Choqing Liu,Houwen Chen,Min Song,Jin-Feng Nie

aState Key Laboratory of Powder Metallurgy,Central South University,Changsha 410083,China

bInternational Joint Laboratory for Light Alloys(MOE),College of Materials Science and Engineering,Chongqing University,Chongqing 400044,China

cDepartment of Materials Science and Engineering,Monash University,Victoria 3800,Australia

Abstract The major interface between β′-Mg3Sn precipitate plate and the α-Mg matrix in a Mg-9.8wt.%alloy has been investigated using aberrationcorrected scanning transmission electron microscopy and first-principles calculations.It is found that Sn atoms orderly distribute in the single layer of the α-Mg matrix immediately adjacent to the broad surface of β′at the early stage of ageing.These Sn atoms substitute Mg atoms located at the centers of equilateral triangles constituted by three Mg columns in the outmost layer of β′.First-principles calculations suggest that the ordered Sn distribution is energetically favored and it not only decreases the interfacial energy of the β′-matrix interface but also hinders the occurrence of 1/3<01ˉ10>α shear that thickens the β′plate.

Keywords:Mg-Sn alloys;Ordered distribution of solute atom;HAADF-STEM;First-principles calculations.

1.Introduction

Mg-Sn based alloys have received increasing attention in the past two decades due to their great potential to develop high strength and low cost wrought magnesium alloys[1–15].The precipitation sequence of these alloys has been reported to be:Supersaturated solid solution→GP zone→β′-Mg3Sn phase→β-Mg2Sn phase[10].Although theβphase is the main strengthening phase,theβ′phase is also a key precipitate as it can act as heterogeneous nucleation site for the precipitation ofβstrengthening phase[10].Theβ′phase has a L12structure and a plate-like morphology with its habit plane parallel to the basal plane ofα-Mg matrix.The formation mechanism ofβ′structure from hcpα-Mg matrix was reported in our previous study[10],which is similar to the classical hcp→fcc transformation that involves a 1/3<01ˉ10>αshear on every second(0002)αplane.According to our previous study[10],the interface structure between theβ′structure and theα-Mg matrix can be established easily,but the distribution of Sn solute atoms around the interface remains unclear.

It has been reported that distribution of enriched solute atoms in precipitate/matrix interface often occurs during ageing[16–28],and the distribution of solute atoms in the precipitate/matrix interface usually plays an important role in the processes of nucleation and growth of the precipitate[19,21,23,26],e.g.,the Zn segregation inβ-Mg2Sn/α-Mg interfaces improves the nucleation rate ofβprecipitate and reduces its coarsening rate,resulting in a finer distribution ofβprecipitate[23].Therefore,it is necessary to investigate the Sn distribution around theβ′/α-Mg interface and to reveal its potential effect on the nucleation and growth ofβ′.Such findings are important to a deeper understanding of theβ′precipitation behavior.

2.Material and methods

Alloy with a nominal composition of Mg–9.8wt.%Sn was cast using the method reported in a previous study[23].Small specimens cut from the ingot were firstly solution treated at 300 °C for 24 h,400 °C for 24 h and at 500 °C for 4 h,followed by quenching to water at room temperature.The quenched specimens were aged at 100 °C for 720 h and 4320 h,and 200 °C for 88 h.Thin foil specimens for high-angle annular dark-field scanning transmission electron microscopy(HAADF-STEM)observations were prepared by mechanical polishing from 500 μm to 50–70 μm and ionbeam milling.HAADF-STEM observations were conducted in a Cs-corrected FEI Titan G260-300 ChemiSTEM operated at 300 kV.The HAADF-STEM images were smoothed in a Gatan DigitalMicrograph package.

To rationalize the ordered Sn distribution and to determine the positions of Sn atoms immediately adjacent to the habit plane ofβ′,first-principles calculations based on density functional theory(DFT)calculations were carried out.These calculations are operated within the ViennaAb InitioSimulation Package(VASP)code[29]and use the Generalized-Gradient Approximation exchange-correlation functional of Perdew-Burke-Ernzerhof[30].Atoms involved in the calculations were treated using projector augmented-wave(PAW)pseudopotentials[31,32].The cut-off energy was set at 380 eV.Gamma centered grids were used for the k-point grids automatic generation and an equivalent(25×25×15 for anα-Mg unit cell)k-point mesh was used.An interface supercell including 352 atoms in total and twoβ′generated by two opposite shears was built,Fig.3a,to maintain the periodic boundary condition.The energy differences(ΔE)between one Sn atom distributed in the layer ofα-Mg matrix that is immediately adjacent to theβ′habit plane and one Sn atom dissolved inα-Mg matrix far fromβ′,are given by the equation:

whereEx-Mg319Sn33andEMg320Sn32are the total energies of the interface supercell with and without one Sn substituting one Mg atom in the layer ofα-Mg matrix,respectively.As there are two difference positions within the layer,xcan be 1 and 2.EMg144andEMg143Sn1are the total energies of a Mg matrix supercell containing 144 Mg atoms without and with a dissolved Sn atom,respectively.To investigate the influence of the Sn distribution on interfacial energy,we calculated the interfacial energies of interfaces betweenβ′andα-Mg matrix without and with Sn distribution using the interface supercell in Fig.3a.The interfacial energy(γ)was calculated according to the equation:

Fig.1.(a)HAADF-STEM image showing an edge-on β′precipitate plate with its end connected to a GP zone in a sample aged at 100 °C for 720 h.(b)Enlarged HAADF-STEM image of the β′in(a)showing ordered Sn distribution in the layer of α-Mg matrix that is immediately adjacent to the β′.Two orange dashed lines in(b)indicate the habit planes of β′.Yellow arrow marks the layer of α-Mg matrix that is immediately adjacent to the β′and small green arrow indicates the Sn-rich column.A,B and C represent three different closely packed planes in α-Mg and β′precipitate in terms of stacking sequence.Electron beam direction is parallel to[2ˉ1ˉ10]α.

whereEtotis the total energy of the interface supercell,Eβ′is the energy ofβ′constrained byα-Mg matrix,andEmatrixis the energy ofα-Mg matrix constrained byβ′,S is the area of the interface,and the factor 4 is because there are four interfaces in the supercell.Similar calculation method of interfacial energy has been reported in aluminum alloys[33].Moreover,the effect of ordered Sn distribution on thickening ofβ′was also investigated by first-principles calculations.In this case,the supercell was built to include two four-layerβ′generated by two opposite shears,Fig.4,as thickening ofβ′structure involves a shear of 1/3<10ˉ10>α[10].To calculate the energy change during the shear,the shear was divided into ten shear segments and the energy change(ΔE′)caused by each segment was given by the equation:

whereExis the total energy of a supercell that experiencedxshear segments(xcan be any of numbers from 1 to 10),E0is the total energy of the initial supercell with two four-layerβ′,and the factor 2 is because the shear occurs on two habit planes simultaneously.

3.Results and discussion

Fig.1a shows a HAADF-STEM image of a small edge-onβ′precipitate plate in a sample aged at 100 °C for 720 h.Theβ′plate is 7 nm in length,and its right end is connected to a GP zone,confirming that reported in a previous study[10].Fig.1b shows an enlarged HAADF-STEM image of theβ′plate.Thisβ′has an orientation relationship of(11ˉ1)β′//(0001)αand[011]β′//[2ˉ1ˉ10]αwithα-Mg matrix[10].Theβ′plate has four atomic layers in thickness and its bottom and top habit planes are marked by the orange dashed lines,Fig.1b.In addition,orderly distributed atomic columns that have a brightness lower than Sn-rich columns in theβ′but higher than Mg columns in theα-Mg matrix are observed in the layers of theα-Mg matrix that are immediately adjacent to the habit planes of theβ′plate.These columns are Sn-rich,and the Sn concentration in this layer is lower than that ofβ′but higher than that of theα-Mg matrix.This is abnormal since the region immediately adjacent to the broad surface of a growing precipitate plate usually has a lower solute concentration than the matrix region remote from the precipitate-matrix interface[34].

Fig.2a shows a largerβ′plate in a sample aged at 100 °C for 4320 h(still under-aged).Its length is 23 nm,while its thickness is only four atomic layers.Orderly distributed Snrich columns are again visible within the layers of theα-Mg matrix immediately adjacent to theβ′habit planes,as indicated in Fig.2b,even though these columns have a slightly lower brightness than those in Fig.1b.After ageing at 200 °C for 88 h(approximately peak-aged condition),the ordered Sn distribution within the layers of theα-Mg matrix that are immediately adjacent to theβ′habit planes are absent,as indicated in Fig.2c.Moreover,the brightness of some Sn-rich columns within the outmost layer of theβ′becomes lower than those insideβ′,which indicates the Sn concentration in this layer decreases during to the peak-aged condition.

In order to understand the ordered Sn distribution immediately ahead of theβ′/α-Mg interface,we calculated the energy differences(ΔE)between one Sn atom distributed in the layer ofα-Mg matrix immediately ahead of theβ′/α-Mg interface and one Sn atom dissolved in theα-Mg matrix using the supercell shown in Fig.3a.Fig.3b shows the atomic arrangement of the layer ofα-Mg matrix and the habit plane ofβ′along[0001]α.Careful analysis indicates that there are two different Mg positions in the layer of theα-Mg matrix,as marked by numbers 1 and 2,respectively.Positions 1 are in the centers of equilateral triangles constituted by three Mg atom columns,and positions 2 are in the centers of equilateral triangles constituted by two Mg atom columns and one Sn atom column.The energy differences are-62.1 meV and 141.8 meV,Fig.3c,when one Sn atom substitutes a Mg atom at positions 1 and 2,respectively.This indicates that the distribution of Sn at positions 1 is energetically favored.Fig.3d illustrates the perspective view ofβ′and its nearest layers of theα-Mg matrix.When the Sn atoms substitute some Mg atoms at positions 1,the distribution of the Sn-rich columns in the layer of theα-Mg matrix is fully consistent with that of bright dots observed experimentally within the layer ofα-Mg matrix immediately ahead of theβ′/α-Mg interface,Figs.1b and 2b.To reveal the origin of the Sn distribution at positions 1,we further calculated and plotted the electron charge density,after one Sn atom has substituted a Mg atom at the position 1,Fig.3e.Charge distribution between the Sn atom

Fig.2.(a)HAADF-STEM image showing an edge-on β′precipitate plate in a specimen aged at 100 °C for 4320 h.(b)Enlarged HAADF-STEM image of the β′in(a)showing ordered Sn distribution in the layer of α-Mg matrix that is immediately adjacent to β′.Small green arrow indicates the Sn-rich column.(c)HAADF-STEM image of a β′precipitate in a specimen aged at 200 °C for 88 h showing absence of Sn distribution in the layer of α-Mg matrix immediately adjacent to β′.Orange dashed line represents the habit plane of β′.Yellow and red arrows indicate the layers of α-Mg matrix with and without ordered Sn distribution,respectively.Electron beam direction is parallel to[2ˉ1ˉ10]α.

in the layer of theα-Mg matrix and its nearest Sn atom in the habit plane ofβ′is very similar to that between two neighbouring Sn atoms inside theβ′lattice,as indicated by blue arrows in Fig.3e.This suggests that the chemical bonding between the Sn atom in the layer of theα-Mg matrix and its nearest Sn atom in the habit plane ofβ′resembles that between two neighbouring Sn atoms in theβ′.Since formation ofβ′phase is energetically favored[10],the chemical bonding between two neighbouring Sn atoms insideβ′is expected to be relatively stable.Therefore,the substitution of Mg by Sn at position 1 is probably caused by the chemical bonding between it and its nearest Sn atom in the habit plane ofβ′.Note that the Sn distribution within the layer of theα-Mg matrix immediately ahead of theβ′/α-Mg interface is absent in the peak-aged condition,Fig.2c.This might be caused by the fact that Sn atoms have a stronger tendency to formβequilibrium precipitate to further decrease the total energy of the system during ageing[7,10],and when the alloy is aged to peak-aged condition or when the supersaturated Sn concentration drops to its equilibrium solubility in the solidα-Mg at the ageing temperature,the low Sn concentration in theα-Mg matrix(～0.45wt.%[35])probably causes the Sn atoms enriched in the Mg layer immediately ahead of theβ′/α-Mg interface to diffuse away to formβ,Fig.2c.This phenomenon of the presence of a Sn-rich layer immediately ahead of theβ′/α-Mg interface at the early stage of ageing but disappeared in the later stage of ageing is similar to the Ag-rich layer immediately adjacent toγ′precipitate in Al-Ag alloys[18]and Cu-rich layer in theθ′/Al-matrix interface in Al-Cu alloys[27].

Fig.3.(a)Schematic diagram illustrating the supercell used to calculate energy differences when Sn substitutes Mg in the layer of α-Mg matrix that is immediately adjacent to the habit plane of β′.(b)Atomic arrangement in the layer of α-Mg matrix and the habit plane of β′marked by red arrows in(a),viewed along[0001]α.Numbers 1 and 2 represent two different Mg positions in the layer of α-Mg matrix.(c)Energy difference when one Sn atom substitutes one Mg atom at position 1 or 2 in(b).(d)Perspective view of β′and its nearest layers of α-Mg matrix(planes C and B)showing the ordered distribution of Mg atoms at position 1 within the layers of α-Mg matrix along[2ˉ1ˉ10]α.Yellow ball in(d)represents Mg atom in position 1.(e)Valence electron charge density plot showing charge distribution on a(ˉ12ˉ10)α plane when one Sn atom substitutes one Mg atom at position 1.Dark and light green balls represent Mg atoms at different height along[ˉ12ˉ10]α.Two black dashed lines indicate the outermost layers of β′.A,B and C represent three different closely packed planes.

Since the ordered Sn distribution occurs at the early stage of ageing,it would significantly affect the nucleation and thickening ofβ′.As interfacial energy is the most important factor affecting precipitation nucleation,we calculated the interfacial energies before and after the ordered Sn distribution occurs.The interfacial energy is 67.0 mJ/m2for the absence of Sn distribution,but decreases to 58.6 mJ/m2after a quarter of Mg atoms at positions 1 are substituted by Sn atoms.This indicates that the Sn distribution decreases the interfacial energy of theβ′/α-Mg interface.As a result,the presence of this Sn-rich layer would reduce activation energy barrier to the nucleation ofβ′precipitate and consequently enhance its nucleation rate.This is similar to the Zn segregation in Mg2Sn/α-Mg interfaces in Mg-Sn-Zn alloys[23],and the Zn or Ag segregation in Mg17Al12/α-Mg interfaces in Mg-Al-Zn or Mg-Al-Ag alloys[19,21].

Fig.4.(a,b)Schematic diagrams showing supercells used to calculate energy change during thickening of four-layer β′structures.Supercell in(a)does not include Sn distribution in the layer of α-Mg matrix immediately adjacent to β′,while supercell in(b)does,as indicated by blue hollow arrows.Parts of Mg matrix at the top and middle of the supercells are omitted to get a clear visualization of β′and its nearest layer of α-Mg matrix.(c)Energy change curves for the β′thickness increase from four-layer in(a,b)to six layers by 1/3[01ˉ10]α shear on the layer of α-Mg matrix(marked by blue hollow arrows),respectively.(d,e)Atomic arrangement in the habit plane of β′and its nearest layer of α-Mg matrix,marked by red arrows in(b),viewed along[0001]α,(d)before and(e)after 1/3[01ˉ10]α shear.

To study the effect of the Sn-rich layer on thickening ofβ′,we investigated its influence on the occurrence of 1/3<01ˉ10>αshear in the layer of theα-Mg matrix immediately ahead of theβ′/α-Mg interface,asβ′thickens by the shear[10].Fig.4a,b illustrated schematically supercells used to calculate energy changes associated with the thickening of two four-layerβ′structures without and with Sn atoms in the shear occurrence layer,respectively.Fig.4c shows the energy change curves during the occurrence of 1/3[01ˉ10]αshear without and with the Sn distribution.In the absence of Sn distribution,thickening a four-layerβ′needs to overcome an energy barrier,i.e.maximum value of the curve,of 63.0 mJ/m2and reaches to a minimum value of-10.8 mJ/m2.When Sn atoms orderly distribute in the shearing layer,the energy barrier is increased to 64.4 mJ/m2,and the thickening of the four-layerβ′structure would require an extra energy of 60.4 mJ/m2.This indicates that the ordered Sn distribution can hinder the occurrence of 1/3[01ˉ10]αshear,i.e.,thickening ofβ′,which is unexpected since the Sn distribution within the layers ofα-Mg matrix immediately adjacent toβ′can increase the Sn concentration and provide the chemical environment forβ′thickening.To understand this phenomenon,Fig.4d presents the atomic arrangements within the habit plane(plane A)ofβ′and its nearest layer ofα-Mg matrix(plane C),marked by red arrows in Fig.4b,along[0001]α.The orderly distributed Sn atoms are at the centers of equilateral triangles constituted by three Mg atom columns,i.e.,positions 1 in Fig.3b.Once the 1/3[01ˉ10]αshear has occurred on the layer of theα-Mg matrix,all atoms within that layer would be moved from positions C to positions B,Fig.4e,and the Sn atoms are moved to the centers of equilateral triangles constituted by two Mg atom columns and one Sn atom column,i.e.the positions 2 in Fig.3b.As the distribution of Sn is energetically favored at positions 1,but is energetically unfavored at positions 2,Fig.3c,this 1/3[01ˉ10]αshear moving the Sn atoms from positions 1 to positions 2 would naturally increase the system total energy.This explains why the ordered Sn distribution within the habit plane ofβ′hinders thickening ofβ′precipitate.

4.Conclusion

In summary,ordered distribution of Sn atoms occurs in the layer ofα-Mg matrix immediately ahead of theβ′/α-Mg interface at the early stage of ageing of Mg-9.8wt.%Sn alloy.The Sn atoms substitute Mg atoms located at the centers of equilateral triangles constituted by three Mg atom columns lying parallel to[0001]αin the habit plane ofβ′.First-principles calculations suggest that the ordered Sn distribution is energetically favored,and it decreases the interfacial energy of theβ′/α-Mg matrix interface and impedes the occurrence of 1/3[01ˉ10]αshear and thus thickening of theβ′precipitate.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work is financially supported by National Natural Science Foundation of China(52101167 and 52071033),Natural Science Foundation Project of CQ(cstc2020jcyjmsxmX0832),and the Fundamental Research Funds for the Central Universities(2020CDJ-LHZZ-085).Project also supported by State Key Laboratory of Powder Metallurgy,Central South University,Changsha,China.This work was supported in part by the High Performance Computing center of the Central South University.JFN acknowledges the support from the Australian Research Council and computational resources provided by the Australian Government through Pawsey under the National Computational Merit Allocation Scheme and the use of the National Computational Infrastructure.