I) and red colored boundaries, sitting in a stiff matrix, is initially activated, say at the boundary towards grain (1) to rotate by ω into orientation (II), which might form a single grain.A stiff rotation would result in the blue boundary, which is incompatible with the matrix.Mass transport is necessary though lattice or boundary diffusion to conserve the shape, as indicated by straight arrows, then activating other grain boundaries.During this rotation, it may happen that some other plane family (III) of the same lattice (II) is energetically attracted by a competing neighbor (2) changing the torque and leading to zigzag rotations, which can be extended with further neighbors to 2D reorientation pathways.