{102}twinning nucleation in magnesium assisted by alternative sweeping of partia

Zhen Zhng,Jin-Hu Peng,Ji’n Hung,Peng Guo,Zho Liu,Shi-Cho Song,Yu Wng,∗

a School of Materials Science and Engineering,Hefei University of Technology,Hefei 230009,China

bCAS Key Laboratory of Mechanical Behavior and Design of materials,Department of Modern Mechanics,University of Science and Technology of China,Hefei 230027,PR China

Received 24 February 2020;received in revised form 18 May 2020;accepted 5 June 2020 Available online 11 October 2020

Abstract Molecular dynamic simulation and transmission electron microscopy(TEM)characterization was employed to investigate the{102}twinning mechanism in magnesium.A partial dislocation assisted twinning nucleation mechanism was proposed based on simulation results,in which the twin lattice was reconstructed from parental matrix by two-step sweeping of partial dislocations on different close packed planes from matrix and the subsequently formed twin precursor respectively.A{102}twin precursor was observed adjacent to matrix/twin interface by a spherical aberration corrected TEM,which indicated the hexagonal-close-packed(hcp)matrix→quasi face-centered cubic(fcc)twinning precursor→h.c.p twin transformation sequence during{102}twinning process.

Keywords:Magnesium;Twinning;Basal slip.

1.Introduction

Magnesium and its alloys are being increasingly and widely used in many fields,due to their low density and other prominent properties such as high specific strength,electromagnetic shielding performance and thermal conductivity etc.However,the poor formability restricts their wider application in industry.The reason is widely believed to be the less symmetrical hexagonal close packed(hcp)structure,which provides limited slip systems in magnesium alloys[1].Twinning thus always participates as an important plastic mechanism[2,3].The most common twinning type in magnesium alloy is{102}twinning,which gives extension along the caxis[4,5].Such twinning is quite common because of its low CRSS and usually occurs at early stain stage during which a characteristic basal texture is readily developed accordingly[6].

On the other hand,when taking more account of lattice correspondence,{102}twinning in magnesium could be also treated as a finite shear;which entailed the atoms move to their theoretical position by shearing plus shuffling[2,23],without action of dislocations[24].However,the underlying reason for such complex and irregular motion of these atoms was less understood in terms of both kinetics and energetics.Considering the extraordinary anisotropy of Mg showing much lower CRSS(∼1/100)for both basal slip and{102}twinning than for other plastic carriers like non-basal slip and contraction twinning,as well as the fact that basal slip has been frequently observed accompanying{102}twinning in magnesium[20,25,26],it is reasonable to think of a potential connection between basal slip and{102}twinning and it is also interesting to know whether the atomic shuffling during twinning could be explained in this manner.This,however,did not receive adequate attention yet.In this paper,we revisit the{102}twinning mechanism in magnesium by using both atomic simulation and TEM characterization.The purpose is to find the role of the most comfortable plastic mode-basal slip in triggering{102}twinning in magnesium and to explain the atomic shuffling that was involved during twinning with the assistance by basal dislocations.

2.Simulation method

Atomic simulation was performed with empirical interatomic potentials developed by Sun[27],using large-scale atomic/molecular massively parallel simulator(LAMMPS)[28].A perfect single-crystal model containing 393 thousand atoms was constructed for calculations based on a rectangular simulation block with x and y axis parallel to110and102direction respectively,as shown in Supplementary Fig.S1.Free boundary condition was set forx,yandzdirections.Compression was exerted along z axis at a constant strain rate for about 0.02nm per step on the 1.0-nmthick top layer,while the 1.0-nm-thick bottom layer was fixed.Such orientation was chosen because it would facilitate both{102}twinning and basal slip[29]due to the low CRSS of these two plastic carriers[7].The twinning process is thus expected to be slackened in simulation,which rendered the capture of atomic mechanism for twinning nucleation possible.The simulation was performed with a NVT ensemble using a Velocity-Verlet integrator.The temperature was controlled at 0.1K by the Nose–Hoover thermostat.

3.Experimental procedure

Experimental compression tests were performed on submicron scale Mg single crystals by a Hysitron PicoIndenter(PI95)inside a JEOL 2100FEG TEM(200keV).Submicron pillars were cut from a Mg single crystal by using focus ion beam milling.The cross-section of the pillars were in square shape,with a side length of∼400nm;and the thickness direction(view direction)was set to be20.The height of the pillars was∼800nm in the direction of100.The compression direction was set to be perpendicular to c-axis,because it was the most representative orientation to activate{1012}twinning that was commonly used for compression tests for single crystals.This ideal orientation could get round ductile failure from excessive basal slip when loading in a deviated orientation like the case for atomic simulation.The strain rate was at the level of 10−2s−1.After loading,the strained sample was further thinned to 200nm and examined inside a FEI Titan spherical aberration-corrected TEM.

4.Results

4.1.Atomic simulation

The simulation results indicated that when the strain reached about 4%,a small twin nucleus was formed at the edge of the crystal,as shown in Supplementary Fig.S2a.This small twin could be identified as{102}type based on its orientation relationship∼86◦110with matrix.The twinning process was found accomplished by direct{100}T→(0002)Ptransformation(Fig.1a).In a similar way,the(0002)plane in matrix was transformed into a new{100}plane in twinned region.Similar results have also been reported recently for submicron sized samples[30].Considering the similarity of the stacking periodicity between these two atomic planes-{100}and{0002}plane,as shown in Fig.1b,it was believed to be reasonable for atoms to complete such intertransformation.However,it did not seem kinetically possible for atoms to shuffle independently inside any periodic crystal structure to form new basal planes.

Interestingly,it was found in our present work that the twin nuclei tended to form in the region where basal dislocations have swept,as shown in Fig.2.After sweeping of two partial dislocations with a Burgers vector of 1/3100,as indicated by the two black“”symbols in Fig.2c,on adjoining basal planes in matrix,or to be more specific,between A-B layers,a f.c.c structure with a thickness of four-layer atoms was identified behind the leading partial dislocations by CNA algorithm.The corresponding atoms were highlighted in green in Fig.2b,c.Meanwhile,the atoms from the corrugated{100}planes in parental lattice,reconstructed flat atomic planes,indicated by the atoms numbered as 1–4 that were selected from the blue rectangles in Fig.2.On further straining,a local h.c.p structure with two-layer atoms in thickness was identified in the f.c.c structure,as framed by yellow rectangle in Fig.2c.This small h.c.p structure then grew and obtained a misorientation of∼86◦110with matrix,which was the theoretical {102}twin orientation,as shown in Fig.2d.It could thus be considered as a twin nucleus formed in the precursor f.c.c structure,since the observed{102}twin did grow on basis of this local f.c.c region.Moreover,interestingly,two partial dislocations could be observed at the edge of basal plane of the twin nucleus,as indicated by the two“”symbols in the yellow rectangles.

Fig.1.The atomic image from molecular simulation viewed from110direction(a)before and(b)after{102}twinning in magnesium;A comparison between atomic arrangement on(c)(0002)and(d){100}plane.

Fig.2.Nucleation of a{102}twin in matrix:(a)Initial matrix,(b)the activation of a100/3 leading partial dislocation producing a stacking fault behind,(c)two partial dislocations on adjoining basal planes producing four layers of atoms identified as f.c.c structure by CNA algorithm,(d)a{102}twin nucleated on basis of the precursor.

Fig.3.{102}twinning nucleation by two-step alternative sweeping of partial dislocations(a)Initial matrix;(b)a f.c.c precursor produced by the 1st step sweeping of partial dislocations on basal planes in matrix;(c)twin nucleation on basis of the precursor by the 2nd step on another cognate close packed plane.

Based on atomic simulation results,we proposed a basal slip assisted nucleation model for{101}twining,as shown in Fig.3.Such twinning nucleation process can be decomposed in two steps:Firstly,by successive sweeping of partial dislocations(=[010]/3)on basal plane in h.c.p matrix,as indicated by the black⊥”symbol in Fig.3b,a f.c.c structure was produced in the dislocation swept region,the newly formed flat atomic plane essentially became a close packed plane-(111)plane in the fresh f.c.c.structure(highlighted in red in Fig.3b),whereas the previous basal planes in matrix became another cognate(11)plane(highlighted in green in Fig.3b).At this stage,a potential precursor was well prepared for{102}twinning nucleation.However,the newly formed(111)planes still presented an A-B-C-A-B-C…stacking sequence at this stage.Secondly,by successive sweeping of partial dislocations(=[2]/6)on(111)plane in the f.c.c structured precursor,as indicated by the green“⊥”symbol in Fig.3c,such(111)planes then transformed into new basal planes which constructed the h.c.p twin lattice,as shown in Fig.3c.This could well explain why partial dislocations were associated on basal plane in the twin nucleus in Fig.3c and d.

However,a question then arises that if the twin lattice was formed on basis of the{111}plane in an ideal f.c.c structure it would then form a∼70◦20misorientation with matrix(i.e.the inclined angle between two close packed planes in f.c.c structure)rather than the theoretical twinning misorientation(∼86◦20).A close examination into the twinning precursor region revealed that the lattice was actually distorted from the ideal f.c.c structure;the two close packed planes presented a higher inclined angle(∼82°)which was closer to the theoretical twining misorientation.The subsequently formed twin lattice then produced the observed twining misorientation(∼86◦20).The schematic atomic paths were mapped in unit cells for a comparison between the ideal and distorted f.c.c structure as shown in Fig.3b,c.It could be seen that the atomic shuffling directions were both the same in the close packed direction;however the shuffling magnitude was smaller to form the distorted f.c.c structured twinning precursor.

4.2.TEM characterization of{102}twinning

In order to seek experimental evidence for the proposed twinning mechanism,we triggered{102}twinning by compressing a submicron sized Mg single crystal along the100direction in TEM and further thinned the strained sample to examine the microstructurepost morteminside a spherical aberration-corrected TEM.The compressed sample was viewed along the110of the parental crystal,along which the∼86.3° twinning orientation relationship was created.(110is theηdirection of the observed{102}twinning system.)It could be clearly seen that quite a few stacking faults were also produced both in twinned and matrix region after the propagation of twin boundaries,as indicated by arrows in Fig.4.The density of stacking faults was found to be rather high;and the average spacing distance was measured to be∼10nm.

Fig.4.TEM image of stacking faults both in matrix and twin area near a{102}twin boundary in magnesium.

Since atomic simulation indicated that twin precursor was usually formed near matrix/twin interface,we then took a close examination locally in this region,where the proposed atomic paths for twinning might be captured,as shown in Fig.5a.The parental matrix and twin area were colored in blue and red respectively.The atomic images from both matrix(Area b)and twin(Area c)were shown in Fig.5b and c,which indicated an ideal h.c.p lattice from both regions.However in a region adjacent to matrix/twin interface(Area D),an unexpected structure,different from parental h.c.p lattice,was clearly observed(Fig.5d).The atomic image shows a quasi-cubic shape with the angleαof∼89°.This was considered as the intermediate structure produced by slipping of partial dislocations on basal plane in matrix,which served as metastable precursor for{102}twinning nucleation.The region of twinning precursor region was enclosed in green lines in Fig.5a,and the size was estimated to be∼10nm.

It is also worth noticing that basal stacking faults were also frequently found in bulk samples when{102}twins were activated during compression under the same loading orientation.A typical example was shown in Fig.6,in which stacking faults were investigated by contrast analysis.Firstly,the stacking faults could be identified by their characteristic fringe patterns both within matrix and twinned area(Fig.6a,b).Then under double beam conditions,dislocations associated with these stacking faults lying on the(0002)plane in matrix were analyzed.According to·criterion,the dislocations were expected to have a Burgers vector()lying on the basal plane due to their extinction with(0002)reflection(Fig.6d).The only possiblethat can be bonded to a stacking faults is expected to be[010]/3.This was consistent with the sharp contrast of these stacking faults when={100}was used for TEM bright image(Fig.6c).The above TEM analyses indicate a potential connection between twinning and partial dislocations induced stacking faults on basal planes,which could be considered as an experimental evidence for twinning mechanism proposed based on simulation.

5.Discussion

Classical theory treated twinning as a homogenous shearing mode,in which twinning dislocations are needed in mediating twin boundary(TB)migration.It works well for f.c.c.metals,in which spiral sweeping of pole dislocation is well accepted to be the underlying mechanism;and the migration of twin boundary is always mediated by gliding of Shockley partial dislocation on twinning planes.This is believed to be reasonable since the twinning plane is the same as the slipping plane in f.c.c.metals.It is,however,a different story for{102}twining in h.c.p magnesium,for which both homogeneous twining shear and atomic shuffling are involved.The homogeneous shear is an affine shear that maps crystallographic planes/directions of the parent into the planes/directions of the twin.The burgers vectorbTof elementary twinning dislocation,which was calculated by[12],was so small(0.024nm,less than 1/10 of ordinary dislocations in magnesium)tha t it could be considered that the twin lattice almost exists in parental lattice prior to any twinning shear.Based on this presumptions,Li proposed that{102}twinning nucleation could be accommodated by pure atomic shuffling[31].It was confirmed in the present work that inter-transformation between basal and prismatic plane was completed between matrix and{102}twin.In fact,the twin lattice could be directly constructed from parental lattice.This was,from atomic scale,akin to displacive martensite transformation,although the crystal structure was kept unchanged for‘twinning transformation’.However it was different in that{102}twinning involves transformation of atoms from corrugated planes({100}plane)into a flat atomic plane((0002)plane);the displacive tensor is not considered to be homogeneous on atomic scale.A question was then raised how could the irregular and complex atomic shuffling occur inside a regularly packed crystal lattice?

The simulation results showed that such atomic shuffling was accomplished by two-step slipping of partial dislocations on different close packed planes from matrix and the subsequently formed twin precursor respectively.It needs to be stressed that after the 1st step the atoms from the corrugated prismatic plane already transformed into a flat closely packed plane,which,ideally speaking,presented f.c.c stacking sequence(…A-B-C…)at this stage.After subsequent gliding on such new planes in the 2nd step,a h.c.p lattice was reconstructed.

As a matter of fact,such process was quite similar to the famous pole mechanism for twinning in f.c.c.metals.However,they differ fundamentally in that,in twinning pole theory for f.c.c metals the sweeping of partially dislocation proceeds consecutively on only one series of twinning plane;whereas for{102}twinning in magnesium the sweeping of partial dislocations occurred alternately on two equivalent close packed planes across a metastable precursor region.Such basal slip assisted twinning nucleation mechanism was believe to be reasonable for magnesium since the strongly anisotropic h.c.p structure always presented a much lower critical stress for basal slip than other slip modes.As supporting evidence,a recent in-situ tension test on Mg crystal clearly indicated the dislocation slip induced twin growth and the formation of stacking faults in the way of the advancing TB[32].In addition,similar basal stacking faults were also frequently found related with{102}twins for bulk samples(Fig.6).The above phenomenon implies the importance of basal slip in{102}twinning nucleation.

Fig.5.(a)High resolution TEM image at twin/matrix interface;atomic image of crystal lattice from(b)matrix;(c)twin and(d)twinning precursor region.

Fig.6.Fringepatterns characteristic ofstackingfaults froma bulk single crystal compressed along101both in(a)matrix and(b)twin area;the bright fieldimage contrastwith(c)={101}and(d)=(0002).

As described above,on the other hand,the twinning transformation could be ideally considered as a h.c.p matrix→f.c.c precursor→h.c.p twin sequence.The transformations between intermediate stages were both mediated by partial dislocations on closely packed planes.However the observed precursor was usually distorted from rigorous f.c.c structure.The main difference was the angle between close packed planes,which was∼70° for the ideal f.c.c structure and were∼81°and∼89° respectively for simulation and experimental results.Such orientation deviation was expected to show up when a smaller atomic shuffling displacement was involved in h.c.p↔f.c.c transformation(inset in Fig.3)than in the proposed model that ideally assumes successive sweeping of partial dislocations on every single closed packed plane,which might require unreasonably high stresses.Actually,as found in the present work,twinning precursor usually formed behind several parallel partial dislocations,which kept certain interval,rather than ideally on every basal plane,and concurrently proceeded during the migration of twin boundary.In this way,the atomic shuffling involved in such twinning precursor was expected to be smaller than the ideally proposed model.This leads to a deviation from the ideal 70°between close packed planes.Such orientation deviation,or say the extent of lattice distortion in twinning precursor,was expected to be closely related with the density of basal dislocation that dragged the migration of twin boundary.For the observed twinning precursor with an angle of∼89° between close-packed planes,the required average spacing distance is expected to be around∼10nm,which was consistent with the TEM results shown in Fig.4.Thus the smaller atomic shuffling could be well mediated in such region across which the burgers vectors of partial dislocations were gradually dissipated and disassociated across multiple basal planes.Such would essentially influence the practical misorientation angle between the subsequently formed twin and the parental lattice.It could explain the deviation from well-defined twin misorientation angle as found in the present as well as in other previous work[30,31].

6.Conclusion

•The twinning precursor was confirmed by atomic images obtained in spherical aberration-corrected TEM.The precursor was close to f.c.c structure.Distortion did exist to some extent,which might be related with the density of basal dislocation that dragged the migration of twin boundary.

Declaration of Competing Interest

The authors declare no competing financial interests.

Acknowledgment

This work was supported by the National Natural Science Foundation of China(No.51871084 and No.51401072)and the Fundamental Research Funds for the Central Universities JZ2019HGTB0072.The authors thanks Pro.Boyu Liu(Xi’an Jiaotong University)for TEM characterization and Pro.Zhiwei Shan(Xi’an Jiaotong University)for the valuable discussion.

Supplementary materials

Supplementary material associated with this article can be found,in the online version,at doi:10.1016/j.jma.2020.06.012.