Ehsn Bhrmi Motlgh ,Peter A.Lynch,b ,Thoms Dorin ,Pvel Cizek ,Alirez Ghderi ,Mtthew R.Brnett ,Sitrm R.Kd,*

aInstitute for Frontier Materials,Deakin University,75 Pigdons Road,Waurn Ponds,VIC 3216,Australia

b CSIRO,Manufacturing,Geelong 3216,Australia

Abstract In-situ transmission X-ray diffraction based compression deformation experiments are performed to study the twinning behaviour in asextruded (non-aged) and peak-aged Mg-7Sn-3Zn-0.04Na alloy.The axial lattice strains were measured in the parent grains,twins and the precipitates as a function of applied stress.The critical shear stress for achieving 5% twinning was found to be increased by～26MPa by the presence of 7% of Sn and by～50MPa by the presence of the particles formed after 10 h of aging.The evolution of twin volume fraction with plastic strain is similar in both non-aged and aged conditions,indicating no change in the relative activities of slip and twin in the ideally oriented (10ˉ10) parent grains.Predictions made in previous studies of twin thickening stresses and twin bypass stresses agree reasonably well with the measured values,given the experimental error.Considerable relaxation was seen in the precipitate lattice reflections This is attributed to relaxation effects continuing during X-ray data collection.Macroscopic fl w curves confir that precipitate hardening in the present system is particularly sensitive to relaxation effects.This is likely to be an important consideration for fatigue loading of precipitate hardened samples.

1.Introduction

In precipitate strengthened Mg alloys,slip and twinning modes harden to differing extents.The difference depends on the morphology,orientation and size of the precipitates [1,2].Common precipitates in Mg alloys include prismatic plates(in Mg-RE alloys),basal plates (in Mg-Al-Zn alloys) and prismatic rods (in Mg-Zn alloys).The expected impact of these particles on relative strengthening can be readily established from geometrical considerations assuming the particles do not deform.That is,the most hardened mode will tend to be the mode with the smallest inter-particle spacings on the plane of the deformation mode.Thus,prismatic plate precipitates are expected to strengthen the basal slip more than the prismatic slip [3],while basal plate precipitates should show the opposite effect,strengthening prismatic slip to a larger extent than basal slip [2,4].Basal plate precipitates will tend to be effective at hardening againsttwinning [4-6] and prismatic rod precipitates should exhibit effective hardening of both slip and twin modes that intersect the precipitate long axis [7-9].A near equiaxed precipitate,of course,should impact on all modes similarly.This,however,has not been tested.The present study examines the effect of Mg2Sn precipitates,which can adopt a relatively low aspect ratio in magnesium alloys while appearing in quite high number densities[10-12].Alloys hardened by these precipitates show appreciable hardening increments (by up to 30 VHN on a 45 VHN base),high temperature stability and improved creep resistance [10].The present article focusses on the impact of these precipitates ontwinning in Mg-Sn-Zn-Na.

The interaction of dispersions of precipitates with deformation twinning in magnesium alloys has been reviewed in a number of places recently [13-15].A point of contention has arisen over the role of the precipitate induced ‘back stress’[7,9,16].The back stress is a uniform stress that develops in the matrix to balance the high stresses that arise in ‘hard’non-deforming precipitates.Simply put,the hard precipitates accept more of the applied load than the matrix does so the stress available to drive twinning in the matrix is less than the applied load.The stress in the matrix is given by the applied stress minus the back stress.Analytical,FEM and fullfiel calculations suggest that the stress developed in the nondeforming precipitates,and hence the balancing back stress in the matrix,should be substantially relaxed during deformation due to glide in the vicinity of the precipitates[13,17,18].Thus only in certain cases will the back stress account substantially for the observed increment in the applied stress required for twinning dominated deformation [13].Instead,Orowan type hardening of non-deforming particles has been proposed to exert a significan impact on twin growth,either in the processes of twin propagation or thickening [1,7,8,14,15].

The problem has been recently examined in considerable detail using full-fiel simulations [13].It is seen that the stresses required for deformation dominated by the traverse of a {10ˉ12} twin boundary through an array of nondeforming particles increases with particle fraction,particle refinement particle (plate) aspect ratio and proximity of the particle (plate) habit plane to the twin plane.In the simulations,the lattice dislocation density was frequently found to follow the same trend.This reflect the role of lattice dislocation activity in accommodating the misfi stresses generated when a twin interacts with a non-deforming particle.Appreciable hardening of the twin mode was observed in cases where the back stress was negligible,pointing to the role of Orowan-like hardening effects (and associated dislocation activity).In other instances,the back stress rose to values as high as～40% of the observed increase the stress associated with twin boundary movement.In general,the back stress effect was seen to be more dominant when the twin aspect ratio was high and when the angle between the precipitate plates and the twin plane was in the vicinity of 45deg [13].Despite this advance in understanding,we are still unable to confi dently generalize across systems and precipitate species.It is unclear,for example,what we should expect in the present case of Mg2Sn precipitates.

There is clearly a need to pay particular attention to the stresses born by the reinforcing particles.This is something that can readily be established,as a volume average,using diffraction techniques [6,19].A number of us have recently[6] used synchrotron X-ray diffraction to monitor the evolution of precipitate lattice strains during in-situ compression of alloy AZ91.We observed that plate shaped Mg17Al12precipitates habiting the basal plane develop significan forward stresses.Battacharyya et al.[20]applied a multi-phase Elasto-Visco-Plastic Self-consistency (EVPSC) code to the problem and found that the precipitate lattice strains could be reproduced without the introduction of any particular local relaxation effects.That is,the precipitate stresses follow,in an average sense,what one would expect from homogeneous plasticity acting to relax part but not all of the precipitate forward stress.In the present study,we set out to measure the forward stresses developed within Mg2Sn precipitates in material deformed in compression,to activate copious amounts of twinning.

Low aspect ratio precipitate rod Mg2Sn particles were produced by aging of an extruded Mg-7Sn-3Zn-0.04 Na (in wt.%) alloy.The precipitates are characterised using Smallangle X-ray scattering (SAXS) and Transmission Electron Microscopy (TEM) studies.The critical stresses for twinning were experimentally measured using synchrotron X-ray diffraction during in-situ compression deformation performed along the extrusion direction.

2.Materials and methods

The Mg alloy used in the current study has a nominal composition of Mg-7.3Sn-3.4Zn-0.04Na (in wt.%).The alloy was cast into a～30mm in diameter billet,which was homogenised using a two-step heat treatment (335°C for 2 h followed by 530?C for 20 h under Argon atmosphere) [10].The solidus temperature for this alloy composition is approximately 550°C.Following homogenization,the billets were quenched in water to suppress the precipitation of any Mg-Zn intermetallics or Mg2Sn precipitates.The homogenised billets were then hot extruded at 475?C from 30mm to 5mm diameter (extrusion ratio～ 30) using a MTS 385 KN universal testing machine.To prevent the non-isothermal precipitation and grain growth,the extrudates were quenched in water at the exit of the extrusion.Small samples were cut along the extrusion direction of the extrudate for aging heat treatment at 200°C under argon atmosphere.

To determine the volume fraction of precipitates,Small Angle X-ray scattering (SAXS) measurements were carried out in a SAXS/WAXS beamline at the Australian Synchrotron.X-rays of beam dimensions approximately 100×200μm and energy of 12KeV was incident on the sample perpendicular to the extrusion direction.The scattered Xrays from the sample were recorded on Pilatus 1M area detector.The measured data was reduced using the ScatterBrain software to extract the intensity changes with the scattering vector,q,denoted by I(q).

The morphology of the precipitates and their orientation relationship (OR) with magnesium matrix was determined in section perpendicular to extrusion direction using JEOL JEM 2100F FEG transmission electron microscopy (TEM) operating at 200kV.The TEM foils were obtained by punching small discs of 3mm from the thin foils (～ 60 μm) and by grinding using dimple grinder.Finally,the dimpled region was made transparent to electrons by thinning using Gatan 691 Precision Ion Polishing unit.

Fig.1.a) The EBSD Microstructure of the as-extruded alloy with the grains coloured according to extrusion direction inverse pole figur (inset) and b) the contour plot of ED IPF shows the strength of texture.

The effect of aging on the CRSS for basal slip and tensile twinning activities during compression deformation was carried out using in-situ transmission based synchrotron Xray diffraction technique in the Powder diffraction (PD) beam line at Australian Synchrotron.The diffraction geometry set up is similar to Kada et al.[6].The in-situ compression tests were performed with a strain rate of 2×10-4s-1at room temperature.The compression samples of 2.5mm in diameter and 4mm high were deformed such that the compressive forces act along the extrusion direction using a micro deformation stage equipped with a 5kN load cell.Monochromatic X-rays of energy～21KeV (=0.58998 °A wavelength) and a beam cross section of 3×2 mm2were incident on the sample perpendicular to the loading direction.The transmission diffracted X-rays were detected by a linear microstrip Mythen detector [21],which enabled the measurement of the (hkil)reflection from 5 -85?range of 2θsimultaneously.To improve the grain sampling statistics,the compression sample was rocked from -8° to +12° about the direction perpendicular to incident beam and applied load direction.For X-ray data collection,the samples were held at a constant extension at the desired applied load for～480 s,the time needed for two complete rockings.The obtained reflection are thus averages.However,we will refer to the reflection in terms of a diffraction vector in the ‘a(chǎn)xial’ direction of the loaded sample.

X-ray line profil analysis was carried out using TOPAS software [22].Following the calibration and peak fittin methodology reported in Kada et al.[6,23],the diffraction geometry was calibrated using LaB6SRM660b material[24] and single peak fittin was carried out by fittin individual peaks using Pseudo-Voigt function.The extracted peak parameters such as peak position,2θhkiland integrated intensity,Ihkilare then used to calculate the elastic lattice strain and twin volume fraction changes with applied stress.The elastic lattice strains at a particular applied loadεhkilis calculated by the relative change in lattice spacingdhkilfrom the strain-free lattice spacinggiven by

The twin volume fraction in the grains contributing toparent grain reflections were calculated from the relative change in the intensities of theand (0002) reflections according to the relation given by

where,TVF(hkil)is the twin volume fraction in a given (hkil)reflectionIis the intensity of the (hkil) reflectio corrected for Lorentz polarization and structure factor at any applied load,Iois the corrected intensity at nominal applied load.It is assumed that the parent to twin volume change is due to one-to-one flipping due to the 86.4° reorientation of basal poles in magnesium.

3.Results

3.1.Microstructure characterisation

The EBSD microstructure of the as-extruded (non-aged)alloy is shown in Fig.1a.The microstructure consists of equiaxed grains with a mean linear intercept grain size of～37μm.The grains are coloured based on the inverse pole figur (IPF)shown in the inset.It can be seen that the majority of the grains are blue and green in color showing the characteristic extrusion texture for magnesium,with theandplane normals aligned parallel to the extrusion direction.The contour plot of the extrusion direction inverse pole figur (Fig.1b) shows a Inverse Pole Figure (IPF) density of(10ˉ10)grains～9 times of the random orientation.This texture favours tensile twinning during compression test performed along the extrusion direction [25].

Fig.2.a) The intensity distribution of the scattered X-rays during Small Angle X-ray Scattering are plotted as a function of scattering angle,|→q|.b) The raw data is replotted in the form of Kratky convention to determine c) precipitate volume fraction,Guinier radius,and d) the number density of Mg2Sn precipitates as a function of aging time.

The Mg alloy exhibited a steady increase in the hardness during aging at 200°C for up to 24 h due to the formation of Mg2Sn precipitates [26].SAXS measurements were performed to quantify the size and volume fraction of the Mg2Sn precipitates as a function of aging time (Fig.2).The raw SAXS patterns (inset in Fig.2a) are radially integrated to extract intensities (I) as a function of scattering angle,q.Fig.2a shows thevalues for all the aging conditions.The increase in the spread of intensity to higher scattering angles following 2h of aging,clearly indicates the formation of precipitates.In order to determine the respective volume fraction,thedata is replotted in the form of Kratky convention (Iq2vsq) in Fig.2b.The area under Kratky plot is directly proportional to the precipitate volume fraction.However,the asymmetry in the Iq2vsqindicate the presence of two distinct type of precipitate types in the current alloy.TEM investigations shows that the majority of precipitates are of Mg2Sn and a small fraction of Mg-Zn based precipitates are also seen in the microstructure (Fig.3).The smaller Mg-Zn precipitates contribute more to scattering at higher values of‘q’ leading to a slight asymmetry in the Kratky plot.Considering the apparent differences in the electronic densities of the precipitates,the volume fractions of the two types are deconvoluted based on the asymmetry in the Kratky plot (using the commercial IRENA software package) [27].Fig.2c shows the change in volume fraction and the Guinier radius of the Mg2Sn precipitates as a function of aging time.It can be seen that the precipitate volume fraction and size increase with aging time.Following 10 h of aging,approximately 3.8±0.3vol.% of Mg2Sn precipitates were formed with an equivalent sphere radius of～19nm.However,the number density of precipitates,obtained by dividing the precipitate volume fraction with the equivalent spherical volume of precipitateremained relatively constant (Fig.2d).It is known from atom-probe tomorgraphy studies that heterogeneously formed Na clusters act as nucleation sites for Mg2Sn particles.[28].The current results also revealed that the number density of Mg2Sn precipitates are unchanged with aging time.This is believed to be due to the saturation of the nucleation of Mg2Sn precipitates at pre-existing Na clusters formed early in the aging treatment [12].The number density of precipitates is approximately 1.35×1021m-3following 10h of aging.

Fig.3.a) TEM bright fiel micrograph and b) corresponding EDS color mapping of Mg2Sn (green) and Mg-Zn (red) precipitates.c) TEM image showing the T-shape configuratio of the precipitates.

Fig.4.(a) TEM bright-fiel micrograph,obtained along the [0001]Mg direction,showing uniform distribution of Mg2Sn particles,(b) high resolution and high magnificatio image of Mg2Sn particles,labelled 1 and 2,having distinct ORs and elongation directions.(c) and (d) Nano-beam diffraction patterns,together with their indexing,corresponding to the particles 1 and 2,respectively,showing the [0001]Mg and [110]Mg2Sn zone axes.The fille and open circles represent diffraction spots of the Mg matrix and Mg2Sn particle,respectively.

Fig.3a,b shows the bright fiel STEM micrograph and the corresponding EDS colour mapping of the Mg2Sn and Mg-Zn precipitates formed after 10h of aging.The images were taken with beam direction close to [2-1-10].There is no obvious segregation of zinc observed at the Mg2Sn interface,however,using atomic resolution TEM,Liu et al.[29] observed atomic scale zinc segregation for a similar alloy.The two kinds of precipitates exhibit a characteristic T-shape configuratio uniformly distributed in the magnesium matrix.The T-shape configuratio was reported previously in the literature[30,31].The mean width (d) and length (lrod) of the Mg2Sn precipitates calculated from the TEM images are 25±7nm and 75±20nm.The Guinier radius obtained in the SAXS analysis evidently falls closer to the smaller dimension of the particles.Fig.3c shows relatively low magnificatio image of the precipitates taken in general orientation without tilting.Precipitate free zones are also seen at the grain boundary region.

Fig.4a and b shows the high magnificatio bright fiel TEM micrographs viewed down the[0001]Mg direction.The microstructure reveals Mg2Sn precipitate particles with a lathor rod-like morphology,uniformly distributed in the Mg matrix.This is quite consistent with the literature[10]and shows that a majority of Mg2Sn particles are aligned with their long axis along one of thedirections.

The orientation relationship (OR) of the precipitates with Mg matrix is confirme using nano-beam diffraction in TEM(Fig.4c,d).Two types of ORs,each associated with the particular particle elongation direction,are present.Fig.4c and d show an example of a diffraction analysis for two Mg2Sn particles marked 1 and 2 in Fig.4b.The analysis reveals that the particle labelled 1 which is elongated in the directiondirection,exhibits an OR:(0001)Mg// (110)Mg2Snand// [001]Mg2Sn.Whereas,the particle labelled 2 exhibits an OR:(0001)Mg// (110)Mg2Snandand the particle elongation direction isBoth the above ORs between Mg2Sn particles and the Mg matrix and the corresponding particle elongation directions are consistent with those reported previously[30,31].

Fig.5 shows typical stress-strain curves of the non-aged and aged samples obtained during the in-situ compression test.Prior to the in-situ measurements,the machine compliance of the deformation stage was determined by performing ex-situ compression loading and by simultaneously monitoring the strain on the compression sample using a Instron video strain measurement system [6].Fig.5 reveals that the yield strength at 0.2% offset increased by 60MPa following 10h of aging.Relaxation in the stress values were observed during the holding time for X-ray data collection,with the drop in the stress (～15MPa) significantl higher in the aged alloy.This is an interesting effect also seen in other age hardened alloy systems such as Mg-Al-Zn [6,32].We have also seen it in Mg-Zn.Evidently,the presence of non-deforming precipitates stimulates local plastic activity in the highly stressed regions that surround the precipitates and this is highly rate sensitive,manifesting as a creep like phenomenon during the measurements.We will need to return to this observation below when interpreting our measurements of the precipitate forward stresses.

Fig.5.In-situ compression stress-strain curves of the non-aged and aged alloys.The data points correspond to the applied loads where the XRD data is collected.

3.2.Matrix reflection

Fig.6a and b shows the evolution of elastic lattice strains in the(hkil)reflection with planes normal to the applied load(extrusion direction).The elastic lattice strain values are reproduced within the strain resolution of ±2×10-4based on three repeated in-situ compression tests [33].The anticipated Young’s modulus of 45GPa is reproduced at low strains in thereflections Twin reflection ((0002),andfirs appear at an applied stress of～-65MPa in both non-aged and aged samples.The lattice strains in thefollow very closely to the elastic line over the entire loading range,which indicates the dominance of these reflec tions in the texture.Thus,the axial stress within these grains is equivalent to the applied axial stress.Fig.6c shows the change in twin fraction in thereflection as a function of the applied stress.Although twin reflection are seen to appear at stresses considerably lower than the macroscopic yield stress,the twin fraction is only seen to increase significantl with applied stress once yielding is underway (Fig.6c).This is quite consistent with other studies [34,35],which show a close correlation between yielding and the onset of twinning activity.The twinning stress (macroscopic stress where the very firs twin reflection are observed) is highly sensitive to the presence of any microstructural or geometrical irregularity within the sample.It is thus not a sufficientl robust term for analysis.Instead,for the present purposes,we take a twin fraction threshold of 5% as an indication of the ‘twinning stress’ in thereflections In the non-aged sample,we determine the axial twinning stress to be 88 +/-5MPa and after aging,152 +/-5MPa.

To isolate the impact of precipitation,the effect of solute depletion must be considered.This requires a reference value for the effective critical resolved shear stress(CRSS)for twinning in pure Mg for a similar grain size [36],an estimate of which is 18 +/-6MPa [37].Applying a scalar Schmid factor analysis (SF=0.5) to the twinning stress for thereflection in the present non-aged condition,we obtain a value of 44±5MPa.Thus we see that the presence of 7wt% Sn(neglecting the effect of solute Zn [38]) contributes 26 +/-11MPa to the critical stress fortwinning.According to the phase diagram of Mg-Sn,the equilibrium level of Sn in the matrix following aging at 200°C is 0.6wt.% Sn.Assuming a square root solute strengthening term,we can estimate that this level of solute Sn contributes 7.5 +/-3MPa to the twinning stress in the aged condition.Thus,after aging,the resolved shear stress fortwinning attributable to the precipitates themselves can be estimated as 76±3MPa -18±6MPa -7.5 +/-3MPa=50.5±12MPa.

Fig.6d plots the twin fraction in thereflection against plastic strainThis gives an indication of what effect,if any,aging has upon the balance between slip and twinning in the dominantreflections Clearly,the difference between the twin fractions between the non-aged and aged samples is negligible in the present case.This contrasts with previous measurements made on alloy AZ91 (also shown in Fig.6d),which show a marked drop in twin fraction with aging [39].In that case,aging facilitated slip while retarding twinning.However,there is no evidence for a similar relative change in mode activity in the current material;it thus seems that both the slip and tensile twinning modes experience similar increases in critical stresses to activate and sustain them.

The elastic strain level in the twin reflection is low -even zero in one case -when they firs appear in the diffraction profile This reflect the stress drop that is often seen to accompany twinning.It arises from the interaction between the misfi back stress in the twin and the applied stress (see[17,40-43]).Fig.6 reveals that as the level of applied stress is increased,the twin reflection also increase in the degree of axial elastic strain they bear.The twins increasingly behave like grains.It is interesting to note that the (0002) reflec tions,however,accumulate axial strain more rapidly than thereflection such that they become appreciably harder in the axial direction.One consequence of this is that at higher stresses,the difference in axial elastic strains born by theparent reflection and the (0002) daughter reflection diminishes significantl .

3.3.Precipitate reflection

Fig.7 shows the elastic lattice strains corresponding to the(111),(200) and (220) reflection of the cubic Mg2Sn precipitates.The Young’s modulus of the precipitate reflection calculated from the elastic compliance matrix (C11=83.71,C12=39.79,C44=21.69) is～58GPa [44].The lattice strains in Fig.7 initially follow a common slope equivalent to this Young’s modulus.At an applied stress of approximately 75MPa,the (200) precipitate reflection in Fig.7 begin to accumulate higher lattice strains compared to the (111) and(220) reflections which depart only slightly from the elastic prediction.This is due to the plasticity in the matrix grains either due to onset of basal slip (See (10-13) matrix reflec tions in [45]) or due to premature twinning (Fig.6a,b).This causes a relaxation in lattice strain in the respective matrix orientations thereby shedding load to the relatively harder precipitates.Due to the cubic symmetry of precipitates,the (200)reflection are soft compared to (111) and (220).Therefore,the (200) reflection bare the load shed by the surrounding matrix and accumulates more lattice strains.At the point of macroscopic yielding,the lattice strains in these three reflec tions correspond to forward axial stresses of between 5 and 40MPa in the precipitate reflections Correcting for precipitate fraction (3.5%) and Schmid factor,these stresses correspond to negligibly small uniform matrix resolved back stresses of between 0.1 and 0.7MPa.

Fig.6.The evolution of elastic lattice strains along the matrix and twin reflection in a) non-aged and b) aged alloy.The change in the twin volume fraction in the (10ˉ10) axial reflection is shown as a function of c) applied stress and d) the macroscopic plastic strain.

Fig.7.The evolution of the elastic lattice strains along the Mg2Sn precipitates in the aged Mg-Sn-Zn-Na alloy.

With further increase in applied load,the lattice strains in the (200) and (111) precipitate reflection decrease,while the lattice strains in the (220) reflection remain unchanged.The relaxation in precipitate lattice strains is most likely a consequence of plastic relaxations in the vicinity of the particles.During deformation,this could occur by a ‘rotational’fl w [7,46,47].During the hold period,static processes such as climb or even some degree of slip could be active,locally and this could facilitate relaxation.Precipitate shearing[48]has been reported in other age-hardened Mg alloys.However,post-mortem TEM investigation of the deformed precipitates (Fig.8) reveals no indication of precipitate shearing or plasticity in the current alloys.Although no diffraction pattern was acquired for Fig.8,the literature suggests no significan change in the orientation relationship between precipitate and matrix during deformation [46,49].Upon subsequent unloading,the lattice strains in the particles drop nearly but not exactly along the expected elastic lines,leaving a range of positive residual strains in the precipitates,which shows that relaxation of precipitate stresses was not via decohesion of particle or the interface,consistent with lack of any evidence of these mechanisms in the microstructure.

Fig.8.Bright fiel TEM micrograph of an aged and deformed Mg-Sn-Zn-Na alloy.The beam direction is along [0001]Mg.The precipitates within the twin do not show any signs of shear or plasticity.

4.Discussion

In-situ transmission X-ray diffraction was employed to measure the axial lattice strains in the grains and precipitates,and subsequently estimate the critical stresses for active deformation mechanisms during in-situ loading.Some comments are firs in order in regards to the experimental uncertainties.Based on the repeated measurements of macroscopic stress-strain data,the estimated uncertainty in the applied stress was less than 5MPa.Further,during holding time for X-ray data collection for the aged alloy,the applied stress drops by～15MPa.So although we report the maximum value(after [32]),there are relaxation effects that are not captured in the present analysis and which are more prevalent in the data for the aged condition than in the non-aged data.The lattice strain resolution for a given reflectio depends on the intensity and shape of the reflections the accuracy of the strain-free reference lattice spacing (do),and the accuracy of the profil fitting Based on the optimised calibration methodology (discussed in methods),the peak positions are reproduced with an uncertainty of ± 0.0025°2θfor consecutive in-situ loading tests.This equals to an uncertainty in thedoof～±1.6×10-4which translates to～7MPa in axial stress.However,the lattice strains in the multiple order reflection from the same families of grains are reproduced to much higher certainty of ±2×10-5(e.g.see (0002) and (0004) reflection in Fig.6a,b).While the stresses are well captured by the technique,the challenge is in identifying the time step corresponding to the onset of a given mechanism,which in this case is twinning.It is this challenge that accounts for the rather large values of experimental uncertainty in the present values,coupled with the need to subtract values,which of course compounds the uncertainty.

Aging of the present extruded samples produced a dispersion of precipitates dominated by Mg2Sn but with also the presence of a number of Zn containing rod shaped particles that formed upon the Mg2Sn precipitates,as has been previously reported [10].The Zn rich particles are present in volume fractions less than an order of magnitude lower than for the Mg2Sn precipitates and are thus neglected in the following analysis of the dominant mechanisms.

The recent simulation study carried out by Liu et al.[13] (for the ideal case neglecting phenomena relating to elastic differences between the particle and the matrix) reported a strength increment of～27 -35MPa fortwin thickening through a fiel of equiaxed particles with the approximate fractions and sizes employed in the present work[13].The experimental value obtained in the present study -50.5±12MPa -falls a little higher than this range.The difference may relate to effects stemming from the differences in the elastic moduli between the matrix and the particles.This is readily incorporated in principle into the simulation approach adopted in [13],what is not clear is if the thickening of a twin is the stress controlling step for thetwinning mode in magnesium [37].

One of us recently considered the propagation step [1].For a mean particle dimension of 50nm (dmean) and volume fraction of 0.035 (f),the interparticle spacing (λ) calculated using the equation,is 170nm[1].This value can be employed to estimate the stress expected for a thin propagating twin to bypass an array of non-deforming particles [14]:

where,τois the reference stress in the absence of particles(i.e.CRSS of the aged alloy minus the contribution of precipitates,18+7.5=25.5MPa),Gis the shear modulus (17GPa),νis Poissons ratio (0.3),is the harmonic mean of interparticle spacing,λand particle width,is the number of leading twinning dislocations that bow between the particles andγis the twin surface energy (0.12J/m2).For a particle dimension of 50nm,the value ofn′bis seen in dislocation dynamics simulation to be around 2.5 nm [14].Using these values gives the estimateΔτp=43MPa.This value agrees reasonably well with measurements and with the simulation values [13],given the errors involved.The need to estimate the number of bowing dislocations is a large source of error in Eq.(3) and this hampers true predictability.Differentiating between the importance of twin thickening and twin propagation in this case will require spatially resolved real-time in-situ testing.

Although not apparently contributing significantl to the observed twinning stresses,it is necessary to consider the drop in axial stresses seen in the precipitates at higher levels of applied stress.The axial internal stress present in the(111) and (200) precipitate reflection drop from～200MPa to a level lower than the softest twinning reflectio (164MPa).Inspection of the precipitate axial strains reveals that the observed strains are less by～0.0025 than the strains that would be expected if the precipitates accepted load during deformation in a linear manner (dashed line in Fig.7).There is no sign of shearing,plastic deformation,fracture or voids at the precipitate-matrix interface.

We now recall that appreciable lowering of the macroscopic applied stress is seen to accompany the experimental measurements for the aged but not the non-aged samples(Fig.5).It is proposed that the drop in the internal stress in the precipitates at high levels of applied load is due to additional thermally activated relaxation that occurs while the deformation is halted to allow measurement of the diffraction spectra.To perform a rough calculation,we note that a drop in lattice strain of 0.0025 corresponds to a drop in axial stress of～145MPa.For a precipitate fraction 3.5%,this corresponds to an expected relaxation in the applied axial stress of～5MPa.

In Fig.5,the applied stresses in the aged sample are seen to drop by～15MPa during the measurement.Given that the observed lattice strains are an integral over time,it is quite reasonable to assume that the actual drop in lattice strain will exceed the present estimate of 0.0025 (at least for the (111)and (200) reflections) Thus it is quite conceivable that the drop in macroscopic stress seen in Fig.5 during the measurement and the low lattice strains seen in the particles at higher strains both reflec the same phenomenon.That is,precipitate hardening in the present material is subject to enhanced relaxation effects that become particularly obvious when deformation is halted while under load.This is likely to be an important consideration for fatigue loading.

5.Conclusions

The Mg-7Sn-3Zn-0.04Na (wt.%) alloy was cast and extruded to produce characteristic extruded microstructure with a grain size of～37μm.The extruded alloy was aged at 200 °C to produce Mg2Sn precipitates with an approximate volume fraction of 0.035,as determined by SAXS investigations.In-situ synchrotron X-ray diffraction measurements were performed to investigate the evolution of axial lattice strains in both twin and precipitates during compression along extrusion direction.

·The critical shear stress for achieving 5% twinning was found to be increased by～26MPa by the presence of 7%of Sn and by～50MPa by the presence of the particles formed after 10 h of aging.The errors are however large,amounting to approximately plus or minus one quarter of the measured values.

·The evolution of twin volume fraction with plastic strain is similar in both non-aged and aged conditions,indicating no change in the relative activities of slip and twin in the ideally oriented (10ˉ10) parent grains.

·The observed strength increment of 50MPa due to precipitates was estimated using Orowan strengthening mechanism for twin propagation (Δτp).The predictions made in previous studies of twin thickening stresses and twin bypass stresses in the current study agree reasonably well,given the errors present.More sophisticated measurement techniques will need to be developed to enable differentiation between active strengthening mechanisms.

·Relaxation of the internal stress within the particles is proposed to continue during the hold period required for measurement of the x-ray spectra.This is manifest in lower than expected precipitate lattice strains and an appreciable drop in the applied stress during the measurement.No drop in applied stress is seen during measurement of the nonaged samples and it is proposed that precipitate hardening in the present system is particularly sensitive to relaxation affects,which may prove important for understanding fatigue.

Declaration of Competing Interest

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

Acknowledgments

This research was supported by the Australian Research Council’s Discovery research grant (DP150101577).This research was undertaken in part on the powder diffraction and SAXS beamline at the Australian synchrotron,part of ANSTO.The Deakin University’s Advanced characterisation facility is acknowledged for the use of electron microscopes.