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Al2(Mg,Ca) phases in MgAlCa ternary system:First-principles prediction and experimental identification

Yu Zhong,a,* Jing Liu,b Ron A. Witt,c Yong-ho Sohnb and Zi-Kui Liua

aDepartment of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USAbAdvanced Materials Processing and Analysis Center, University of Central Florida, Box 162455,

4000 Central Florida, Orlando, FL 32816-2455, USAcEBSD Analytical Inc., 2044 North 1100 East, Lehi, Utah 84043, USA

Received 25 January 2006; revised 22 March 2006; accepted 22 March 2006Available online 21 June 2006

First-principles calculations of three Laves phase structures at Al2Ca and Al2Mg compositions predict the existence ofAl2(Mg,Ca) Laves phase. To validate this prediction, a diffusion couple between Mg30 wt.%Ca alloy and pure Al was assembledand heat-treated at 688 K for 2 weeks. From the cross section of the diffusion couple, backscatter electron microscopy coupled withelectron probe microanalysis indicated the existence of Al2(Mg,Ca). Two Laves phases, i.e. C36-Al2(Mg,Ca) and C14-Al2(Mg,Ca),were identified by indexing the electron backscatter diffraction pattern with predicted lattice parameters by first-principles calcula-tions and by diffraction analysis using transmission electron microscopy independently. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Phase identification; First-principles calculation; Mg alloy; Laves phase

MgAlCa is an important ternary system for itsextensive application in Mg alloys and Al alloys. Manyinvestigations have been carried out to examine the con-stituent binary systems, i.e. AlMg, MgCa, and AlCa;however, there has been a lack of experimental investi-gations of the ternary system due to the reactive natureof Ca.

Experiments by Catteral et al.[1], Ninomiya et al.[2],and Ozturk et al.[3]concentrated on the Mg rich corner.Recently, there have been quite a few experiments tostudy the phase equilibria in the Al2CaMg2Ca pseu-do-binary system [46] and Ca rich corner [5], and anew C36-(Mg,Al)2Ca Laves phase was discovered inthe Al2CaMg2Ca pseudo-binary system. Theoretical

calculations and experimental investigations of C36-(Mg,Al)2Ca were done in our work. The details will bepublished elsewhere.

In the present investigation, first-principles calcula-tions were used to study the stability of Laves phasesin the Al2CaAl2Mg section. Coupled with the predic-tions from first-principles calculations, diffusion couplesof an MgCa alloy and pure Al were made to examinethe existence of new phases in the Al2CaAl2Mg section.

Detailed microstructure analysis was carried outusing scanning electron microscopy (SEM), electronprobe microanalysis (EPMA), orientation imagingmicroscopy (OIM), and scanning transmission electronmicroscopy (STEM) via specimen preparation by the fo-cused ion beam (FIB) in situ lift-out (INLO) technique.

Ultrasoft pseudopotentials were used in the first-principles calculations of total energies [7,8], as imple-mented in the Vienna Ab-initio Simulation Package(VASP)[912]. The generalized gradient approximation(GGA) [13,14] calculations were employed. We usedVanderbilt ultra-soft pseudopotentials [7,8] and thecut-off energies for pure Al, Mg, and Ca were chosensimilar to the choice made in the previous publication

[15]. Extensive tests ofk-point sampling indicated thatthe total energy differences converged to within0.1 kJ/mole.

A general two-sublattice model (Mg,Al,Ca)2(Mg,Al,Ca)1 was used to model the three Laves phases, C14,C15, and C36. First-principles calculations were carriedout to provide the enthalpies of formation of all the nineend-members, including Al2Ca and Al2Mg. Surpris-ingly, the enthalpies of formation of Al2Mg break theconvex hull from the previous modeling [16] as shownin Figure 1. Thus the thermodynamic database of theAlMg binary system has been updated[17].

1359-6462/$ - see front matter

2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.doi:10.1016/j.scriptamat.2006.03.068

* Corresponding author. E-mail:yqz100@psu.edu

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The total energies and the enthalpies of formation ofthe three Laves crystal structures at Al2Mg and Al2Ca

compositions were calculated as reported in Table 1.The enthalpies of formation of the three Laves phasestructures of Al2Mg vary from 2.301 kJ/mol to2.802 kJ/mol, while those of Al2Ca vary from32.722 kJ/mol to 33.981 kJ/mol. The C15 structure,which has the lowest enthalpy of formation at the Al2Cacomposition, is the stable phase in the AlCa binarysystem. The C36 structure has the lowest enthalpy offormation at the Al2Mg composition among the threeLaves phase structures, while none of them is stable inthe AlMg system. However, the enthalpies of forma-tion of C14 and C36 are only 0.312 kJ/mol and0.223 kJ/mol higher than the stable convex hull asshown inFigure 1is a very small difference in enthalpies

of formation among these three Laves phase structures.The maximum difference is only 0.501 kJ/mol for Al2Mgand 1.259 kJ/mol for Al2Ca. These differences are verysmall considering the uncertainty of first-principles cal-culations, viz., 1 kJ/mol, and indicate that a ternaryLaves phase Al2(Mg,Ca) may exist in the Al2CaAl2Mgsection. The existence of the ternary Laves phase is thusmainly determined by the entropies of formation of allnine end-members and the ternary interaction parame-ters of these three Laves phases, which is not availableyet. To verify the prediction from first-principles calcu-lations, experiments are carried out.

The Mg30 wt.%Ca alloy was acquired from Timm-

inco Ltd. The diffusion couple was prepared using Mg30 wt.%Ca alloy with pure Al (99.99%). The tube was

placed in a furnace and isothermally heat treated for 2weeks at 688 K. The diffusion couple was then quenchedin water, and its cross section was prepared using stan-dard metallographic techniques.

The cross-sectional specimen was first examinedusing backscatter electron image via SEM. EPMA anal-ysis was performed on the diffusion couple to quantita-

tively determine the composition of phases across thediffusion zone by using Cameca SX50.OIM was used to identify the crystal structures of the

phases developed in the diffusion couple. The FIB-INLO technique was employed to prepare a site-specificTEM specimen [18,19], as shown in Figure 2. TEM/STEM using FEI/Tecnai F30 equipped with high angleannular dark field (HAADF) and X-ray energy disper-sive spectroscopy (XEDS) was employed for phase iden-tification by electron diffraction.

Figure 3 shows a backscatter electron image fromthe cross section of the diffusion couple. The dark regionwas identified as hexagonal close-packed (hcp) Mgphase. The lightest region contained the highest amount

of Ca. EPMA analyses were used to identify the phasesinvolved, such as b-Al140Mg49, c-Al12Mg17, C15-Al2Ca,C14-Mg2Ca, and hcp-Mg.

A broad region above the b phase region was identi-fied as Al2(Mg,Ca) as indicated in Figure 3. DetailedEPMA analysis was carried out starting from points inthe Al2(Mg,Ca) phase region to points in theb phase re-gion. The concentration profiles within this phase showthat Al2(Mg,Ca) contains about 66.7 at.% Al, while Mgconcentrations vary from 17.3 at.% to 22.5 at.% asshown in Figure 4. Al2(Mg,Ca) was labeled in the iso-thermal section of the MgAlCa ternary system at688 K with this updated data as shown in Figure 5.

The possible diffusion path is also plotted in Figure 5in dash line. Because of the appearance of Al2(Mg,Ca),

Figure 1. The calculated enthalpy of formation at 298 K as a functionof Mg concentration in the AlMg system [17] in comparison withfirst-principles calculation results (*) for C14, () for C15, (+) for C36,and previous modeling[16](dotted line).

Table 1. Structure properties and enthalpies of formation for the AlMg binary system in a variety of order structures

Lattice constants(A)

Total energy(eV/atom)

Enthalpies offormation

(kJ/mol-atom)

hcp-Mg a= 3.177, c = 5.172 1.4852 fcc-Al a= 4.041 3.6892 fcc-Ca a= 5.486 1.9477 C14-Al2Ca a= 5.670, c = 9.231 3.4478 32.722C15-Al2Ca a= 8.005 3.4609 33.981C36-Al2Ca a= 5.686, c = 18.347 3.4571 33.617C14-Al2Mg a= 5.448, c = 8.742 2.9827 2.713C15-Al2Mg a= 7.667 2.9784 2.301C36-Al2Mg a= 5.450, c = 17.514 2.9836 2.802

Figure 2. Typical procedure of TEM specimen preparation by usingfocused ion beam in situ lift-out technique.

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the thermodynamic database of the MgAlCa ternarysystem needs to be updated in the future. More calcula-

tions and experiments are needed to understand theentropies, interaction parameters, and solubility and sta-bility ranges of ternary Laves phases.

There is a significant possibility that Al2(Mg,Ca) maybe one of these Laves phases from the first-principlescalculation results. With the lattice parameters of thetwo end-members of these three Laves phases (Al2Ca

and Al2Mg), simple linear approximation was used toestimate the lattice parameter ranges of the three candi-dates as listed inTable 2, which serves as the input forthe OIM analysis. Candidates 1, 2, and 3 representAl2(Mg,Ca) phase with C15, C14, and C36 structures,respectively.

Based on the composition determined by EPMA,possible candidates with different lattice parametersfrom first-principles calculations were proposed, andOIM analysis was performed to identify the crystalstructure of the Al2(Mg,Ca) phase as shown in Figure3. EBSP matches only to that of the Laves C36 phase(candidate 3) with lattice parameters a= 5.450 A,c= 17.514 A. EBSPs for b-Al140Mg49, C15-Al2Ca, and

C14-Mg2Ca are also shown in Figure 3. The phasemap in Figure 6(a) clearly shows the phase regions inthe cross section of the diffusion couple by comparing theEBSP of each phase.Figure 6(b)(f) also shows the ori-entation color coded maps for C15-Al2Ca, c-Al12Mg17,C14-Mg2Ca, Candidate 3(C36), and Mg-hcp phases.

Figure 7(a) and (b) shows the bright field andHAADF images of theb phase and Al2(Mg,Ca), respec-tively. XEDS with resolution of approximately 200 nmconfirms the presence of Al, Ca, and Mg in this newphase as shown in Figure 7(c). Al2(Mg,Ca) was identi-fied as C14 hexagonal Laves phase with lattice parame-ters of a= 5.56 A and c= 9.02 A based on electron

diffraction analysis, which lies in the range of our pre-dicted lattice parameter for C14 Laves phase.Two different Laves phases, i.e. C36 and C14, were

thus found surprisingly by using OIM analysis andTEM independently. It is not unusual that two or threeLaves phases exist in an A2BA2C or AB2AC2sectionin an ABC ternary system. This may be due to thevery small energy difference among the three Lavesphase structures. Our first principles calculations of all25 end-members of three Laves phase structures inMgAlCaSrZn quinary system show the three Lavesphases have very similar enthalpies of formation at 0 K,by comparing the results at each composition [20]. Thedifference of these three structures are typically around

Figure 3. OIM identification of phases in SEM backscatter electronimage of the cross section of the MgCa alloy and pure Al diffusioncouple. The EBSP are shown in pairs with the un-indexed pattern onthe left and the indexed pattern on the right.

Figure 4. Composition profile for Al2(Mg,Ca) measured by EPMA.

Figure 5. Isothermal section of the MgAlCa ternary system at688 K.

Table 2. Crystal structure information for phases in the MgAlCasystem

Phase Pearson symbol a c

fcc-Al cF4 4.0495 4.0495hcp-Mg hP2 3.1775 5.1717b-Al140Mg89 cF1832 28.239 28.239e-Al30Mg23 hR159 12.718 21.848c-Al12Mg17 cI58 10.544 10.544C15-Al2Ca cF24 8.02 8.02C14-Mg2Ca hP12 6.212 10.050Candidate 1 cF24 7.6678.02 7.6678.02Candidate 2 hP12 5.4485.670 8.7429.231

Candidate 3 hP24 5.4505.686 17.51418.347

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12 kJ/mol for all the stable and non-stable end-mem-bers, which are reasonable as the only difference between

these three Laves phases is the stacking sequences ofatoms[4].In summary, first-principles calculations of three

Laves phase structures at Al2Ca and Al2Mg composi-tions have been shown to predict the existence ofAl2(Mg,Ca) Laves phases. Backscatter electron micros-copy coupled with EPMA analysis verified the existenceof Al2(Mg,Ca). C36-Al2(Mg,Ca) Laves phase was iden-tified by indexing EBSP with predicted lattice parame-ters by first-principles calculations. C14-Al2(Mg,Ca)Laves phase was identified by TEM and electrondiffraction via site-specific specimen preparation byFIB-INLO with lattice parameters of a= 0.556 nmand c= 0.902 nm. Investigations are being carried out

to determine the temperature stability range and solubil-ity range of these two new ternary Laves phases.

This work is supported by the NSF CAREERAwards under the grant DMR-9983532 and DMR-0510180 (Liu) and DMR-0238356 (Sohn). First-principles calculations were carried out at the Materials

Simulation Center (MSC) of Penn State University.FIB-INLO specimen preparation and TEM analysiswere carried out at Materials Characterization Facility(MCF) of University of Central Florida. Authors wouldalso like to express their appreciation to J. Boynes, D.Artis, L. Farlow, E. Lipe and J. Mercer participated inthe diffusion couple experiments in connection with theSEEMS program (Summer Experience in Earth andMineral Science) at Penn State, a program organizedat Penn State in cooperation with the Upward BoundMath and Science Center and Drs. Carelyn E. Campbelland William J. Boettinger for providing this collabora-tive research opportunity with semiannual workshopsentitled High Throughput Analysis of MulticomponentMultiphase Diffusion Data (www.ctcms.nist.gov/~ce-camp/Present.html).

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Figure 6. Phase map (a) and orientation color coded maps for Al2Ca(b), c-Al12Mg17(c), Mg2Ca (d), Candidate 3 (e), and Mg-hcp (f) of thecross section of MgCa alloy and pure Al diffusion couple from OIManalysis.

Figure 7. (a) and (b) Bright field and HAADF images of the b phaseand Al2(Mg,Ca), respectively; (c) XEDS results of the Al2(Mg,Ca)phase as marked in (b); (d) the corresponding diffraction pattern of themarked phase in (b).

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