Composition of β ″ precipitates in Al–Mg–Si alloys by atom probe tomography and firstprinciples calculationsHåkon S. Hasting, Anders G. Frøseth, Sigmund J. Andersen, Rene Vissers, John C. Walmsley, Calin D.Marioara, Frédéric Danoix, Williams Lefebvre, and Randi Holmestad Citation: Journal of Applied Physics 106, 123527 (2009); doi: 10.1063/1.3269714 View online: http://dx.doi.org/10.1063/1.3269714 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/106/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Early precipitation during cooling of an Al-Zn-Mg-Cu alloy revealed by in situ small angle X-ray scattering Appl. Phys. Lett. 105, 101908 (2014); 10.1063/1.4894768 Alloying effects on the elastic parameters of ferromagnetic and paramagnetic Fe from first-principles theory J. Appl. Phys. 110, 073707 (2011); 10.1063/1.3644907 Combined electron beam imaging and ab initio modeling of T 1 precipitates in Al–Li–Cu alloys Appl. Phys. Lett. 98, 201909 (2011); 10.1063/1.3590171 The influence of composition and natural aging on clustering during preaging in Al–Mg–Si alloys J. Appl. Phys. 108, 073527 (2010); 10.1063/1.3481090 Nanobelts in multicomponent aluminum alloys Appl. Phys. Lett. 93, 093115 (2008); 10.1063/1.2978405

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Composition of �� precipitates in Al–Mg–Si alloys by atom probetomography and first principles calculations

Håkon S. Hasting,1 Anders G. Frøseth,1 Sigmund J. Andersen,2 Rene Vissers,1

John C. Walmsley,1,2 Calin D. Marioara,2 Frédéric Danoix,3 Williams Lefebvre,3 andRandi Holmestad1,a�

1Department of Physics, Norwegian University of Science and Technology NTNU, Høgskoleringen 5,Trondheim N-7491, Norway2SINTEF Materials and Chemistry, Trondheim N-7465, Norway3Groupe de Physique des Matériaux, Université de Rouen, UMR CNRS 6634, Saint Etienne du RouvrayCedex 76801, France

�Received 15 July 2009; accepted 3 November 2009; published online 29 December 2009�

The composition of �� precipitates in an Al–Mg–Si alloy has been investigated by atom probetomography, ab initio density functional calculations, and quantitative electron diffraction. Atomprobe analysis of an Al-0.72% Si-0.58% Mg �at. %� alloy heat treated at 175 °C for 36 h shows thatthe �� phase contains �20 at. % Al and has a Mg/Si-ratio of 1.1, after correcting for a localmagnification effect and for the influence of uneven evaporation rates. The composition differenceis explained by an exchange of some Si with Al relative to the published ��-Mg5Si6 structure. Abinitio calculations show that replacing the Si3-site by aluminum leads to energetically favorablecompositions consistent with the other phases in the precipitation sequence. Quantitative electronnanodiffraction is relatively insensitive to this substitution of Al by Si in the ��-phase. © 2009American Institute of Physics. �doi:10.1063/1.3269714�

I. INTRODUCTION

A. Al–Mg–Si alloys

Al–Mg–Si alloys are versatile heat treatable alloys withhigh strength/weight ratios. They have good extrudabilityand hardening characteristics as well as excellent corrosion,surface, and welding properties. They find applications in awide range of areas, such as in the construction, automobile,and aerospace industries. There is an increasing demand forimproved control of properties, which requires knowledge ofthe finest details of the precipitation sequence. This includesdiffusion and solute clustering, nucleation, growth, and trans-formation of the precipitates. In this context, it is obviousthat better knowledge and understanding of the atomic struc-tures of the precipitates and their interfaces are particularlyimportant.

The precipitation sequence in Al-Mg-Si1–4 alloys isatomic clusters → GP-zones → ��→�� ,U1,U2,B�→� ,Si,where the U1, U2, and B� phases are also referred to as typesA, B, and C, respectively.2,5 Except for the equilibrium phase�, with composition Mg2Si, and Si, all phases are meta-stable. Historically, all the precipitates were assumed to havethe Mg2Si composition. It is now known that compositionsrange from the Si-rich U1 to the Mg-rich �� phase.1–4 Everystage of the sequence is complex and is a function of alloycomposition, heat treatment �including cooling and heatingrates�, and storage time at room temperature prior to aging.During aging a tremendous increase in strength takes place,caused by the growth of a high density of semicoherentprecipitates within the aluminum matrix. At peak hardness

these are usually ��, or a combination of pre-�� type GuinierPreston �GP� zones and �� in Si-rich alloys.1,6 In Mg-richalloys, the formation of pre-�� is suppressed1 and anothertype of GP zone forms, which consists of monolayers�plates� with Mg /Si=1 parallel with �100� type Al planes.7

B. The previously published �� structure

The structure of �� has been determined in an earlierstudy by a combination of transmission electron microscopy�TEM� and quantitative electron diffraction.8,9 The conven-tional unit cell was found to be monoclinic, space groupC2/m, with composition Mg10Si12 and cell parameters a=15.16 Å, b=4.05 Å, c=6.74 Å, and �=105.3°. Themodel had been derived from high resolution TEM exit wavereconstructed images by matching known atomic radii toconsistent interatomic distances. The Si/Mg ratio was mea-sured using energy dispersive x-ray spectroscopy �EDS�. Theratio of Si/Mg was found to be about one, with a standarderror of about 10%, which was sufficiently close to Mg5Si6to support the model. Systematic deviations were not consid-ered. Because of the small precipitate cross sections, strayelectrons, and scattering of electrons into the matrix, EDSmeasurements cannot exclude the presence of some Al in theprecipitates, since an Al-signal from the matrix will alwaysbe present. Refinements of the model using diffraction inten-sities gave very good R-values �goodness of fit betweenmodel and experiment�. With the proposed composition, theinteratomic distances in the structure fit the atomic radii well.Al has a smaller covalent radius than Mg. A substitution ofMg by Al would, therefore, produce a less dense unit cell.Substitution of Si by Al was not investigated because Al hasa larger covalent radius than Si and Si–Si distances were

a�Author to whom correspondence should be addressed. Tel.: �4773593880.FAX: �4873597711. Electronic mail: randi.holmestad@ntnu.no.

JOURNAL OF APPLIED PHYSICS 106, 123527 �2009�

0021-8979/2009/106�12�/123527/9/$25.00 © 2009 American Institute of Physics106, 123527-1

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already small and near the covalent distances. Aluminumwas therefore considered unlikely in the structure.

Indirect support for the Mg5Si6 composition of the ��phase comes from the fact that many alloys with solute ratiosMg /Si=5 /6 have high strength. On conventional age heattreatment, they develop a microstructure with a homoge-neous distribution of �� precipitates, rarely disordered,which have sharp �310� and �320� type habit planes. By con-trast, precipitates in alloys with different Mg/Si ratios tend tohave less regular morphologies1 and are often disordered.Furthermore, the Mg5Si6 composition found support in abinitio calculations10 which confirmed the atomic structure de-rived from experiments8,9 and demonstrated the existence ofa network of covalently bonded Si-atoms throughout theMg5Si6 structure. Subsequently, the electronic bonding andstructural stability of �� and several other phases in the pre-cipitation sequence for Al–Mg–Si and Al–Mg–Si–�Cu� al-loys were studied by density functional theory �DFT�calculations.5,11 More recently, it has been suggested that aSi-backbone structure �nanopillars�, which may be regardedas an extension of the Si-network proposed by Andersen etal.,12 can also be found for the pre-�� phase, and that it isinvariant in the transformation from the pre-�� to the ��phase.13 The stoichiometric Mg5Si6 composition was foundto be the energetic minimum of all �� Al5−xMgxSi6configurations.13

The possibility of having Al at the Si sites of the original�� Mg5Si6 has not to our knowledge been previously inves-tigated by ab initio calculations. A reason for this is probablythat Si and Al are not considered interchangeable, due totheir different metallic and covalent ground state bondingcharacteristics, as described above. However, calculations ofthe electronic bonding in the U1 and U2 phases showed thatAl can assume a tetrahedral coordination in Al–Si bonds,which is made possible by the donation of charge from theMg atoms.5 This suggests that a complete ab initio study ofthe �� phase should include the possibility of Al substitutionat the Si sites.

C. The current studies of ��

Atom probe tomography �APT� is perhaps the best tech-nique available for measurements of chemical compositionin the fine-scale precipitates of aluminum alloys, as demon-strated in Al–Zn–Mg14–16 and Al–Sc–Zr17,18 alloys. For Al–Mg–Si alloys, it has been used to investigate the early stagesof the precipitation sequence.19–21 The �� phase is reportedto contain Al, in general more than 50%, and have a Mg/Siratio of about 1.1 in Si-rich alloys �Mg /Si�1� when mea-sured by APT.4,19 Also, more uncertain EDS measurementsindicated Al contents in the �� phase.20 However, these mea-surements are not consistent with the Mg5Si6-structure. Inorder to understand this discrepancy it is found necessary toconsider some aspects of the APT technique in more detail.In the present paper, we account for the two major artifactsleading to earlier overestimation of the Al content in thecomposition of �� and give a more accurate measurement forthe composition.

The major aim of the current study is to re-evaluate thestructure of �� precipitates in light of the identified sourcesof error in order to resolve the differences in the reportedcompositions. Experimental data have been acquired usingmore advanced APT equipment and data processing proce-dures �Sec. IV�. DFT calculations have been performed totest the energy of different configurations of �� �Sec. V�. Inaddition, �� diffraction data have been revisited to investi-gate the sensitivity of multislice least squares �MSLS� elec-tron refinement22 to the presence of Al in the structure �Sec.VI�. TEM observations are presented to confirm precipitatemorphology and number density �Sec. III�. The correspon-dence between experiments and calculations is discussed inSec. VII.

II. EXPERIMENTAL

The chemical composition of the studied alloy was 0.72at. % Si and 0.58 at. % Mg balanced with Al. Extruded barswere cut into pieces of 25�25�2 mm3. These were ho-mogenized for 1 h at 570 °C, then water quenched andstored for 4 h at room temperature. The samples were heattreated at 175 °C for 36 h to optimize growth of ��.1 Forquantitative electron diffraction experiments, the same alloywas used, but it was heat treated for 45 min at 220 °C toobtain larger cross sections of the �� needles.

TEM samples were prepared by electropolishing, usingan electrolyte of 1/3 HNO3 in methanol in a Tenupol-3 ma-chine. Conventional TEM analysis was carried out using aPhilips CM30 operating at 150 kV, equipped with a Gatanparallel electron loss spectrometer that was used for samplethickness measurement, and a JEOL 2010F operating at 200kV. Diffraction experiments were performed in a PhilipsCM30-UT/FEG electron microscope operated at 300 kV. Thelatter was equipped with a Photometric 1024�1024 slowscan charge coupled device camera �12 bits dynamical range�controlled by TIETZ software. The beam diameter was 2 nmand exposure times were 1–2 s.

Samples for APT were first cut into 20 mm long rodswith a cross section of 0.3�0.3 mm2. The rods were pre-pared into needles by electropolishing. First a “neck” wasproduced in a 25% percloric acid, 75% acetic acid solution atroom temperature. Final polishing, to separate the neck, wasperformed with a 5% percloric acid, 95% butoxyethanol so-lution. Back polishing to give the final needle-shaped samplewas performed with a 2% percloric acid, 98% butoxyethanolsolution at room temperature. The APT analyses were per-formed with an energy compensated tomographic atomprobe,23 equipped with an advanced delay line detector.24

The analyses were performed with a pulse fraction of 20%and a pulse repetition rate of 2 kHz, under vacuum betterthan 2�10−8 Pa. In earlier works by 1 dimensional atomprobe, it has been suspected that a temperature of analysislarger than 25 K would lead to an underestimation of the Mgconcentration.4 However, two recent investigations clarifiedin detail the influence of analysis parameters on compositionmeasurement by APT for Al–Mg–Si alloys.25,26 Both con-cluded that an analysis temperature of 40 K gives reliableprecipitation measurements. In addition, working at 40 K for

123527-2 Hasting et al. J. Appl. Phys. 106, 123527 �2009�

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AlMgSi alloys is found to reduce the likelihood of thesample breaking during analysis. Consequently, all APTanalyses in the present work were performed at 40 K. Inaddition, it should be noted that the alloy composition deter-mined by APT agrees well with the nominal composition, asshown in Table I, showing that the level of Mg is measuredaccurately.

The APT data were analyzed using software developedat the University of Rouen. Details of the cluster identifica-tion procedure that was applied to distinguish particles fromthe matrix are given elsewhere.27,28 Because of defocusingeffects due to local magnifications �described further in Sec.IV�, the cluster identification procedure tends to include ashell of matrix within a particle �precipitate�, which influ-ences the composition data.14,29 This shell represents an ap-parent matrix/particle interface, while the true particle inter-face lies within the identified particle. A more correctmeasure of the particle composition can be obtained by asubsequent “erosion” process. An erosion profile29 is a com-position profile, stretching from the apparent matrix/particleinterface to the middle of the particle. For each atom belong-ing to the particle the distance to the apparent matrix/particleinterface is calculated. The particle is further eroded step-wise, by removing the atom closest to the interface. For eachstep the composition of the remaining atoms is calculated.The erosion composition profile is obtained by plotting thecalculated composition for each step. Typically, such plotsshow an increasing content of solute atoms as the outermost

atoms are eroded. A distinct change in the slope of the curveis observed at the transition point between the overlap regionand the true matrix/particle interface.

Erosion profiles were used to measure the core compo-sition of the elongated precipitates found by cluster identifi-cation. In this paper, precipitate compositions measured bycomposition profiles are called composition profile values.Values of composition measured at the precipitate core byerosion profiles after cluster identification are called erosionvalues.

III. TEM OBSERVATIONS OF THE MICROSTRUCTURE

A typical TEM bright field image of the microstructureof the investigated alloy is shown in Fig. 1�a�. The imageshows the general morphology of the precipitates. Theneedle-shaped �� precipitates are aligned along one of thethree Al �100 directions. Figure 1�a� is a �001 Al zone axis.The �� needles appear as double weak lines along �100 and�010 Al. Needles along the �001 viewing direction havecross-section shapes that are parallelograms. A single pre-cipitate is shown in more detail in Fig. 1�b�. The numberdensity, as estimated from TEM images at lower magnifica-tions, is �3.70�0.13��1022 particles /m3. Close to 70% ofthe precipitates were ��. The remaining 30% had a disor-dered structure, showing partial �� atomic structure.1 Perfect�� particles are easy to recognize in their a-c cross-sectionplane, where the two unit cell edges line up with �310 and�230 Al directions. The identification was based on high-resolution TEM images of precipitates viewed in cross sec-tion, as shown for a �� precipitate in Fig. 1�b�. Similar im-ages were also used to measure the mean needle crosssection as 5.27�0.23 nm2.

IV. �� COMPOSITION BY APT

For APT measurements of �� precipitate compositions,errors can be traced to both the field evaporation phenom-enon and the detection system. Their combined effect pre-cludes a simple extraction of composition by standard meth-ods, such as composition profiles or cluster identification

TABLE I. Nominal alloy composition and experimental alloy compositionmeasured by APT. The value of 2� �� is the standard deviation for compo-sition measurements in atom probe� is indicated in brackets. Compositionswere estimated for three distinct APT analyses with a total of 754 000 ions.

Al�at. %�

Mg�at. %�

Si�at. %� Mg/Si

Nominal composition 98,70 0,58 0,72 0,81Composition determinedby APT

98,74 �0,03� 0,57 �0,02� 0,69 �0,02� 0,83

FIG. 1. TEM images of �a� alloy microstructure consisting of �� needles oriented along the �100 Al directions and �b� high resolution image of a ��precipitate.

123527-3 Hasting et al. J. Appl. Phys. 106, 123527 �2009�

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routines. The local magnification30,31 is related to the fieldevaporation process and was not accounted for in two earlierstudies.4,19 Because of the larger evaporation field of precipi-tates with respect to the Al matrix, a fraction of the ionsevaporating from the particles is detected in a shell ofsurrounding matrix because of a defocusing of theirtrajectories.32 More detailed consideration of the evaporationprocess30,31 and improved data treatments allow the relatederrors to be corrected.29

Another source of error is related to uneven precipitateevaporation rates.23 This leads to ions being released inbursts rather than at a uniform rate. For earlier designs of theoptical detection system, the Al content in �� was found tobe overestimated due to a selective loss of counts of Mg andSi when they arrive at the detector separated by only veryshort time intervals.26,33,34 This problem is eliminated by thenew generation of detectors.24 As a consequence, the currentmeasurements only require a correction related to the localmagnification effect.

Reconstructed volumes from APT experiments are typi-cally of the order of 10−5 �m3. Examples of the precipitatesstudied are presented in Fig. 2. Precipitates are identified bynumbers or letters which refer to the composition data givenin Table II. Erosion composition profiles are calculated forall precipitates having circumferences within the analyzedvolume. An example of the procedure applied to a volumecontaining a precipitate is shown in Fig. 3�a�. Figure 3�b�shows the same precipitate, isolated by cluster identification,with the volume tilted so that the precipitate is viewed alongits long axis. Atoms associated with the cluster are displayedusing a larger size than the ones corresponding to the matrix.The true matrix/precipitate interface is indicated by a dashedline in the profile of Fig. 3�c�. The core of the precipitate, asfound from the erosion profiles shown in Fig. 3�c�, is indi-cated in Fig. 3�b�.

Erosion values of Al-composition and Mg/Si-ratio in theprecipitates shown in Fig. 2 are listed in Table II. There aresignificant variations in measured composition between theobserved precipitates, mainly in the level of Al. This illus-trates how the local magnification error prevents a directmeasurement of precipitate composition. From Fig. 2, it isclear that the precipitates have a bimodal size distribution.By TEM it was found that more than 70% of the precipitatesin the analyzed condition were ��. It is likely that precipi-tates 1–6 and 8 are of this type, whereas some of the smallercluster features, labeled A to G, are more probably are GP

zones and were therefore not used for the �� compositionmeasurement. Particles F and G correspond to �� precipitatespartly intercepted by the APT volume.

The influence of the local magnification effect is illus-trated in Fig. 3�b�. Here defocused Mg- and Si-atoms, whichactually originate from the precipitate, are instead found inthe Al-rich shell surrounding the core of the particle that waslocated by the cluster identification. This shows that a simpleselection of the core of each particle �e.g., by plotting a com-position profile across it� can fail and lead to a systematicunderestimation of the solute content of a precipitate. A bet-ter measure of the precipitate composition is achievable byreassigning the Mg and Si atoms of the overlap region withthe core atoms. The protocol introduced by De Geuser26 isused here and can be summarized as follows. �i� An erosionprofile is calculated. �ii� The true precipitate-matrix interfaceis identified by a corresponding change in slope of the curverepresenting the Al concentration. �iii� The number of Alatoms in the precipitate structure is defined as the number ofAl atoms inside the true interface. �iv� All solute atoms �i.e.,in the core and in the surrounding shell together� are countedas originating from the precipitate. This will correct for dif-ferences in composition between precipitates of different size

TABLE II. Al-content measured in �� precipitates core by erosion profiles,the Al defocusing corrected value obtained by gathering all Mg and Si atomsfrom the overlap region in the core of the precipitates, and correspondingMg/Si-ratio.

Precipitate

Al erosionvalue �2��

�%�

Al defocusingcorrectedvalue �2��

�%� Mg/Si

1 35.6 �4.3� 21.9 �3.3� 1.09�0.152 51.0 �3.3� 22.5 �1.8� 1.11�0.093 43.6 �6.3� 20.9 �3.6� 1.17�0.184 52.4 �6.0� 20.8 �3.1� 1.01�0.135 36.0 �5.1� 20.0 �3.2� 1.24�0.176 35.6 �4.3� 19.9 �2.7� 1.03�0.127 44.3 �5.7� 27.7 �4.1� 0.99�0.178 40.5 �3.1� 22.2 �1.9� 1.05�0.09A ¯ ¯ 1.14�0.47B ¯ ¯ 0.98�0.33C ¯ ¯ 1.05�0.32D ¯ ¯ 1.23�0.44E ¯ ¯ 1.06�0.62F 66.1 �4.2� 33.1 �2.9� 0.98�0.24G 62.0 �3.1� 28.4 �1.9� 1.08�0.18H ¯ ¯ 1.11�0.52

FIG. 2. �Color� Reconstructed volumes containing �� precipitates, obtained by APT.

123527-4 Hasting et al. J. Appl. Phys. 106, 123527 �2009�

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that is introduced by the defocusing effect. The correspond-ing effect from Al atoms being part of the precipitate struc-ture is more difficult to determine, due to the low Al concen-tration in the overlap region, relative to the matrix.Therefore, the defocusing corrected composition will definea lower limit of Al in the precipitates. The defocus-correctedvalues of Al-concentration for several precipitates listed inthe second column of Table II show a much narrower spreadthan the uncorrected erosion values. Seven of the ten mea-sured precipitates shown in Table II have corrected Al con-centrations between 19.9% and 22.5%, while three weremore Al-rich. Furthermore, the corrected Mg/Si ratios givean average value of around 1.1. The convergence of the dataobtained for �� �i.e., Al concentration and Mg/Si ratio� withthe use of our protocol confirms that it is necessary to con-sider the influence of local magnification for this type ofanalysis.

V. DENSITY FUNCTIONAL THEORY SIMULATIONS

DFT simulations were used to investigate the possible Alcontent in the �� phase. Simulations were carried out usingthe Vienna Ab initio Simulation Package35–37 and ultrasoftpseudopotentials.38 We use the generalized gradient approxi-mation parametrized by Perdew and Wang.39 Using a primi-tive unit cell �half the conventional unit cell�, we label thesymmetrically inequivalent sites Mg1, Mg2, Mg3 and Si1, Si2,Si3 with basis in the original Mg5Si6 compound, illustrated inFig. 4. Mg1 has a multiplicity of one, while the remainingsites have a multiplicity of two. In principle, we would liketo explore all compounds where these sites can be occupiedby any of the elements Al, Mg, and Si. However, we restrictourselves to compounds where the Mg-sites can be occupiedby either Al or Mg and the Si-sites can be occupied by eitherAl or Si, while keeping the C2/m symmetry. Additionally, weonly investigate compounds for which the Al content is be-low 60%. This leaves 42 nonequivalent structures. For eachof these we fully relax both unit cell parameters and coordi-nate positions �keeping the C2/m symmetry� in order to findthe minimum energy configuration. The equilibrium forma-

tion enthalpy �T=0� for each compound is given by

�HEq = ETot − aESidc − bEMg

hcp − cEAlfcc,

where ETot is the cohesive energy of the compound contain-ing a, b, and c atoms of Si, Mg, and Al, respectively. ESi,EMg, and EAl are the corresponding cohesive energies peratom. In order to get closer to the energetics of the precipi-tation sequence, we would ideally like to compare the cohe-sive energies of the precipitates with the energies of the sol-ute elements in solid solution. In the following we willtherefore use the formation enthalpy with respect to the sub-stitutional energies of Mg and Si given by

�HSS = ETot − aESiSS − bEMg

SS − cEAlfcc.

The energies for Mg and Si as substitutional elements in Al,calculated using 64 atom fcc supercells, are then given by

ExSS = Efcc�Al63x� − 63

64EAlfcc�Al64�

for the substitutional element x. The substitutional energy ofelement x is related to the corresponding impurity energy by

�HxImp = Ex

SS − ExEq.

For all of our calculations we used a wave function energycutoff of 170 eV. For the �� structures, we used the 11 atom

FIG. 3. �Color� �a� Reconstructed volume containing a �� precipitate. �b� Same precipitate identified by cluster identification. �c� Erosion profile withmatrix/precipitate interface indicated.

FIG. 4. �Color� The �� Mg5Si6 atomic model with denotations of symmetri-cally inequivalent atomic sites used in the text. The external cell parametersof the monoclinic conventional unit cell are indicated.

123527-5 Hasting et al. J. Appl. Phys. 106, 123527 �2009�

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primitive unit cell and 10�10�10 -centered Monkhorst–Pack k-point grids. A 10�10�10 grid was also used for the64 atom supercell calculations. For the single element calcu-lations, substantially denser k-point grids were needed. Testsshowed that the resulting energy differences were convergedto within 0.01 eV per atom. Figure 5 shows the calculatedformation enthalpies per atom of solute �Mg, Si� as a func-tion of the fraction xMg / �xSi+xMg�. We label the variouscompounds AlxMg5−xAlySi6−y, where x is the number of Alatoms at the Mg-sites in the unit cell and y is the number ofAl atoms at the Si-sites. For a given Mg/Si ratio, there are upto ten possible permutations for Al substitutions at the vari-ous Mg- and Si-sites. The structure showing the lowest for-mation enthalpy contains 18% Al and has a Mg/Si-ratio of

1.25−Mg5Al2Si4. In this structure, two Al atoms occupy theSi3 sites. The second lowest formation enthalpy is obtainedby AlMg4Al2Si4, containing 27% Al and with a Mg/Si-ratioof 1. Interestingly, also in this case, the Al occupies the Si3sites in addition to a single Al atom at the Mg1 site. Thecorresponding structures with Al at either the Si1 or Si2 sitesproduced significantly higher formation enthalpies. As canbeen seen from Fig. 5, the Mg5Si6 phase does not constitutea vertex of the convex hull, but lies above the tie line formedby the AlMg4Al2Si4 and the Al3Mg2Al2Si4. For structureswith Al-contents above 30%, the structural relaxation per-formed in the calculations produced unit cells with latticeparameters differing significantly from the experimental re-sults. However, for structures with lower Al-contents, theunit cell parameters obtained are in good agreement withexperiment.

The third column in Table III shows the unit cell param-eters and atomic coordinates of the Mg5Al2Si4 structure asresulted from the ab initio DFT calculations. In conclusionour calculations indicate that the lowest energies �� phasescontain a substantial amount of Al and a Mg/Si-ratio 1.

When only considering the ground state energy in com-paring the various configurations, we are in effect ignoringany contribution to the enthalpy from entropy at T�0. En-tropy contributions have been shown to be significant for therelative energetic ordering of the � and �� phases in theAl–Cu alloy system.40 DFT calculations demonstrated thatvibrational entropy favored the tetragonal � phase over thecubic �� phase for temperatures above �200 °C. We cannotrule out a significant effect from entropy terms to the relativeordering of the structures under consideration in the presentstudy. However, as opposed to the case for Al–Cu, we arecomparing structures which are structurally/symmetricallyidentical except for the varying Al-content. Moreover, DFTcalculations of phonon modes, electronic and configurationalentropy terms are outside the scope of this paper.

TABLE III. First and second columns: quantitative electron diffraction �MSLS� refinements of unit cell param-eters and atomic positions for the original Mg5Si6 model �Ref. 9� and the proposed Mg5Al2Si4 model, respec-tively, using the same experimental data set. Temperature factors B are also given. Third column: ab initio�DFT� refinements of unit cell parameters and atomic positions for the proposed Mg5Al2Si4 model.

Property MSLS results with Mg5Si6-model MSLS results with Mg5Al2Si4-model DFT on Mg5Al2Si4

a�� 15.16 15.16 15.50b�� 4.05 4.05 4.05c�� 6.74 6.74 6.74� �deg� 105 105 106Mg1 x,y,z Mg:0.0,0.0,0.0 Mg:0.0,0.0,0.0 Mg:0.0,0.0,0.0B 0.5�2� 0.8 �2�Mg2 x,y,z Mg:0.3444�11�,0.0,0.094�2� Mg:0.3419�11�,0.0,0.099�3� Mg:0.347,0.0,0.074B 0.8�3� 0.8�2�Mg3 x,y,z Mg:0.4248�10�,0.0,0.650�3� Mg:0.4225�9�,0.0,0.659�3� Mg:0.423,0.0,0.636B 1.05�19� 0.79�17�Si1 x,y,z Si:0.0500�11�,0.0,0.684�3� Si:0.0501�10�,0.0,0.678�3� Si:0.054,0.0,0.661B 1.3�3� 1.3�3�Si2 x,y,z Si:0.1867�14�,0.0,0.216�4� Si:0.1876�14�,0.0,0.225�5� Si:0.190,0.0,0.232B 0.9�3� 0.9�3�Si3 x,y,z Si:0.2174�13�,0.0,0.621�3� Al:0.2213�14�,0.0,0.618�3� Al:0.211,0.0,0.626B 2.3�4� 1.5�3�

FIG. 5. Fully relaxed formation enthalpies �eV/solute atom� for various ��compounds as a function of the Mg / �Si+Mg� fraction. Solid lines representthe convex hull.

123527-6 Hasting et al. J. Appl. Phys. 106, 123527 �2009�

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VI. QUANTITATIVE ELECTRON NANODIFFRACTION

To explore the sensitivity of quantitative electron diffrac-tion to the presence of Al in the ��-phase, five additionalelectron diffraction patterns of �� in the �010� �� orientationwere analyzed with the same MSLS software used for theearlier structure refinement.8,9 The refinement was performedusing both the original Mg5Si6 model and the energeticallymore favorable Mg5Al2Si4 structure. Crystal model param-eters �atom positions and temperature factors�, specimen tilt�center of Laue circle�, and specimen thickness were refined.As can be seen from the first two columns of Table III, therefined positions differ only marginally between the twomodels and the R-values, which quantify the goodness of fit,are nearly identical. The most significant difference is in thetemperature factor of the Si3 atom, which is substituted byAl. In the original model it has by far the highest value, yetin the adjusted model the Al atom replacing Si3 has a tem-perature factor comparable to that of the other atoms. Theeffect of a higher temperature factor of a certain atom on theelectron diffraction intensities is quite similar to that of re-placing this atom with a slightly weaker scatterer �a lighteratom�. An atom with a higher temperature factor appears“smeared” out over a larger area, resulting in a lower localscattering power. In the Mg5Si6 model this means that thetwo Si3 atoms �which have a high temperature factor� couldbe replaced by Al, giving support to the Mg5Al2Si4 compo-sition of ��. This is consistent with the plausible transfer ofcharge from Mg to Al �see Sec. I B� implying that Al appearselectronically more similar to Si in this structure. In conclu-sion, although solely on the basis of diffraction data, it isdifficult to clearly distinguish between the two models; thenew Mg5Al2Si4 model is more favorable due to the lowertemperature factor of the Si3 atom when it is replaced by Al.

VII. DISCUSSION

An Al-content of about 20% and a Mg/Si-ratio of about1.1 in the �� precipitates measured by APT is not in corre-spondence with the Mg5Si6-model.8,9 At the same time, theMg/Si-ratio is in good agreement with earlier atom probestudies.4,19,41 Previously, it has been assumed that Mg is mostlikely to replace Al during the transformation from pre-�� tothe Mg5Si6-��, due to the common metallic character of Aland Mg and to the interatomic distances for Al, Mg, andSi.6,42 By contrast, the atom probe experiments indicate thatAl is more likely to be included in the �� structure at theexpense of Si. These experimental findings are supported byab initio calculations of the �� structure. The structure withthe lowest equilibrium formation enthalpy �even lower thanMg5Si6� was found by replacing the Si3 position in theMg5Si6 model with Al, yielding the composition Mg5Al2Si4�18% Al�, see Table III. This result was previously not con-sidered, as it implies that the Al-atoms in this site bond co-valently to their neighbors. This model of �� offers a betterexplanation of the experimental data presented earlier.1 Un-like Si-rich alloys, that favor the formation of pre-�� GP-zones, Mg-rich alloys display only one hardness peak, asso-ciated with ��, suggesting the direct formation of ��.Moreover, the alloys with Mg/Si ratios 6/5 and 2/1 achieve

higher peak hardness as compared to the corresponding al-loys with compositions Mg /Si=5 /6 and 1/2, respectively.

Our earlier paper suggested a model for a Si-rich�� /matrix interface,9 which was subsequently investigatedby ab initio calculations.42 It was found that, when Si-atomsin the interface were replaced by Al-atoms, the resultant pe-riodic interface phase was more energetically favorable.More precisely, in the Al �310� interface plane, it was foundthat a lower energy was obtained when the Si3 site was sub-stituted with an Al-atom. Even if this only applied for theinterface, it would mean that the overall Si/Mg ratio in the ��phase should be closer to one for small particles.

Another observation, described in Sec. 6, is the value ofthe temperature factor of the Si3 position. When reconsider-ing the original quantitative electron diffraction data,9 it wasnoticed that this was higher than for all other atomic posi-tions. This was regarded as possibly due to anisotropic ther-mal parameters, probably caused by Si–Si covalent bonding,but was not confirmed. For the new model, this factor iscomparable with the other positions.

The substitution of Al on the Si3-site makes �� evenmore structurally related to the U2 phase.43 Al showing amore covalent nature is also demonstrated in the Al-containing U1 phase. Here, according to calculations of theelectronic bonding, Al–Si pairs are found to receive chargefrom Mg.5 Both U1 and U2 phases are obtained on overagingof ��. The Mg5Al2Si4-�� phase is therefore consistent withthe structures of the Al-containing subsequent phases in theprecipitation sequence. Furthermore, the calculations showthat there are several other �� structures with a solubilityenthalpy equal to or lower than that of Mg5Si6. It is thereforereasonable to believe that several ��-type phases with differ-ent compositions can be present in the microstructure and theaverage stoichiometry will be some energetically weightedaverage of these, most of which contain a substantial amountof Al. Also, depending on the heat treatment, one or more ofthese structures could become dominant in the microstruc-ture. It is beyond the scope of this paper to investigate thedetails further. However, Mg5Al2Si4 stands out as the lowestenergy configuration, and therefore this composition is themost likely to be found in any given �� precipitate.

The conclusion from DFT calculations that the energiesof bulk Mg5Al2Si4-�� and Mg5Si6-�� are highly similar ap-pears of fundamental interest to the understanding of thebonding within the �� precipitate. The three sets of Si atomsin Mg5Si6-�� have clearly inequivalent surroundings �seeFig. 4�. Moving from Si1 to Si3, the local environmentchanges from involving a majority of Mg nearest neighboratoms into a Si-rich arrangement closely resembling the dia-mond structure.10 On the basis of this observation, and thetheoretically reported Si covalent bond formation throughoutthe material,10 it would seem likely that the bonds betweenSi2 and Si3, i.e., the Si nanopillars,13 were integral to theformation of ��. The present theoretical studies, however,oppose this conclusion. The Si atoms at the Si3 sites are theones that can be replaced by Al without any significant en-ergy penalty, whereas a clear energy increase is obtained forattempted substitution of other Si atoms by Al. This ques-tions the suggested function of the nanopillars as integral to

123527-7 Hasting et al. J. Appl. Phys. 106, 123527 �2009�

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the formation of hardening precipitates in Al–Mg–Sialloys,13 as the most crucial bonds appear to be located else-where in the structure. This will count even if the composi-tion of �� is Mg5Si6.

In a preliminary study, we reported a �� precipitate witha content of 15 at. % Al after an initial attempt at correctingexperimental artifacts.33 The atom probe experiments in thepresent study showed a higher Al content. However, in thepreliminary study composition data were measured as com-position profile values. Due to the small sizes of the precipi-tate cross sections, giving a small number of atoms in thecomposition measurements, a high uncertainty level is attrib-uted to this result. The defocus corrected method used forcomposition measurement in the present study is far morerobust as it takes all the Mg and Si atoms detected for eachprecipitate into account. The main uncertainty in the inter-pretation of the experiments is to define the precipitate core.We have shown that there is an overlap region around pre-cipitates where a higher concentration of Mg and Si atoms ispresent, compared to the matrix, due to the known localmagnification artifact.30,32 Utilizing erosion profiles, the Al-content of the precipitate is fixed at a measured matrix/precipitate interface, while all Mg- and Si-atoms defocusedoutside the interface are added to the particle. This gives acorrected composition value with a more stable Al content inthe precipitates, of around 20%. The relative uniformity ofthe corrected composition value supports the interpretationof the local magnification effect. The Al value is probably alower limit as some Al from the precipitates would also beexpected to be lost into the overlap region due to the samedefocusing effect.

VIII. CONCLUSIONS

The Mg5Al2Si4-structure of �� in Al–Mg–Si alloys sug-gested in this paper is supported by the experimental resultsfrom APT, ab initio calculations, and quantitative electrondiffraction. The difference from the earlier published Mg5Si6�Ref. 9� structure is a replacement of Si with Al at one posi-tion in the unit cell. While this substitution was unexpectedand therefore not considered earlier, the Mg5Al2Si4-structureis consistent with the structure of the subsequent phaseformed in the alloy precipitation sequence and is found tohave the lowest formation energy of the configurations inves-tigated. However, this composition cannot be concluded tobe unique for �� as other compositions are also found tohave low formation enthalpies. Rather, it is reasonable tothink that precipitates with the �� structure can take severalcompositions, most of them Al-containing. The calculationssupport that Si atoms form a spacious network with strongbonds �Si1, Si2 in Fig. 4� where the penalty for substituting Siwith Al is high, whereas smaller changes in the energy be-tween Si and Al exist regarding the atom sites �Si3� in be-tween. Since the earlier suggested Si nanopillars13 wouldconsist of Si-atoms in the network together with additionalSi-atoms in the intervening positions �Si3�, the current calcu-lations therefore do not support such features. The peak hard-ness, Si-rich, alloy investigated in this study by APT had amicrostructure consisting of mostly �� with composition cor-

responding to Mg5Al2Si4. APT investigations of this phasedemand correction of local magnification artifacts in order tomeasure a consistent composition among different precipi-tates. This correction resolves earlier uncertainties, wheremuch higher levels of Al were measured in the precipitatesby APT when no correction was applied. Quantitative elec-tron diffraction also shows that the Mg5Al2Si4 structure givesa better fit with the experimental data than Mg5Si6, althoughthis method alone is not sensitive enough to clearly distin-guish the two structures.

ACKNOWLEDGMENTS

H.S.H., R.V., and J.C.W. acknowledge financing fromthe Norwegian Research Council through the SUP program“Micro- and nanostructural materials development.” S.J.A.and C.D.M. are funded by the Research Council through twoprojects: �i� the research project “Fundamental investigationsof solute clustering and precipitation” and �ii� the BIAproject “Nucleation control,” the latter partly financed byindustry, �Hydro Aluminum AS and Steertec Raufoss AS�.Financial support from the Aurora program for the coopera-tion between NTNU and UR is also gratefully acknowl-edged. H.S.H. would in particular like to thank Dr. FrédéricDe Geuser for his original and clever effort in interpretationof atom probe data used in this work. C.D.M. wishes tothank Delft University of Technology, the Netherlands fortechnical �equipment� support. We want to acknowledge Dr.Flemming Ehlers, NTNU for useful discussions and inputaround the DFT calculations.

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