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Acta Materialia 78 (2014) 245–253

HAADF-STEM and DFT investigations of the Zn-containing b00

phase in Al–Mg–Si alloys

Takeshi Saito a,⇑, Flemming J.H. Ehlers a, Williams Lefebvre b,David Hernandez-Maldonado b, Ruben Bjørge a,1, Calin D. Marioara c,

Sigmund J. Andersen c, Randi Holmestad a

a Department of Physics, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norwayb Universite de Rouen, GPM, UMR CNRS 6634, BP 12, Avenue de I’Universite, 76801 Saint Etienne du Rouvray, France

c SINTEF Materials and Chemistry, N-7465 Trondheim, Norway

Received 13 May 2014; accepted 23 June 2014Available online 24 July 2014

Abstract

The Zn-containing b00 phase in Al–Mg–Si alloys was investigated by aberration corrected high angle annular dark-field scanningtransmission electron microscopy (HAADF-STEM), combined with density functional theory (DFT) calculations. The mean intensityof one Si site of the b00 phase is higher than that of the other Si sites, suggesting partial Zn occupancy. DFT studies support that thisSi site is competitive for Zn incorporation. While HAADF-STEM image simulations show an influence of the Zn distribution alongthe b00 main growth direction, total energy calculations predict a weak Zn–Zn interaction. This suggests that Zn atoms are not clustering,but uniformly distributed along the atomic columns. The Zn incorporation has a weak influence on the b00 phase, where Zn is admitted asa “defect” according to the DFT studies.� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Aluminium alloys; Precipitate; High angle annular dark-field scanning transmission electron microscopy; Density functional theory; Atomicstructure

1. Introduction

Al–Mg–Si alloys are heat-treatable materials used inmany industrial applications on the basis of their character-istic properties: high strength-to-weight ratio, good form-ability and corrosion resistance. The main property ofthese heat-treatable materials is a significant increase inhardness during a final isothermal heat treatment (artificial

http://dx.doi.org/10.1016/j.actamat.2014.06.055

1359-6454/� 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights r

⇑ Corresponding author. Present address: Hydro Aluminum Researchand Technology Development, N-6601 Sunndalsøra, Norway. Tel.: +4773 59 07 30.

E-mail address: takeshi.saito@ntnu.no (T. Saito).1 Present address: SINTEF Materials and Chemistry, N-7465 Trond-

heim, Norway.

aging) at an adequate temperature and time. This is due tothe formation of large numbers of nano-sized semi-coherentmetastable precipitates, hindering dislocation movement.The precipitates form from a supersaturated solid solution(SSSS) and are controlled by the alloy composition andthe thermo-mechanical history. The materials strength ulti-mately depends on the precipitate structure and the micro-structures they produce (sizes, numbers and orientations).Further, composition, morphology and aspect ratio for aprecipitate may be affected by small amounts of a differenttype of solute atoms. This could be triggered by direct incor-poration of these additional solute atoms in the existingprecipitate, either in the bulk (change of cell dimensions)or at the interface (change of interfacial energies). Such alloymodifications are of growing interest, owing to specific

eserved.

246 T. Saito et al. / Acta Materialia 78 (2014) 245–253

industrial requirements for materials properties and focuson recycled aluminium.

The precipitation sequence of Al–Mg–Si alloys is as fol-lows [1–9]:

SSSS! atomic clusters! GP zones ðpre-b00Þ! b00 ! b0; U1; U2; B0 ! b; Si ð1Þ

The U1, U2 and B0 phases are also known as Type A,Type B and Type C, respectively [10].

The b00 phase is the most important metastable phaseencountered together with GP zones, leading to the finestmicrostructure at peak hardness condition [1]. The mono-clinic structure (space group C2/m) of the b00 phase,described in Fig. 1a and Table 1, was identified more thana decade ago [2,9]. By contrast, the b00 composition hasbeen widely discussed [3,11–15]. The b00/Al matrix inter-faces are coherent, with {130}Al and {320}Al as habitplanes. The orientation relationships with the face-centredcubic (fcc) Al matrix are

½230�Al==½100�b00; ½001�Al==½010�b00; ½�310�Al==½001�b00

ð2ÞThe lattice misfits along these directions are in the order

of 3.8%, 0% and 5.3%, respectively [2,9], from which a nee-dle-shaped precipitate, directed along [010]b00, results.Recent extensive experimental atom probe tomography(APT) studies suggested [3,12,13] that the Mg/Si ratio isclose to 1.1, which differs from the originally proposedb00-Mg5Si6 phase. Both experimental studies and theoreticaldensity functional theory (DFT) calculations [3,12–14]have supported the Mg5Al2Si4 composition, most likelythe b00 configuration in Fig. 1a. The most recent DFT cal-culations [14] deduced very weak formation enthalpy differ-ences for b00-Mg5+xAl2�xSi4 (�1 < x < 1). Further, the b00

phase could have compositional variations within a singleprecipitate, as suggested by the most recent experimentalstudy [15]. These results imply the possibility of a strongsensitivity for the b00 phase composition, aspect ratio andultimately the microstructure, to incorporation of “for-eign” solute atom types.

The present work investigates the incorporation of Zn inb00, using a series of experimental and theoretical methods,from the perspective of a general analysis of foreign solute

Table 1Structural overview and atomic site positions (x,y,z) in the b00 phase [2,3];each atomic site is shown schematically in Fig. 1a.

Composition Mg5Al2Si4

Space group C2/mLattice parameter (nm) a = 1.516, b = 0.405, c = 0.674, b = 105.3�Mg1 site 0, 0, 0Mg2 site 0.3419, 0, 0.099Mg3 site 0.4225, 0, 0.659Si1 site 0.0501, 0, 0.678Si2 site 0.1876, 0, 0.225Si3/Al site 0.2213, 0, 0.618

atom types in this phase. It has previously been demon-strated [16] by high-angle annular dark-field scanningtransmission electron microscopy (HAADF-STEM) thatZn is confined to the Si3/Al sites of the b00 phase; seeFig. 1b. The contrast of these Zn-containing atomic col-umns was weak, which indicates a low Zn partial occupa-tion on the site [16]. The main interest in this work ishow to clarify, to the largest possible degree, the state of“a well-known phase with foreign solute atom types”: here,the b00 phase with Zn incorporation.

It is well known that information acquired fromHAADF-STEM images is limited, owing to the “projec-tion” of the three-dimensional (3-D) atomic structure andcomplicated scattering mechanisms [17,18]. The presentauthors aim to circumvent this limitation by using both astatistical analysis and simulations of the HAADF-STEMintensities, as well as DFT calculations. This attemptshould serve to highlight the present limitations of the gen-eral structural analysis, as well as the key areas where fur-ther investigations are needed.

2. Experimental details and methodologies

2.1. Materials and HAADF-STEM images

An alloy with measured composition Al–0.52Mg–0.38Si–0.42Zn (at.%) was prepared by extrusion from castbillets. This composition is close to the commercial 6060Al alloy, except for the Zn addition. Other impuritiesare <0.01 at.%. The alloy was solution heat treated at540 �C for 1 h, kept for 4 h at room temperature andisothermally heat treated at 185 �C for 12 h. This heattreatment procedure gives a peak hardness condition.The preparation and heat treatment are identical to theprevious work [16].

HAADF-STEM specimens were prepared by electro-polishing with a Tenupol 5 machine (Struers, Denmark).The electrolyte consisted of 1/3 HNO3 in methanol andthe solution was kept at a temperature between �20and �35 �C. In order to reduce contamination duringobservation, all specimens were ion-milled by a precisionion polishing system (PIPS Gatan). In addition, all speci-mens were plasma cleaned before HAADF-STEM imag-ing in order to reduce the effect of contamination, usinga Model 1020 Plasma Cleaner (Fischione Instruments).The HAADF-STEM images were taken by a sphericalaberration (Cs) probe-corrected JEOL ARM200F STEMwith a Schottky field emitter operating at 200 kV. Theprobe size was 0.1 nm. The collection angle of the HAADFdetector was in the range. 45–150 mrad. The thickness ofthe specimen was near 50 nm. The HAADF-STEMtechnique provides atomic number (Z) contrast with theintensity proportional to Z1.7–1.9 [17,18]. This enables todistinguish the heavier Zn (ZZn = 30) enriched atomiccolumns from those containing only Mg (ZMg = 12),Al (ZAl = 13) and Si (ZSi = 14) in the precipitatestructures.

Fig. 1. (a) Projected unit cell of the b00 phase along the b-axis. The labelling of atoms refers to Table 1. The characteristic 4-fold atomic coordinationaround the Mg1 site is indicated by a triple solid black line. The dashed large boxes in (a, b) represent a unit cell and the dotted blue one in (a) shows theprimitive cell used in DFT calculations. (b) HAADF-STEM image of a b00 cross section taken along h0 0 1iAl (same orientation as in (a)) for an alloycontaining 0.42 at.% Zn after isothermal heat treatment for 12 h at 185 �C. The image has been filtered using Fast Fourier transform with a circular bandpass mask that removed all periods (noise) shorter than 0.15 nm (adopted from Ref. [16]). (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

T. Saito et al. / Acta Materialia 78 (2014) 245–253 247

2.2. Analysis of HAADF-STEM intensity by a statistical

approach

The intensities of atomic columns of the precipitateexamined were estimated using a statistical analysis[19,20]. The HAADF-STEM intensity I(R) can be approx-imated as a convolution of an object function and a probefunction as follows [18]:

IðRÞ ¼ OðRÞ � P ðRÞ ð3ÞHere, R is the position of the STEM probe, O(R) is the

object function, and P(R) is the probe function. The probefunction represents the intensity distribution of the conver-gent scanning beam, which depends on acceleration volt-age, objective aperture, convergence angle and defocus[18]. The object function describes the scattering, relatedto the projected potential of atomic columns. This functionis peaked at the atomic column positions and can be mod-elled as a superposition of Gaussian peaks [19,20]. Thescattered intensity for an atomic column is expected to beidentical for columns with the same chemical composition.In this manner, histograms of the estimated peak intensityof the atomic columns can be drawn [19]. This methodol-ogy [19,20] has been developed to count the atoms innano-sized particles from HAADF-STEM images. Themethod was applied here to identify the atom types in thevarious columns, assuming the same number of atoms ineach column of a precipitate. This approach has recentlybeen followed to investigate the b00 phase without Zn incor-poration, deducing atomic column types [15].

Following the methodology proposed by van Aert et al.[19,20], integrated column intensities were measured foreach atomic column in the experimental images (i.e. with-out any filtering). Histograms of column intensities werethen fitted with a Gaussian “mixture model”, using a

statistical analysis in which the amounts of Gaussiancomponents [19,20] are estimated from the variation ofthe integrated classification likelihood (ICL) criterion. Thisapproach enables the intensity distribution of each atomiccolumn to be estimated and discussed.

2.3. HAADF-STEM image simulations

In order to clarify how a partial occupancy of Zn at theSi3/Al site in the b00 phase influences the HAADF-STEMintensity, three different Zn occupancies, 0%, 5% and10% on this site were simulated. The composition of theb00 phase was assumed to be Mg5Al2Si4. In addition, toinvestigate how the intensity varies with Zn distributionalong a precipitate needle, three different distributionsalong the electron beam direction were considered: evendistribution throughout the column, and top and bottomZn enrichments (see Fig. 2). In this manner, one can extract3-D information on the precipitate atomic structure fromthe projected HAADF-STEM images.

The HAADF-STEM image simulations were conductedusing the frozen phonon multislice program provided bythe QSTEM package [21] with slice thickness of 0.205 nm(half a unit cell; see Table 1). The convergence semi angleof the electron probe was 20 mrad, and the HAADF collec-tor angles were between 45 and 150 mrad. These valueswere the same as in the experiment. The simulatedstructures were assumed (see Table 1) to adopt the experi-mentally reported [2] b00 cell dimensions, regardless of Zncontent and distribution. The HAADF-STEM images werecalculated for every two slices. Each simulation was aver-aged over 30 frozen phonon configurations. The chosenDebye–Waller factors for each site matched those of theelemental phases at 300 K: 0.8333, 1.8837, 0.5261 and1.1782 A2 for Al, Mg, Si and Zn, respectively [22].

Fig. 2. Schematic image of precipitate columns for different distributionsof Zn along the electron beam direction: (a) even distribution of Zn atomsthroughout the column; (b) top and (c) bottom Zn atom enrichments. Theprecipitate column represents one primitive b00 unit cell (repeated along theb-axis).

248 T. Saito et al. / Acta Materialia 78 (2014) 245–253

2.4. DFT calculations

The DFT [23,24] calculations for the Zn-containing b00

phase have three key purposes. It is attempted to: (i) com-pute the energy gain for a Zn atom incorporated in b00

(named “replacement energy” below), as obtained relativeto having this atom in solid solution (SS); (ii) clarify thelevel of Zn-induced changes to the b00 composition; (iii) elu-cidate the strength of Zn–Zn interactions in b00 (and thus, inturn, the expected degree of Zn clustering in theprecipitate).

To capture the state of Zn in the precipitate, calculationson a bulk b00 system are needed. Owing to the expected lowZn occupancy in b00, the precipitate was modelled usingsupercells, comprising Na � Nb � Nc primitive b00 unit cells(see Fig. 1a) along ab00, bb00 and cb00, respectively. Initially,one Zn atom was incorporated in a 1 � 4 � 1 cell, testingthe preference for each non-equivalent site in b00, in a man-ner described below. To examine Zn clustering tendencies,a second Zn atom was introduced on an equivalent site,varying the Zn–Zn separation. Those studies involved boththe 1 � 4 � 1 cell as well as 1 � 2 � 2 and 2 � 2 � 1 cells.For the description of Zn in SS, one Zn atom was includedin a 108 atom fcc Al supercell, comprising 3 � 3 � 3 con-ventional fcc unit cells.

To accommodate b00 configurations with space groupsymmetry lower than C2/m in calculations, all atom sitesN for the Zn-free structure (labelled b000 for brevity below)were treated as formally non-equivalent. This yielded 11different sites within the primitive cell of Fig. 1a. The drivefor Zn incorporation on any of these sites was addressed asfollows: whenever a solute atom was present at site N in b000,

an “artificial” Al defect was introduced here, for each prim-itive cell making up the full supercell (four Al atoms intro-duced in total). Two possible scenarios were thenconsidered: (i) one Zn atom removed from the fcc Al super-cell and incorporated on site N, with the Al atom presenthere expelled to the Al matrix; (ii) the same substitutionprocess examined for the solute atom occupying site Nbefore the introduction of the artificial Al defects.

In this manner, not only was the drive for Zn incorpora-tion on each given site in b00 probed, but also the level ofcompetition with the solute atom most likely occupyingthis site when no Zn is present in the alloy. Labelling theincorporation of a given atom X on site N as “{X! N}”,the system enthalpy change DH(b000; X! N) due to one ofthe above described substitution processes may be writtenas

DHðb000; X! NÞ ¼ H b000; 3� fAl! Ng; 1� fX! Ng� �

þ Hðfcc AlÞ � H b000; 4� fAl! Ng� �

� Hðfcc Al;1 � fX! SgÞ ð4Þ

Here, H denotes the calculated enthalpy for the systemdescribed in parenthesis (first argument: host material;remaining arguments: replacement processes), with X spec-ifying the solute atom incorporated in the precipitate, andS denoting a substitutional site in the Al matrix. FollowingRefs. [3,14], the present authors considered three different(energetically competitive) b000 configurations; Mg4Al3Si4(Al on Mg1, Si3 sites in Fig. 1a), Mg5Al2Si4 (Al on Si3sites) and Mg6AlSi4 (Al on one Si3 site). For sites N hostingAl in b000, the replacement processes “{Al! N}” have nopractical effect. However, even for this situation, incorpo-ration of the most likely solute atom Mg/Si on site N wasconsidered for comparison with the Zn incorporation.

All computational studies were performed at 0 K,employing Vanderbilt ultrasoft pseudopotentials [25] asimplemented in the plane wave (PW) based Vienna Ab ini-tio Simulation Package (VASP) [26,27]. For the descriptionof the exchange–correlation functional, the Perdew–Wanggeneralised gradient approximation [28] was used. The cho-sen PW cut-off in simulations was 234 eV, with (12,6,14)Monkhorst–Pack [29] k-point grids used for the 1 � 4 � 1b00 supercell, and compatible grids for other cells. Gener-ally, all structural parameters (cell dimensions, basis vectorangles and atomic positions) were relaxed. The use ofenthalpies over formation energies E in Eq. (4) relates tothe present authors’ neglecting the influence of the (small)pressure–volume (PV) term distinguishing these quantities.

3. Results

3.1. HAADF-STEM intensity distribution of atomic columns

by statistical analysis

Fig. 3 shows an unprocessed HAADF-STEM image of ab00 precipitate cross section taken along h0 0 1iAl and thecorresponding average HAADF-STEM intensity map.

Fig. 3. (a) Unprocessed HAADF-STEM image of a Zn-containing b00 precipitate cross section taken along h0 0 1iAl. (b) Corresponding HAADF-STEMintensity map. Each coloured dot overlaying an atomic column represents an integrated HAADF-STEM intensity of a square area of 1.25 � 1.25 nm2 (i.e.much larger than the size of the projected column). The overlay therefore represents the average thickness variations for the specimen. The HAADFintensity is displayed in arbitrary units. The precipitate orientation is the same as in Fig. 1a. (For interpretation of the references to colour in this figurelegend, the reader is referred to the web version of this article.)

T. Saito et al. / Acta Materialia 78 (2014) 245–253 249

The intensity map shows thickness variations over the spec-imen, deduced by integrating the intensity over a square arealarger than the size of a projected column. This means thateach dot overlaid a column in Fig. 3b is a centre, with colourrepresenting the (average) intensity of the surrounding area.Fig. 4 shows the intensity map of the Si3/Al sites, and inten-sity distributions for each Mg and Si site in the precipitate.The following observations can be made from Figs. 3 and 4.

� The intensity map shows a strong intensity variation,reflecting thickness variations of the scanned area. Inaddition, the intensity from the bulk precipitate is rela-tively lower than the Al matrix. This could be attributedto elastic lattice strain in the precipitate [30]. Here, it

Fig. 4. (a) Colour mapping of the integrated intensity on the Si3/Al sites of thearbitrary units. In (b) and (c), the respective intensity distributions for Mg andprecipitate had non-systematically higher intensity (shown by white arrow ininterpretation of the references to colour in this figure legend, the reader is re

cannot be excluded that the actual thickness of the bulkprecipitate and the Al matrix might be different, owingto the results of specimen preparation.� While the intensity distributions for the Mg sites are

similar to each other, those for the Si sites show cleardifferences among the sites. The mean intensity of theSi3/Al sites is clearly higher than other Si sites. This isin good agreement with a partial occupation of Zn onthe Si3/Al sites.� Intensities for the Si3/Al sites are lower close to the

interfaces along [230]Al; the higher intensity comesfrom the bulk Si3/Al sites, not from either near or atinterfaces along [230]Al. Interestingly, this tendencyappears weaker for the interfaces along [�3 10]Al.

Zn-containing b00 precipitate. The HAADF-STEM intensity is displayed inSi sites in the precipitate are shown. The columns at the bottom part of the

(a)) and were excluded in the statistics of intensity distributions. (Forferred to the web version of this article.)

Table 2HAADF-STEM intensity gradients as a function of specimen thickness,deduced by linear interpolation of selected data sets from Fig. 5; the linearfunctions were fitted with zero intercept term, i.e. zero intensity at zerothickness is assumed.

Si3/Al sites Gradient (�10�3)

Without Zn occupation 1.35% Zn with even distribution 2.25% Zn with top enrichment 2.35% Zn with bottom enrichment 2.110% Zn with even distribution 2.610% Zn with top enrichment 3.010% Zn with bottom enrichment 2.5

250 T. Saito et al. / Acta Materialia 78 (2014) 245–253

� A small part of area on the interface along [�310]Al isnon-systematically brighter than the bulk (bottom partof the precipitate shown in Fig. 4a). This might be dueto local Zn enrichment at the precipitate/matrix inter-face. Similar observations were made for disordered pre-cipitates examined in previous work [16].� The widths of the intensity distributions for the Si2 and

Si3/Al sites exceed that of the Si1 site.

3.2. Simulated HAADF-STEM intensity

Fig. 5 shows the simulated intensities for the Si3/Al siteas a function of thickness for 5% and 10% Zn occupancieswith different Zn distributions along the electron beamdirection as shown in Fig. 2. As a reference, the intensityfor all Si sites (Si1, Si2 and Si3) in the b00 phase withoutZn occupation are also shown in Fig. 5. As expected, theintensity increases with increasing specimen thickness.Since the intensity variation in a HAADF-STEM imageis approximately linear with increasing thickness [18], anintensity gradient was deduced by linear interpolation.Table 2 lists the fitted intensity gradients of Fig. 5. The fol-lowing observations can be made from Fig. 5 and Table 2.

� The intensity differences between Si sites are negligiblysmall compared with the intensity variations in the casewith partial Zn occupation.� Regardless of the Zn distribution imposed along the

electron beam direction, the presence of Zn increasesthe intensity.� The intensity gradient with respect to thickness increases

with Zn occupancy for all distributions.� Differences among the intensity gradients are encoun-

tered, depending on the Zn distribution along the column.These variations are weak in 5% Zn occupancy. For 10%Zn occupancy, the variation has increased. In both cases,

Fig. 5. Simulated intensities of the Si3/Al site in the b00 phase (points) as a functdistributions along the electron beam direction, as given in the legend. The co(lines), the intensities of all Si sites (Si1, Si2 and Si3 sites) in the b00 phase withouwith the intensity for Al on the Si3/Al site (assuming the Mg5Al2Si4 or Mg4Athickness. The right bottom rectangle shows enlarged the dashed rectangle co

Zn top enrichment yields higher interties. Note that devi-ations from linear behaviour in the actual curves makethis scatter most pronounced at realistic specimen thick-ness (>�40 nm). None of the selected Zn distributionscan be excluded as unphysical, based on the informationin Fig. 3a. These results indicate that determining the levelof partial Zn occupancy from HAADF-STEM imageintensities is not a trivial problem.

3.3. Calculated Zn replacement energies

Fig. 6 shows the calculated energies DH(b000; X! N)obtained when considering incorporation of X = Zn/Mg/Si on the various sites N in an initially Zn-free precipitateb000, as described by Eq. (4). Given the chosen supercell sizes(see Section 2.4), the examined Zn occupancy is 12.5% forall sites except Mg1, where the occupancy is twice as high.In the presentation of the data, two simplifications weremade: first, for the Si3/Al site in Mg6AlSi4, Zn (Mg) wasonly incorporated on the Al bearing (Mg bearing) site.Secondly, whenever symmetry breaking produced morethan one energy for a selected case in Fig. 6, only the lowestenergies were included. This latter simplification had no

ion of specimen thickness for 5% and 10% Zn occupancies with different Znmposition of the b00 phase was assumed to be Mg5Al2Si4. As a referencet Zn occupation (assuming the Mg5Si6 composition) are also shown, alongl3Si4 composition). See Table 2 for the estimated intensity gradients with

rresponding to thicknesses >40 nm.

Fig. 6. Calculated replacement energies for Zn and alternative soluteatoms Mg/Si on the different sites of three different b00 configurations. 1:Mg4Al3Si4, 2: Mg5Al2Si4 and 3: Mg6AlSi4. Zn and Mg/Si replacementenergies are labelled with grey and white bars, respectively. Mg wasincorporated for comparison with Zn on the Si3/Al site.

T. Saito et al. / Acta Materialia 78 (2014) 245–253 251

significant influence on the results outlined below. The fol-lowing observations can be made.

� For the Si3/Al sites, where Zn atoms were observedexperimentally, theory predicts weak binding(�0.18 eV/Zn atom or higher), with little variation forthe three different b000 configurations and a minimum atthe Mg5Al2Si4 composition.� Compared with Zn, Mg may occupy the Si3/Al sites at a

similar energy gain, but with the Mg2, and Mg3 sitesclearly favoured (�0.60 eV/Mg atom or lower).� Compared with the Si3/Al site, Zn is predicted to bind

more strongly on the Si1 and Si2 sites. Here, however,the “competing” Si atom is always binding more favour-ably. The only exception is the Si1 site in b00-Mg4Al3Si4,where Zn incorporation is “competitive” (�0.51 eV/Znatom vs. �0.56 eV/Si atom).

Additional studies probing the level of Zn–Zn interac-tions in b00 were performed only for Zn on Si3/Al sites inb00-Mg5Al2Si4. The results suggest an almost completeindifference of the system energy to the Zn separation,implying that Zn is statistically distributed on the Si3/Alsites, as opposed to clustering; see Fig. 7a. In further sup-port of this conclusion, it is noted that the Zn replacementenergy is unchanged compared with Fig. 6, although the Znconcentration has been doubled.

The variation in the Zn replacement energy as a functionof distance from the interface was also examined for Zn onthe Si3/Al site in b00-Mg5Al2Si4; see Fig. 7b. The resultsindicate that Zn atoms are preferentially incorporated inbulk b00, i.e. not close to the interface.

4. Discussion

Although strong intensity variations due to thicknesschanges and elastic strain are seen in the analysed b00 precip-itate, the statistical analysis of the HAADF-STEM image

intensities in Fig. 4 clearly indicates that the Si3/Al sites dis-play a larger mean intensity compared with the Si1 and Si2sites of the b00 phase. In addition, the intensity distributionfor the Si3/Al sites is broader. The HAADF-STEM imagesimulations in Fig. 5 suggest that the intensity differencebetween Si sites is negligibly small, compared with intensityvariations obtained with partial Zn occupations. Further-more, DFT calculations predicted (see Fig. 6) that theSi3/Al site should be the most favourable site for Zn incor-poration in the b00 phase. These results are in good agree-ment with a partial occupation of Zn atoms on the Si3/Alsites. Note that the intensity distribution for the Si2 sitesis also broader and has slightly higher intensity than thatfor the Si1 sites. However, DFT calculations suggest thatZn is effectively less likely on the Si2 sites, compared withthe Si3/Al (and even the Si1) sites. The broader intensitydistribution for the Si2 sites might result from the Zn pres-ence on the neighbouring Si3/Al sites, i.e. the increasedintensity is due to electron channelling or cross-talk arte-facts [31] between these sites. This could influence intensitiesalong h0 0 1iAl for a specimen thickness >50 nm [32]—roughly the value in the present studies. The intensity onthe Mg sites was lower than on the Si sites. This suggeststhat the Mg sites are not occupied by Zn atoms, a conclu-sion also supported by the DFT calculations.

The higher intensities in Fig. 4a come from the bulk Si3/Al sites, as opposed to the precipitate/Al matrix interfacesand their vicinity, in case of the interface along [230]Al. Itis stressed here that the average intensity in the bulk region(Fig. 3b) is also higher than near the interface. This may beattributed to the elastic lattice strain on the b00 precipitate;see the strain map in Ref. [15]. One cannot exclude, on thebasis of the present work, that this strain is appreciablyaffecting the Zn binding energy reduction near the inter-face, e.g. owing to different bonding with surroundingatoms. In particular, it is noted that the DFT results inFig. 7b do not predict differences in the Zn behaviour atthe two interfaces. Further, the Zn binding energy in b00

is always weak and as such susceptible to remaining errorsin the calculations, e.g. finite temperature effects. To clarifywhether strain or chemical effects are the more influential,DFT studies on strained supercells (e.g. following themethodology in Ref. [33]) as well as a closer experimentalexamination of compositional variations within the precip-itate of Fig. 3a would be of interest.

The DFT results suggest (see Fig. 6) that Zn on the Si3/Al site has only very weak preference for a particular b00

composition. Since the Zn-free b00 energy contours areequally weak, one cannot deduce solely from the aboveinformation how Zn may affect b00 chemically. However,the results of Fig. 6 also suggest that, in addition to theSi3/Al site, the Si1 site could be a competitive site for Znincorporation in b00-Mg4Al3Si4. Experimentally, no Zn onthe Si1 site is observed. Further, the intensity distributionsfor the Mg sites in Fig. 4b are highly similar. Those twoobservations suggest that the analysed b00 precipitate isunlikely to be dominated by local regions with the Mg4Al3Si4

Fig. 7. Zn binding energies at the Si3/Al site as a function of (a) distance between the Zn atoms along the precipitate needle direction, and (b) the columndistance from the interfaces. Zero energy denotes the formation enthalpy of isolated Zn in SS. In (b), the zero value on the x-axis represents the first Si3/Alsite at the interface [14] and negative and positive values correspond to b00 bulk side and Al matrix side, respectively.

252 T. Saito et al. / Acta Materialia 78 (2014) 245–253

composition. Even with the significant theoretical incorpo-ration of Zn in b00, the cell dimensions and the structure ofthis phase change only weakly, preferably along the b00 nee-dle direction. It is inferred that Zn has a weak interactionwith the b00 phase, where it can be considered “a defect”preferentially located at the Si3/Al site.

The precise level of Zn occupancy at the Si3/Al sitedepends not only on the projected location within the pre-cipitate, but also on the Zn distribution along the precip-itate needle, as seen in the HAADF-STEM intensityanalysis and simulations, respectively. The dependenceon the distribution is weak at low Zn occupancy (5%).However, if the occupancy is 10% and the specimen thick-ness exceeds 40 nm, the intensities for top enrichment inFig. 5 are non-negligibly higher than the other distribu-tions. The main reason for this dependence is a largeinfluence of electron channelling (and/or de-channelling).In addition, the HAADF-STEM intensity generallydepends on several factors: crystal structure and bonding,Debye–Waller factors, thickness and background inten-sity. These factors are decoupled influences on theHAADF-STEM intensity. As an example of the remain-ing complexities present here, a recent study [34] showedthat the HAADF-STEM intensity depends greatly onthe Debye–Waller factors. Interestingly, the results indi-cated that the Z-contrast of the HAADF-STEM intensitywas no longer truly valid, but depending on crystal struc-ture and bonding. Other examples of complexities to beconsidered can be mentioned: an inhomogeneousHAADF detector intensity [35] and static disorder inatomic columns, due to occupation of more than one typeof atom in the column—so-called “static atomic displace-ments” [36].

The DFT calculations indicate that the Zn–Zn interac-tions are weak for the Si3/Al site in the b00 phase. Zn isinferred to be in favour of a uniform (statistical) distribu-tion throughout the Si3/Al site column, as opposed tothe “clustering” tendencies reflected by the proposed top

and bottom Zn enrichment in the HAADF-STEM imagesimulation; see Fig. 2. In a previous work [16], Zn wasshown to induce only a low increase in precipitate numberdensity, compared with Zn-free alloys, consistent with theweak Zn influence proposed in the present study. Here,one thing may have to be considered: in principle, a newsuperstructure with different symmetry would arise if theZn atoms were periodically distributed. The Zn distribu-tion could be determined from an HAADF-STEM imagetaken in the direction normal to the precipitate needle(90� tilted from the present orientation). As the needlesare thin (<10 nm), however, observation may be difficultbecause of the huge projected atomic overlap with fcc Alin this direction.

As stated in the introduction, a key motivation in thepresent work has been to address the limits to the under-standing of the state of “a well-known phase with foreignsolute atom types”. The present investigations have high-lighted the example of Zn in b00, which is characterised byits simple nature. Since Zn was shown from previous work[16] to occupy a single site (Si3/Al) in the precipitate, agreatly eased analysis was implied. The results discussedabove have indicated that a combination of HAADF-STEM statistical analysis, HAADF-STEM image simula-tions and DFT calculations may provide highly usefulinformation, not achievable by these techniques indepen-dently. HAADF-STEM statistical analysis in combinationwith DFT calculations suggests that Zn is confined to theSi3/Al sites and statistically distributed, with non-negligi-ble consequences to the relation between Zn occupancyand intensity, as shown in HAADF-STEM image simula-tions. A combination of HAADF-STEM statistical analy-sis and simulations may quantify the Zn occupancy, withsimilar considerations applying to the b00 composition.However, this is not straightforward because of thicknessvariations and decoupled factors influencing HAADF-STEM intensity as discussed earlier. To further clarifythe state of the system, different experimental techniques,

T. Saito et al. / Acta Materialia 78 (2014) 245–253 253

e.g. APT, may support the analysis to overcome the inher-ent limitation.

5. Conclusion

A combination of statistical analysis and simulations ofHAADF-STEM intensities has been used along with DFTcalculations to clarify the state of the Zn-containing b00

phase in Al–Mg–Si alloys. Statistical analysis ofHAADF-STEM intensities shows that the intensity distri-bution of the Si3/Al sites in the b00 phase is broader, withmarkedly higher intensities, for atomic site columns pre-sumed to contain Zn. DFT calculations support that theseSi3/Al sites are preferential sites for Zn incorporation, withZn admitted as a weakly binding “defect” in b00. The occu-pancy of Zn atoms on the Si3/Al site depends on the regionin the precipitate, while the HAADF-STEM intensity var-ies as well with the Zn distribution along the precipitateneedle. DFT calculations suggest a negligible Zn–Zn inter-action, implying statistically distributed Zn in b00. Quantifi-cation of the Zn content remains problematic, as a directcomparison of HAADF-STEM image simulations withexperiment is complicated by several independent sourcesof errors. Improving the reliability of this comparisonshould be the main target of future work attempting aquantitative description of a precipitate accommodatinglow amounts of foreign solute atoms.

Acknowledgements

This research is supported by Hydro Aluminum and theResearch Council of Norway though the bilateral KMBproject: 193619 “The Norwegian-Japanese Al–Mg–SiAlloy Precipitation Project”. The authors would like tothank Dr. Olaf Engler, Hydro Bonn Germany, for compo-sition measurement by inductively coupled plasma opticalemission spectroscopy. W.L. acknowledges the AgenceNationale pour la Recherche for financial support throughthe Programme Jeune Chercheur – Jeune Chercheuse TIP-STEM. The DFT calculations were performed throughaccess to NOTUR facilities.

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