Rotational and translational domains of beta precipitate in aged binary Mg−Ce alloys

B.Z.Sun,H.X.Zhng,Y.Dong,J.X.Ren,Y.Tin,G.M.Xie,J.Tn,c,Y.H.Sun,N Xio,∗∗

aSchool of Materials Science and Engineering,Northeastern University,Shenyang 110819,China

b State Key Lab Rolling & Automat,Northeastern University,Shenyang 110819,China

cKey Laboratory for Anisotropy and Texture of Materials,Ministry of Education,Northeastern University,Shenyang 110819,China

dAnalytical and Testing Center,Northeastern University,Shenyang 110819,China

Abstract The structural evolution fromβ1(Mg3Ce)toβ(Mg12Ce)precipitates,which takes place at the over-aged stage of binary Mg−Ce alloys,are investigated by high-angle annular dark-field scanning transmission electron microscopy.The structural transformation mainly occurs in the{111}β1 crystallographic planes,where the newly formedβlattices exhibit two categories of domain structures,namely rotational and translational domains.The rotational domain is composed of threeβdomains(βRA,βRB andβRC),which are related by a 120° rotation with respect to each other around the〈111〉β1 axis of theirβ1 parent phase.The{111}β1 crystallographic planes can provide four sets of sublattices with the same orientation for an initial nucleation ofβlattice.It leads to the formation of four translationalβdomains(βTA,βTB,βTC and βTD),among which any two differ by a vector of 1/6〈112〉β1.We deduce theoretically that there exist twenty-fourβdomains during this transition.However,considering the interfacial misfit,only one-third of domains can grow up and eventually formsβribbon.Furthermore,a majority ofβribbons overlap partiallyβ1 plate,which is beneficial to relax interfacial strain amongβ,β1 andα-Mg matrix(α/β/β1).The configuration of multipleβdomains can effectively regulate interfacial misfit ofα/βandβ/β1,which are responsible for enhancing the hardness and strength of Mg−Ce alloy.Additionally,this study aims to provide some clues to improve the over-aged performance of magnesium alloys by constructingβdomains and optimizing theα/β/β1 interface.© 2020 Chongqing University.Publishing services provided by Elsevier B.V.on behalf of KeAi Communications Co.Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/)Peer review under responsibility of Chongqing University

Keywords:Magnesium alloys;HAADF-STEM;Rotational domain;Translational domain;Phase transition;Interfacial misfit.

The metastableβ′andβ1precipitates appear successively with the extended aging.Since theβ′precipitate corresponds to the traditional peak-aged stage of age-hardening response[21,22],it serves as an important and key strengthening precipitate in the majority of binary Mg−RE alloys.In contrast to GP zones orβ′′,some microstructural features of theβ′precipitates,including the morphology,composition,lattice type and orientation,have been characterized explicitly[23,24].Theβ′precipitate has a Mg7RE composition and an orthorhombic structure,and it can be divided into two categories,namelyβL′(a≈2aα≈6.40,b≈≈22.40,c≈cα≈5.20)[25,26]andβ′S(a≈2aα≈6.40,b≈≈11.40A˚,c≈cα≈5.20)[26,27]based on the different lattice parameterb.Here,the parametersaαandcαdenote the lattice constants ofα-Mg matrix.No matter which kind ofβ′precipitate,the orientation relationship(OR)betweenβ′andα-Mg matrix was such that[001]β′//[0001]αand(100)β′//{110}α[28],and both have a coherent interfacial relation(IR)toα-Mg matrix.Apparently,the specific OR and coherent IR will be responsible for the strengthening effects ofβ′precipitate.Unfortunately,with a conversion fromβ′intoβ1precipitates,it is admitted commonly that the hardness value of alloys is declining gradually and the precipitation begins to step into the over-aged stage[29].With a Mg3RE composition,theβ1precipitate crystallizes usually in a face-centered cubic structure(FCC,a≈7.40).Although the ORs betweenβ1andα-Mg matrix(β1/α)are reported to be〈110〉β1//[0001]αand{112}β1//{100}α[30],the IR between both has been worsened noticeably.It may be an explanation for the deterioration in mechanical properties of aged Mg−RE alloys.Here,it must be mentioned that theβ1precipitate can barely be formed in some binary Mg−RE alloys,such as Mg−Y[31]and Mg−Dy[7,32]alloys,where theβ′precipitate is converted directly into the equilibriumβprecipitate.

With an appearance ofβphase,the aging has stepped completely into the traditional over-aged stage,when the performance of Mg−RE alloys are declining dramatically[21,33].Compared toβ′′andβ′coherent precipitates[34–36],some coarsenedβparticles formed at the over-aged stage exhibit a terrible IR toα-Mg matrix in spite of the existence of OR betweenβandα-Mg matrix(β/α)[37].Consequently,the microstructural characterizations of Mg−RE binary alloys are generally disregarded in case that the aged alloys proceed to the over-aged stage.Relevant literature[38]reveals that the composition and crystal structure ofβprecipitate vary with binary Mg−RE system.In binary Mg−Ce and Mg−Nd alloys,theβprecipitate is characteristic of Mn12Th-type structure with a tetragonal unit cell(a≈10.33andc≈5.96)[39–41].Meanwhile,a definite OR ofβ/αcan be claimed as[100]β//[0001]αand(002)β//{100}αin Mg−Ce alloy[42].Theβprecipitate has an FCC structure(space groupFBZ_340_2288_1400_2309_14503manda≈22.34)and a Mg5RE composition in binary Mg−Sm[43]and Mg−Gd[44-47]alloys.It is also found that an OR ofβ/αis[11]β//[20]αand(110)β//(0001)αin Mg−Gd alloy[21].As RE element is replaced with Dy or Y,theβprecipitate can be characterized as a body-centered cubic structure(BCC,a≈11.28)with space groupIBZ_340_2288_1400_2309_14503m[48].The composition ofβprecipitate is approximate more to Mg24RE5,such as Mg24Dy5[49]and Mg24Y5[50].Regrettably,the OR ofβ/αhas been ambiguous and remain to be established,implying that the coherent IR ofβ/αis difficult to be constructed.Anyhow,it is realized that theβprecipitate undergoes a structural evolution from Mg12RE tetragonal lattice to Mg5RE FCC lattice and then to Mg24RE5BCC lattice with an increase in RE atomic number.

As rare earth element Ce has a relatively low solid solubility(only 0.52wt% at eutectic temperature 590 °C)[51,52]in magnesium,an inefficient age-hardening response may be expected for the Mg−Ce alloy.However,according to some studies[53,54]on correlations between precipitation strengthening and microstructural evolution,the aged Mg−Ce alloy can also provide plenty of precipitates taking the forms of linear and curved segments with a thickness of sub-nm,leading to its hardness maximized(VHN～61)at a stage of top-aging[41].Although theβ1andβprecipitates formed at the over-aged stage have been fully identified or characterized on the structural basis[33,42,53],little attention is paid to the evolution mechanisms fromβ1toβprecipitates and how it affects the performance of magnesium alloys.Thus,many microstructural details,such as theβ1/βstructural evolution and the interfacial matching between various precipitates andα-Mg matrix,still remain to be thoroughly checked and studied particularly.In this research,the age-hardening response of a series of aged binary Mg−Ce alloys is investigated.Synchronously,by means of aberration corrected HAADF-STEM,the microstructural characterizations are focused on Mg−3.0wt% Ce alloys aged at 200 °C for 150 to 900h.Theβ1andβprecipitates formed at the aging stage are characterized in detail.It is confirmed that the multipleβdomain can be formed during phase transition fromβ1toβprecipitates.The interfacial matching between various precipitates andα-Mg matrix is also discussed emphatically,providing an explanation for a second peak hardness at age-hardening response.Importantly,this study has made a substantial contribution towards redesigning and optimizing the alloy composition according to the evolution mechanisms fromβ1toβprecipitates and the interfacial matching.

2.Materials and methods

The binary Mg−3.0wt% Ce alloys were prepared by melting pure Mg(99.9wt%)and Mg−30Ce(wt%)master alloys in the induction furnace with protection of the argon atmosphere.After staying at 760 °C for 5 min,the molten alloys were poured into a steel mold preheated to 300 °C.As-cast samples were solution-treated at 520 °C for 12h,and then quenched into water.A series of samples was aged at 200 °C for 1,2,4,8,12,24,48,100,150,200,300,450,600 and 900h in sequence.The age-hardening response of all samples in the whole Mg−Ce system was measured by a Vickers hardness tester(WOLPERT 401MVD)with a load of 0.1kg and a loading time of 15s.The microstructural characterization aims mainly at the four categories of Mg−Ce alloys with different aging times,whose specimens for STEM characterization were first cut into 0.5mm thick slices using wire-electrode cutting.Discs with 3mm in diameter were punched from these slices,and then ground to 100μm thickness.Afterwards,specimens were prepared by twin jet electro-polishing at−40 °C in mixture solution of 5.3g lithium chloride,11.2g magnesium perchlorate,500ml methanol and 100ml 2-butoxy ethanol.Gatan PIPSПion milling was used for the thinning and cleaning of specimens with low energy electron beam.

HAADF-STEM observations were performed on a JEMARM200F microscope,which is fitted with an energydispersive X-ray spectroscopy(EDS).A newly developedCscorrector brings the resolution of HAADF-STEM image up to sub-angstrom level(0.8),and the convergence semi-angle was set to a conservative 25 mrad,which yields a diffraction limited(Gaussian)probe diameter of 0.1nm.Incident beam is parallel to[0001]α,〈110〉αand〈100〉αdirections ofα-Mg matrix respectively.With a larger atomic number of Ce element,it provides a good contrast between Mg and Ce atoms in HAADF-STEM characterization.Therefore,the bright imaging dots in HAADF-STEM images represent Cerich atomic columns.The constructions of unit cells and interfaces were carried out by Materials Studio software,and then schematic diagrams of perspective views were accomplished by Visualization for electronic and structural analysis(VESTA)software.

3.Results

3.1.Age-hardening response of the aged Mg−Ce alloys

An age-hardening response curve of the Mg−Ce alloys aged at 200 °C is shown in Fig.1.As the aging time equals to zero,the alloy is as-solutioned and there is no precipitation hardening within the alloy.The hardness value at this point is 57 HV,which is close to that provided by Yamashita et al.[39].At the early aged stage,the hardness of alloys exhibits a slightly escalating trend with the advance of aging,which should originate from the Ce-rich solute clusters,GP zones and some atomic-size substructures,such as zig-zag chain or hexagonal ring.Subsequently,the hardness value reaches a maximum of 88 HV as aged for 24h,as indicated by blue elliptical rings.It corresponds to the traditional peak-aged stage,at which the corresponding microstructure contains a large proportion of multiple rows of zig-zag chains[42].Afterward,the hardness value decreases rapidly and arrives at a minimum of 68 HV at 48h,which should be attributed to the nucleation and growth of theβ1precipitate.However,it is unexpected that the alloy arrives at its another peak-aged condition with an unprecedented peak hardness of 108 HV when aged at 300h.According to some pertinent literatures[33,53,54],this aging condition has already entered the traditional over-aged stage,when the morphology of precipitates and the microstructure of alloy are ignored generally.In our opinions,the abnormal recovery of the hardness value should be associated with the structural evolution at this stage.Besides the hardness of the precipitate itself,it may involve the OR and the IR between precipitates andα-Mg matrix.To make certain the origin of the second peak-aging behavior and the relationship between performance and microstructure,the four Mg−Ce alloy samples(as marked by red elliptical rings in Fig.1)attached to the second peak-aged stage were characterized particularly by atomic scale HAADF-STEM techniques.

Fig.1.The age-hardening response curve of the Mg−3.0wt% Ce alloys during isothermal aging at 200 °C.

3.2.Microstructural evolution corresponding to the second peak-aged stage

Fig.2a is a low magnification HAADF-STEM image taken from Mg−Ce alloy aged at 200 °C for 150h with the beam parallel to[0001]αzone axis.A typical microstructural feature is the distribution of precipitate plates with the three{100}αhabit planes.Another characteristic is that some tiny particles with a darker contrast are located in the ends of many plates,as indicated by dashed yellow circles.Fig.2b and c are the two enlarged images of the ends.With an atomic arrangement along a〈110〉β1direction,the body of precipitate plate with a bright contrast can be identified as theβ1precipitate with aDO3structure(a≈0.742nm)and an Mg3Ce composition[55].In contrast,the ends with a dark contrast present an approximate regular triangular arrangement of atomic columns,which is identical completely to those along[100]βor[010]βprojections.As a basic unit cell highlighted by red balls in Fig.2c,the ends can be confirmed as theβprecipitate with a tetragonal lattice(a≈1.033nm,c≈0.596nm)and a Mg12Ce composition[56].At this stage,a majority of theβ1plates always make their ends attached to theβparticles,bringing up a coupled configuration ofβandβ1precipitates(β1−βconfiguration).Actually,it is very similar to the coupledβ1/βplates in the binary WE54 alloy[57].

Fig.2.(a)A low magnification[0001]αHAADF-STEM images in Mg−Ce alloys aged at 200 °C for 150h.(b,c)High magnification images of the linkedβ1 andβprecipitates.(d)A perspective view of theβsupercell along the[100]βdirection.

Four groups of[0001]αHAADF-STEM images are indicated in Fig.3,showing the multipleβ1−βconfigurations in Mg−Ce samples aged at 200 °C for 150,300,450 and 900h,respectively.From Fig.3a and b,it is seen that theβparticles at this stage are relatively small and only in the range of 10nm or less.As the aging time prolonged to 300h,theβparticles either combine with each other(Fig.3c)or oneself grow up(Fig.3d).The aging treatment for 450h reveals that theβparticles are obviously coarsened and far beyond the size of the shrinkingβ1precipitates,as shown in Fig.3e and f.Finally,theseβ1−βconfigurations are distributed in the form of“butterfly knot”,where theβprecipitates serve as the inflated wings and theβ1precipitates have withered away to the knots(Fig.3g and h).Comparing four sets of morphological features,it is concluded that a phase evolution from theβ1plates to the expandingβparticles has taken place with an advance of aging.

Fig.4a shows a representative[0001]αHAADF-STEM image taken from the Mg−Ce alloy aged at 200 °C for 300h.Distinctly,it is a case that two growingβparticles encounter and combine,and then constitute aβ1−β−β1configuration.The magnified image of the dashed white box in Fig.4a is displayed in Fig.4b,showing a fine microstructural feature of the junction.As previously characterized,it is recognized easily that the middle area enclosed by red lines represents the typicalβprecipitate.However,for the two triangular regions enclosed by yellow and green lines,a close examination reveals that the atomic arrangements are exactly in accordance with the〈103]βprojections of theβtetragonal unit cell.Here,the〈103]βdenotes a family of equivalent crystallographic directions of the tetragonal structure.For the sake of discussion,the threeβregions are defined asβRA,βRBandβRC,(where the subscript“R”denotes a rotational domain mentioned below).Noticeably,the intergrowth of theseβlattices with the different crystal orientation is so far unreported and should be associated closely with the crystallography of phase transition fromβ1toβprecipitates.In the same aging condition,a[0001]αHAADF-STEM image of anotherβ1−βconfiguration is demonstrated in Fig.4c,where theβparticle has expanded significantly and reached a size of～30nm.A corresponding EDS mapping of Ce is demonstrated in Fig.4d,hinting clearly that the Ce-concentration of the bulgyβparticle is distinctly lower than that of theβ1plate.It undoubtedly confirms the validity of phase identification of Mg12Ce and Mg3Ce.The two magnified images of the red and yellow dashed boxes in Fig.4c are displayed in Fig.4e and f,respectively,where a category of mixedβlattice can also be noticed.

3.3.STEM characterization from〈110〉αand〈100〉α directions

Aiming at the second peak hardness,the following HAADF-STEM characterization along〈110〉αand〈100〉αdirections focus mainly on the Mg−Ce alloy aged at 200 °C for 300h.A[110]αHAADF-STEM image of aβ1−βconfiguration is shown in Fig.5a,from which theβ1plate with a brighter contrast can be discerned readily.Combining the observations from[0001]αand[110]αdirections,it is found that theβ1plate is the shortest along a〈100〉αdirection and the longest along the[0001]αdirection,up to 250nm.Furthermore,theβparticle generally overlaps theβ1plate and has an evident expansion along the〈100〉αdirection.The two magnified images of the dashed red and yellow boxes in Fig.5a are displayed in Fig.5b and c,respectively,showing the atomic arrangements of a singleβ1region and an overlapping region.In Fig.5b,three sets of{220}β1planes with an interplanar distance of～0.522nm are related to each other by a 120° rotation,exhibiting a three-fold rotational symmetry in the{111}β1crystallographic planes.Meanwhile,the specific OR ofβ1/αis determined as:〈110〉β1//[0001]αand{111}β1//{110}α.In Fig.5c,a pair of arrows mark clearly off the regions ofβandβ1precipitates and confirm a partial overlap of both.Owing to the equivalence of[100]βand[010]βcrystallographic directions,the imaging dots in theβregion are also characteristic of an approximate regular triangular arrangement.Owing to an exactlyratio ofatoc,three sets of crystallographic planes almost provide the same interplanar distance(10.31),as highlighted by three pairs of yellow lines in Fig.5c.Assuming only Ce-rich atomic columns considered,the array of bright dots also exhibit a three-fold rotational symmetry in theβregion.Corresponding to the overlapping region,an EDS mapping of Ce element given in Fig.5d reveals a similar compositional result to Fig.4d.

Fig.3.A series of[0001]αHAADF-STEM images of theβ1−βconfigurations in Mg−Ce alloys aged at 200 °C for 150h(a,b),300h(c,d),450h(e,f)and 900h(g,h).

Fig.4.Two groups of[0001]αHAADF-STEM images showing theβ1−βconfigurations in Mg−Ce alloys aged at 200 °C for 300h.(a,c)Low magnification images of theβ1−βconfiguration.(b)The enlarged image of the dashed white box in(a).(d)An EDS mapping of Ce element corresponding to(c).(e,f)High magnification images of dashed yellow and red boxes in(c),respectively.

Another overlapping example of two precipitates is provided in Fig.5e.As enclosed by dashed red boxes,the two ends of the precipitate plate are magnified and displayed in Fig.5f and g,respectively,presenting a singleβ1region.In contrast,an enlarged image of the yellow dashed box in Fig.5e is shown in Fig.5h,from which it is perceived intuitively that some regular imaging dots are noticeably brighter than others.A closer examination of the image reveals that the region is constituted by an overlap of two sets of triangular meshes assigned to theβ1andβprecipitates,respectively,as highlighted by white and red balls.The side length is 0.596nm for theβmesh and approximately to the twice than that(0.301nm)for theβ1mesh.The similar atomic configurations can result in an excellent IR and a moderate interfacial matching between{100)βand{111}β1crystallographic planes({100)β/{111}β1,similar form is used throughout the paper in case not specified otherwise).Therefore,the brighter imaging dots should come from the mutual contribution of the Cerich atomic columns inβ1andβlattices.The observations along both directions unravel that the{111}β1crystallographic planes act as a basal plane during the structural evolution fromβ1toβprecipitates.In other words,the{100)βplanes are constructed by consuming{111}β1planes ofβ1parent phases,and the initial{100)βplane is formed by occupying a set of sublattice in{111}β1planes.Based on it,the ORs amongβ,β1andα-Mg matrix(α/β/β1)can be identified as:〈100]β//〈110〉β1//[0001]αand{100)β//{111}β1//{110}α.

Fig.5.(a,e)Two low magnification〈110〉αHAADF-STEM images of theβ1−βconfigurations in Mg−Ce alloys aged at 200 °C for 300h.(b,c)High magnification images of the dashed red and yellow boxes in(a),respectively.(d)An EDS mapping of Ce element corresponding to(c).(f,g)High magnification image of the two dashed red boxes in(e).(g)High resolution HAADF-STEM image of the overlappingβandβ1 plates.

Fig.6 shows four groups of low magnification〈110〉αHAADF-STEM images of theβ1−βconfigurations and the corresponding magnified images of dashed boxes.In the magnified image of dashed red box in Fig.6a,a film of newly formedβprecipitate still overlap partiallyβ1plate.Peculiarly,along the normal(a〈100〉α)direction ofβ1plate,theβtriangular meshes are discontinuous and interrupted by a mixed or irregular region,where the imaging dots of atomic columns are crowded and weaker.As highlighted by a triangular array of red balls,two sets ofβtriangular meshes separated by the mixed region are attached to the same sublattice.A seemingly similarβmixed region is revealed in the magnified image of dashed green box in Fig.6b.Nevertheless,when two triangular arrays of red and green balls encounter,the Ce-rich atomic columns arrange alternately.The two sets ofβtriangular meshes misplace each other by a tiny displacement,hinting that both may be located in the different sublattices.Analogous impingement between two sets ofβmeshes is also provided in the magnified image of Fig.6c.Two sets ofβtriangular meshes are staggered and the shift vector between both is not perpendicular to[0001]αdirection,which is different from the case occurred in Fig.6b.Likewise,several types of situations can occur simultaneously and are displayed in the magnified image of Fig.6d,where theseβlattices occupying different sublattices are named asβTA,βTB,βTCandβTD,(where the subscript“T”means the translational domain mentioned below).Undoubtedly,the formation of theseβlattices should also be related to the structural transformation fromβ1toβprecipitates.

Fig.7a−f shows a group of experimental results obtained by an in-situ tilting from a〈110〉αto a neighboring〈100〉αzone axes.Fig.7a indicates a low magnification[110]αHAADF-STEM image of severalβ1−βconfigurations,among which aβ1−βconfiguration is enclosed by dashed yellow box and enlarged in Fig.7b.Microstructural observations reveal that all precipitate plates are arranged uniformly along the[0001]αdirection and reach a length of 200–400nm.An enlarged atomic-resolution HAADF-STEM image of the red box is demonstrated in Fig.7c,where a singleβlattice(marked byβTAorβTB)and the mixed regions between them can be recognized.When an in-situ 30° tilting aroundreciprocal axis is fulfilled,the obtained[010]αHAADF-STEM image is shown in Fig.7d,in which the dashed yellow box points out the tracked precipitate plate.Correspondingly,the middle and high magnification HAADF-STEM images are displayed in Fig.7e and f,showing a nearly square meshes with a side length of～0.510nm,as highlighted by red or green balls.Fig.7g illustrates two projections ofα-Mg matrix along a〈110〉αand the[0001]αdirections,with a 90° difference.In the[0001]αprojection,〈110〉αand〈100〉αzone axes are represented by blue and red dashed lines,respectively,with a 30° difference between the adjacent zone axes.Therefore,a titling experiment from the[110]α(thick blue line)to the adjacent〈100〉αdirections is done in the(0001)αbasal plane,meaning that two adjacent〈100〉αdirections(thick red lines)may be obtained.Meanwhile,a schematic diagram of theβlattice titling is given in Fig.7h,where the corresponding[100]βand[010]βprojections are provided.With a 30° titling around the[0001]αaxis,a[100]βzone axis(parallel to incident beam)of theβlattice switches exactly to a[101]βor a[10]βzone axes owing to the specialratio ofaβtocβ.Fig.7i gives the〈101]βprojections ofβlattice,consistent well with experimental image shown in Fig.7f.However,two abnormal regions need attention.As marked by red arrows,one is that the weak imaging dots have appeared in the midpoint of a pair of edges of a square mesh on the both sides of Fig.7f.Another feature is that the mixed regions still exist as highlighted by the interlaced red or green balls.We speculate that it should be a result of mixedβlattices imaging.

Fig.6.The four sets of low and high magnification〈110〉αHAADF-STEM images of theβ1−βconfigurations in Mg−Ce alloys aged at 200 °C for 300h.High magnification image is pointed out by dashed box and arrow in the corresponding low magnification image.

Fig.8a is a low magnification〈100〉αHAADF-STEM image,showing multiple parallel precipitate plates.The inset presents the magnified micrograph of dashed yellow box,from which a typical ofβ1−βconfiguration with the different contrast can be observed.The interfacial area between both phases,enclosed by dashed red box,is furtherly magnified and displayed in Fig.8b.The interface ofβ/β1is very straight,and can extend about 200nm before forming a wedge edge,as marked by dashed white box.Fig.8c and d show atomic-resolution HAADF-STEM images of the flat and wedged interfaces tagged by solid and dashed white boxes.In Fig.8c,an excellent interfacial matching can confirm that the OR ofβ/β1are[001]β//[11]β1and(100)β//(10)β1,which agrees well with the above mentioned ORs.However,in the wedged interfaces shown in Fig.8d,the different interplanar spacings of(010)βand(111)β1crystallographic planes result in a significantly mismatch,as marked by symbol“⊥”.Intriguingly,in theβregion,two types of periodic meshes can be discerned easily due to the ununiform brightness of imaging dots,as labeled by solid and hollow yellow balls in Fig.8c and d.It may be associated closely with the multipleβstructural entanglement.

4.Discussion

4.1.Rotational domain inβprecipitates

According to the crystallography of phase transformation,crystals break up into multiple domain structures at a phase transition.Generally,the symmetry of each domain structure is lower than the parent-crystal symmetry,but the arrangement of the domains in the crystal is determined by the symmetry elements lost at the transition.In this study,the phase transition fromβ1toβprecipitates is a structural transformation from FCC to tetragonal lattices,suggesting that the three-fold rotational axis is deprived as a consequence of the lowering of the symmetry.As observed in Fig.4,it is conjectured that the threeβlattices with the different orientation are exactly theβdomains caused by phase transition.The hypothesis can be verified by a set of schematic diagrams showing the ORs of theβ1/βand the atomic coordinates in the(111)β1/(100)βinterface shown in Fig.9.By the contrast,it is found that all of Ce-rich atomic columns inβphase can be aligned with those inβ1parent phase along the projected direction.So,that is to say,the basicβtranslation lattice(solid rectangle in Fig.9b)is a close approximation of theβ1dashed rectangular lattice in Fig.9a,which lays the foundation for the construction of a coherentβ1/βinterface.However,distinguished fromβ1lattice,the newly nucleatedβtetragonal lattice has lost its a 120° rotational symmetry.Based on these near coincidence site lattices(CSL),it is easy to imagine that threeβtetragonal lattices can nucleate on the(111)β1plane.A schematic diagram of the overlapping(111)β1/(100)βinterface is revealed in Fig.9c,where the threeβtetragonal lattices are related to each other by a rotation of 120° about their mutual[100]βzone axis.In crystallography,the threeβlattices belong to the same rotational domain(RD)and are defined asβRA,βRBandβRC,respectively.Furthermore,the nucleation probability of threeβRDs is perfectly even owing to a three-fold rotational symmetry ofβ1parent phase.Analogous structural transformations have been also referred to actually in aged binary or ternary Mg−RE alloys.For example,Nie[58]proposed that the nucleation ofβ1precipitates involves the evolution of threeβ′structures.A similar 120° rotational symmetry is supported by threeβ3metastable structures during the growth ofβ1precipitate in binary Mg−Nd alloy[59].

Fig.7.(a–c)A group of〈110〉αHAADF-STEM images of theβ1−βconfiguration in Mg−Ce alloys aged at 200 °C for 300h.(d–f)A group of〈100〉α HAADF-STEM images obtained by an in-situ tilting.The dashed yellow boxes in(a,d)and the solid red boxes in(b,e)are enlarged in sequence.(g)A pair of〈110〉αand[0001]αprojections ofα-Mg matrix.(h)A pair of[100]βand[010]βprojections ofβunit cell.(i)A perspective view of theβsupercell along the[001]βdirection.

Fig.8.(a)A low magnification〈100〉αHAADF-STEM images of Mg−Ce alloys aged at 200 °C for 300h,the inset is the enlarged image of the dashed yellow box.(b)The enlarged image of the dashed red box in inset of(a).(c,d)Atomic resolution HAADF-STEM images of the white solid and dashed boxes in(b).

On the basis of the constructed(111)β1/(100)βinterface,a supercell includingβ1,βRA,βRBandβRC(β1/βRA/βRB/βRC)is designed and its projection along the[0001]αdirection(parallel to[10]β1direction)is shown in Fig.10a.TheβRAdomain exhibits a perfect[010]βorientation,which corresponds to the dashed red box area with a triangular atomic arrangement in Fig.4b.Whereas,both theβRBand theβRCdomains give a denser lattice,representing a projection along[013]βor[01]βdirection,which is exactly in accord with the dashed green and yellow lines regions in Fig.4b.Meanwhile,the atomic arrangements of threeβdomain structures in theβ1/βinterface are displayed in Fig.10b,from which a 120°rotational relationship can be seen clearly.Fig.10c and d shows the[100]αprojections ofβ1/βRA/βRBandβ1/βRA/βRCinterfaces,respectively.As marked by solid black boxes,Cerich atomic columns exhibit two categories of square lattices,which is identical to the two types of square meshes in experimental images of Fig.8c and d.Undoubtedly,it originates from the overlap of twoβdomains.Therefore,based on the comparison of experimental images and projection models in three directions,it is deemed that the proposed threeβRDs with a 120° rotational symmetry each other are reasonable.

4.2.Translational domain inβprecipitates

Fig.9.Schematic diagrams showing a 120° rotational domain ofβprecipitate in the(111)β1 crystallographic plane.(a,b)The atomic coordinates in the matching(111)β1 and(100)βplanes.(c)A perspective view of the overlapping(111)β1 and(100)βplanes along their normal direction.

As described previously,theβparticles have expanded with the transition fromβ1toβprecipitates due to a relatively low Ce-content.Likewise,the Ce-concentration in the newly formed{100)βplanes is much less than that in the{111}β1planes ofβ1parent phase.Therefore,a basic rectangular translational period in the initial{100)βcrystallographic plane,will have four sets of CSL with the{111}β1crystallographic planes.Fig.11a reveals the four possible collocation forms of{100)βand{111}β1planes.Assuming only theβlattice with a single orientation considered,there are theoretically four types of collocation forms of{100)β/{111}β1.In other words,all lattice points in the{111}β1crystallographic planes are exactly occupied by the four sets ofβlattices,as represented by balls with different colors.Distinguished from the above-mentionedβRD,the four sets ofβlattices have no difference in the orientation and only have a minimum translational vector of 1/6〈112〉β1each other along the three equivalent〈112〉β1directions in a{111}β1plane,as shown in the right inset of Fig.11a.Apparently,the four sets ofβlattices can be regarded asβtranslational domain(TD)and named asβTA,βTB,βTCandβTD,respectively.Furthermore,it is considered that the nucleation possibilities ofβTA,βTB,βTCandβTDshould be identical completely and the nucleation positions are also random.A schematic diagram of the four incipientβTDs is indicated in Fig.11b,where the fourβTDs with the same orientation show a state of non-contact with each other.However,with a consumption of{111}β1planes and an expansion of{100)βplanes,several neighboringβTDs may encounter or impinge each other.As a result,someβmixed regions composed of twoβTDs may be generated,as the shadow regions shown in Fig.11c.The atomic columns attached to the differentβTDs are arranged alternately and constitute theβmixed regions,which are in accord well with the staggered meshes in some experimental images shown in Figs.5 and 6.A remarkable feature ofβmixed region is that the imaging intensities of Ce-rich atomic columns are weakened significantly as shown in the enlarged images of Fig.6b and c.We think that a slope model designed for theβmixed region can successfully explain it,as shown in Fig.11d.The left model shows the two isolatedβTDs,which have a tendency to expand in all directions along the{111}β1plane.With an encounter of the twoβTDs,a sloping or nearly sloping domain boundary is most likely to form,as the mixed region shown in the right model.Furthermore,if the Ce-rich atomic columns affiliated to individualβTDs are misaligned up and down along the[110]αdirection in mixed region,it brings about an increase in Ce−Mg mixed atomic columns and averages the projection potential.

Fig.10.Schematic diagrams showing the[0001]α(a),[110]α(b)and two[100]α(c,d)perspective views of the interface betweenβ1 andβdomains.

Based on the sloping domain boundary,aβTA/βTBsupercell model is constructed and its[0001]αprojection and corresponding HAADF-STEM images are indicated in Fig.12a and b,respectively.In Fig.12a,aβTA/βTBTD boundary is about 60° from the{111}β1growth planes,corresponding well to the sloping domain boundary pointed out by black arrows in experimental image of Fig.12b.Meanwhile,one[110]αand two adjacent〈100〉αprojections are indicated in Fig.12c,e and g,respectively,from which the mixed region of twoβTDs can be seen clearly.Fortunately,theseβmixed regions are strongly supported by some experimental images shown in Fig.12d,f and h,respectively.Additionally,along two〈100〉αdirections,both the projections of supercell model and experimental images present a different breadth ofβmixed regions,which should be closely related to the observed direction of the sloping domain boundary.For instance,with incident beam parallel to[010]α,theβTA/βTBTD boundary is nearly parallel to the electron beam and exhibits a single line,as marked by a pair of black arrows in Fig.12h.For the case in Fig.12,a translational vector ofβTA/βTBTDs is the 1/6[11]β1,which is perpendicular to the[0001]αdirection andβplates,as described in Figs.6a,b and 7.Another situation is that the translational vectors of both TDs are 1/6[11]β1or 1/6[11]β1,which are not is perpendicular to the[0001]αdirection andβplates.As given in Fig.13c,the{100)βplanes ofβTAandβTDdomains are not aligned and the translational vector between both is the 1/6[11]β1,corresponding to these experimental images shown in Fig.6c and d.As viewed along the[0001]αdirection,the supercell model exhibits a projection shown in Fig.13a.The TD boundary ofβTA/βTDis about 30° from the{111}β1planes,which is consistent well with boundary pointed out by black arrows in experimental image of Fig.13b.Two〈100〉αprojections of theβTA/βTDsupercell model are illustrated in Fig.13d and e,respectively,from which the staggered layer between two TDs can also be noticed.Unfortunately,as it is no chance to accomplish a tilting from[110]αto[100]αor[010]αzone axes,the corresponding experimental images have never been captured.

Fig.11.Schematic diagrams showing a set of translational domains ofβprecipitate in the(111)β1 crystallographic plane.(a)The four possibleβtranslational domains occupying different sublattice in the(111)β1 plane.(b)The isolatedβtranslational domains formed randomly at initial nucleation stage.(c)The extension and impingement ofβtranslational domains at the growth stage.(d)A schematic diagram of isolated and connectedβtranslational domains on the(111)β1 plane.

Fig.12.A set of schematic diagrams and related HAADF-STEM images ofβTA andβTB translational domains.The corresponding directions of projection and incident beam are(a,b)[0001]α([010]β),(c,d)[110]α([100]β),(e,f)[100]α([101]β)and(g,h)[010]α([10]β).

4.3.The possibleβdomains in crystallographic theory

As we know,the crystal symmetry lowering at a phase transition occurs both as a result of a decrease in the number of rotational symmetry elements and as a result of the reduction of some translations.According to phase transition theory,the structure transformation fromβ1toβprecipitates can be formulated by a transformation matrix(R,T).It is composed of the matrix of fundamental vector transformation(R)and the translation of coordinate origin(T).Therefore,the whole symmetry operation is generally expressed as an augmented matrix:

In the above,allβdomains proposed,including threeβRDs and fourβTDs,are derived fromβ1parent phase and can be formulated by the augmented matrix.

Only when a RD considered,taking theβRAas an example,its relation toβ1parent phase only includes the part of rotational operation of the augmented matrix and can be described as:

Fig.13.A set of schematic diagrams and related HAADF-STEM images ofβTA andβTD translational domains.The projection directions are(a)[0001]α([010]β),(c)[110]α([100]β),(d)[100]α([101]β),(e)[010]α([10]β).(b)A[0001]αHAADF-STEM image ofβTA andβTD translational domains corresponding to(a).

Here,the matrixRβRAdenotes a matrix of fundamental vector transformation fromβ1toβRAphases.Since thea-axes of allβdomains are parallel to the[111]β1zone axis ofβ1parent phase,theμis a scale factor between two unit vectors along[100]βand[111]β1directions and has nothing to do with the subsequent matrix operations.Similarly,the other two matricesRβRBandRβRCare also deduced.Furthermore,a transformation matrixRβamongβRA,βRBandβRCcan be given as:

A 120° rotational relationship between the three RDs can be supported by an identity matrixIobtained by three matrix operations ofRβ,namely

As described previously,for eachβRD,there are four sets of CSL in{111}β1planes.In other words,as far as one RD is concerned,four possible translational vectors give rise to the formation of four TDs.According to the inset of Fig.11,the four possible translational vectors(Tn)could be concluded as:

Table 1The augmented matrix M describing possible formed twelveβdomain structures during phase transition fromβ1 toβprecipitates only when a{111}β1 crystallographic plane and a〈100]βcrystallographic direction considered.

It is the part of translational operation of the augmented matrix and can be expressed as:

Therefore,taking the combined operation ofβRAandβTBas an example,the augmented matrix can be described as:

Similarly,when the other translational vectors,such asTACandTAD,are taken effect,some other the augmented matrixMis also obtained.Thus,the combination of three RDs and four TDs can evolve twelveβdomain structures in theory,and corresponding transformation matrix is listed in Table 1.Since both[100]βand[010]βare a four-fold axis symmetry element and both directions are completely equivalent,the[010]βaxis is also completely preset to be perpendicular to the{111}β1crystallographic planes.Therefore,as far as a{111}β1plane is concerned,the number of the possible nucleatedβdomains can add up to twenty-four(3×4×2=24).

4.4.Interfacial matching amongβ,β1 andα-Mg matrix

4.4.1.Growth rates of threeβrotational domains

As previously mentioned,the nucleation chances of threeβRDs(βRA,βRBandβRC)are equal theoretically,nevertheless,lots of HAADF-STEM images demonstrate statistically that the observedβRARD is more than the other two RDs.The most likely scenario is that threeβRDs have an entirely different growth rate along a〈110〉αdirection,involving the OR and IR of theβ/α,especially the interfacial misfit ofβ/αinterface.Fig.14a shows a schematic diagram ofβRA,βRBandβRCat initial nucleation stage,when three nucleatedβRDs with a small size randomly stay on the(111)β1planes.With a decomposition of(111)β1planes and a thickening of(111)βplanes,a group of brand-newβ/αinterfaces have showed up and the area is increasing.The group ofβ/αinterfaces have been highlighted by dark gray in Fig.14b,exhibiting threeβRDs at their growth stage.Distinctly,the mismatch on these newβ/αinterfaces has to be investigated comparatively because it will significantly affect the growth rate.In view of the ORs ofβRA/α,βRB/αandβRC/α,the indices,interplanar spacings and calculated mismatches of corresponding crystallographic planes are listed in Table 2.Regardless of whichβRD,it is noticed that the(100)βcrystallographic planes are consistently parallel to(110)αand(111)β1planes.For threeβRDs,the mismatch of(100)β/(110)αinterface is completely identical and reaches 7.045%,severely inhibiting a growth ofβdomains along the[110]αdirection.Similarly,along the[100]αdirection,the mismatches are 6.984% for(001)βRA/(100)αinterface and 7.034% for(03)βRB/(100)αand(031)βRC/(100)αinterfaces,hinting that the[100]αis also a slower growth direction.However,along the[0001]αdirection,the interfacial mismatches are only 0.84% for(020)βRA/(0001)αand 0.89%for(011)βRB/(0001)αand(01)βRC/(0001)α.As a result,it is found that allβdomains have a greater rate of growth along the[0001]αdirection and are easier to formβribbon.Furthermore,theβRAdomain has a relatively smaller interfacial mismatch withα-Mg matrix than the other two domains along the[0001]αand the[00]αdirections,which is conducive to a rapid expansion of theβRAdomain in(111)β1plane.As provided in Fig.4b,theβRBandβRCRDs with the[011]βand the[01]βorientations have been obviously restrained.Thus,among the proposed twenty-fourβdomains,only one-third ofβdomains can grow up and the rest may delay growth or decays.

Fig.14.Schematic diagrams showing the nucleation,growth and interfacial relationships of variousβdomains.(a)The nucleation stage and(b)The growth stage ofβRA,βRB andβRC domains on the(111)β1 crystallographic plane,(c)The interfacial strain relations betweenβ,β1 andα-Mg matrix.(d)Random distribution along the[10]β1 direction ofβTA,βTB,βTC andβTD domains on the(111)β1 plane.

Table 2Corresponding interplanar spacings and the interfacial mismatch betweenβRA,βRB,βRC andα-Mg matrix.

4.4.2.Accommodation of interfacial strain ofβprecipitates

Table 3Corresponding interplanar spacings(),the interfacial mismatch(%)and the types of stress amongβ,β1 andα-Mg matrix.

Table 3Corresponding interplanar spacings(),the interfacial mismatch(%)and the types of stress amongβ,β1 andα-Mg matrix.

β1 precipitate βprecipitate α-Mg matrix Mismatch(%)ofβ/β1 Mismatch(%)ofβ/α(1images/BZ_345_1047_2283_1068_2334.png0) 5.2603 (020) 5.165 (0001) 5.2112 1.8282 0.8905(111) 4.2949 (200) 5.165 (33¯60) 4.8141 – −7.0327(11images/BZ_118_729_1599_748_1637.png) 3.0372 (002) 2.980 (images/BZ_345_1047_2283_1068_2334.png100) 2.7793 1.9012 −6.9696

4.4.3.Performance prediction and optimization design of Mg−RE alloys

In our age-hardening response of binary Mg−Ce alloys,the second peak-aging behavior should be the main contribution from theβprecipitated phase itself.Theβphase with a tetragonal structure and a Mg12RE composition,mainly exist in aged binary Mg−RE(RE=Ce,Pr and Nd)alloys[2,42,60].It is reported that all Mg12RE,such as Mg12Ce,Mg12Pr and Mg12Nd,exhibit a high hardness[61].Especially,the Mg12Ce precipitate takes a form of“butterfly knot”and has a relatively large volume fraction,which will contribute remarkably to the second peak of hardness.Here,the high hardness of the Mg12RE itself will not be considered in this investigation.On the other hand,it is confirmed that all Mg12RE behave in a brittle manner according to the calculated modulus and Poisson’s ratio based on DFT[60].This should be an important cause of the decrease in strength of alloy and also a reason why the mechanical properties and microstructure of alloys at the over-aged stage have little attention.Assuming that theβ1−βconfiguration composed of multipleβdomains andβ1plate is constructed purposefully,a better IRs ofα/β/β1can be acquired.In a sense,a pair of comfortable IRs ofα/βandβ/β1has demonstrated that the formedβribbon could serve as a bridging role betweenβ1andα-Mg matrix.At least,theβ1−βconfiguration should be very effective barriers to preventing the basal slip of dislocation,and furtherly be capable of improving the strength of alloys.

At the traditional over-aged stage,however,it is commonly admitted that the strength and hardness of alloys have a significant declining in some binary Mg−RE alloys.In Mg−Gd or Mg−Sm alloys,βprecipitates are identified as a Mg5RE(Mg5Gd and Mg5Sm)phase with an FCC structure(space groupF3manda≈22.34)rather than the tetragonal Mg12RE phase.Furthermore,the Mg5RE plate,attached to theβ1parent plate,has a{100}αhabit plane,different from the Mg12Ce ribbon with a{110}αhabit plane.It suggests that the nucleation and growth mechanisms of Mg5RE plate should be distinguished from those of the Mg12Ce ribbon.Thus,the above-mentionedβdomain can hardly occur and the interfacial strength may deteriorate.For binary Mg−Y and Mg−Dy alloys,the high strength and hardness of alloys are derived from the solid solution effect to a large extent owing to the higher solid solubility of Y or Dy atoms.However,the precipitation strengthening is proved to so sluggish in aged binary Mg−Y and Mg−Dy alloys.Especially in binary Mg−Y alloy,the equilibriumβprecipitate can hardly be found regardless of the extended aging time.Theβprecipitates in Mg−Y and Mg−Dy alloys take the form of a Mg24RE5composition and a BCC structure(space groupI3manda≈11.25).Besides,since theβ1precipitate is absence in the precipitation sequence and theβprecipitate originates directly fromβ′precipitate,multipleβdomains can hardly be formed in these binary Mg−RE alloys.Meanwhile,the lattice parameters and individual(hkl)interplanar spacings of the Mg24RE5precipitate are not close to those ofα-Mg matrix,which is difficult to obtained a good atomic matching in the correspondingβ/αinterface.In turn,the poor interfacial relations result in that a majority of Mg5RE precipitates are only able to take the form of a polyhedron shape particles,not a ribbon-like or lamellar Mg12Ce precipitate observed in this paper.

For the moment,Mg−Nd alloy may be considered a promising alloy.On the one hand,it benefits by the higher solid solubility of Nd in magnesium.Another important factor is that theβprecipitate in Mg−Nd alloy has also been identified as the Mg12Nd tetragonal structure.Since the Mg12Nd has the same lattice type and similar parameters as the Mg12Ce,we imagine that there also exist multipleβdomain structures during the structural transformation fromβ1toβprecipitates in binary Mg−Nd alloy.It will provide a strongβ1/βinterfacial strength and a clue to the performance of the alloy.Unfortunately,some studies relevant to binary Mg−Nd alloy have shown that the Mg12Nd precipitate can hardly be formed by prolonging aging time at the conventional aging temperature(200 °C)and the acquisition of Mg12Nd precipitate can only be fulfilled by quenching treatment[11].A feasible method is to select an appropriate alloying element in order to accelerate the formation of Mg12RE-type precipitate.However,the only thing to avoid is the formation of some unnecessary precipitates,such as Mg14YNd2[62]and Mg14Y4Nd[63].In addition,this method is also attempted in other Mg−RE alloys,such as Mg−Gd,Mg−Sm and Mg−Dy alloys,aiming to change the original structure ofβphase and obtain the tetragonal Mg12RE precipitate.However,these assumptions need to be confirmed by a large number of experiments and theoretical calculations.

5.Conclusions

Aiming at the aged binary Mg−3.0wt% Ce alloys,we have investigated systematically multipleβdomains formed during phase transition fromβ1toβprecipitates by means of HAADF-STEM.The main conclusions are as follows:

(1)At the traditional over-aged stage,the precipitation behavior is mainly a phase transition fromβ1(Mg3Ce)toβ(Mg12Ce)precipitates.Owing to a similar atomic configuration in{100)βand{111}β1planes,it is deemed that the structural transformation fromβ1toβprecipitates mainly occurs in the{111}β1planes.Both the decomposition ofβ1phase and the nucleation ofβphase are accomplished in the{111}β1planes.

(2)The{111}β1crystallographic planes are characteristic of three-fold rotational symmetry,which leads to the formation ofβrotational domain during structural evolution.The rotational domain is composed of threeβdomains(βRA,βRBandβRC),which are related by a 120° rotation with respect to each other around the mutual〈111〉β1axis of theirβ1parent phase.

(3)The{111}β1crystallographic planes provide four sets of homologous sublattices,acting as the coincidence site lattices ofβprecipitates.It gives rise to the formation ofβtranslational domain including fourβdomains(βTA,βTB,βTCandβTD).These translational domains have the identical orientation and any twoβtranslational domains differ by a vector of 1/6〈112〉β1.

(4)Considering the four-fold rotational symmetry ofβlattice,it is deduced theoretically that twenty-fourβdomain structures can nucleate during phase transition.However,with the growth along the〈110〉αdirection,theβ/αinterfacial misfits have to be taken into account.Therefore,only one-third of domains can grow up and eventually formβribbons.

(5)A majority ofβribbons overlap partiallyβ1plate,which is helpful to relax theα/β/β1interfacial strain.The multipleβribbons can construct a comfortableβ/β1andα/βinterfaces,which is responsible for improving the hardness and strength of binary Mg−Ce alloy.The constructed multipleβdomains can be extended to other Mg−RE alloys in order to improve the over-aged performance of magnesium alloys.

Conflict of interest statement

The authors declared that they have no conflicts of interest to this work.

Acknowledgments

The authors acknowledge the access to TEM instruments at the Institute of Advanced Material Technology of Northeastern University of China and acknowledge the access to the Vickers hardness tester at the Northwest Institute for Nonferrous Metal Research of China.This research did not receive any specific grant from funding agencies in the public,commercial,or not-for-profit sectors.