1. Introduction

As materials are pushed to extremes of temperatures and stresses, they become increasingly sensitive to their internal microstructure. For instance, aero-engine turbines would fail at service temperatures if blades crept beyond certain tolerances. Yet, the strength and plastic deformation of metals and alloys are largely achieved and controlled by linear defects, the dislocations, which carry an elemental distortion, represented by their Burgers vector. The mutual interactions between dislocations or between dislocations and obstacles determine microstructural self-organization and give rise to hardening effects. However, the mechanism of hardening is still "the most difficult remaining problem", since various hardening theories fail to provide comprehensive explanations to such a phenomenon. Transmission electron microscopy (TEM) observations and dislocation dynamics simulations show that, at the early stage of hardening, there is a wealth of dislocation reactions, where dislocation dipoles may play an important role. But TEM results are limited by resolution and due to the lack of long-range strain field of the dipole, several crucial features were left unattended.

In this review, first, the history of dislocation dipole annihilation is revisited. Then, recent progresses in elucidating the atomic-scale processes during dipole annihilation are presented with examples from representative systems. Last, the consequence of dipole annihilation, as well as experimental verifications are introduced.

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2. History of Dislocation Dipole Annihilation

Dislocation annihilation by cross-slip of screw dislocations and by climb otherwise, plays a key role in recovery processes. Of particular importance is the mutual annihilation of edge dipolar configurations within dislocation entanglements such as walls of persistent slip bands in fatigued samples. The investigation originates from the old question of dislocation patterning discovered in FCC metals associated with the end of stage Ⅰ and the transition to stage Ⅱ ^[1,2], where self-organization under single slip is particularly intriguing since dislocations under interaction then share the same operating Burgers vector. With the origin of such patterning still unclear ^[3], and with a lack of documentation and direct observations, it is agreed that a substantial number of prismatic loops of finite length exist after the formation of the tangles (e.g., see Refs. ^[4,5]).

The mechanism of athermal annihilation of edge dipoles was first introduced by Essmann and Rapp ^[6] to model the experimental strain dependence of the dislocation density in stages Ⅰ and Ⅱ of neutron-irradiated Cu (see Figure 1 for a review). This model hypothesizes that below a certain approach distance, defined as the distance between the two glide planes of the approaching dislocations, edge dipolar dislocations annihilate athermally forming invisible debris of almost atomic dimension. Fitted to experimental data, the model leads to a critical dipole height of 1.6 nm (~7d₁₁₁, where d₁₁₁ is the {111} interplanar distance) for spontaneous dipole disintegration. The notion of a minimum dipole height plays a pivotal role in certain models of the plastic strain localization and of the dislocation patterning associated with persistent slip bands in fatigued FCC metals ^[7,8,9]. In these models, the contribution of the debris resulting from dipole annihilation is merely ignored.

In an experimental and theoretical analysis conducted in relation with tensile and cyclic deformation tests of Cu, Essmann and Mughrabi were led to postulate that an edge dipole less than 1.6 nm in height transforms into a chain of point defect clusters whose subsequent role in deformation was however not elaborated ^[7]. Transmission electron microscopy (TEM) studies in Cu concluded to a minimum edge dipole height of about 3 nm, down to 1 nm ^[4,10,11,12]. Reporting a minimum average dipole height of approximately 4 nm and 6 nm at 77 K and 750 K, respectively in fatigued Ni, Tippelt et al. ^[13] later confirmed the analysis made in Cu, thus implying that this critical distance is not strongly material dependent. In a similar TEM analysis in AISI 316L stainless steel, Catalao et al. claimed critical heights of 1 and 5 nm at 300 K and 900 K, respectively ^[14]. Recent simulations of TEM images of dipoles of undissociated dislocations, however, revealed that below 5 to 6 nm, dipole heights cannot be measured in practice by the TEM method designed for this purpose, and they showed that the analysis worsens if dissociated dipolar dislocations are to be dealt with ^[15,16].

In early simulations of dipoles, static relaxation was performed by Duesbery and Joos ^[17] on Kr and Xe and by Rabier and Puls ^[18] on NaCl and MgO. However, with the ignorance of point defect diffusion, as well as the strong Coulomb effect in ionic compounds, these results do not have a common sense. For metals, Tichy and Essmann ^[19] arrived at an annihilation distance of 1d much smaller than the commonly accepted critical height of 1.6 nm. This result was somewhat questioned in subsequent numerical simulation ^[20] that yielded critical heights of 0.42 nm and 1.6 nm for copper and aluminum, respectively. Both computer investigations were, however, carried out on cavities as starting configurations and at 0 K thus including neither thermal vibration nor diffusion. Indeed, there is general agreement that the by-products of dipole annihilation should not just evaporate but their nature has received little attention. In annihilating at finite temperatures, the dipoles are thought to transform either into Frank loops subsequently transformed and swept out by gliding dislocations ^[19,20], or else into point defects or point defect agglomerates whose properties at a macroscopic scale are for instance manifested by surface extrusions in fatigue-tested Cu ^[21,22]. There is experimental evidence that nano-sized defects are indeed present in significant densities in the walls of persistent slip bands in fatigued Cu ^[23,24].

Currently, it is commonly accepted that narrow dislocation dipoles will spontaneously disintegrate. However, the product is believed unimportant during plastic deformation with their evolution almost undocumented. In fact, the stability of narrow dislocation dipoles relates closely to a number of mechanical properties, including the critical annihilation distance ^[7] and back stress ^[25,26], and contributes to the localization of deformation through the formation of deformation debris by dipole disintegration ^[5,27,28]. Dipole annihilation and subsequent point defect evolution not only has atomic-scale importance, but also affect meso-scale models, e.g., dislocation dynamics and constitutive laws. As an example, the discrepancy between elastic and MD predictions on the partial dissociation distance was revealed in Al ^[29]. Therefore, in the following context, we will review firstly the issue of dipole annihilation in various metals and alloys with face-centered cubic (FCC), body-centered cubic (BCC) and hexagonal close-packed (HCP) lattices; secondly the nature of the atomic-sized debris resulting from dipole annihilation; and lastly dipole-induced strengthening.

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3. Recent Progresses

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3.1. Athermal and Thermal Annihilation

In a series of recent studies ^{[5,27,28,29,30,31,32]} focusing on the atomic-scale interaction between dipolar dislocations, some new features were revealed regarding both athermal and thermal annihilations. At low temperature without thermal agitation, dipoles spontaneously rearrange. At very small height, 1d or 2d (d is the interplanar distance of the dislocation glide planes), vacancy or interstitial tubes are formed. At intermediate height, i.e., 3d to 6d, reconstructed cores are formed. Higher than 6d, classical vertical or inclined configurations are formed. Note that the above range is materials dependent. At high temperature with thermal agitation, the above configurations gradually transform into vacancy/interstitial clusters, stacking fault tetrahedral, interstitial loops, etc. Athermal and thermal annihilation configurations are exemplified in Figure 2 and Figure 3 for 1d to 4d edge dipoles in typical FCC, BCC and HCP systems, Cu, Fe and Ti, respectively.

Apart from the above similarity, at both low and high temperature, the atomic structures of the annealed configurations depend strongly on materials, dipole height and orientation. For detailed comparison, please refer to Refs. ^[28,31]. In general, low temperature stability is mostly relevant to the stacking fault energy, which determines the separation of partial dislocations and affects the mutual interaction of the constitutive dislocations; while high temperature stability is also influenced by vacancy/interstitial migration energy.

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3.2. Defect Formation and Consequence

Some of the annihilation debris are stable against thermal annealing and moreover, as indicated in Refs. ^[28,30], certain atomic diffusion paths correspond with activation energies significantly lower than bulk diffusion, which indeed accelerates the overall formation processes. Employing saddle-point search methods, activation energies of the atomic processes therein are obtained and the lifetime of the above by-products is estimated, showing the stability of certain clusters and loops on the experimental timescale (for details, see Refs. ^[31,33,34]). Using objective kinetic Monte Carlo simulations, clustering and its influence on metal properties can also be revealed ^[33,34]. Among the annihilation debris, interstitial loops may be of interest due to their role during plastic deformation. Atomic simulations have suggested their strengthening effect ^[35]. A thorough review of debris induced intermittent plastic flow can be found in Ref. ^[36].

Figure 4 exemplifies the atomic diffusion processes in Al ^[28] and Ti ^[31] during annihilation. Local short circuit diffusion operates, transforming the linear dipoles into vacancy or interstitial clusters. Unique diffusion paths, in particular those with activation energies significantly lower than bulk diffusion, were analyzed in FCC systems ^[30,37] during the initial clustering stage. Stable dipole and debris produce strengthening by locking the constitutive dislocation and interacting with mobile dislocations, respectively. The breaking stress is significantly increased by the formation of stable dipolar configurations ^[29,38], while in annihilation debris, e.g., interstitial loops, strongly interact with incoming dislocations by forming decoration ^[35].

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3.3. Experimental Verifications

Dipole and debris structures were frequently observed in deformed TiAl alloys by transmission electron microscopy (TEM) ^{[5,40,41,42,43,44,45,46,47]}. Most recent high-resolution TEM observations ^[5] have made good verifications of the above atomic-scale simulations. In a series of experiments on intermetallic TiAl alloys, Appel and coworkers have observed plenty of dipoles in deformed samples. It is thus believed that dipolar interaction and dipole annihilation should be well considered in meso-scale models and constitutive laws to count for their contribution on internal stresses ^[25,26], dynamic recovery ^[7] and the temperature retention of strain hardening ^[5]. In particular for faulted dipoles in TiAl, simulations are in full agreement with experiments in 1) atomistic simulations ^[38] predicts exactly the same atomic structure as high-resolution TEM observations ^[5]; and 2) the long-term stability of faulted dipoles indicated by atomistic simulations ^[38] is consistent with their abundance in deformed samples ^[45].

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4. Conclusion

In summary, despite the long-time investigation on dipole annihilation, there are still several key questions remain unanswered. Recently, narrow dislocation dipoles have been systematically investigated with atomistic simulations and high-resolution experiments. The atomic structures of narrow dipolar configurations, their formation energies and the activation energies during their evolution were determined. The atomic-scale structure and long-term stability of faulted dipoles are in full agreement with high-resolution and ordinary TEM observations. This indicates the importance of incorporating dipole effects in the various models of predicting mechanical properties.

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Acknowledgements

This work is supported by the National Key Research and Development Program of China (2016YFB0701304), the Natural Science Foundation of China (51671195) and the Youth Innovation Promotion Association of Chinese Academy of Sciences (2015151). HW is grateful to Dr. Patrick Veyssière (1947–2011), Dr. Dongsheng Xu, Dr. David Rodney, Dr. Fritz Appel, Dr. Yunzhi Wang, Dr. Ju Li for fruitful discussions.

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Conflict of Interest

There's no conflict of interest.

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