thermodynamic description of the al-fe-mg-ni-si and al-cu ......2015/01/01 · thermodynamic...

Thermodynamic Description of the Al-Fe-Mg-Ni-Siand Al-Cu-Fe-Mg-Ni Quinary Systems and Its

Application to Solidification SimulationBiao Hu, Song Qin, Yong Du, Zhiyong Li, and Qingping Wang

(Submitted January 1, 2015; in revised form April 20, 2015; published online May 8, 2015)

Based on the critical review of the available experimental phase equilibrium data for the con-stituent quaternary systems in the Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni quinary systems, a set ofself-consistent thermodynamic parameters for these systems has been obtained using theCALPHAD approach. In combination with the constituent binary, ternary and quaternarysystems, the thermodynamic database for the quinary Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Nisystems was developed. Comprehensive comparisons between the calculated and measuredphase diagrams and invariant reactions showed that the experimental data were satisfactorilyaccounted for by the present thermodynamic description. The established database was used todescribe the solidification behaviors of Al alloys 6063 (Al-0.39Si-0.20Fe-0.43Mg, in wt.%) and2618 (Al-2.24Cu-1.42Mg-0.9Fe-0.9Ni, in wt.%) under Gulliver-Scheil non-equilibrium condition.The reliability of the present thermodynamic database was also verified by the good agreementbetween the Gulliver-Scheil calculation and experiment.

Keywords Al alloys, Al-Cu-Fe-Mg-Ni, Al-Fe-Mg-Ni-Si, CAL-PHAD, solidification

1. Introduction

Casting Al alloys containing nickel and silicon are widelyused in the automotive industry in piston applications.Casting Al alloys usually contain several major components(i.e. Cu, Fe, Mg, Ni and Si) and are known to have verycomplex phase compositions.[1] The mechanical and chemi-cal properties as well as the corrosion resistance of solidifiedAl alloys are heavily dependent on the microstructureobtained after solidification.[2] In order to obtain optimalmaterial properties, accurate predictions of the reactionsduring solidification are essential to design solidificationprocess and subsequent heat treatments. Hence, knowledge ofthe phase diagrams and thermodynamic properties of the six-component Al-Cu-Fe-Mg-Ni-Si system is the theoreticalbasis to understand the performance of casting Al alloys.

The CALculation of PHAse Diagrams (CALPHAD)approach has become a valuable tool in the calculation ofcomplex multi-component phase equilibria of industrial alloysbased on experimental thermodynamic and phase diagramdata. However, assessment of the six-component Al-Cu-Fe-Mg-Ni-Si system is a very challenging task. In general, theassessment of high-order alloying systems starts with theevaluation of phase diagrams and thermodynamic properties inlow-order alloying systems. In the present work, the thermo-dynamic description of the two quinary Al-Fe-Mg-Ni-Si andAl-Cu-Fe-Mg-Ni systems that constituent the commerciallyimportant Al-Cu-Fe-Mg-Ni-Si alloying system is performed.

The aims of the present work are: (1) to establish athermodynamic database for the quinary Al-Fe-Mg-Ni-Si andAl-Cu-Fe-Mg-Ni systems on the basis of the constituentbinary, ternary and quaternary systems using the CALPHADapproach; and (2) to apply the present database to simulatesolidification behaviors of Al alloys 6063 (Al-0.39Si-0.20Fe-0.43Mg, in wt.%) and 2618 (Al-2.24Cu-1.42Mg-0.9Fe-0.9Ni,in wt.%) under Gulliver-Scheil non-equilibrium condition.

2. Evaluation of Phase Diagram Information in theLiterature

In order to facilitate reading, information on the phasesof the Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni systems in Al-rich corner investigated in the present work is listed inTable 1.

2.1 The Binary Systems

There are 14 binary systems in the quinary Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni systems. The thermodynamic

Biao Hu, School of Materials Science and Engineering, AnhuiUniversity of Science and Technology, Huainan 232001 Anhui,People’s Republic of China and State Key Laboratory of PowderMetallurgy, Central South University, Changsha 410083 Hunan,People’s Republic of China; Song Qin and Yong Du, State KeyLaboratory of Powder Metallurgy, Central South University, Changsha,Hunan, 410083, People’s Republic of China; and Zhiyong Li andQingping Wang, School of Materials Science and Engineering, AnhuiUniversity of Science and Technology, Huainan, Anhui, 232001,People’s Republic of China. Contact e-mail: [email protected] [email protected].

JPEDAV (2015) 36:333–349DOI: 10.1007/s11669-015-0388-01547-7037 �ASM International

Journal of Phase Equilibria and Diffusion Vol. 36 No. 4 2015 333

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parameters of these binary systems are all taken fromliterature. The selection of these thermodynamic parametersis briefly described as follows.

The Al-Fe system was thermodynamic described byseveral groups of authors.[3-5] The thermodynamic assess-ment of the Al-Fe system most used in databases was bySeierstein[3] from the COST 507 project. Recently, Jacobsand Schmid-Fetzer[4] improved the representation of thebcc_A2, bcc_B2 and fcc_A1 phases based on the descrip-tion from Seierstein.[3] Sundman et al.[5] reassessed thestable and metastable equilibria in the Al-Fe system using afour-sublattice model to describe disordered A2 and the B2,D03 and B32 ordering. Based on the work of Seierstein,[3]

Du et al.[6] modified the thermodynamic parameters for theAl13Fe4, Al5Fe2 and Al2Fe phases in order to reflect thecongruent melting behavior of Al13Fe4. All of the thermo-dynamic assessments could represent the experimental datafairly well. The four-sublattice model presented by Sund-man et al.[5] was not compatible with a two-sublattice modelin other binary systems. To be compatible with ourestablished Al-based thermodynamic database, the thermo-dynamic parameters from Du et al.[6] based on the modelingof Seierstein[3] were finally adopted in this work.

The recent thermodynamic description of theAl-Mg systemcould be obtained in the work of Liang et al.,[7] Zhong et al.[8]

and Aljarrah.[9] Liang et al.[7] and Zhong et al.[8] applied therandommixingmodel for the liquid phase, andAljarrah[9] usedthe modified quasichemical model to described the liquidphase. The experimental data could be well reproduced by thethermodynamic modeling mentioned above. In order tocoincide with our established Al-base thermodynamic data-base, the modeling by Liang et al.[7] was adopted in this work.

The widely adopted thermodynamic modeling of the Al-Cu systems was from Saunders[10] in the COST 507 project.

The parameters of the liquid and c_D83 phases weremodified by Witusiewicz et al.[11] based on the work ofSaunders.[10] There were no obvious differences betweenthem except the c_D83 phase field at temperatures below600 K. Due to the slightly influence of the c_D83 phase tophase relationships in higher-order systems at low tem-perature, the thermodynamic assessment of the Al-Cusystem by Saunders[10] was adopted in the present work.

The Fe-Ni phase diagram has been constructed byseveral groups[12-14] by means of CALPHAD approach.Servant et al.[12] assessed the Fe-Ni system using a four-sublattice model to describe the order/disorder transforma-tion. Keyzer et al.[13] calculated the stable Fe-Ni phasediagram showing a large discrepancy between computedand experimental melting equilibria. Cacciamani et al.[14]

also assessed the Fe-Ni system using a four-sublattice modelto describe both stable and metastable fcc-based orderedphases as well as the bcc-based ordered phases. Zhang andDu[15] have been converted the parameters of the Ni3Fephase in the Fe-Ni system[12] from a four-sublatticeformalism to a two-sublattice one in order to maintain theconsistency with the other binary systems. Considering ofthe accuracy of the thermodynamic parameters and theconsistency of the models, the thermodynamic parameters inthe Fe-Ni system were taken from Zhang and Du[15] basedon the modeling of Servant et al.[12] in the present work.

The widely accepted thermodynamic assessment of theFe-Si system was from Lacaze and Sundman.[16] Later on,Miettinen[17] did a slight modification of the solution phasesand Tang and Tangstad[18] reassessed the phase equilibria inthe Si-rich domain of the Fe-Si system based on the work ofLacaze and Sundman.[16] All of the thermodynamic modelingcould represent well experimental data. In order to coincidewith our established Al-base thermodynamic database, the

Table 1 List of the symbols to denote the phases of the Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni systems in the Al-richcorner

Symbol Phase Pearson symbol/space group/prototype

L Liquid -, -, -

(Al) Solid solution based on Fcc_A1 Ni cF4, Fm�3m, Cu

(Si) Solid solution based on Diamond_A4 Si cF8, Fd�3m, C(diamond)

Al13Fe4 Solid solution based on Al13Fe4 mC102, C2/m, Al13Fe4Al3Ni Solid solution based on Al3Ni oP16, Pnma, Fe3C

Al3Ni2 Solid solution based on Al3Ni2 hP5, P�3m1, Al3Ni2Mg2Si Solid solution based on Mg2Si cF12, Fm�3m, CaF2b_AlMg Solid solution based on Al140Mg89 cF112, Fd�3m, Cd2Na

Al2Cu Solid solution based on Al2Cu tI12, I4/mcm, Al2Cu

AlFeSi_T2 Ternary compound Al0.5Fe0.2Si0.1(Al, Si)0.2 m**, mC*, Al3FeSi

AlFeSi_T4 Ternary compound (Al, Si)5Fe1 tI24, I4/mcm, GaPd5Al8Fe2Si Ternary compound Al71Fe19Si10 hP244, P63/mmc, Al7.4Fe2Si

Al9Fe2Si2 Ternary compound Al9Fe2Si2 mC52, C2/c, Al9Fe2Si2Al9FeNi Ternary compound Al9(Fe, Ni)2 mP22, P21/c, Al9Co2Al7Cu2Fe (N) Ternary compound Al7Cu2Fe tP40, P4/mnc, Al7Cu2Fe

Al2CuMg (S) Ternary compound Al2CuMg oC16, Cmcm, BRe3Al6CuMg4 (T) Ternary compound Mg26(Al,Mg)6 (Al,Cu,Mg)48Al1 -, -, -

Al6(CuFe) (D) Ternary compound Al62Cu25Fe13 -, -, -

Al7Cu4Ni Ternary compound Al1(Cu,Ni)1 hR42, R�3m, -

Al9FeMg3Si5 Quaternary compound Al18Fe2Mg7Si10 hP18, P�62m, Al9FeMg3Si5

334 Journal of Phase Equilibria and Diffusion Vol. 36 No. 1 2015

thermodynamic parameters from Lacaze and Sundman[16]

were finally used in this work.In the case of the Cu-Mg system, there were three

available thermodynamic descriptions from Coughanowret al.,[19] Zuo and Chang[20] and Zhou et al.[21] Coughanowret al.[19] and Zuo and Chang[20] treated the liquid andMg2Cu phases as a regular solution and a stoichiometriccompound, respectively. Accordingly, Zhou et al.[21] usedan association model for the liquid phase and a two-sublattice model to describe the Mg2Cu phase. From theoverall, these thermodynamic modeling could represent theexperimental data fairly well. In order to coincide with ourestablished Al-base thermodynamic database, the modelingby Coughanowr et al.[19] was finally accepted in this work.

TheMg-Ni systemwas formerly assessed by four groups ofauthors.[22-25] The experimental Mg-Ni phase diagram couldbe represented by all of the parameter sets mentioned above.However, this is not the case for the thermodynamic properties,especially for the measured heat capacities of the Mg2Ni andMgNi2 phases. Only the thermodynamic parameters from thework of Jacobs and Spencer[24] could describe the heatcapacity of MgNi2 phase in the Mg-Ni system satisfactory.Hence, the thermodynamic parameters from Jacobs andSpencer[24] were adopted in the present work.

The recent thermodynamic assessment of the Mg-Sisystem has been conducted by several groups of au-thors.[26-30] Yan et al.[26] and Kevorkov et al.[27] used 6and 4 parameters, respectively, to describe the liquid phase.Jung et al.[28] modeled this system using the modified quasi-chemical model to describe the liquid phase, in which 4parameters were introduced for the liquid phase. Yuanet al.[29] applied an exponential formulation to describe theexcess Gibbs energy of the liquid phase. Schick et al.[30]

reassessed the Mg-Si system to resolve the uncertainties inthe Gibbs energy of the Mg2Si phase by means of a hybridapproach of ab initio, experimental and CALPHAD.Considering of the consistency of the models, the thermo-dynamic parameters in the Mg-Si system were taken fromKevorkov et al.[27] in the present modeling.

For the Ni-Si system, the lasted two thermodynamicassessments were carried out by Du and Schuster[31] andTokunaga et al.[32] Both thermodynamic modeling could wellreproduce the experimental data. In order to coincide with ourestablished Al-base thermodynamic database, the modelingby Du and Schuster[31] was finally adopted in this work.

The latest thermodynamic parameters of the Al-Ni,[33]

Al-Si,[34] Fe-Mg,[35] Cu-Fe[36] and Cu-Ni[37] systems areadopted in the present thermodynamic database.

2.2 The Ternary Systems

There are 16 ternary systems in the quinary Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni systems. The thermodynamicparameters of these ternary systems are all taken fromliterature. The selection of these thermodynamic parametersis briefly described as follows.

The lasted thermodynamic parameters for the Al-Fe-Nisystem assessed by Zhang et al.[38] were adopted in thepresent work. However, the published parameters cannotwell describe the Al9FeNi phase stabilizing at low tem-

peratures in the Al-Fe-Ni system. Therefore, the thermody-namic parameters of the Al9FeNi phase were slightlymodified in our previous work.[39]

Thermodynamic assessments have been performed for theAl-Fe-Si ternary system several times. The most recentassessment over the whole composition range have been doneby Du et al.[6] Eleno et al.[40] recently reassessed the Al-richphase equilibria of the Al-Fe-Si system and refined thedescriptions of a-AlFeSi, b-AlFeSi, s2-AlFeSi and s4-AlFeSiwithin the COST507 database. However, the Al-Fe-Si descrip-tion in the COST507 database is relatively outdated comparedwith that of Du et al.[6] A further thermodynamic reassessmentof the Al-Fe-Si system in the Al-rich corner was carried out inour previous work[39] based on the work of Du et al.[6]

For the Al-Mg-Si system, a thermodynamic optimizationwas carried out by Feufel et al.,[41] which was included inthe COST507 project. Lacaze and Valdes[42] modifiedslightly the description of the liquid phase in the Al-Mg-Si system with respect to the COST 507 data. The calculatedresults were similar with the work of Feufel et al.[41] In orderto avoid an artificial miscibility gap at high temperaturesautomatically without adding any thermodynamic con-straint, Tang et al.[43] used an exponential formulation todescribe the excess Gibbs energy of the liquid phase.Considering of the consistency of the models in ourestablished Al-base thermodynamic database, the thermo-dynamic parameters in the Al-Mg-Si system were takenfrom Feufel et al.[41] in the present modeling.

The recent thermodynamic assessment of the Cu-Fe-Nisystem has been carried out by several groups of au-thors.[12,44,45] Servant et al.[12] assessed the Cu-Fe-Ni systemtaking into account the disorder/order transformation betweenfcc-Al and (Cu,Ni)3Fe base on the new experimental data.Turchanin et al.[44] improved the description of the miscibilitygap and phase equilibria involving liquid phase. But theorder/disorder phase transformations have not been consid-ered. Dreval et al.[45] updated the thermodynamic descriptionof the Cu-Fe-Ni system considering the newly availableexperimental data based on the work of Turchanin et al.[44]

The thermodynamic parameters of the Cu-Fe and Cu-Ni sub-systems adopted in the work of Dreval et al.[45] wereinconsistent with the ones accepted in our established Al-basethermodynamic database. Hence, the thermodynamic pa-rameters of the Cu-Fe-Ni system assessed by Servant et al.[12]

were adopted in our thermodynamic database.The latest thermodynamic parameters of the Al-Fe-

Mg,[46] Al-Mg-Ni,[47] Al-Ni-Si,[48] Al-Cu-Fe,[49] Al-Cu-Mg,[50] Al-Cu-Ni,[51] Fe-Mg-Ni,[52] Fe-Mg-Si,[53] Mg-Ni-Si,[54] Cu-Mg-Ni[55] and Fe-Ni-Si[56] systems are adopted inthe present thermodynamic database.

The remaining ternary system Cu-Fe-Mg is assumed tobehave as ideal solutions, i.e. the thermodynamic pa-rameters are extrapolated from the corresponding sub-binary sides.

2.3 The Quaternary Systems

2.3.1 The Al-Fe-Ni-Si System. Since the review of theexperimental phase equilibria of the Al-Fe-Ni-Si systemhave been reported by our previous work,[39] they are briefly


presented here. Gusev[57] and Belov[58] employed about 80quaternary alloys to study the microstructure, phase com-position, and thermograms of cast and heat-treated alloys,which were reviewed and summarized in detail by Belovet al. in 2002[59] and 2005.[60] On the basis of theexperimental results from Gusev[57] and Belov,[58] thedistribution of phase fields in the solid state and twovertical sections: Al94Si5Fe1-Al92Ni2Si5Fe1 and Al91Si8Fe1-Al89Ni2Si8Fe1 in wt.% were constructed by Belovet al.[59,60] Most recently, 6 alloys along two verticalsections (Al94Si5Fe1-Al92Ni2Si5Fe1 and Al91Si8Fe1-Al89Ni2-Si8Fe1 in at.%) were prepared by our previous work.[39] Therelated phase equilibria, phase transition temperatures, andsolidified microstructure were determined in both annealedand as-cast alloys by means of XRD, SEM/EDX, EPMA,TEM and DTA techniques. On the basis of the experimentalequilibria from the present work and the literature, a set ofself-consistent thermodynamic parameters for the quater-nary Al-Fe-Ni-Si system in Al-rich corner was simultane-ously obtained and adopted in the present work.

2.3.2 The Al-Fe-Mg-Si System. Phillips[61] investigatedthe phase equilibria in the Al-rich corner of the Al-Fe-Mg-Siin the composition range from 0 to 12 wt.% Mg, 0 to 14wt.% Si, and 0 to 2.5 wt.% Fe using thermal analysis andoptical microscopy. Gul’din and Dokukina[62] measured thesolubility of Fe and Si in Al-Mg melts and the eutecticreaction temperature for L = (Al) + Al13Fe4 + Mg2Si +b_AlMg. The experimental data on the liquidus and thephase distribution in the solid state for this quaternarysystem have been reviewed by Barlock and Mondolfo.[63]

Backerud et al.[64] presented the solidification data for thealuminum 6063 alloy (Al-0.39Si-0.2Fe-0.43Mg, in wt.%).The solidification begins with the Fcc_A1 phase at 655 �C.Next Al8Fe2Si forms at 618 �C, Al9Fe2Si2 at 613 �C, andfinally Mg2Si begins to solidify.

No thermodynamic data have been reported for thisquaternary system. The only quaternary compound Al9-FeMg3Si5 was found by Phillips.[61] Belov et al.[60] reporteda series of isothermal and vertical sections for the quaternarysystem and showed that the quaternary Al9FeMg3Si5 phaseis stable at low temperature. By means of single-crystalautomatic, the stoichiometry of the Al9FeMg3Si5 phase wasdetermined to Al18Fe2Mg7Si10 by Krendelsberger et al.[65]

The thermodynamic description of the Al-Fe-Mg-Siquaternary system in the Al-rich corner has been succes-sively performed by Daniel[66] and Du et al.[67] However,the calculated liquid phase compositions of the invariantreactions by Daniel[66] show noticeable discrepancies fromthe experimental ones and the Al9FeMg3Si5 phase stabilizedat low temperature cannot be well described by both of thework.[66,67] Thus, the thermodynamic parameters of thequaternary Al9FeMg3Si5 phase are slightly modified in thepresent work.

2.3.3 The Al-Mg-Ni-Si System. A limited amount ofexperimental data for the Al-Mg-Ni-Si system was availablein the literature. The Al-Mg-Ni-Si phase diagram wasexperimentally studied by Belov[68] in the region of the Al-Mg2Si-Si-Al3Ni tetrahedron, inside which no quaternarycompound was found. The Mg2Si, Al3Ni and (Si) phaseshave almost the same compositions as in the corresponding

ternary system. In addition, two invariant eutectic reactions,i.e. L = (Al) + Mg2Si + Al3Ni + (Si) and L = (Al) + Mg2-Si + Al3Ni + b_AlMg, and one quasi-ternary eutectic reac-tion, i.e. L = (Al) + Mg2Si + Al3Ni, were reported byBelov[68] in the Al-rich corner of the Al-Mg-Ni-Si system.Considering the lack of experimental information and theabsence of the quaternary compound, direct extrapolationcalculations for the Al-Mg-Ni-Si system were carried out inthe present work. The experimental data reported byBelov[68] were used to compare with the present calculationresults.

2.3.4 The Al-Cu-Fe-Mg System. No quaternary phasewas found in the Al-Cu-Fe-Mg system. The phases Al2Cu,Al13Fe4, b_AlMg, Al7Cu2Fe, Al2CuMg, Al6CuMg4 andAl6(CuFe) from the constitutive systems are in equilibriumwith (Al). The liquidus projection and the distribution ofphase regions in solid state and six invariant reactions inAl-rich corner of the Al-Cu-Fe-Mg system were reportedby Mondolfo.[69] The compositions of Fe in liquid phaseare extremely limited for these invariant reactions and thecorresponding invariant points are close to the invariantpoints of the Al-Cu-Mg ternary system. Just as thequaternary Al-Mg-Ni-Si system, direct extrapolation cal-culations for the Al-Cu-Fe-Mg system are also carried outin the present work due to the lack of any reliableexperimental information and the absence of the quater-nary compound.

2.3.5 The Al-Cu-Fe-Ni System. Until now, only onepiece of experimental measurement of phase diagram in theAl-corner of the Al-Cu-Fe-Ni system has been reported byRaybor and Ward.[70] In the work of Raybor and Ward, 74specimens containing 10 and 15 wt.% of solute metals inaluminum were prepared. After annealing for 10 weeks at530 �C, the specimens were examined by metallographic, x-ray diffraction, and electrode-potential measurements. Twoisothermal sections with 90 and 85 wt.% Al at 530 �C wereconstructed. In the composition range investigated, the (Al)solid solution was in equilibrium with the Al2Cu phase, theternary Al7Cu2Fe phase, or the ternary Al7Cu4Ni phase. Thecompound Al7Cu2Fe was shown to be capable of dissolvingNi up to a limit of approximately 6.8 wt.% at 530 �C. Thesolubility of Fe in Al7Cu4Ni is much smaller and is about0.8 wt.%. The experimental data published by Raybor andWard[70] are used in the present thermodynamic modeling.

2.3.6 The Al-Fe-Mg-Ni, Al-Cu-Mg-Ni, Fe-Mg-Ni-Si andCu-Fe-Mg-Ni Systems. No quaternary phase was re-

ported in the quaternary Al-Fe-Mg-Ni, Al-Cu-Mg-Ni, Fe-Mg-Ni-Si and Cu-Fe-Mg-Ni systems. In the literature, therewas no experimental information on the phase diagrams ofthe above four quaternary systems. Consequently, thethermodynamic properties for the above three quaternarysystems are extrapolated from the descriptions of theconstituent ternary systems.

2.4 The Quinary Systems

2.4.1 The Al-Fe-Mg-Ni-Si System. For the quinary Al-Fe-Mg-Ni-Si system, only one piece of experimentalinformation has been reported by Belov et al.[1] Accordingto the work of Belov et al.,[1] three invariant reactions, i.e.


L + Al9Fe2Si2 = (Al) + (Si) + Al9FeMg3Si5 + Al9FeNi, L +Al9FeNi = (Al) + (Si) + Al9FeMg3Si5 + Al3Ni and L = (Al) +(Si) + Mg2Si + Al3Ni + Al9FeMg3Si5, with participation of(Al) and (Si) in the Al-rich region of the Al-Fe-Mg-Ni-Sisystem were reported. The distribution of phase fields in thesolid state, the polythermal projection of solidificationsurfaces, one isothermal section Al84Mg2Si13Ni1-Al86Si13Ni1-Al84Fe2Si13Ni1 in wt.% at 300 �C, and one verticalsection Al85Mg1Ni1Si13-Al84.4Fe0.6Mg1Ni1Si13 in wt.%were constructed by Belov et al.[1] Direct extrapolationcalculations for the Al-Fe-Mg-Ni-Si system were carried outin the present work. The experimental data reported byBelov et al.[1] were used to compare with the presentcalculation results.

2.4.2 The Al-Cu-Fe-Mg-Ni System. The information ofthe experimental phase equilibrium for the quinary Al-Cu-Fe-Mg-Ni system was very limited. Aluminum alloy 2618 withthe composition range of Al-1.9-2.7Cu-0.9-1.3Fe-1.3-1.8Mg-0.9-1.2Ni-0.1-0.25Si (in wt.%) attracted extensive research.[71-74] According to the work of Belov et al.,[60] the microstructureof the 2618 alloy in the as-cast state contains particles of theAl9FeNi and Al2CuMg phases. The Al9FeNi phase probablyforms through the binary eutectic reaction L = (A1) + Al9Fe-Ni, which occurs over a wide temperature range fromapproximately 640-645 �C down to 505-515 �C due to thepresence of copper andmagnesium in an alloy. The appearanceof the Al2CuMg phase in the as-cast structure is a consequenceof non-equilibrium solidification. During homogenizing an-nealing, it completely dissolves in solid solutiom (Al). Inaddition, quasi-ternary section Al-Al9FeNi-Al2CuMg of theAl-Cu-Fe-Mg-Ni phase diagram was tentatively constructedbyBelov et al.[60] Themicrostructure of the as-cast Al-2.24Cu-1.42Mg-0.9Fe-0.9Ni (in wt.%) alloy, consisting of (Al)matrix,Al/Al2CuMg eutectic structure, Al7Cu2Fe, Al7Cu4Ni andAl9FeNi compounds, were studied by Wang et al.[71] After16 h homogenization at 520 �C, the lamellar eutectic phasesdissolved into the matrix, and the intermetallics containing FeorNiwere remained in themicrostructure. Direct extrapolationcalculations for the Al-Cu-Fe-Mg-Ni system were also carriedout in the present work. The experimental data from Belovet al.[60] and Wang et al.[71] were used to compare with thepresent calculation results.

3. Thermodynamic Modeling

In the present work, the quaternary phase Al9FeMg3Si5 istreated as a stoichiometric phase Al18Fe2Mg7Si10, and itsGibbs energy is expressed relative to the mechanical mixingof the pure elements by the following equation:

GAl9FeMg3Si5m � HSER ¼ Aþ B � T þ 18 � 0GFcc A1

Al

þ 2 � 0GBcc A2Fe þ 7 � 0GHcp A3

Mg

þ 10 � 0GDiamond A4Si

ðEq 1Þ

in which the coefficients A and B are to be evaluated fromthe experimental phase diagram data.

In view of the solubilities for Ni in the Al7Cu2Fe phaseand Fe in the Al7Cu4Ni phase,[70] the Al7Cu2Fe andAl7Cu4Ni phases are described with the sublattice models(Fe, Ni)1Cu2Al7 and Al1(Cu, Fe, Ni, Va)1, respectively.Taking the Al7Cu2Fe phase as an example, its Gibbs energyof per mole-formula can be expressed as:

GAl7Cu2Fem ¼y0Fe � 0G

Al7Cu2FeFe:Cu:Al þ y0Ni � 0G

Al7Cu2FeNi:Cu:Al

þ RT � ðy0Fe ln y0Fe þ y0Ni ln y0NiÞ

þ y0Fe � y0Ni � 0LAl7Cu2FeFe;Ni:Cu:Al

þ y0Fe � y0Ni � ðy0Fe � y0NiÞ � 1LAl7Cu2FeFe;Ni:Cu:Al

þ � � �

ðEq 2Þ

where y¢Feandy¢Ni are the site fractions of Fe and Ni in thefirst sublattice of the model (Fe, Ni)1Cu2Al7. The twoparameters denote 0GAl7Cu2Fe

�:Cu:Al (also called compound en-ergies) are expressed relative to the Gibbs energies of pureAl, Cu, Fe, and Ni at the same temperature. The interactionparameters 0LAl7Cu2FeFe;Ni:Cu:Al and

1LAl7Cu2FeFe;Ni:Cu:Al can be evaluated onthe basis of the experimental data in the present work.

4. Results and Discussion

The thermodynamic parameters were evaluated by theoptimization module PARROT[75] of the program Thermo-Calc, which works by minimizing the square sum of thedifferences between measured and calculated values. Theoptimized thermodynamic parameters in the Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni quinary systems are listed inTable 2.

Table 2 Summary of the optimized thermodynamicparameters in the Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Nisystems

Al9FeMg3Si5: Model Al18/37Fe2/37Mg7/37Si10/37

0GAl9FeMg3Si5Al:Fe:Mg:Si ¼ �12959þ 1:54 � T þ 18=37 � 0GFcc A1

Al þ 2=37 � 0GBcc A2Fe

þ 7=37 � 0GHcp A3Mg þ 10=37 � 0GDiamond A4

Si

Al7Cu2Fe: Model (Fe, Ni)1Cu2Al70GAl7Cu2Fe

Ni:Cu:Al ¼ �24200þ0 GFcc AlNi þ 2 �0 GFcc Al

Ni þ 7 �0 GFcc AlNi

0LAl7Cu2FeFe;Ni:Cu:Al ¼ �30000

Al7Cu4Ni: Model Al1(Cu, Fe, Ni, Va)10GAl7Cu4Ni

Al:Fe ¼ �50000þ0 GFcc AlAl þ0 GBcc A2

Fe

0LAl7Cu4NiAl:Fe:Cu ¼ �450000LAl7Cu4NiAl:Fe:Ni ¼ �1700000LAl7Cu4NiAl:Fe:Cu;Ni ¼ �400000

Al2Cu: Model Al2(Cu, Fe, Ni, Va)1

0GAl2CuAl:Ni ¼ �120000þ 2 �0 GFcc Al

Ni þ0 GFcc AlNi

0LAl2CuAl:Cu;Ni ¼ �50000

0LAl2CuAl:Cu;Fe ¼ �75000


4.1 The Al-Fe-Mg-Si System

In the present work, the Gibbs energy of formation forthe quaternary Al9FeMg3Si5 phase relative to its constituentelements is optimized to be �12,959 + 1.54T J/(mol-atoms)by using the measured invariant reactions[61,62] and thephase equilibria at low temperature.[60]

Figure 1 presents the calculated vertical sections (inwt.%) of the Al-Fe-Mg-Si system along with the experimen-tal data from Phillips[61]: (a) Al99Fe0.5Si0.5-Al91Mg8Fe0.5-Si0.5, (b) Al98.5Fe0.5Si1-Al90.5Mg8Fe0.5Si1, (c) Al99Fe0.5Mg0.5-Al85Si14Fe0.5Mg0.5, (d) Al98.5Fe0.5Mg1-Al84.5Si14Fe0.5Mg1, (e) Al95.5Mg4Si0.5-Al93Fe2.5Mg4Si0.5, and (f)Al91.5Mg8Si0.5-Al89Fe2.5Mg8Si0.5. The compositions aregiven in weight percents. The calculated phase equilibriaagree reasonably with the experimental data.

Figure 2(a) and (b) show the presently calculatedisothermal sections Al97.8Si2Fe0.2-Al99.8Fe0.2-Al97.8Mg2Fe0.2 in wt.% at 450 �C and Al98.5Fe1Si0.5-Al99.5Si0.5-Al97.5Mg2Si0.5 in wt.% at 400 �C of the Al-Fe-Mg-Sisystem, respectively. The calculated phase equilibria arealso consistent with the work from Belov et al.[60]

The calculated liquidus projection is shown in Fig. 3 andthe correspondingly calculated temperatures and liquidphase compositions of the invariant reactions of the Al-Fe-Mg-Si system in the Al-rich corner along with ex-perimental data[61,62,69] and calculated results from otherresearchers[66,67] are listed in Table 3. Again, the calculatedresults agree reasonably with the experimental data.[61,62,69]

The reaction scheme of the quaternary system in the Al-richcorner is constructed, as shown in Fig. 4.

4.2 The Al-Mg-Ni-Si System

Figure 5 is the calculated section Al90Si10-Al90(Al3Ni)10-Al90(Mg2Si)10 in at.% at 500 �C. It can be seen from thisfigure, the four phases, i.e. (Al), (Si), Al3Ni and Mg2Si, arebalanced and the solubilities of the third component, i.e. Niand Si, in the Mg2Si, Al3Ni and (Si) phases are relativelylow. These calculated results are consistent with the workreported by Belov.[68]

The liquidus projection of the Al-Mg-Ni-Si system in theAl-rich corner is also constructed, as shown in Fig. 6. Thecalculated temperatures and liquid phase compositions ofthe invariant reactions of the Al-Mg-Ni-Si system in the Al-rich corner are listed in Table 4. As can be seen from thistable, all the experimental data[68] can be well accounted forby the present calculation within the estimated experimentalerrors.

4.3 The Al-Cu-Fe-Mg System

Figure 7 shows the liquidus projection of the Al-Cu-Fe-Mg system in the Al-rich corner according to the presentwork. Since all invariant points are close to the invariantpoints of the Al-Cu-Mg ternary system, the compositions ofthe invariant reactions are not considered in this schematic.The presently calculated liquid phase compositions andtemperatures of the corresponding invariant reactions arecompared with the experimental values,[69] as presented inTable 5. Again, the calculated results agree with theexperimental data,[69] except for two invariant reactions.According to the present work, the calculated invariantreactions are L + D = (Al) + S + N and L + Al13-Fe4 = (Al) + D +T, whereas the measured ones[69] areL + N = (Al) + D + S and L + D = (Al) + Al13Fe4 + T,respectively. In view of the difficulty in measuring theinvariant reaction for the multi-component system, furtherexperiments are needed to verify it. The reaction scheme forthe Al-Cu-Fe-Mg system in the Al-rich corner according tothe present work is also constructed, as shown in Fig. 8.

Fig. 2 Calculated isothermal sections in the Al-Fe-Mg-Si system: (a) Al97.8Si2Fe0.2-Al99.8Fe0.2-Al97.8Mg2Fe0.2 in wt.% at 450 �C, and(b) Al98.5Fe1Si0.5-Al99.5Si0.5- Al97.5Mg2Si0.5 in wt.% at 400 �C

bFig. 1 Calculated partial vertical sections (in wt.%) of the Al-Fe-Mg-Si system along with the experimental data from Phil-lips[61]: (a) Al99Fe0.5Si0.5-Al91Mg8Fe0.5Si0.5, (b) Al98.5Fe0.5Si1-Al90.5Mg8Fe0.5Si1, (c) Al99Fe0.5Mg0.5-Al85Si14Fe0.5Mg0.5, (d)Al98.5Fe0.5Mg1-Al84.5Si14Fe0.5Mg1, (e) Al95.5Mg4Si0.5-Al93-Fe2.5Mg4Si0.5, and (f) Al91.5Mg8Si0.5-Al89Fe2.5Mg8Si0.5


Fig. 3 Calculated liquidus projection of the Al-Fe-Mg-Si system in the Al-rich corner. The compositions are given in mole fractions

Table 3 Calculated invariant reactions of the Al-Fe-Mg-Si system in the Al-rich corner along with experimentaldata[61,62,69] and calculated results from others[66,67]

Type Invariant reactions

Compositions in liquid phase, wt.%

T, �C ReferencesFe Mg Si

EI,max L = (Al) + Al13Fe4 + Mg2Si �1.0 �10.0 �7.0 >587 [69]

0.85 9.23 4.45 586 This work

UI L + Al13Fe4 = (Al) + Mg2Si + Al8Fe2Si 1.35 7.25 7.05 586 [69]

0.97 7.82 5.92 584 This work

UII L + Al8Fe2Si = (Al) + Mg2Si + Al9Fe2Si2 0.82 6.45 9.50 576 [69]

0.60 7.03 6.84 585 [66]

0.92 6.88 7.25 581 This work

UIII L + Mg2Si + Al9Fe2Si2 = (Al) + Al9FeMg3Si5 0.55 6.00 11.40 568 [61]

0.29 7.75 6.91 568 [66]

0.60 5.39 11.29 570 [67]

0.71 5.87 9.11 574 This work

UIV L + Al9Fe2Si2 = (Al) + (Si) + Al9FeMg3Si5 0.52 2.90 12.15 567 [61]

0.09 5.52 13.17 559 [66]

0.50 3.79 13.40 560 [67]

0.49 3.09 12.46 563 This work


Fig. 4 Reaction scheme of the Al-Fe-Mg-Si system in the Al-rich corner

Table 3 continued



T, �C ReferencesFe Mg Si

EI L = (Al) + (Si) + Mg2Si + Al9FeMg3Si5 0.15 4.90 12.90 555 [61]

0.86 7.44 18.83 556 [66]

0.22 4.79 13.62 557 [67]

0.12 4.47 12.50 559 This work

EII L = (Al) + Al13Fe4 + Mg2Si + b_AlMg 0.11 33.30 0.35 448 [62]

0.0001 33.90 0.092 451 [66]

0.005 33.92 0.095 450 [67]

0.002 33.86 0.03 450 This work


4.4 The Al-Cu-Fe-Ni System

Figure 9(a) and (b) show the presently calculatedisothermal sections at 530 �C, 90 wt.% Al and 530 �C, 85

wt.% Al of the Al-Cu-Fe-Ni system along with experimentaldata from Raybor and Ward,[70] respectively. As can beenseen from these figures, the calculated phase relationshipsare consistent with the measured ones. However, thediscrepancies between calculated and measured composi-tions for phase regions are about 1.5 wt.% Fe and 0.5 wt.%Ni. The discrepancies derive from the Al-Cu-Fe and Al-Cu-Ni boundaries ternary systems.

4.5 The Al-Fe-Mg-Ni-Si System

A thermodynamic database for the Al-Fe-Mg-Ni-Sisystem is established on the basis of the constituent binary,ternary and quaternary systems. Table 6 lists the calculatedand experimental[1] invariant reactions for the Al-Fe-Mg-Ni-Si system in the Al-rich corner, showing a good agreementbetween the reactions.<Dummy RefID="Tab6

Figure 10 presents the calculated isothermal sectionAl84Mg2Si13Ni1-Al86Si13Ni1-Al84Fe2Si13Ni1 in wt.% ofthe Al-Fe-Mg-Ni-Si system at 300 �C. Figure 11 showsthe calculated vertical section Al85Si13Ni1Mg1-Al84.4Fe0.6-Si13Ni1Mg1 in wt.%. The ‘‘experimental data’’ pointsderived from the experimental phase diagram in the workof Belov et al.[1] were added in the present calculated phasediagram. It can be seen from the two figures that thecalculated phase relationships are consistent with the

Fig. 5 Calculated section Al90Si10-Al90(Al3Ni)10-Al90(Mg2Si)10in at.% at 500 �C of the Al-Mg-Ni-Si system

Fig. 6 Calculated liquidus projection of the Al-Mg-Ni-Si system in the Al-rich corner. The compositions are given in mole fractions


Table 5 Calculated invariant reactions of the Al-Cu-Fe-Mg system in the Al-rich corner along with experimentaldata[69]



T, �C ReferencesCu Fe Mg

UI L + N = (Al) + D + S 25 <1 <5 <517 [69]

L + D = (Al) + S + N 55.51 0 4.8 534 This work

EI L = (Al) + Al2Cu + N + S 33 0.3 5 505 [69]

30.75 0 6.9 508 This work

UII L + S = (Al) + D + T 10 <1 20-25 465 [69]

10.13 0.16 23.64 477.7 This work

UIII L + D = (Al) + Al13Fe4 + T 5 <1 25-30 450 [69]

L + Al13Fe4 = (Al) + D +T 34.78 0 9.15 459.8 This work

EII L = (Al) + Al13Fe4 + b_AlMg + T 2 0.1 33 445 [69]

1.3 0 33.4 447.6 This work

E1,max L = (Al) + S + D 59.68 0 6.65 543.8 This work

E3,max L = (Al) + Al13Fe4 + T 17.24 0.006 18.95 481.9 This work

E4,max L = (Al) + D + T 38.09 0 7.59 450.0 This work

S: Al2CuMg; T: Al6CuMg4; N: Al7Cu2Fe; D: Al6(CuFe)

Table 4 Calculated invariant reactions of the Al-Mg-Ni-Si system in the Al-rich corner along with experimentaldata[68]



T, �C ReferencesMg Ni Si

EI,max L = (Al) + Mg2Si + Al3Ni 7.4 3 4.8 590 [68]

8.5 2 4.4 584 This work

EI L = (Al) + Mg2Si + Al3Ni + (Si) 3.5 2 13 550 [68]

4.1 1.7 12 556 This work

EII L = (Al) + Mg2Si + Al3Ni + b_AlMg �32 <1.7 <0.4 �447 [68]

33.8 0.03 0.03 450.24 This work

Fig. 7 Schematic liquidus projection of the Al-Cu-Fe-Mg system in the Al-rich corner


experimental data.[1] The differences between the calculatedand experimental compositions are less than 0.4 wt.%. Dueto the relatively small number of alloys investigated byBelov et al.,[1] the two sections can be considered semi-quantitative, and the present calculated results are accept-able.

4.6 The Al-Cu-Fe-Mg-Ni System

A thermodynamic database for the Al-Cu-Fe-Mg-Nisystem is established on the basis of the constituent binary,ternary and quaternary systems. Figure 12 presents thecalculated vertical section Al96.78Mg1.42Fe0.9Ni0.9-Al93.78-Cu3Mg1.42Fe0.9Ni0.9 in wt.% of the Al-Cu-Fe-Mg-Ni systemalong with the experimental data from Wang et al.[71] Thecalculated results are consistent with the experimentaldata.[71] In addition, it can be confirmed that the Al2CuMgphase forms in the non-equilibrium solidification of the Al-2.24Cu-1.42Mg-0.9Fe-0.9Ni (in wt.%) alloy and complete-ly dissolves in solid solution (Al) during homogenizingannealing.

4.7 Solidification Simulation of Al Alloys

Various approximations and simplifications are alwaysneeded in simulating the complicated solidification process.One qualitative approximation is to use the Gulliver-Scheilmodel.[76,77] It has been realized that there is a reasonableagreement between prediction and experiment by applyingthe model to the description of solidification process.[67,78]

In the present work, Gulliver-Scheil simulations are per-formed to describe the solidification behaviors of Al alloys6063 (Al-0.39Si-0.20Fe-0.43Mg, in wt.%) and 2618 (Al-2.24Cu-1.42Mg-0.9Fe-0.9Ni, in wt.%).

Figure 13 shows the calculated solidification curves of6063 alloy (Al-0.39Si-0.20Fe-0.43Mg, in wt.%) under theequilibrium and Gulliver-Scheil non-equilibrium conditions.The solidification begins with the (A1) phase at 655 �C.Next Al13Fe4 forms at 630 �C, Al8Fe2Si at 609 �C,Al9Fe2Si2 at 591 �C, Al9FeMg3Si5 at 575 �C, and Mg2Siin the final eutectic at 572 �C. Compared with the ex-perimental data from Backerud et al.,[64] the phases andreactions simulated in the present work are consistent with

Fig. 8 Reaction scheme of the Al-Cu-Fe-Mg system in the Al-rich corner


experimental data, except the Al13Fe4 and quaternaryAl9FeMg3Si5 phases. According to the work of Backerudet al.,[64] the solidified microstructure of the 6063 alloy was(Al) + Al8Fe2Si + Al9Fe2Si2 + Mg2Si. The two phasesAl13Fe4 and Al9FeMg3Si5 were not detected in theirexperiments. The reason of the discrepancy may be due tothe fact that such low amount of the Al13Fe4 andAl9FeMg3Si5 phases could not be determined by using thetemporal experimental techniques. This discrepancy sug-gests that additional experiments should be conducted toconfirm the existence of the two phases Al13Fe4 andAl9FeMg3Si5.

Figure 14 shows the calculated solidification curves of2618 alloy (Al-2.24Cu-1.42Mg-0.9Fe-0.9Ni, in wt.%) underthe equilibrium and Gulliver-Scheil non-equilibrium condi-tions. It can be seen that the solidified microstructure of the2618 alloy resulting from the Gulliver-Scheil model is(Al) + Al9FeNi + Al7Cu4Ni + Al2CuMg, which is consis-tent with the work reported by Belov et al.[60] However,there exists a discrepancy with the experimental microstruc-ture, i.e. (Al) + Al9FeNi + Al7Cu4Ni + Al2CuMg + Al7-Cu2Fe, measured by Wang et al.[71] Further experiments

are needed to verify the existence of the Al7Cu2Fe phase. Inaddition, the presently calculated results confirm that theAl9FeNi phase forms through the binary eutectic reactionL = (A1) + Al9FeNi over a wide temperature range fromapproximately 640-645 �C down to 505-515 �C reported byBelov et al.[60]

The information about phase equilibria and thermo-dynamic properties in multi-component alloys is usuallymissing in the literature due to their complex nature. Bymeans of the thermodynamic modeling, the present workdemonstrates a successful study on the phase equilibriaof the quinary Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Nisystems in Al-rich corner. The approximate compositionranges for each element are Al 80-100, Cu 0-6, Fe 0-5,Mg 0-10, Ni 0-5 and Si 0-20 in wt.%. It should be notedthat this given composition range is rather conservative.In the sub-systems, many of these elements can beapplied to a much wider composition range. Thethermodynamic database is updated continuously toreliably predict the phase equilibria and phase formationin multi-component alloy systems and industrial alu-minum alloys.

Fig. 9 Calculated partial isothermal sections of the Al-Cu-Fe-Ni system along with experimental data from Raynor and Ward[70]: (a)530 �C and 90 wt.% Al, and (b) 530 �C and 85 wt.% Al

Table 6 Calculated invariant reactions of the Al-Fe-Mg-Ni-Si system in the Al-rich corner along with experimentaldata[1]


Compositions in liquid phase, in wt.%

T, �C ReferencesFe Mg Ni Si

UI L + Al9Fe2Si2 = (Al) + (Si) + Al9FeMg3Si5 + Al9FeNi <0.5 �3 �1 �12 560-565 [1]

0.45 2.90 1.40 12.04 561.8 This work

UII L + Al9FeNi = (Al) + (Si) + Al9FeMg3Si5 + Al3Ni <0.5 �3 �1 �12 550-560 [1]

0.30 3.14 1.83 11.93 559.2 This work

EI L = (Al) + (Si) + Mg2Si + Al9FeMg3Si5 + Al3Ni <0.15 �3.5 �2 �13 �548 [1]

0.11 4.12 1.68 11.99 555.8 This work


Fig. 11 Calculated partial vertical section Al85Si13Ni1Mg1-Al84.4Fe0.6Si13Ni1Mg1 in wt.% of the Al-Fe-Mg-Ni-Si system

Fig. 10 Calculated partial isothermal section Al84Mg2Si13Ni1-Al86Si13Ni1-Al84Fe2Si13Ni1 in wt.% of the Al-Fe-Mg-Ni-Si sys-tem at 300 �C

Fig. 13 Calculated solidification curves of 6063 alloy (Al-0.39Si-0.20Fe-0.43Mg, in wt.%) under the equilibrium and Gul-liver-Scheil non-equilibrium conditions

Fig. 12 Calculated partial vertical section Al96.78Mg1.42Fe0.9-Ni0.9-Al93.78Cu3Mg1.42Fe0.9Ni0.9 in wt.% of the Al-Cu-Fe-Mg-Nisystem along with the experimental data from Wang et al.[71]


5. Conclusions

• The thermodynamic database for the quinary Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni systems is obtained onthe basis of the constituent binary, ternary, and quater-nary systems. Particularly, the quaternary Al-Fe-Mg-Siand Al-Cu-Fe-Ni systems were thermodynamic opti-mized based on all the available phase equilibria in theAl-rich corner.

• Gulliver-Scheil non-equilibrium solidification behaviorsof Al alloys 6063 (Al-0.39Si-0.20Fe-0.43Mg, in wt.%)and 2618 (Al-2.24Cu-1.42Mg-0.9Fe-0.9Ni, in wt.%)are investigated. The reliability of the established data-base is verified by good agreement between calculationand experiment for phase diagrams, invariant reactionsand Gulliver-Scheil non-equilibrium solidification be-haviors.

• The application of the presently thermodynamic data-base to control phase transitions throughout solidifica-tion process for Al alloys indicates the importance ofthermodynamic databases in material design.

Acknowledgments

The financial support from the National Basic ResearchProgram of China (Grant No. 2011CB610401), Thermo-Calc Software AB under the Aluminum Alloy DatabaseProject, Sino-German Center for Research Promotion (GrantNo. GZ755), and the Scientific Research Starting Founda-

tion for the Introduced Talents of Anhui University ofScience and Technology (Grant No. ZX979) are greatlyacknowledged.

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