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Thermodynamic Description of the Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni Quinary Systems and Its Application to Solidification Simulation

Abstract

Based on the critical review of the available experimental phase equilibrium data for the constituent quaternary systems in the Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni quinary systems, a set of self-consistent thermodynamic parameters for these systems has been obtained using the CALPHAD approach. In combination with the constituent binary, ternary and quaternary systems, the thermodynamic database for the quinary Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni systems was developed. Comprehensive comparisons between the calculated and measured phase diagrams and invariant reactions showed that the experimental data were satisfactorily accounted for by the present thermodynamic description. The established database was used to describe the solidification 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. The reliability of the present thermodynamic database was also verified by the good agreement between the Gulliver-Scheil calculation and experiment.

Introduction

Casting Al alloys containing nickel and silicon are widely used 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 very complex phase compositions.[1] The mechanical and chemical properties as well as the corrosion resistance of solidified Al alloys are heavily dependent on the microstructure obtained after solidification.[2] In order to obtain optimal material properties, accurate predictions of the reactions during solidification are essential to design solidification process and subsequent heat treatments. Hence, knowledge of the phase diagrams and thermodynamic properties of the six-component Al-Cu-Fe-Mg-Ni-Si system is the theoretical basis to understand the performance of casting Al alloys.

The CALculation of PHAse Diagrams (CALPHAD) approach has become a valuable tool in the calculation of complex multi-component phase equilibria of industrial alloys based on experimental thermodynamic and phase diagram data. However, assessment of the six-component Al-Cu-Fe-Mg-Ni-Si system is a very challenging task. In general, the assessment of high-order alloying systems starts with the evaluation of phase diagrams and thermodynamic properties in low-order alloying systems. In the present work, the thermodynamic description of the two quinary Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni systems that constituent the commercially important Al-Cu-Fe-Mg-Ni-Si alloying system is performed.

The aims of the present work are: (1) to establish a thermodynamic database for the quinary Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni systems on the basis of the constituent binary, ternary and quaternary systems using the CALPHAD approach; and (2) to apply the present database to simulate solidification 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.

Evaluation of Phase Diagram Information in the Literature

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

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-rich corner

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 parameters of these binary systems are all taken from literature. The selection of these thermodynamic parameters is briefly described as follows.

The Al-Fe system was thermodynamic described by several groups of authors.[3-5] The thermodynamic assessment of the Al-Fe system most used in databases was by Seierstein[3] from the COST 507 project. Recently, Jacobs and Schmid-Fetzer[4] improved the representation of the bcc_A2, bcc_B2 and fcc_A1 phases based on the description from Seierstein.[3] Sundman et al.[5] reassessed the stable and metastable equilibria in the Al-Fe system using a four-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 the Al13Fe4, Al5Fe2 and Al2Fe phases in order to reflect the congruent melting behavior of Al13Fe4. All of the thermodynamic assessments could represent the experimental data fairly well. The four-sublattice model presented by Sundman et al.[5] was not compatible with a two-sublattice model in other binary systems. To be compatible with our established Al-based thermodynamic database, the thermodynamic parameters from Du et al.[6] based on the modeling of Seierstein[3] were finally adopted in this work.

The recent thermodynamic description of the Al-Mg system could 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 the random mixing model for the liquid phase, and Aljarrah[9] used the modified quasichemical model to described the liquid phase. The experimental data could be well reproduced by the thermodynamic modeling mentioned above. In order to coincide with our established Al-base thermodynamic database, 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 γ_D83 phases were modified by Witusiewicz et al.[11] based on the work of Saunders.[10] There were no obvious differences between them except the γ_D83 phase field at temperatures below 600 K. Due to the slightly influence of the γ_D83 phase to phase relationships in higher-order systems at low temperature, the thermodynamic assessment of the Al-Cu system by Saunders[10] was adopted in the present work.

The Fe-Ni phase diagram has been constructed by several 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 transformation. Keyzer et al.[13] calculated the stable Fe-Ni phase diagram showing a large discrepancy between computed and experimental melting equilibria. Cacciamani et al.[14] also assessed the Fe-Ni system using a four-sublattice model to describe both stable and metastable fcc-based ordered phases as well as the bcc-based ordered phases. Zhang and Du[15] have been converted the parameters of the Ni3Fe phase in the Fe-Ni system[12] from a four-sublattice formalism to a two-sublattice one in order to maintain the consistency with the other binary systems. Considering of the accuracy of the thermodynamic parameters and the consistency of the models, the thermodynamic parameters in the Fe-Ni system were taken from Zhang and Du[15] based on the modeling of Servant et al.[12] in the present work.

The widely accepted thermodynamic assessment of the Fe-Si system was from Lacaze and Sundman.[16] Later on, Miettinen[17] did a slight modification of the solution phases and Tang and Tangstad[18] reassessed the phase equilibria in the Si-rich domain of the Fe-Si system based on the work of Lacaze and Sundman.[16] All of the thermodynamic modeling could represent well experimental data. In order to coincide with our established Al-base thermodynamic database, the 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 Coughanowr et al.,[19] Zuo and Chang[20] and Zhou et al.[21] Coughanowr et al.[19] and Zuo and Chang[20] treated the liquid and Mg2Cu phases as a regular solution and a stoichiometric compound, respectively. Accordingly, Zhou et al.[21] used an association model for the liquid phase and a two-sublattice model to describe the Mg2Cu phase. From the overall, these thermodynamic modeling could represent the experimental data fairly well. In order to coincide with our established Al-base thermodynamic database, the modeling by Coughanowr et al.[19] was finally accepted in this work.

The Mg-Ni system was formerly assessed by four groups of authors.[22-25] The experimental Mg-Ni phase diagram could be 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 and MgNi2 phases. Only the thermodynamic parameters from the work of Jacobs and Spencer[24] could describe the heat capacity of MgNi2 phase in the Mg-Ni system satisfactory. Hence, the thermodynamic parameters from Jacobs and Spencer[24] were adopted in the present work.

The recent thermodynamic assessment of the Mg-Si system has been conducted by several groups of authors.[26-30] Yan et al.[26] and Kevorkov et al.[27] used 6 and 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 4 parameters were introduced for the liquid phase. Yuan et al.[29] applied an exponential formulation to describe the excess Gibbs energy of the liquid phase. Schick et al.[30] reassessed the Mg-Si system to resolve the uncertainties in the Gibbs energy of the Mg2Si phase by means of a hybrid approach of ab initio, experimental and CALPHAD. Considering of the consistency of the models, the thermodynamic parameters in the Mg-Si system were taken from Kevorkov et al.[27] in the present modeling.

For the Ni-Si system, the lasted two thermodynamic assessments were carried out by Du and Schuster[31] and Tokunaga et al.[32] Both thermodynamic modeling could well reproduce the experimental data. In order to coincide with our established Al-base thermodynamic database, the modeling by 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 are adopted in the present thermodynamic database.

The Ternary Systems

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

The lasted thermodynamic parameters for the Al-Fe-Ni system assessed by Zhang et al.[38] were adopted in the present work. However, the published parameters cannot well describe the Al9FeNi phase stabilizing at low temperatures in the Al-Fe-Ni system. Therefore, the thermodynamic parameters of the Al9FeNi phase were slightly modified in our previous work.[39]

Thermodynamic assessments have been performed for the Al-Fe-Si ternary system several times. The most recent assessment over the whole composition range have been done by Du et al.[6] Eleno et al.[40] recently reassessed the Al-rich phase equilibria of the Al-Fe-Si system and refined the descriptions of α-AlFeSi, β-AlFeSi, τ2-AlFeSi and τ4-AlFeSi within the COST507 database. However, the Al-Fe-Si description in the COST507 database is relatively outdated compared with that of Du et al.[6] A further thermodynamic reassessment of the Al-Fe-Si system in the Al-rich corner was carried out in our previous work[39] based on the work of Du et al.[6]

For the Al-Mg-Si system, a thermodynamic optimization was carried out by Feufel et al.,[41] which was included in the COST507 project. Lacaze and Valdes[42] modified slightly the description of the liquid phase in the Al-Mg-Si system with respect to the COST 507 data. The calculated results were similar with the work of Feufel et al.[41] In order to avoid an artificial miscibility gap at high temperatures automatically without adding any thermodynamic constraint, Tang et al.[43] used an exponential formulation to describe the excess Gibbs energy of the liquid phase. Considering of the consistency of the models in our established Al-base thermodynamic database, the thermodynamic parameters in the Al-Mg-Si system were taken from Feufel et al.[41] in the present modeling.

The recent thermodynamic assessment of the Cu-Fe-Ni system has been carried out by several groups of authors.[12,44,45] Servant et al.[12] assessed the Cu-Fe-Ni system taking into account the disorder/order transformation between fcc-Al and (Cu,Ni)3Fe base on the new experimental data. Turchanin et al.[44] improved the description of the miscibility gap and phase equilibria involving liquid phase. But the order/disorder phase transformations have not been considered. Dreval et al.[45] updated the thermodynamic description of the Cu-Fe-Ni system considering the newly available experimental 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] were inconsistent with the ones accepted in our established Al-base thermodynamic database. Hence, the thermodynamic parameters 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 in the present thermodynamic database.

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

The Quaternary Systems

The Al-Fe-Ni-Si System

Since the review of the experimental phase equilibria of the Al-Fe-Ni-Si system have been reported by our previous work,[39] they are briefly presented here. Gusev[57] and Belov[58] employed about 80 quaternary alloys to study the microstructure, phase composition, and thermograms of cast and heat-treated alloys, which were reviewed and summarized in detail by Belov et al. in 2002[59] and 2005.[60] On the basis of the experimental results from Gusev[57] and Belov,[58] the distribution of phase fields in the solid state and two vertical sections: Al94Si5Fe1-Al92Ni2Si5Fe1 and Al91Si8Fe1-Al89Ni2Si8Fe1 in wt.% were constructed by Belov et al.[59,60] Most recently, 6 alloys along two vertical sections (Al94Si5Fe1-Al92Ni2Si5Fe1 and Al91Si8Fe1-Al89Ni2Si8Fe1 in at.%) were prepared by our previous work.[39] The related phase equilibria, phase transition temperatures, and solidified microstructure were determined in both annealed and as-cast alloys by means of XRD, SEM/EDX, EPMA, TEM and DTA techniques. On the basis of the experimental equilibria from the present work and the literature, a set of self-consistent thermodynamic parameters for the quaternary Al-Fe-Ni-Si system in Al-rich corner was simultaneously obtained and adopted in the present work.

The Al-Fe-Mg-Si System

Phillips[61] investigated the phase equilibria in the Al-rich corner of the Al-Fe-Mg-Si in the composition range from 0 to 12 wt.% Mg, 0 to 14 wt.% Si, and 0 to 2.5 wt.% Fe using thermal analysis and optical microscopy. Gul’din and Dokukina[62] measured the solubility of Fe and Si in Al-Mg melts and the eutectic reaction temperature for L = (Al) + Al13Fe4 + Mg2Si + β_AlMg. The experimental data on the liquidus and the phase distribution in the solid state for this quaternary system have been reviewed by Barlock and Mondolfo.[63] Backerud et al.[64] presented the solidification data for the aluminum 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, and finally Mg2Si begins to solidify.

No thermodynamic data have been reported for this quaternary system. The only quaternary compound Al9FeMg3Si5 was found by Phillips.[61] Belov et al.[60] reported a series of isothermal and vertical sections for the quaternary system and showed that the quaternary Al9FeMg3Si5 phase is stable at low temperature. By means of single-crystal automatic, the stoichiometry of the Al9FeMg3Si5 phase was determined to Al18Fe2Mg7Si10 by Krendelsberger et al.[65]

The thermodynamic description of the Al-Fe-Mg-Si quaternary system in the Al-rich corner has been successively performed by Daniel[66] and Du et al.[67] However, the calculated liquid phase compositions of the invariant reactions by Daniel[66] show noticeable discrepancies from the experimental ones and the Al9FeMg3Si5 phase stabilized at low temperature cannot be well described by both of the work.[66,67] Thus, the thermodynamic parameters of the quaternary Al9FeMg3Si5 phase are slightly modified in the present work.

The Al-Mg-Ni-Si System

A limited amount of experimental data for the Al-Mg-Ni-Si system was available in the literature. The Al-Mg-Ni-Si phase diagram was experimentally studied by Belov[68] in the region of the Al-Mg2Si-Si-Al3Ni tetrahedron, inside which no quaternary compound was found. The Mg2Si, Al3Ni and (Si) phases have 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) + Mg2Si + Al3Ni + β_AlMg, and one quasi-ternary eutectic reaction, i.e. L = (Al) + Mg2Si + Al3Ni, were reported by Belov[68] in the Al-rich corner of the Al-Mg-Ni-Si system. Considering the lack of experimental information and the absence of the quaternary compound, direct extrapolation calculations for the Al-Mg-Ni-Si system were carried out in the present work. The experimental data reported by Belov[68] were used to compare with the present calculation results.

The Al-Cu-Fe-Mg System

No quaternary phase was found in the Al-Cu-Fe-Mg system. The phases Al2Cu, Al13Fe4, β_AlMg, Al7Cu2Fe, Al2CuMg, Al6CuMg4 and Al6(CuFe) from the constitutive systems are in equilibrium with (Al). The liquidus projection and the distribution of phase regions in solid state and six invariant reactions in Al-rich corner of the Al-Cu-Fe-Mg system were reported by Mondolfo.[69] The compositions of Fe in liquid phase are extremely limited for these invariant reactions and the corresponding invariant points are close to the invariant points of the Al-Cu-Mg ternary system. Just as the quaternary Al-Mg-Ni-Si system, direct extrapolation calculations for the Al-Cu-Fe-Mg system are also carried out in the present work due to the lack of any reliable experimental information and the absence of the quaternary compound.

The Al-Cu-Fe-Ni System

Until now, only one piece of experimental measurement of phase diagram in the Al-corner of the Al-Cu-Fe-Ni system has been reported by Raybor and Ward.[70] In the work of Raybor and Ward, 74 specimens containing 10 and 15 wt.% of solute metals in aluminum were prepared. After annealing for 10 weeks at 530 °C, the specimens were examined by metallographic, x-ray diffraction, and electrode-potential measurements. Two isothermal sections with 90 and 85 wt.% Al at 530 °C were constructed. In the composition range investigated, the (Al) solid solution was in equilibrium with the Al2Cu phase, the ternary Al7Cu2Fe phase, or the ternary Al7Cu4Ni phase. The compound Al7Cu2Fe was shown to be capable of dissolving Ni up to a limit of approximately 6.8 wt.% at 530 °C. The solubility of Fe in Al7Cu4Ni is much smaller and is about 0.8 wt.%. The experimental data published by Raybor and Ward[70] are used in the present thermodynamic modeling.

The Al-Fe-Mg-Ni, Al-Cu-Mg-Ni, Fe-Mg-Ni-Si and Cu-Fe-Mg-Ni Systems

No quaternary phase was reported in the quaternary Al-Fe-Mg-Ni, Al-Cu-Mg-Ni, Fe-Mg-Ni-Si and Cu-Fe-Mg-Ni systems. In the literature, there was no experimental information on the phase diagrams of the above four quaternary systems. Consequently, the thermodynamic properties for the above three quaternary systems are extrapolated from the descriptions of the constituent ternary systems.

The Quinary Systems

The Al-Fe-Mg-Ni-Si System

For the quinary Al-Fe-Mg-Ni-Si system, only one piece of experimental information has been reported by Belov et al.[1] According to 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-Si system were reported. The distribution of phase fields in the solid state, the polythermal projection of solidification surfaces, one isothermal section Al84Mg2Si13Ni1-Al86Si13Ni1-Al84Fe2Si13Ni1 in wt.% at 300 °C, and one vertical section Al85Mg1Ni1Si13-Al84.4Fe0.6Mg1Ni1Si13 in wt.% were constructed by Belov et al.[1] Direct extrapolation calculations for the Al-Fe-Mg-Ni-Si system were carried out in the present work. The experimental data reported by Belov et al.[1] were used to compare with the present calculation results.

The Al-Cu-Fe-Mg-Ni System

The information of the experimental phase equilibrium for the quinary Al-Cu-Fe-Mg-Ni system was very limited. Aluminum alloy 2618 with the 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 microstructure of the 2618 alloy in the as-cast state contains particles of the Al9FeNi and Al2CuMg phases. The Al9FeNi phase probably forms through the binary eutectic reaction L = (A1) + Al9FeNi, which occurs over a wide temperature range from approximately 640-645 °C down to 505-515 °C due to the presence of copper and magnesium in an alloy. The appearance of the Al2CuMg phase in the as-cast structure is a consequence of non-equilibrium solidification. During homogenizing annealing, it completely dissolves in solid solutiom (Al). In addition, quasi-ternary section Al-Al9FeNi-Al2CuMg of the Al-Cu-Fe-Mg-Ni phase diagram was tentatively constructed by Belov et al.[60] The microstructure 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 and Al9FeNi compounds, were studied by Wang et al.[71] After 16 h homogenization at 520 °C, the lamellar eutectic phases dissolved into the matrix, and the intermetallics containing Fe or Ni were remained in the microstructure. Direct extrapolation calculations for the Al-Cu-Fe-Mg-Ni system were also carried out in the present work. The experimental data from Belov et al.[60] and Wang et al.[71] were used to compare with the present calculation results.

Thermodynamic Modeling

In the present work, the quaternary phase Al9FeMg3Si5 is treated as a stoichiometric phase Al18Fe2Mg7Si10, and its Gibbs energy is expressed relative to the mechanical mixing of the pure elements by the following equation:

$$\begin{aligned} G_{m}^{{{\text{Al}}_{ 9} {\text{FeMg}}_{ 3} {\text{Si}}_{ 5} }} - H^{\text{SER}} = & A + B \cdot T + 18 \cdot {}^{0}G_{\text{Al}}^{{{\text{Fcc\_A1}}}} \\ &\quad + 2 \cdot {}^{0}G_{\text{Fe}}^{{{\text{Bcc\_A2}}}} + 7 \cdot {}^{0}G_{\text{Mg}}^{{{\text{Hcp\_A3}}}} \\ &\quad + 10 \cdot {}^{0}G_{\text{Si}}^{{{\text{Diamond\_A4}}}} \\ \end{aligned}$$
(1)

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

In view of the solubilities for Ni in the Al7Cu2Fe phase and Fe in the Al7Cu4Ni phase,[70] the Al7Cu2Fe and Al7Cu4Ni 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 energy of per mole-formula can be expressed as:

$$\begin{aligned} G_{\text{m}}^{{{\text{Al}}_{ 7} {\text{Cu}}_{ 2} {\text{Fe}}}} = & y^{\prime}_{\text{Fe}} \cdot {}^{0}G_{\text{Fe:Cu:Al}}^{{{\text{Al}}_{ 7} {\text{Cu}}_{ 2} {\text{Fe}}}} + y^{\prime}_{Ni} \cdot {}^{0}G_{\text{Ni:Cu:Al}}^{{{\text{Al}}_{ 7} {\text{Cu}}_{ 2} {\text{Fe}}}} \\ & + RT \cdot (y^{\prime}_{\text{Fe}} \ln y^{\prime}_{\text{Fe}} + y^{\prime}_{\text{Ni}} \ln y^{\prime}_{\text{Ni}} ) \\ & + y^{\prime}_{\text{Fe}} \cdot y^{\prime}_{\text{Ni}} \cdot {}^{0}L_{\text{Fe,Ni:Cu:Al}}^{{{\text{Al}}_{ 7} {\text{Cu}}_{ 2} {\text{Fe}}}} \\ & + y^{\prime}_{\text{Fe}} \cdot y^{\prime}_{\text{Ni}} \cdot (y^{\prime}_{\text{Fe}} - y^{\prime}_{\text{Ni}} ) \cdot {}^{1}L_{\text{Fe,Ni:Cu:Al}}^{{{\text{Al}}_{ 7} {\text{Cu}}_{ 2} {\text{Fe}}}} \\ & + \cdots \\ \end{aligned}$$
(2)

where yFeandyNi are the site fractions of Fe and Ni in the first sublattice of the model (Fe, Ni)1Cu2Al7. The two parameters denote \({}^{0}G_{{ * : {\text{Cu:Al}}}}^{{{\text{Al}}_{ 7} {\text{Cu}}_{ 2} {\text{Fe}}}}\)(also called compound energies) are expressed relative to the Gibbs energies of pure Al, Cu, Fe, and Ni at the same temperature. The interaction parameters \({}^{0}L_{\text{Fe,Ni:Cu:Al}}^{{{\text{Al}}_{ 7} {\text{Cu}}_{ 2} {\text{Fe}}}}\) and \({}^{1}L_{\text{Fe,Ni:Cu:Al}}^{{{\text{Al}}_{ 7} {\text{Cu}}_{ 2} {\text{Fe}}}}\) can be evaluated on the basis of the experimental data in the present work.

Results and Discussion

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

Table 2 Summary of the optimized thermodynamic parameters in the Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni systems

The Al-Fe-Mg-Si System

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

Figure 1 presents the calculated vertical sections (in wt.%) of the Al-Fe-Mg-Si system along with the experimental data from Phillips[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-Al93Fe2.5Mg4Si0.5, and (f) Al91.5Mg8Si0.5-Al89Fe2.5Mg8Si0.5. The compositions are given in weight percents. The calculated phase equilibria agree reasonably with the experimental data.

Fig. 1
figure 1

Calculated partial vertical sections (in wt.%) of the Al-Fe-Mg-Si system along with the experimental data from Phillips[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-Al93Fe2.5Mg4Si0.5, and (f) Al91.5Mg8Si0.5-Al89Fe2.5Mg8Si0.5

Figure 2(a) and (b) show the presently calculated isothermal 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-Si system, respectively. The calculated phase equilibria are also consistent with the work from Belov et al.[60]

Fig. 2
figure 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

The calculated liquidus projection is shown in Fig. 3 and the correspondingly calculated temperatures and liquid phase compositions of the invariant reactions of the Al-Fe-Mg-Si system in the Al-rich corner along with experimental data[61,62,69] and calculated results from other researchers[66,67] are listed in Table 3. Again, the calculated results agree reasonably with the experimental data.[61,62,69] The reaction scheme of the quaternary system in the Al-rich corner is constructed, as shown in Fig. 4.

Fig. 3
figure 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 experimental data[61,62,69] and calculated results from others[66,67]
Fig. 4
figure 4

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

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 this figure, the four phases, i.e. (Al), (Si), Al3Ni and Mg2Si, are balanced and the solubilities of the third component, i.e. Ni and Si, in the Mg2Si, Al3Ni and (Si) phases are relatively low. These calculated results are consistent with the work reported by Belov.[68]

Fig. 5
figure 5

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

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

Fig. 6
figure 6

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

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

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 present work. Since all invariant points are close to the invariant points of the Al-Cu-Mg ternary system, the compositions of the invariant reactions are not considered in this schematic. The presently calculated liquid phase compositions and temperatures of the corresponding invariant reactions are compared with the experimental values,[69] as presented in Table 5. Again, the calculated results agree with the experimental data,[69] except for two invariant reactions. According to the present work, the calculated invariant reactions are L + D = (Al) + S + N and L + Al13Fe4 = (Al) + D +T, whereas the measured ones[69] are L + N = (Al) + D + S and L + D = (Al) + Al13Fe4 + T, respectively. In view of the difficulty in measuring the invariant reaction for the multi-component system, further experiments are needed to verify it. The reaction scheme for the Al-Cu-Fe-Mg system in the Al-rich corner according to the present work is also constructed, as shown in Fig. 8.

Fig. 7
figure 7

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

Table 5 Calculated invariant reactions of the Al-Cu-Fe-Mg system in the Al-rich corner along with experimental data[69]
Fig. 8
figure 8

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

The Al-Cu-Fe-Ni System

Figure 9(a) and (b) show the presently calculated isothermal sections at 530 °C, 90 wt.% Al and 530 °C, 85 wt.% Al of the Al-Cu-Fe-Ni system along with experimental data from Raybor and Ward,[70] respectively. As can been seen from these figures, the calculated phase relationships are consistent with the measured ones. However, the discrepancies between calculated and measured compositions 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.

Fig. 9
figure 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

The Al-Fe-Mg-Ni-Si System

A thermodynamic database for the Al-Fe-Mg-Ni-Si system is established on the basis of the constituent binary, ternary and quaternary systems. Table 6 lists the calculated and experimental[1] invariant reactions for the Al-Fe-Mg-Ni-Si system in the Al-rich corner, showing a good agreement between the reactions.

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

Figure 10 presents the calculated isothermal section Al84Mg2Si13Ni1-Al86Si13Ni1-Al84Fe2Si13Ni1 in wt.% of the Al-Fe-Mg-Ni-Si system at 300 °C. Figure 11 shows the calculated vertical section Al85Si13Ni1Mg1-Al84.4Fe0.6Si13Ni1Mg1 in wt.%. The “experimental data” points derived from the experimental phase diagram in the work of Belov et al.[1] were added in the present calculated phase diagram. It can be seen from the two figures that the calculated phase relationships are consistent with the experimental data.[1] The differences between the calculated and experimental compositions are less than 0.4 wt.%. Due to the relatively small number of alloys investigated by Belov et al.,[1] the two sections can be considered semi-quantitative, and the present calculated results are acceptable.

Fig. 10
figure 10

Calculated partial isothermal section Al84Mg2Si13Ni1-Al86Si13Ni1-Al84Fe2Si13Ni1 in wt.% of the Al-Fe-Mg-Ni-Si system at 300 °C

Fig. 11
figure 11

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

The Al-Cu-Fe-Mg-Ni System

A thermodynamic database for the Al-Cu-Fe-Mg-Ni system is established on the basis of the constituent binary, ternary and quaternary systems. Figure 12 presents the calculated vertical section Al96.78Mg1.42Fe0.9Ni0.9-Al93.78Cu3Mg1.42Fe0.9Ni0.9 in wt.% of the Al-Cu-Fe-Mg-Ni system along with the experimental data from Wang et al.[71] The calculated results are consistent with the experimental data.[71] In addition, it can be confirmed that the Al2CuMg phase forms in the non-equilibrium solidification of the Al-2.24Cu-1.42Mg-0.9Fe-0.9Ni (in wt.%) alloy and completely dissolves in solid solution (Al) during homogenizing annealing.

Fig. 12
figure 12

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

Solidification Simulation of Al Alloys

Various approximations and simplifications are always needed in simulating the complicated solidification process. One qualitative approximation is to use the Gulliver-Scheil model.[76,77] It has been realized that there is a reasonable agreement between prediction and experiment by applying the model to the description of solidification process.[67,78] In the present work, Gulliver-Scheil simulations are performed to describe the solidification 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.%).

Figure 13 shows the calculated solidification curves of 6063 alloy (Al-0.39Si-0.20Fe-0.43Mg, in wt.%) under the equilibrium 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 Mg2Si in the final eutectic at 572 °C. Compared with the experimental data from Backerud et al.,[64] the phases and reactions simulated in the present work are consistent with experimental data, except the Al13Fe4 and quaternary Al9FeMg3Si5 phases. According to the work of Backerud et al.,[64] the solidified microstructure of the 6063 alloy was (Al) + Al8Fe2Si + Al9Fe2Si2 + Mg2Si. The two phases Al13Fe4 and Al9FeMg3Si5 were not detected in their experiments. The reason of the discrepancy may be due to the fact that such low amount of the Al13Fe4 and Al9FeMg3Si5 phases could not be determined by using the temporal experimental techniques. This discrepancy suggests that additional experiments should be conducted to confirm the existence of the two phases Al13Fe4 and Al9FeMg3Si5.

Fig. 13
figure 13

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

Figure 14 shows the calculated solidification curves of 2618 alloy (Al-2.24Cu-1.42Mg-0.9Fe-0.9Ni, in wt.%) under the equilibrium and Gulliver-Scheil non-equilibrium conditions. It can be seen that the solidified microstructure of the 2618 alloy resulting from the Gulliver-Scheil model is (Al) + Al9FeNi + Al7Cu4Ni + Al2CuMg, which is consistent with the work reported by Belov et al.[60] However, there exists a discrepancy with the experimental microstructure, i.e. (Al) + Al9FeNi + Al7Cu4Ni + Al2CuMg + Al7Cu2Fe, measured by Wang et al.[71] Further experiments are needed to verify the existence of the Al7Cu2Fe phase. In addition, the presently calculated results confirm that the Al9FeNi phase forms through the binary eutectic reaction L = (A1) + Al9FeNi over a wide temperature range from approximately 640-645 °C down to 505-515 °C reported by Belov et al.[60]

Fig. 14
figure 14

Calculated solidification curves of 2618 alloy (Al-2.24Cu-1.42Mg-0.9Fe-0.9Ni, in wt.%) under the equilibrium and Gulliver-Scheil non-equilibrium conditions

The information about phase equilibria and thermodynamic properties in multi-component alloys is usually missing in the literature due to their complex nature. By means of the thermodynamic modeling, the present work demonstrates a successful study on the phase equilibria of the quinary Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni systems in Al-rich corner. The approximate composition ranges 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 noted that this given composition range is rather conservative. In the sub-systems, many of these elements can be applied to a much wider composition range. The thermodynamic database is updated continuously to reliably predict the phase equilibria and phase formation in multi-component alloy systems and industrial aluminum alloys.

Conclusions

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

  • Gulliver-Scheil non-equilibrium solidification 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.%) are investigated. The reliability of the established database is verified by good agreement between calculation and experiment for phase diagrams, invariant reactions and Gulliver-Scheil non-equilibrium solidification behaviors.

  • The application of the presently thermodynamic database to control phase transitions throughout solidification process for Al alloys indicates the importance of thermodynamic databases in material design.

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Acknowledgments

The financial support from the National Basic Research Program of China (Grant No. 2011CB610401), Thermo-Calc Software AB under the Aluminum Alloy Database Project, Sino-German Center for Research Promotion (Grant No. GZ755), and the Scientific Research Starting Foundation for the Introduced Talents of Anhui University of Science and Technology (Grant No. ZX979) are greatly acknowledged.

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Hu, B., Qin, S., Du, Y. et al. Thermodynamic Description of the Al-Fe-Mg-Ni-Si and Al-Cu-Fe-Mg-Ni Quinary Systems and Its Application to Solidification Simulation. J. Phase Equilib. Diffus. 36, 333–349 (2015). https://doi.org/10.1007/s11669-015-0388-0

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  • DOI: https://doi.org/10.1007/s11669-015-0388-0

Keywords

  • Al alloys
  • Al-Cu-Fe-Mg-Ni
  • Al-Fe-Mg-Ni-Si
  • CALPHAD
  • solidification