Structural Phase Transformations In Metallic Grain Boundaries

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ARTICLEReceived 22 Dec 2012 Accepted 18 Apr 2013 Published 21 May 2013DOI: 10.1038/ncomms2919Structural phase transformations in metallicgrain boundariesTimofey Frolov1, David L. Olmsted1, Mark Asta1 & Yuri Mishin2Structural transformations at interfaces are of profound fundamental interest as complexexamples of phase transitions in low-dimensional systems. Despite decades of extensiveresearch, no compelling evidence exists for structural transformations in high-angle grainboundaries in elemental systems. Here we show that the critical impediment to observationsof such phase transformations in atomistic modelling has been rooted in inadequate simulation methodology. The proposed new methodology allows variations in atomic densityinside the grain boundary and reveals multiple grain boundary phases with different atomicstructures. Reversible first-order transformations between such phases are observed byvarying temperature or injecting point defects into the boundary region. Owing to thepresence of multiple metastable phases, grain boundaries can absorb significant amounts ofpoint defects created inside the material by processes such as irradiation. We propose a novelmechanism of radiation damage healing in metals, which may guide further improvements inradiation resistance of metallic materials through grain boundary engineering.1 Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA. 2 School of Physics, Astronomy andComputational Sciences, George Mason University, Virginia 22030, USA. Correspondence and requests for materials should be addressed to T.F.(e-mail: timfrol@berkeley.edu).NATURE COMMUNICATIONS 4:1899 DOI: 10.1038/ncomms2919 www.nature.com/naturecommunications& 2013 Macmillan Publishers Limited. All rights reserved.1

ARTICLENATURE COMMUNICATIONS DOI: 10.1038/ncomms2919ResultsGB structures at 0 K. To demonstrate this new approach, westudied two representative high-angle, high-energy S5(210)and S5(310) symmetrical tilt GBs in several FCC metals withatomic interactions described by embedded-atom method (EAM)(ref. 13) potentials. The choice of the S5(310) GB was motivatedby the recent diffusion measurements described above11,12. Thelong-accepted structure of these S5 boundaries is an array ofkite-shaped structural units (Fig. 1b,d). This structure is easilyobtained by joining two perfect crystallites along (210) or (310)planes and applying various grain translations followed by staticrelaxation. It has been suggested, however, that in order to sampleall possible structures of a GB its density must be also varied byadding or removing atoms14–19. We applied an algorithm whichfinds equilibrium GB structures at 0 K by varying the GB densityalong with grain translations and static relaxation. In Fig. 1, weplot the obtained energies of the S5 GBs in Cu versus the extranumber of atoms relative to a perfect crystal plane. The minimain this plot correspond to three different equilibrium structures:(i) the normal kites b and d, (ii) split kites c and e having extra2/5 of the (310) plane or 7/15 of the (210) plane, respectively; and20.039Excess GB energy(a.c44)Phase transformations at interfaces in crystalline materialsare of significant fundamental interest and practicalimportance due to their possible impact on the macroscopicmechanical, transport and thermal properties of polycrystals1,2.To date, the studies of interfacial phase transitions have beenfocused primarily on ‘complexions’ of intergranular thin filmsin ceramics3,4,5 and pre-melting transitions in metallic alloys6.Little is known about grain boundary (GB) transformations insingle-component metals apart from the recently founddislocation pairing transition in low-angle GBs composed ofdiscrete dislocations7. Despite decades of research, no convincingexperimental or simulation evidence exists for structuraltransformations in high-angle GBs. Direct experimentalobservations of interfacial phase transitions by high-resolutiontransmission electron microscopy (HRTEM) are extremelydifficult8,9,10, and to date evidence for the possibility of GBtransformations has been obtained by less direct experimentalmethods. For example, recent measurements of diffusion in theCu S5(310) GB (S being the reciprocal density of coincidentsites1) revealed a marked change in the temperature dependenceof the diffusivity at about 800–850 K11,12, suggesting a possiblestructural transformation in this boundary. However, theconcurrent molecular dynamics (MD) simulations11 did notdetect any structural change other than gradual accumulationof disorder and eventually GB pre-melting at high temperatures.Owing to the difficulty of experimental observations, muchof the current knowledge about GB structures has come fromcomputer simulations. Most of the MD simulations conductedto date have employed periodic supercells that did not permitvariations in atomic density in the GB core region, which arepossible under experimental conditions. This unphysical constraint stabilizes one particular GB structure and prohibitstransformations to other structures with different GB densities.This can explain why transformations in high-angle GBs have notbeen found in the previous simulation work.We proposed a more general simulation approach thatfacilitates variations in GB density allowing the boundary toassume the most thermodynamically favourable structure. Thisapproach reveals the existence of multiple GB phases characterized by not only different structures but also different densities.This opens the door, for the first time, to direct observations oftransitions between GB phases with different densities inatomistic simulations of metallic systems.c0.037eSplit kites (2/5)Split kites (7/15)0.0350.033b Kites (0)d0.0310.0290.00.20.40.60.8fFilledkites (6/7)Kites1.0Fraction of (310) plane0.20.40.60.81.0Fraction of (210) planeΣ5(310)[001]Σ5(210)[001]Figure 1 GB structures and energies at 0 K. Results of structure andenergy calculations for S5(310) and S5(210) GBs at 0 K using anEAM potential for Cu32. (a) GB energy versus atomic density (fractionof atomic plane) for the S5(310) (left) and S5(210) (right) GBs.The horizontal line marks the energy of the kite structure. The densitiescorresponding to local energy minima and the respective GB structures areindicated. Panels (b–f) show the GB structures as viewed parallel tothe [001] tilt axis (left column) and normal to it (right column).(b,d) Normal kites. (c,e) Split kites. (f) Filled kites.(iii) filled kites f having extra 6/7 of the (210) plane. Differentcross-sections of the simulation block containing these structureswere tested as illustrated in the Supplementary Fig. S1.For each structure corresponding to a local minimum ofenergy, we computed the excess GB energy [U]N, excess volume[V]N and two components of the GB stress, tN11 and tN22 , in thedirections parallel and normal to the tilt axis, respectively20,21.The results summarized in Table 1 clearly demonstrate thatthe structures are characterized by significantly differentthermodynamic parameters, including even different signs ofthe GB stress component tN22 .To demonstrate the generality of this important finding,similar calculations were performed with a different EAM Cupotential and for several other FCC metals including Ag, Au andNi (see Supplementary Fig. S2). In all cases tested, the structuresNATURE COMMUNICATIONS 4:1899 DOI: 10.1038/ncomms2919 www.nature.com/naturecommunications& 2013 Macmillan Publishers Limited. All rights reserved.

ARTICLENATURE COMMUNICATIONS DOI: 10.1038/ncomms2919Table 1 Characteristics of different GB phasesStructureS5(310) GBNormal kites (0 K)Split kites (0 K)Split kites (MD)S5(210) GBNormal kites (0 K)Split kites (0 K)Split kites (MD)Filled kites (0 K)Cross-sectionFraction of plane[U]N, J m " 2[V]N, ÅtN11 , J m " 21#110 # 218 # 6 0.5171#115 # 218 # 30.3011.1740.2970.4461.042tN22 , J m " 21.7740.04650.09711.491" 2.12" 1.2762.299Abbreviations: GB, grain boundary; MD, molecular dynamics.S5(310) and S5(210) GBs in Cu modelled with the EAM (ref. 32) potential. Note that the periodic unit cells of the structures are different and can be significantly larger than the repeat unit of the lattice.*The MD unit cell represents the size of the simulation block for which the GB properties were calculated and is larger than the smallest periodic unit.Σ 5(310)2.0GB thickness (nm)GB-phase transformations with temperature. The effect oftemperature on the GB structures was studied by MD simulationswith various boundary conditions starting with the normal-kitestructure. First, we tested the traditional methodology with periodic boundary conditions. In the Cu S5(310) GB, the kitescontinued to exist up to B0.75 of the melting point Tm ¼ 1,327 K.At higher temperatures the GB begins to disorder and eventuallypre-melts near Tm (Fig. 2a). This behaviour known from previouswork21 cannot explain the transformation suggested by thediffusion experiments11,12. A more complex behaviour wasobserved in the S5(210) GB. At about 400 K, the kites werefound to transform into a structure similar to the filled kites(cf. Fig. 1f). In Fig. 2b, a jump in thickness occurs between300 and 400 K due to this change in GB structure. Similarbehaviour was found in simulations with other EAM potentialsfor Cu, Au, Ag and Ni, suggesting that it represents a genericfeature of FCC metals. However, these simulations impose aconstraint on the supply of atoms into the GB core and do notreveal the full picture of possible structural changes.For a more complete investigation, we modified themethodology by letting the GB terminate at an open surface asshown schematically in the Supplementary Fig. S3. The surfaceserves as a source or sink of atoms, which may diffuse in or out ofthe GB to automatically adjust its density. The MD results areillustrated in Fig. 3 for an isothermal anneal at 800 K when theGB meets an open surface at one end and is constrained by a wallof fixed atoms at the other. In the simulation of the S5(310) GBinitiated with the normal-kite structure, a new structure nucleatesat the surface and grows inside the boundary. This structure canbe identified as split kites, whereas the untransformed part of theboundary continues to be composed of normal kites. The extraatoms (40% of the (310) plane) required for the transformationare supplied by diffusion from the surface grove, a process thatkinetically controls the transformation rate. Eventually, the newstructure penetrates through the entire GB and reaches the fixedregion. When the fixed atoms on the left are made dynamic (thusopening another surface), the entire GB reaches the transformedstate (Fig. 3e).The stability of the split-kite structure was tested by a series ofisothermal anneals. It remained stable and well-ordered Temperature (K)2.5Σ 5(210)2.0GB thickness (nm)shown in Fig. 1 represented minima of the GB energy as afunction of GB density. Remarkably, and contrary to the commonbelief, none of the tested potentials predicts the normal kites to bethe lowest-energy structure of the S5(210) GB. The split kites areenergetically more favourable for this boundary and are onlyslightly higher in energy than the normal kites for the 00Temperature (K)Figure 2 MD simulations of GBs using periodic boundary conditions.The thickness of GBs at different temperatures was evaluated from theenergy density profile across the GB. (a) The S5(310) GB graduallyaccumulates disorder and pre-melts near the melting point Tm, whereas(b) the S5(210) GB undergoes a transformation at 400 K before premelting near Tm.800 K and until B1,150 K when it began to disorder and premelt. Upon subsequent cooling from pre-melting temperatures to1,000 K, the ordered split-kite structure reappeared inside the GB.This verifies the thermodynamic stability of the split-kitestructure and eliminates any suspicion that its formation couldbe caused by the presence of the surface grove (an additionalNATURE COMMUNICATIONS 4:1899 DOI: 10.1038/ncomms2919 www.nature.com/naturecommunications& 2013 Macmillan Publishers Limited. All rights reserved.3

ARTICLENATURE COMMUNICATIONS DOI: 10.1038/ncomms2919Figure 4 High-temperature transformation of the R5(210) GB. MDsimulation of the Cu S5(210) GB at 800 K with an open surface allowingvariations in GB density. The boundary undergoes a first-order phasetransformation from filled kites to split kites nucleating and growingfrom the surface.Figure 3 High-temperature transformation of the R5(310) GB. (a) MDsimulation of the Cu S5(310) GB at 800 K with an open surface allowingvariations in GB density. The boundary undergoes a first-order phasetransformation with the split-kite structure nucleating and growing from thesurface. The normal-kite (b) and split-kite (c) structures are separated by a1D-phase boundary accompanied by a step (d). (e) Completelytransformed GB structure in the presence of two open surfaces.proof comes from the point-defect induced transformations inthe absence of surfaces discussed below). We were unableto demonstrate the reversibility of the transformation back tonormal kites by cooling the GB below 800 K because of the slow(on the MD time scale) diffusion rates at low temperatures.However, the zero-temperature results plotted in Fig. 1 establishthat the normal-kite structure has the lowest energy and will bethermodynamically stable at sufficiently low temperatures.Figure 3d demonstrates that the two structures of the S5(310)GB can coexist and are separated by a line defect with an atomicscale cross-section. This allows us to consider the two GBstructures as two-dimensional (2D) phases separated a onedimensional (1D) phase boundary. The phase transformation isfirst order and is kinetically controlled by GB diffusion. To ourknowledge, this is the first observation of coexistence of two GBphases separated by a 1D-phase boundary in atomisticsimulations. It is also evident that this phase boundary isassociated with a GB step22. The exact nature of this 1D defectdeserves a separate study in the future.As the two GB structures have different interface stresses andexcess volumes, long-range elastic stresses could be generatedaround the 1D boundary between them. In principle, suchstresses could affect the stability of the GB phases, for example,via the image forces arising due to the interaction of the stress4field with boundary conditions. In our case, however, this effectwas negligible due to the large size of the simulation block (about12.5 nm in the y direction). For additional verification,simulations were repeated with different boundary conditionsin the y direction and the same GB phases were invariably found.Similar transformations were found in the S5(210) GB insimulations starting from the filled-kite structure formed at400 K. During isothermal anneals at temperatures below 1,050 K,the GB transforms into its thermodynamically stable phase atlow temperatures: the split kites. This new phase grows fromthe surface and eventually penetrates through the entire boundary(cf. Fig. 4). When the boundary with split kites was heatedup to 1,100 K, its structure transformed to filled kites (Fig. 5).In this case, however, we were able to observe the reversetransformation. Upon subsequent cooling down to 1,000 K, theGB structure returned to the split kites, demonstrating fullreversibility of the phase transformation. At temperatures close toTm this GB pre-melts by disordering of the filled-kite structure asobserved earlier23. It is interesting to note that the normal-kitestructure traditionally attributed to this boundary never appearsas its thermodynamically stable phase.GB phase transformations caused by point defects. During thephase transformations, the GB absorbs/ejects large amounts ofatoms from/to the surface. These absorption/ejection processesmay have important implications for properties of polycrystalsunder extreme conditions. For example, in metals subject toradiation by energetic particles, large numbers of vacancies andinterstitials are formed24. Interstitials are much more mobile thanvacancies and reach sinks first, whereas the remaining vacanciescan form clusters, stacking-fault tetrahedra and other defectcomplexes degrading the material properties. GBs can act aseffective sinks of radiation-induced defects and can have a role inthe damage healing. Some of the mechanisms of defect-GBinteractions have been studied by MD simulations25,26. Our worksuggests that the absorption of point defects can strongly modifythe GB structure, causing structural transformations, which,in turn, can greatly increase the absorption capacity ofthe boundary.The proposed effect is illustrated in Fig. 6. The simulationwas intentionally performed in a periodic simulation block toexclude all sources/sinks of atoms other than the GB. TheGB tested is Cu S5(310) and its initial structure consists ofnormal kites. This structure remains unchanged during annealswhen no atoms are added to or removed from the system.We then introduce 80 interstitials into the GB region, which isequivalent to 40% of a (310) atomic plane. This fractionof the plane matches the local minimum of the GB energycorresponding to the split-kite structure (cf. Fig. 1a). Upon annealat 800 K, the interstitials diffuse into the GB core and getNATURE COMMUNICATIONS 4:1899 DOI: 10.1038/ncomms2919 www.nature.com/naturecommunications& 2013 Macmillan Publishers Limited. All rights reserved.

ARTICLENATURE COMMUNICATIONS DOI: 10.1038/ncomms2919Transformation at 1,100 KKitesSplit kitesAdd interstitialsSplit kitesAdd vacanciesFilled kitesReverse transformation at 1,000 KKitesSplit kitesFigure 5 Reversible GB-phase transformations induced by temperature.S5(210) GB terminated at two open surfaces. The initial split-kitestructure taken from a prior anneal at 1,000 K transforms into filled kitesat 1,100 K. Upon subsequent cooling and annealing at 1,000 K, it returnsback to the split kites. Intermediate stages show the two GB structures:one growing from the surface and the other disappearing. It is concludedthat the phase transition temperature is between 1,000 and 1,100 K.absorbed in it initially creating a disordered structure. As theanneal continues, the GB eventually orders into the split-kitephase. To demonstrate the reversibility of this radiation-inducedtransition, we then randomly remove the same number of atomsfrom the GB region, which simulates the insertion of radiationproduced vacancies. After a period of disorder, the GB structuretransforms back to the normal kites. Thus, in the end of thisphase transformation cycle the boundary returns to its initial statehaving annihilated a large amount of radiation-induced defects. Asimilar transformation cycle induced by absorption of pointdefects was observed in the S5(210) GB (Supplementary Fig. S4).Figure 6 Isothermal reversible GB-phase transformations induced bypoint defects. GB-phase transformations in the Cu S5(310) GB induced byinterstitials and vacancies in a simulation block with periodic boundaryconditions at T ¼ 800 K. After 80 interstitials are introduced into a 10 Åthick layer containing the GB, it transforms from the initial normal-kitestructure (a) to a disordered state (b) and then to split kites (c).After the subsequent introduction of 80 vacancies into the same GB layer,the split-kite structure disorders (d) and then transforms back to normalkites (e). The GB states (a) and (e) are identical confirming that thetransformation is fully reversible.Simulations of GB diffusion. As discussed above, experimentalmeasurements of GB diffusion in Cu bicrystals containing theS5(310) GB have been made by Budke et al.12 and more recentlyby Divinsky et al11. Th

Structural phase transformations in metallic grain boundaries Timofey Frolov1, David L. Olmsted1, Mark Asta1 & Yuri Mishin2 Structural transformations at interfaces are of profound fundamental interest as complex examples of phase transitions in low-dimensional systems. Despite decades of extensive research, no compelling evidence exists for structural transformations in high-angle grain .

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