Formation of I 1 stacking fault by deformation defect evolution from grain boundaries in Mg

Yong-Jie Hu,Videhi Menon,Ling Qi,?

a Department of Materials Science and Engineering,University of Michigan,Ann Arbor 48109,USA

b Department of Materials Science and Engineering,Drexel University,Philadelphia 19104,USA

Abstract I1 stacking faults(SFs)in Mg alloys are regarded as the nucleation sites of〈c+a〉dislocations that are critical for these alloys to achieve high ductility.Previously it was proposed that the formation of I1 SFs requires the accumulations of a large number of vacancies,which are difficult to achieve at low temperatures.In this study,molecular dynamics(MD)and molecular statics(MS)simulations based on empirical interatomic potentials were applied to investigate the deformation defect evolutions from the symmetric tilt grain boundaries(GBs)in Mg and Mg-Y alloys under external loading along〈c〉-axis.The results show the planar faults(PFs)on Pyramidal I planes first appear due to the nucleation and glide of〈c+p〉partial dislocations from GBs,where〈p〉=〈100〉.These partial dislocations with pyramidal PFs interact with other defects,including pyramidal PFs themselves,GBs,and〈p〉partial dislocations,generating a large amount of I1 SFs.Detailed analyses show the nucleation and growth of I1 SFs are achieved by atomic shuffle events and deformation defect reactions without the requirements of vacancy diffusion.Our simulations also suggest the Y clusters at GBs can reduce the critical stress for the formation of pyramidal PFs and I1 SFs,which provide a possible reason for the experimental observations that Y promotes the〈c+a〉dislocation activities.

Keywords:Magnesium alloys;I1 stacking faults;〈c+a〉dislocations;Grain boundaries;Defect nucleation and evolution;Molecular dynamics simulations.?Corresponding author.

1.Introduction

Magnesium(Mg)alloys are promising lightweight structural alloys due to their high specific strengths.Their applications can significantly increase energy efficiency and help the transportation industry to achieve the carbon neutrality goal[46].However,their low ductility/formability increases their manufacturing costs[7,26].This drawback is intrinsically related to the lack of active slip systems in their hexagonal close-packed(HCP)structure[77,78].Mg alloys usually have two independent and easily activated slip systems with an〈a〉Burgers vector and a basal{0002}slip plane.These two basal〈a〉slip systems are not sufficient to satisfy the von Mises criterion,which states that a minimum of five independent slip systems are required to achieve arbitrary plastic deformation.Meanwhile,other plastic deformation mechanisms such as deformation twinning often result in strain localization and fracture initialization during macroscopic plastic deformation[8–10,76].A feasible solution is to activate a sufficient amount of dislocations with〈c+a〉Burgers vectors and pyramidal slip planes as plotted in Fig.1(a)[2,3,38].However,in pure Mg and many Mg alloys,〈c+a〉dislocations do not have sufficient activity to achieve high ductility,except in a few cases involving severe plastic deformation or nanoscale sample dimensions[24,30,81].

There are three general strategies to increase the activities of〈c+a〉dislocations in Mg alloys.The first strategy is to enhance the nucleation of〈c+a〉dislocations[42,50–53,77].Experimental characterization and atomistic simulations suggest that〈c+a〉dislocations can nucleate from a special type of defect structure called I1stacking fault(SF)[1,35,79].As shown in Fig.1(b),an I1SF interrupts the normal ABABAB stacking sequence of the basal plane along the〈c〉axis.Different from a typical I2SF in Fig.1(c)generated by the slip of a partial dislocation with a Burgers vector of〈100〉,an I1SF generates only one(instead of two)face-centered cubic(FCC)layer,which is a basal plane with different stacking sequences for its adjacent top and bottom basal planes along the〈c〉axis.First-principles calculations have shown that some rare-earth elements(REs)such as Yttrium(Y)can reduce the energy difference of I1SF relative to the perfect HCP structure,and hence,promote the formation of I1SF and the following nucleation of〈c+a〉dislocations[51,66].These results were used to explain why Y and other alloying elements can promote the activities of〈c+a〉dislocations in Mg alloys and significantly increase their ductility from experimental observations[42,50,52].

Fig.1.Illustrations of HCP structure and its stacking faults(SFs).(a):A plot of HCP structure containing both Pyramidal I{101}and Pyramidal II{112} planes.A Burgers vector of〈c+a〉is plotted along the intersecting line between two pyramidal planes.This〈c+a〉can be decomposed into two〈 c+p〉vectors(〈p〉=〈100〉),each of which connects two neighbor atoms in adjacent basal planes.(b)and(c)show multiple layers of basal planes that contain I 1 and I2 SFs,respectively.Blue,red,and green colors mean the atoms are located at the A,B,and C stacking sequences,respectively.The yellow dashed rectangles indicate the locations of FCC layers.I1 SF generates one FCC layer and I2 SF generates two FCC layers.

The second strategy to enhance〈c+a〉dislocation activities focuses on dislocation mobility[5,6,17,69,70,78].Largescale molecular dynamics(MD)simulations suggest that〈c+a〉dislocations can dissociate into different partial dislocation configurations on two different types of pyramidal planes:Pyramidal I{101}and Pyramidal II{112}plotted in Fig.1(a)[70].A〈c+a〉dislocation has to cross slip between two types of pyramidal planes in the cycles of dislocation dissociation and constriction with large activation barriers,which significantly reduces the mobility of〈c+a〉dislocations and explains the low ductility of pure Mg.Alloying elements such as Y can change the energetics of the dissociation and constriction cycles and increase the mobility of〈c+a〉dislocations,which in turn enhances the ductility of Mg alloys[5,6,14,69].A recent theoretical study has reconciled these two approaches(〈c+a〉nucleation vs.〈c+a〉mobility)by suggesting that the requirements for the alloying elements to reduce I1SF thermodynamic costs are identical to those to reduce the activation barriers for〈c+a〉dislocation cross slip between two pyramidal planes[43].

The third strategy to enhance〈c+a〉dislocation activities is similar to the second one but focuses on the critical resolved shear stress(CRSS)[18,22,23].Atomistic simulations revealed that certain solute atoms have stronger solutedislocation binding and strengthening effects on basal slip planes than those on non-basal planes due to different dislocation core structures on these planes[22,23].These differences in solute-dislocation interactions reduce the large CRSS anisotropy between basal and non-basal slip systems,promoting more〈c+a〉activities.These simulations have been applied to explain both the roles and the optimal compositions of REs[23]and non-REs[18,22]to maximize the〈c+a〉activities and enhance the ductility of Mg alloys.

In this study,we mainly focus on the first strategy by investigating the formation mechanisms of I1SFs.Aside of thermodynamics,there could be large kinetic barriers for an I1SF generation since it can not be formed by a Shockley partial dislocation glide similar to the formation mechanism of I2SFs.A widely accepted mechanism for I1SF formation is the condensation of extra vacancies to a disk on a basal plane,following which an I1SF is created by〈100〉dislocation glide[12].However,vacancy diffusion and concentrations required to form sufficient I1SFs can be difficult to reach,unless under some extreme conditions(elevated temperatures[82]or irradiation[20]).Some experimental and computational studies have proposed I1SF formation mechanisms,which do not involve vacancies or their diffusion,such as:(i)via the dissociation of preexisting〈c+a〉dislocations[1,70,82]and(ii)via the movement/reactions of other deformation defects like incoherent twin boundary migration[28,57,84],point defects generated by jogged migrations of non-basal〈a〉dislocations[82],dislocation transmutation reactions across a{102}twin boundary[60,61].Beyond these studies,ifthere are possible I1SF formation mechanisms without the involvement of preexisting point defects or deformation defects,promoting such mechanisms can further enhance the activities of I1SFs and the consequent〈c+a〉dislocations in conventional Mg alloys under normal loading conditions.

In polycrystalline alloys,grain boundaries(GBs)generally provide sites for the nucleation and growth of various types of defects.This heterogeneous nucleation from GB sites may reduce the nucleation barrier,and there could be stress concentrations near GBs to further increase the driving force for dislocation emission[39,59].For example,it was suggested that the effects of compatibility stress at GBs may enhance nonbasal slip systems like prismatic〈a〉and pyramidal〈c+a〉dislocations[24].Additionally,both experimental and theoretical studies indicate that alloying elements can segregate to GBs and have strong solute drag effects on GB migration,impeding the formation of texture structures in Mg alloys to achieve homogeneous plastic deformation and high ductility[16,41,48,49].Recent experimental characterizations have also indicated that the reduction of grain sizes can increase the activities of non-basal dislocations and enhance ductility in pure Mg[65]and Mg-Gd alloys[33].Thus,it is possible that these alloying elements at GBs can also change the behavior of other defects,such as I1SFs and the consequent〈c+a〉dislocations,near the GBs to impact the mechanical behavior of Mg alloys.

For the above reasons,we applied molecular dynamics(MD)and molecular statics(MS)simulations using classical interatomic potentials to investigate the defect formations and evolution at GBs and their adjacent regions,with an emphasis on the formation mechanisms of I1SFs.We used an evolutionary algorithm to generate bicrystal supercells that contain symmetric-tilt GBs(STGBs)and applied tensile strain to activate defect formations at GBs[73].We chose tensile loading orientations along〈c〉-axis to avoid the activation of basal dislocations in order to focus on the defect reactions that could be connected to〈c+a〉dislocations.Previous experimental studies have shown that,in Mg single-crystal nano-size samples under tensile loading along〈c〉-axis,{102}extension twins appear from surface nucleation[80].MD simulations under the same tensile loading orientation have been applied to pure Mg single-crystal samples and generally show the preference of extension twins[34,58,80].These studies influenced our choice of tensile loading conditions in our simulations,as we wanted to check if GBs and alloying elements at GBs can promote the formation of〈c+a〉dislocations instead of deformation twinning.Details of our simulation methods are described in Section 2.

In Section 3,our simulation results reveal that〈c+p〉(here〈p〉=〈100〉)partial dislocations accompanied by pyramidal planar faults(PFs)are first nucleated from GBs.These partial dislocations can react with other defects,including other〈c+p〉partial dislocations and GBs,to generate and propagate I1SFs.We applied detailed analyses to understand the atomistic mechanisms of I1SF nucleation and growth.Our simulations also show that the Y clusters at GBs significantly reduce the critical stress of〈c+p〉dislocation nucleation from GBs and the consequent formations of I1SFs,potentially promoting〈c+a〉dislocations.As summarized in Section 4,our studies provide an alternative strategy to increase the ductility of Mg alloys by focusing on the role of GBs to boost the activities of I1SFs and〈c+a〉dislocations.

2.Simulation methods

As mentioned previously,we used an evolutionary algorithm combined with MD/MS simulations to generate optimized Mg symmetric tilt grain boundary(STGB)structures[73].Since we intended to avoid the activation of basal dislocations in order to focus on the defect reactions that could be connected to〈c+a〉dislocations,both the rotation axis of the STGBs and the tensile loading axis were along[0001]as shown in Fig.2.In this paper,we investigated three[0001]-tilt GB geometries with tilt angles of 4.72°,5.21°,and 16.10°.For each GB geometry,we have two setups of simulation supercells shown in Fig.2:(i)a single GB plane with free surfaces on either side of the supercell,and(ii)a periodic supercell containing two GB planes without free surfaces.Using these,we can observe different pathways for I1SF formation like〈c+p〉partial dislocation nucleation at GBs,reactions between nucleated dislocations and a second GB plane in the second setup.The single GB supercells have dimensions about～20×57×20 nm3with a 10 nm vacuum layer on either side of the cell parallel to the GB plane,whereas the double GB supercells have dimensions～20×37×20 nm3.On average,the supercells consist of～6×105atoms.All MD and MS simulations are performed using the Large-scale Atomic/Molecular Massively Parallel Simulator(LAMMPS)package[45].

The double GB supercell was constructed using the following steps:we relaxed a single GB supercell using the evolutionary algorithm[73],then the vacuum layer was removed by merging two grains to generate a double GB supercell under periodic boundary conditions.To search for the low-energy structure of the second GB plane,a thin region containing the second GB plane in the double GB supercell was further relaxed by MD simulations using an canonical(NVT)ensemble at 1200 K for 100 ps,which was followed by a second NVT relaxation procedure to gradually lower the temperature to 300 K.After that,the entire supercell was relaxed using an isothermal–isobaric(NPT)ensemble at 300 K to eliminate any residual stresses.The GB structures were deformed by applying a constant tensile loading with the strain rate of 5×107s-1along the[0001]direction,parallel to the GB plane,at a temperature of 300 K.The simulation time step was 1 fs.Before each tensile loading,a MD simulation of 50 ps at 300 K in an NPT ensemble was performed for equilibration.We used the Mg-Al embedded atom method(EAM)potential developed by Liu et al.[32]and the Mg-Y modified embedded atom method(MEAM)potential developed by Ahmad et al.[4]in our simulations.

The results presented in Sections 3.1–3.4 show detailed defect structures for pure Mg obtained using the EAM potential.In Section 3.5,we studied the effects of Y clusters at GBs onthe deformation and I1SF formation mechanisms.The Mg-Y structures were created by randomly distributing spherical Y clusters of the diameter of～2 nm at the GB of the single GB simulation setup to mimic experimentally observed solute segregation[49].The tensile tests were then repeated for pure Mg and Y-decorated GB structures using the same MEAM potential to compare their deformation behavior and I1SF formation mechanisms.All simulation snapshots shown were obtained after carrying out static conjugate gradient minimization to eliminate thermal fluctuations,followed by visualization using the OVITO package[56].We used different methods like centrosymmetry parameter per atom[19]and common neighbor analysis[15]to identify defect structures and defect reaction mechanisms related to I1SF formation.Our results show that these defect structures and mechanisms are not sensitive to the detailed setups of the simulation supercells,such as the tilt angles of STGBs and the supercell boundary conditions illustrated in Fig.2.Thus,only the results from one particular supercell setup were used for each figure in the following sections with details described in the figure captions.

Fig.2.Geometric setups of simulation supercells.(a):A supercell has one[0001]-tilt grain boundary(GB)and two free surfaces.(b):A supercell has two[0001]-tilt GBs without surfaces.

3.Results and discussions

3.1.I1 SF from defect reactions at GBs

Fig.3(a)shows the formation and evolution of defects at and near the[0001]-tilt GB during the MD simulation.Only the defect atoms are plotted and colored according to their centrosymmetry parameter(CSP)[19].At the initial stage(0 ps in Fig.3(a))only atoms at the planar[0001]-tilt GB are shown.When the MD simulation time is 1100 ps,the first defect starts to nucleate from the GB.Due to its planar characteristics,this defect should be a specific type of partial dislocations that generates PFs(atoms with arctic blue color in Fig.3)in HCP structures.This critical point also corresponds to the yielding point of this bicrystal supercell under[0001]tensile loading.More such types of defects are generated from both sides of the GB as the MD simulation time increases.As shown on the left subfigure of Fig.3(b),when the MD simulation time is 1110 ps,such partial dislocations with PFs have occupied a large portion of the whole supercell volume;there are several locations where those partial dislocations with PFs intersect with each other and result in further defect reactions.To reveal the defect characteristics,common neighbor analysis(CNA)was performed on these defect structures in this configuration and the result is plotted in the middle subfigure of Fig.3(b)[15].A key feature is that the I1SF,which is characterized by a single layer of atoms in FCC structure as plotted in Fig.1(b)(a single atomic layer with green color in the CNA algorithm),is formed at multiple locations where the partial dislocations and other defects intersect and react with each other.This I1SF formation is achieved in a short time period of MD simulations,indicating that there are not a large number of vacancy migration and condensation events as suggested by the previous vacancy condensation mechanism[12].

To further investigate whether formations of these I1SFs are merely rare events only found in MD simulations with extremely high strain rates,we performed MD simulationsunder the NVT ensemble to relax the atomistic configurations generated by the MD tensile simulations,such as the middle subfigure of Fig.3(b)in which the I1SF starts to appears.The whole supercell was held under the same applied tensile strain during the MD relaxation at NVT conditions to simulate the normal strain rate condition at the same temperature(300 K)in real experiments.The results in the right subfigure of Fig.3(b)show that the I1SFs can continue to nucleate from defect reactions at different locations and grow into large areas,indicated by multiple single atomic layers of FCC structures.In addition,we performed MD simulations using an NPT ensemble with zero external pressure at 300 K to these supercells after MD relaxations at NVT conditions.The results did not show large changes to the configurations of these I1SFs,confirming these defects are stable even without the external loading.These results at NVT and NPT conditions suggest that,under the normal strain rate in realistic deformation,it is highly possible that these I1SFs can nucleate/grow from these defect reactions near GBs and provide the nucleation sites for〈c+a〉dislocations.To further understand the role of GBs and alloy elements to promote such dislocation activities,it is necessary to first identify the type of these partial dislocations and atomistic mechanisms of the defect reactions that result in the formation of I1SF.

Fig.3.The formation and evolution of defects at and near the[0001]-tilt GB with 16.10° tilt angle in the MD simulation.(a):A partial dislocation with stacking fault(SF)is generated from the GB plane.Only atoms at defects are plotted and colored according to their centrosymmetry parameters(CSP)[19].(b):The formation and growth of I1 SF during the defect evolution in the MD simulations with a fixed applied tensile strain at NVT conditions.Only atoms at defects are plotted and colored according to CSP(the left subfigure)and common neighbor analysis(CNA)algorithm(the middle and right subfigures)[15].In the CNA algorithm,red,blue,green,and grey colors mean atoms is in HCP,BCC,FCC,and other structures,respectively.So I1 SF is indicated by a single atomic layer of a basal plane with green color.

Fig.4 shows the detailed structures of the partial dislocations nucleated from the[0001]-tilt GB based on a typical Burgers circuit analysis.The front edge of a partial dislocation(illustrated by only defect atoms in the left subfigure of Fig.4)is enlarged in the right subfigure of Fig.4,where all atoms are projected along[110]direction and colored by the CNA algorithm.Here atoms in the perfect HCP structure are plotted in red color.It can be clearly observed that the two atomic layers of Mg on the Pyramidal I((011))plane are defects in white color,meaning local atomistic structures different than the typical HCP,BCC,or FCC structures.It indicates the leading partial dislocation generates the PF on Pyramidal I planes.The square made by the solid white lines reveals the Burgers circuit analysis results.The arrow between the two endpoints of the solid white lines connects two neighboring atoms on the adjacent basal planes,indicating the Burgers vector for this partial dislocation is〈203〉.It can be denoted as〈c+p〉partial dislocation,where〈c〉and〈p〉correspond to〈0001〉and〈100〉,respectively.Theglide of a〈p〉dislocation generates the typical I2SF on the basal plane,as shown in Fig.1(c),similar to the Shockley partial dislocations in FCC lattice.The same analyses applied to other defects in Fig.3(b)demonstrate that all these defects generated from the GB can be identified as〈c+p〉partial dislocations with PFs on Pyramidal I planes.These results are consistent with previous MD simulations of Mg single crystal under thec-axis loading,which showed that both the nucleation of leading and trailing partial dislocations of〈c+a〉glide on Pyramidal I planes[58].Our results suggest that the I1SF can be generated by the reactions between〈c+p〉partial dislocations and other defects,including other〈c+p〉partial dislocations.The corresponding mechanisms at atomistic scales are discussed in the following sections.

Fig.4.The detailed atomistic structure of a partial dislocation with PFs nucleated from the 16.10°[0001]-tilt GB based on the Burgers circuit analysis.The left sub-figure only shows atoms at defect sites.The right subfigure shows all the atoms on an across-sectional plane perpendicular to[110]as indicated by a yellow rectangle in the left subfigure.All atoms are colored according to the CNA algorithm.Red,blue,green,and grey colors mean the atom is in HCP,BCC,FCC,and other structures,respectively.The same meaning of colors for the CNA algorithm is used in all the following figures.

Fig.5.Atomistic structures to show the I1 SF formation and growth from the reactions between two〈 c+p〉partial dislocations with Pyramidal I PFs.All plotted atoms are on an across-sectional plane perpendicular to[110]and colored according to the CNA algorithm.An I1 SF is indicated by a single atomic layer of a basal plane with green color.The label at the bottom of each subfigure shows the corresponding time in the MD simulations.

3.2.Mechanisms of I1 SF formation from dislocation reactions

In our MD simulations,a frequently observed formation mechanism of I1SF results from the reactions of two different〈c+p〉dislocations gliding on intersecting Pyramidal I slip planes.One example is plotted in Fig.5.At the initial stage(timet=t0in Fig.5(a)),there are two PFs(white and blue atoms)generated by〈c+p〉partial dislocations on two different Pyramidal I planes.As the simulation goes on(whent=t0+0.5 ps in Fig.5(b)),these two PFs meet each other and generate a complex defect structure at their intersecting line.Interestingly,this defect at the intersection line dissociates into two defects that are separated by several layersof perfect basal planes as shown by the atomistic configuration corresponding tot=t0+1.0 ps in Fig.5(c).One of the dissociated products is the I1SF,which has one FCC layer(green colored atom in Fig.5)and connects two Pyramidal I PFs generated by〈2+p〉dislocations.As the simulation time further increases(t=t0+2.0 ps in Fig.5(d)),I1SF moves downwards along〈c〉-axis direction to another basal plane and its size also increases along the basal plane.As described in Section 3.1,this I1SF can continue to grow in MD simulations at NVT conditions if the simulation supercell is held at the constant tensile strain conditions,indicating this defect reaction and evolution process could be a plausible mechanism for the I1SF formation at the experimental loading conditions.

Fig.6.Illustrations of the detailed atomistic mechanisms of an I1 SF formation from the reaction of two〈 c+p〉partial dislocations plotted in Fig.5.Letters of A,B,and C indicate the stacking sequences of the row of atoms projected along[120]direction.(a)shows the perfect HCP structures.(b)and(c)shows the distributions of stac king s equences after the top-left half in(b)and the top-right half in(c)of the crystal shifts by〈 c+p〉(Here[ c+p1]and c+p2]are two different vectors in the〈 c+p〉family).(f),(e),and(d)show the formation and growth of an I1 SF,which is indicated by a single FCC layer in green color,by the atomic shuffles of atoms in the red dashed-line rectangle in each subfigure.

Fig.6 illustrates the detailed atomistic mechanisms of I1SF format ion from the reactions of two〈+p〉partial dislocations plotted in Fig.5.Fig.6(a)shows the atomistic structure of the HCP structure projected along[110]direction before the shift(slip)due to any plastic deformation.All atoms are categorized into A and B stacking sequences on different basal planes.A solid light blue line in this subfigure indicates the trajectory of a Pyramidal I plane 1(101)projected along[120]direction.In Fig.6(b),one type of 〈+p〉shi fts the top left part of the crystal above the Pyramidal I plane 1 along[023],which can be denoted as[c+p1]here.As indicated by the Burgers vector analysis in Fig.4,a slip with such a Burgers vector moves each atom upward along 〈c〉direction by〈c〉to the adjacent basal plane and changes its stacking sequence as A→B and B→C for all atoms above the Pyramidal I plane 1 as plotted in Fig.6(b).

Fig.7.Illustrations of the detailed atomistic mechanisms of an I1 SF formation from the reaction between a〈 c+p〉partial dislocation and a GB plane with a tilted angle of 16.10°.From(a)to(d),each subfigure shows the evolution of defects as the MD simulation time increases,which reveal a new〈 c+p〉is nucleated and grows from the GB plane,changing the stacking sequences of atoms and producing new segments of I1 SF.The top half of each subfigure shows all atoms colored by the CNA algorithm,and the bottom half of each subfigure shows the corresponding distributions of stacking sequences by labels of A,B,and C letters for each row of atoms.In all subfigures,the I1 SF is indicated by a single atomic layer of FCC structure in green color.

Meanwhile,there are multiple orientations of Pyramidal I planes and〈c+p〉Burgers vectors.As shown in Fig.6(c),above a Pyramidal I plane 2(011)projected along the solid dark blue line,a Burgers vector of[203],denoted as[c+p2],shifts the top right part of the crystal above the Pyramidal I plane 2,so all the shifted atoms move upward by〈c〉and change their stacking sequences as A→B,B→C,and C→A,respectively.As a consequence of these two shifts,there are four different regions in this crystal plotted by different colors in Fig.6(c):the central bottom part without any slip,the left top part shifted by[c+p1],the right top part shifted by[c+p2],and the central top part shifted by both of them.

Since an I1SF can nucleate from the reaction of two〈c+p〉dislocations,the following analyses are conducted by focusing on the intersected region of two Pyramidal I PFs generated by these dislocations.In Fig.6(c),there is a row of atoms with A-stacking highlighted by a red triangle above it in the center of this subfigure.Both of the left and right nearest neighbors of these A-stacking atoms on the same basal plane are in C-stacking,so this row of A-stacking atoms is unstable due to its repulsive interactions with their neighbors.Thus,this row of atoms transforms from A to C stacking through an atomic shuffle mechanism,as plotted in Fig.6(d).Just below this newly formed row of C-stacking atoms highlighted in a red dashed-line rectangle,there are two rows of B-stacking atoms that can be regarded as an I1SF and are highlighted by green color.The basal plane above this area(with C-stacking)and the basal plane below this area(with A-stacking)have different stacking sequences;by only considering its local environment,it is a single atomic layer of FCC structure,the key characteristics of an I1SF.

At the next step,the three rows of A-stacking atoms below this new I1SF can shuffle to C-stacking(highlighted by the red dashed-line rectangle in Fig.6(e))in order to be consistent with the C-stacking atoms on the same basal plane.Consequently,by considering the stacking sequences on the adjacent basal planes,the original single atomic layer of FCC structures in the two rows of B-stacking atoms as the I1SF disappears,and four rows of B-stacking atoms below the newly formed C-stacking atoms can be regarded as the new I1SF(highlighted by the green color in Fig.6(e)).Such a shuffle mechanism can occur continuously,making the I1SF increase its size and move along c-axis directions,as indicated by Fig.6(f),where the A→C shuffle occurs to five rows of atoms in the red dashed-line rectangle and generates a new I1SF due to the changes of stacking sequences.

3.3.Mechanisms of I1 SF formation from reactions between dislocations and GBs

Besides the reactions between two〈+p〉partial dislocations,we also found that I1SF can be generated by the reaction between one〈+p〉dislocation and other types of defects.One typical example is shown in Fig.7,where a〈+p〉dislocation reacts with a[0001]-tilt GB.The top image in each subfigure of Fig.7 displays atoms colored by the CNA algorithm,and the corresponding bottom image in each subfigure illustrates atoms with the letters“A”,“B”and“C”to indicate their stacking sequences in order to explain the defect evolution in the above image.The top image of Fig.7(a),a〈+p〉partial dislocation glides on a Pyramidal I plane(the trace of white-colored atoms in the top image)from the right side and reaches the GB on the left.This〈+p〉dislocation produces a Pyramidal I PF and changes the stacking sequences as A→B of a basal layer above and B→C of a basal layer above.Consequently,the bottom image of Fig.7(a)shows the atoms on basal planes have A+B and B+C stacking sequences below and above the Pyramidal I PF,respectively.This defect configuration is essentially the same as the configurations plotted in the lower parts of Figs.5(d)and 6(f)if the GB is ignored.

3.4.Mechanisms of I1 SF growth from dislocation reactions

After the formation of an I1SF through defect reactions,the continuous growth of this I1SF based on the mechanisms discussed in Section 3.2 and 3.3 requires either atomic shuffles or propagation of〈+p〉partial dislocations.Both mechanisms may have slow kinetics under normal stress and strain rate conditions in real experiments due to their possible large energy barriers[58,70].Alternatively,Fig.8 demonstrates another mechanism of I1SF growth by a reaction between an I1SF and a〈p〉partial dislocation.Here〈p〉=〈100〉,so that its glide on a basal plane in a perfect HCP structure generates an I2SF as shown in Fig.1(c).In Fig.8(a),two sides of an I1SF are terminated by two Pyramidal I PFs,almost identical to the defect configuration in the lower part of Fig.5(d).The stacking sequences of atoms both below and above the I1SF are labeled by letters“A”,“B”and“C”in white color.The I1SF is indicated by a basal plane with B-stacking with the A-stacking below and C-stacking above it,so this basal plane has the FCC structure(green color according to the CNA algorithm)locally.On the right side of this I1SF,a〈p〉partial dislocation is nucleated from the intersection point between the I1SF and the Pyramidal I PF.This〈p〉partial dislocation glides to the left side and changes the stacking sequences of atoms above the slip plane.

As shown in Fig.8(b),when the〈p〉partial dislocation glides along the basal plane,the B and C-stacking sequences(indicated by white letters)change to C and A-stacking sequences(indicated by yellow letters),respectively.As a result,the location of the FCC layer(green color)moves downward along〈c〉direction;atoms on the basal plane with A stacking sequence changes into FCC structure because there are different stacking sequences above(C-stacking)and below(Bstacking)this basal plane.As shown in Fig.8(c),as the〈p〉partial dislocation continues to glide through the basal plane that contains the original I1SF,all the atoms above its slip plane change their stacking sequences(labeled in yellow letters).Thus,compared with Fig.8(a),the I1SF moves downward by〈〉and the FCC layer(green color)also moves to another basal plane just below the original FCC layer.Considering the tilt angles between the Pyramidal I PFs and the basal planes,this transformation due to the〈p〉glide also increases the width of I1SF and the corresponding FCC layer along[100]direction.This newly formed I1can also have the same dislocation reaction as described above,so it can continue to move along〈c〉direction and increase its area.Due to the close-packed structures of basal planes,the nucleation and propagation of a〈p〉partial dislocation has a much lower energy barrier than the atomic shuffles in Section 3.2 and〈+p〉partial dislocation propagation in Section 3.3.Thus,this I1SF growth mechanism could be commonly observed in real experiments.

Fig.8.The mechanism of I1 SF growth by a reaction between an I1 SF and a〈p〉partial dislocation.From(a)to(c),each subfigure shows the evolution of defects as the MD simulation time increases,which reveal a〈p〉partial dislocation is nucleated and glides along the basal plane from the intersection point between the I1 and the pyramidal SF,changing the stacking sequences of atoms and moving the I1 SF along〈c〉axis to the adjacent basal plane.All atoms are colored by the CNA algorithm.The distributions of stacking sequences are labeled with A,B,and C letters for rows of atoms in the middle of each sub-figure.The yellow letters indicate the stacking sequences changed by the〈p〉partial dislocation glide.In all sub-figures,the I1 SF is indicated by a single FCC layer in green color.

Fig.9.Effects of Y clusters at GBs to promote the formation of I1 SFs in Mg.(a):The distributions of Y clusters(yellow colors)at the GB plane in MD simulations.(b):The relation between the calculated stress on the supercell and the applied engineering tensile strain along〈c〉axis for the supercell of pure Mg with the clean GB and the supercell containing the GB with Y clusters as plotted in(a).(c):The nucleation and growth of a〈+p〉dislocation and the sequential I1 SF segment from the GB plane with Y clusters(yellow color)as the MD simulation time increases.All Mg atoms are colored by the CNA algorithm.The label at the bottom of each sub-figure in(c)shows the corresponding time in the MD simulations,where t0 corresponds to the moment just after the yielding.The tilted angle of the shown GB is 4.72°.The I1 SF is indicated by a single FCC layer in green color.

3.5.Effects of Y clusters at GBs

There have been many experimental studies that Y as a solute element can enhance the activities of〈c+a〉dislocations and the ductility/formability of Mg alloys[3,13,25,47,53,55,66–69,83].As discussed in Section 1,the possible reasons for the Y solute effects on〈c+a〉dislocations are:(i)the reduction of the thermodynamic energy cost of I1SFs to provide more〈c+a〉dislocation nucleation sites[51,52],(ii)the enhancement of〈c+a〉dislocation mobility which allows cross slip between two types of pyramidal planes[14,69],and(iii)the reduction of CRSS anisotropy between basal and non-basal dislocations due to different dislocation-solute binding strengths[23].We note that none of these mechanisms mention the role of GBs.However,it has been observed that Y segregates to Mg GBs and forms nanoscale clusters[49].Additionally,a recent study on wrought processed Mg-Y alloys with different grain sizes and Y compositions suggests that GBs are the sources of nonbasal slips,including〈c+a〉dislocations[54].Since the focus of this study is I1SF formation near GBs,our next step was to check whether Y clusters at GBs can affect the kinetics of I1SF formation and the consequent〈c+a〉dislocation activities.We randomly generated Y clusters with diameters of～2 nm at the GB plane as plotted in Fig.9(a).Then tensile loading was applied along〈c〉-axis with the same strain rate compared with those of pure Mg cases.The stress-strain curves of the supercell with the clean GB(Fig.2(a))and the one with GB that contains Y clusters are plotted in Fig.9(b).These two curves are identical when the strain is small because the small number of Y clusters on the GB do not change the elastic behavior of the whole supercell.However,the supercell of the GB with Y clusters has a much lower yield strength(～1500 MPa)than its counterpart of the supercell of the clean GB(～2100 MPa).As discussed in Section 3.1,in the supercell of the clean GB,the yield strength corresponds to the nucleation of a〈+p〉dislocation from the GB.Although these yield strengths are much larger than the experimentally reported values for Mg alloys mainly due to the large MD strain rates and the idealized structures without other defect structures[68,72],the large difference between these two cases indeed suggests that Y clusters play a significant role in reducing the critical stress for the nucleation of a〈+p〉dislocation from the GB.

As plotted in Fig.9(c),the configuration at timet0shows that a defect is nucleated on the left side of the GB plane near two Y clusters exactly at the moment of yielding.Att0+16 ps,shown in the middle subfigure of Fig.9(c),this defect grows into the matrix and the standard Burgers circuit analysis confirms it is a〈+p〉dislocation that generates the Pyramidal I PF.At the next step oft0+23.5 ps shown in the right subfigure of Fig.9(c),an I1SF with the single atomic layer of FCC structure in green color is formed near the GB due to the same formation mechanism discussed in Section 3.3.These results indicate Y clusters can promote the formation of I1SFs near GBs.Since these I1SFs provide the nucleation sites of〈c+a〉dislocations,the Y clusters at GBs possibly can increase the population of〈c+a〉dislocations and enhance the ductility of Mg alloys[51,52,54].Similar mechanisms may contribute to the effects of Ca,Zn and Ag to improve the ductility of Mg alloys by solute segregation and nano-precipitate formation at GBs[37,40,71].

4.Discussions and conclusions

In this study,we focus on tensile loading along〈c〉-axis to generate I1SFs near[0001]-tilt GBs.It is wellknown that deformation modes in Mg and other HCP alloys depend on the loading orientation,which is critical for the ductility and other mechanical properties of both single crystal and textured polycrystalline samples[11,27,34,36,44,58,62,74,75,80,81,85].For example,it has been found by experiments that〈c〉-axis tensile/extension loading favors{102}extension twin activation in singlecrystal samples of pure Mg[80]and Mg-Zn-Ca alloys[11].However,the GBs in our simulation supercells nucleate〈+p〉partial dislocations and I1SFs before deformation twins(although deformation twins appear eventually as tensile load is increased).Therefore,our results indicate that basaltextured polycrystalline Mg and Mg alloys can have higher〈c+a〉dislocation activities under〈c〉-axis tensile/extension deformation due to GB effects and Y solute segregation at these GBs.Considering that〈c+a〉dislocations have been observed to be the major plastic deformation mode for〈c〉-axis compression of highly textured polycrystalline Mg alloys[24],it is likely that the same GB-related I1nucleation mechanisms observed by us in this study are at play under the compressive loading condition.

Additionally,several tensile test studies of basal-textured polycrystalline Mg and Mg alloys,with loading direction perpendicular to〈c〉-axis,have reported significant〈c+a〉dislocation activity near GB regions of AZ31 Mg alloy[2],finegrained Mg-Gd alloys[33],and Mg-Y alloys[69].These aforementioned experimental results imply that the mechanisms proposed by us for GB-related promotion of I1SFs and〈c+a〉dislocations can be found at different GBs under various loading conditions.In fact,MD simulations of[110]-and[100]-textured nanocrystalline pure Mg were performed and showed〈c+a〉dislocations nucleated at GBs[21];however,in these MD studies,there were no detailed analyses of the stability and formation mechanism of I1SFs,which are more likely to serve as the nucleation sites of〈c+a〉dislocations in conventional polycrystalline samples with grain sizes on the μm scale[51,52,54].Future studies will help us build an accurate picture of orientation-dependent effects of GBs in facilitating the plastic deformation.Other non-basal deformation defects,like〈a〉dislocations on prismatic and pyramidal planes have also been observed inside Mg GBs[31,63,64],so these non-basal〈a〉dislocations may also beactivated from GBs and make significant contributions to the plastic deformation of Mg alloys[29,85].

In summary,in this study,MD and MS simulations based on empirical interatomic potentials were applied to investigate the deformation defect evolution from the symmetric[0001]-tilt grain boundaries(GBs)in Mg and Mg-Y alloys under external[0001]tensile loading.We first demonstrated that planar faults(PFs)along the Pyramidal I plane{101}start to appear from the GBs due to the emission of〈+p〉(here〈p〉=〈100〉)partial dislocations.These partial dislocations with PFs then interact with other defects,including other〈+p〉partial dislocations and GBs,generating a large amount of I1stacking faults(SFs),which can serve as the nucleation sites for〈c+a〉dislocation[42,50–53].After detailed analysis of deformed atomistic structures,we described several novel mechanisms for the nucleation and growth of these I1SFs involving:(i)reactions between two〈+p〉partial dislocations followed by atomic shuffle events,(ii)reactions between one〈+p〉and the GB that activates another〈+p〉dislocation,and(iii)the glide of a〈p〉dislocation on the basal plane of an existing I1SF.It is notable that these new mechanisms do not require diffusion events or preexisting defects like vacancies and deformation twin boundaries,which were reported by previous studies[1,12,28,57,60,61,70,82].The addition of Y clusters at GBs largely reduce the critical stress for the formation of〈+p〉partial dislocations and the subsequent I1SFs from GBs,which provides a possible explanation for experimentally observed increase in〈c+a〉dislocation activities due to Y alloying[51,52].Thus,echoed with experimental observations of non-basal dislocations related to GBs and grain sizes in Mg and Mg alloys[2,24,33,54,65],our studies provide an alternative strategy to improve the ductility of Mg alloys by tuning the dislocation activities near GBs,through solute GB segregation or nano-precipitates at GBs.

Data availability

Data will be made available on reasonable request.

Declaration of Competing Interest

The authors declare that they have no conflict of interest.

Acknowledgment

This work was supported by the U.S.Department of Energy,Office of Basic Energy Sciences,Division of Materials Sciences and Engineering under Award DE-SC0008637 as part of the Center for PRedictive Integrated Structural Materials Science(PRISMS Center)at University of Michigan.This work used the Extreme Science and Engineering Discovery Environment(XSEDE)Stampede2 at the TACC through allocation TG-MSS160003.This research also used resources of the National Energy Research Scientific Computing Center(NERSC),a U.S.Department of Energy Office of Science User Facility operated under Contract No.DE-AC02-05CH11231.