- freely available
Metals 2012, 2(3), 377-398; doi:10.3390/met2030377
Published: 14 September 2012
Abstract: Progress in systematic development of a thermodynamic database for Mg alloys with 21 components is reported. Models for multicomponent alloys are built in a methodical approach from quantitative descriptions of unary, binary and ternary subsystems. For a large number of ternary—and some higher—alloy systems, an evaluation of the modeling depth is made with concise reference to experimental work validating these thermodynamic descriptions. A special focus is on ternary intermetallic phase compositions. These comprise solutions of the third component in a binary compound as well as truly ternary solid solution phases, in addition to the simple ternary stoichiometric phases. Concise information on the stability ranges is given. That evaluation is extended to selected quaternary and even higher alloy systems. Thermodynamic descriptions of intermetallic solution phases guided by their crystal structure are also elaborated and the diversity of such unified phases is emphasized.
Thermodynamic simulation of phase formation and calculated phase diagrams have been successfully used as an effective tool in focused alloy design and process optimization of magnesium alloys [1,2,3,4]. While the calculated phase diagrams provide a comprehensive overview of the equilibrium phase assembly, more quantitative details are obtained for simulations at a fixed alloy composition. Even for really multicomponent alloys, far beyond ternary systems, easily interpreted diagrams are obtained for the phase fractions and compositions with varying temperature. Often the as-cast state is reasonably approximated by simulations under Scheil conditions, whereas the other limiting case, complete equilibrium, provides the phases expected after long heat treatment. Thus, the temperature window for solution heat treatment for that specific multicomponent alloy can be predicted and the expected phase transformations, starting from the as-cast state, are revealed. It is evident that the quality of the underlying thermodynamic database is decisive for the success of such applications.
Such thermodynamic databases for multicomponent and multiphase alloys are developed using the Calphad approach [5,6], and comprise all possible phases in the alloy system, including the liquid phase and other complex solution phases. The present work will focus on specific aspects of a thermodynamic Mg alloy database, which is developed in an ongoing effort in the authors’ group since the mid 1990’s  by experiments combined with Calphad modeling as sketched in Figure 1. Some general aspects concerning modeling formalism, quality assurance and applications to multicomponent systems were published in 2001 , 2005  and 2008 .
The major components of the database are given in Figure 2 in a clockwise arrangement from the more conventional to the more advanced alloy systems. The most common alloying systems comprise aluminum (A), zinc (Z) and some manganese (M) in the AZ group or, without zinc, in the AM alloy group. The AS and AL series contain Si (S) or Li (L), in addition to Al. More advanced developments include Ca (X), Sr (J), Sn (T), Y (W) or the important rare earths elements (E) in combinations such as the AXJ, ZE or WZ alloys.
With growing size, the key issues arising are consistency, coherency and quality assurance. These issues also concern extension, maintenance and updating of the database. These specific issues and the application by predicting phase formation during solidification and heat treatment in multicomponent magnesium alloys from thermodynamic calculations are addressed in a recent work . The purpose of the present work is to reveal the necessity of meticulously describing the thermodynamics of intermetallic solid solution phases at least up to the ternary alloy systems. It will be shown that these are abundant in Mg alloy systems and that simplified descriptions focusing on stoichiometric binary or ternary phases must fail dramatically. That aspect is also worked out for the proper thermodynamic modeling of intermetallic solution phases containing many more than three components. In addition to the database, a thermodynamic software package based on the principle of minimizing the Gibbs energy of the multiphase system is required to perform the actual calculations, such as Thermo-calc , FactSage  or Pandat . In the present work, the software Pandat was used for all calculations.
2. Investigated Binary Alloy Systems
The database is built up systematically, from unary to binary to ternary and higher systems. The thermodynamic descriptions for the elements are taken from the unary SGTE data compiled by Dinsdale .
The 20 main components in the database are Ag, Al, Ca, Ce, Cu, Fe, Gd, La, Li, Mg, Mn, Nd, Ni, Sc, Si, Sn, Sr, Y, Zn and Zr. They form a total of 190 possible binary systems. An overview of our critical assessment concerning the Calphad-type modeling status of these binary systems is given in Table 1. All color-marked systems (green/yellow) are modeled in the complete composition range. It should be emphasized that in the process of Calphad modeling, all the experimental data of that binary system are put on the table: phase equilibria and phase boundaries, as well as thermodynamic data, such as enthalpies, specific heat, partial pressures or chemical activities. A self-consistent description of all these data, including the calculated phase diagram, is then produced through models of the Gibbs energy for each phase in the system. Thus, the binary systems marked green in Table 1 (status A, reliable description) are also very well validated by the entity of experimental data.
Less reliable descriptions (status B) are marked yellow. That indicates either scant experimental data or larger deviations between the thermodynamic calculations and the experimental data. Blank fields indicate systems that are not modeled yet (status C). That means that the Gibbs energies of the terminal solution phases, emerging from the elements, are extrapolated, assuming ideal solutions. For example, the calculated Ag-Sr phase diagram shows only the solution phases Liquid, FCC and BCC in this extrapolation but no intermetallic phase. Similarly, the Ag-Fe phase diagram will show complete solubility of the solution phases Liquid, FCC and BCC, but not the miscibility gap.
|Table 1. Classification of the modeling status of basic binary systems.|
|Sn||A||Complete binary modeling, Reliable description|
|Sr||B||Complete binary modeling, Less reliable description|
|Y||C||No binary modeling, extrapolation of terminal solution phases only|
Carbon is not included in Table 1 but in the database, where the two additional binary carbon systems (Al-C, C-Ca) are modeled with status B and two (C-Mg, C-Si) with status A.
For any application to multicomponent Mg alloys, it is important to also consider the binary systems containing no Mg. For example, in ternary Mg-C-Si alloys, the description of the binary system C-Si is of utmost importance because of the very stable compound SiC. This phase precipitates dominantly over a very wide range of conditions from Mg-C-Si alloys, in addition to Mg2Si or graphite. This is just one example why the secondary phases found in multicomponent Mg alloys should never be read from binary Mg-X phase diagrams alone. More detailed comments to the 146 binary systems modeled in the database (status A or B) are beyond the scope of this summary.
3. Investigated Ternary and Multicomponent Alloy Systems
A widely used approach in calculating phase diagrams of ternary and multicomponent systems is to start with the Calphad-descriptions of the binary subsystems and to extrapolate these into the higher system. That often works reasonably well as a first approximation if the proper extrapolation scheme for the binary terminal solution phases is used, such as Liquid, HCP (Mg) and others extending from a pure component . It is also supposed that ternary or higher compounds are less abundant than binary compounds. Ternary interaction parameters are then considered as a refinement only. That gives rise to the rule of thumb: the more components that are included, the less additional information is required. Even though this is generally adequate, it will be shown below that certainly for Mg alloys due diligence is required. The main reason is that intermetallic solid solution phases extending to ternary or higher alloy systems are abundant in Mg alloys. Therefore, calculations that are not based on proper thermodynamic descriptions of at least the important ternary systems may be precarious.
The ternary systems implemented in the database with Calphad-type modeling of the complete composition range are summarized in Table 2 for the 53 modeled ternary Mg-X-Z systems and for the additional 46 non-Mg systems in Table 3. Concerning the experimental validation, the same assessment as for the binary systems applies. The ternary systems marked with green color in Table 2 and Table 3 (status A) are well validated by the entity of experimental data, whereas the less reliable descriptions (status B) are marked yellow. The “year of study” is important information, since the experimental literature for each system up to the year of publication is summarized and critically assessed in the reference given. The key aspect worked out in the present work concerns the solid phases occurring at compositions within each ternary system as stoichiometric or solution phases.
|Table 2. Ternary Mg systems with complete thermodynamic descriptions and their classified modeling status. In ternary intermetallic solid solution phases extending from a binary phase with limited solubility of the third component, the majority component is marked in bold font.|
|System||Modeling status||Ternary intermetallic solid solution phases||Ternary stoichiometric phases||Year of study||Ref.|
|Mg-Al-Ca||A||C14-Ca(Mg,Al)2 C15-Ca(Al,Mg)2 *C36-Ca(Al,Mg)2 Ca8(Al,Mg)3||-||2009||[17,18]|
|Mg-Al-Ce||A||Ce(Mg,Al); Ce(Mg,Al)12; Ce(Mg,Al)2||Al13CeMg6||2002|||
|Mg-Al-Cu||A||*C14-Cu(Mg,Al)2; C15-Cu(Al,Mg)2; *C36-Cu(Al,Mg)2||Al7Cu3Mg6 Al3CuMg V-Al5Cu6Mg2||1998|||
|Mg-Al-Sc||A||Sc(Al,Mg); Sc(Al,Mg)2; Sc(Al,Mg)3||-||1999|||
|Mg-Al-Sr||A||Sr(Mg,Al)2; Sr6(Mg,Al)23; Sr9(Mg,Al)38; Sr2(Mg,Al)17; Sr(Al,Mg)2; Sr(Al,Mg)4||Al38Mg58Sr4||2007|||
|Mg-Al-Zn||A||βMg2(Al,Zn)3; γMg17(Al,Zn)12; (Mg,Al)Zn; (Mg,Al)2Zn3; C14-(Mg,Al) Zn2; (Mg,Al)2Zn11; *θ-AlMgZn; *τ-AlMgZn||-||2006|||
|Mg-Ce-La||A||(Ce,La)Mg; (Ce,La)Mg3;(Ce,La)5Mg41; (Ce,La)Mg12; (Ce,La)2Mg17||-||2012|||
|Mg-Ce-Nd||A||(Ce,Nd)Mg; (Ce,Nd)Mg3; (Ce,Nd)5Mg41; (Ce,Nd)Mg12||-||2011|||
|Mg-Ce-Y||B||(Ce,Y)Mg; (Ce,Y)Mg2; (Ce,Y)Mg3; (Ce,Y)5Mg41; (Ce,Y)Mg12; (Y,Ce)Mg2; (Y,Ce)5Mg24;*(Ce,Y)Mg5||-||2010|||
|Mg-Ce-Zn||A||(Ce,Zn)Mg; (Ce,Zn)Mg3; (Ce,Zn)Mg12||CeMg7Zn12; Ce2Mg53Zn45CeMg3Zn5||2010|||
|Mg-Cu-Si||A||C15- Cu(Mg,Si)2||Cu16Mg6Si7_sigma Cu3Mg2Si_tau||1998|||
|Mg-Cu-Zn||A||C14- Mg(Cu,Zn)2; C15- Mg(Cu,Zn)2; *C36- Mg(Cu,Zn)2 Mg(Cu,Zn)||-||1998|||
|Mg-Gd-Li||A||(Gd,Li)Mg; (Gd,Li)Mg2; (Gd,Li)Mg3; (Gd,Li)Mg5||-||2001|||
|Mg-Gd-Y||B||(Gd,Y)Mg; (Gd,Y)Mg2 (Gd,Y)Mg3; (Gd,Y)Mg5 (Y,Gd)Mg2; (Y,Gd)5Mg24||-||2010|||
|Mg-Gd-Zn||A||(Gd,Zn)Mg; (Gd,Zn)Mg2 (Gd,Zn)Mg3; (Gd,Zn)Mg5||14H-GdMg12Zn I-Gd6Mg38Zn56||2012|||
|Mg-La-Nd||A||(La,Nd)Mg; (La,Nd)Mg3 (La,Nd)5Mg41; (La,Nd)Mg12 (La,Nd)2Mg17||-||2012|||
|Mg-La-Si||A||(La,Mg)5Si4; (La,Mg)3Si2 *(La,Mg)0.6Si0.4||La2Mg4Si4 La25Mg25Si50 La2Mg77Si La32Mg66Si||2010|||
|Mg-La-Zn||B||La(Mg,Zn) ; La(Mg,Zn)3 La2(Mg,Zn)17||I-LaMgZn||2010|||
|Mg-Li-Si||A||(Mg,Li)2Si||Li12Mg3Si4 Li2MgSi Li8MgSi6||2004|||
|Mg-Nd-Y||B||(Y,Nd)Mg; (Y,Nd)Mg3 (Y,Nd)5Mg41; (Y,Nd)Mg2 (Y,Nd)5Mg24; *(Y,Nd)Mg5||-||2008|||
|Mg-Nd-Zn||B||Nd(Mg,Zn) ;Nd(Mg,Zn)3 *Nd8 (Mg,Zn)92||Mg35Nd5Zn60 Mg30Nd15Zn55||2011|||
|Mg-Y-Zn||A||Y(Mg,Zn) ;Y(Mg,Zn)5 *I-YMg3(Mg,Zn)6*Z-Y7Mg28(Mg,Zn)65*W-Y25Mg25(Mg,Zn)50||14H-YMg12Zn 18R-YMg10Zn||2012|||
* indicates a true ternary solution phase, which is the same meaning in the Table 3.
|Table 3. Ternary systems—not containing Mg—with complete thermodynamic descriptions and their classified modeling status. Indication details are the same as in Table 2.|
|System||Modeling status||Ternary intermetallic solid solution phases||Ternary stoichiometric phases||Year of study||Ref.|
|Al-Ca-Sr||A||C15-(Ca,Sr)Mg2 Al4(Ca,Sr) Al4(Ca,Sr)Al2(Ca,Sr) Al7(Ca,Sr)8||-||2009|||
|Al-Ce-Nd||B||(Ce,Nd)3Al11 (Ce,Nd)Al3 (Ce,Nd)Al (Ce,Nd)Al2 (Ce,Nd)3Al (Ce,Nd)3Al||-||2003|||
|Al-Cu-Gd||B||Gd(Al,Cu)2 Gd(Al,Cu)5 Gd(Al,Cu)2||AlCu17Gd2 AlCuGd Al2.1Cu0.9Gd Al3.2Cu7.8Gd Al4.4Cu6.6Gd Al8.9Cu2.1Gd3 Al8Cu4Gd||2009|||
|Al-Cu-Li||B||-||Al2CuLi Al55Cu11Li33 Al57Cu11Li32 Al60Cu32Li8||1994|||
|Al-Fe-Si||B||-||Al35Fe37Si28 Al40Fe25Si35 Al49Fe16Si35 Al54Fe26Si20 Al60Fe15Si25 Al64Fe20Si16 Al66Fe19Si15||1999|||
|Al-Li-Si||A||-||LiAlSi Li5.3Al0.7Si2 Li8Al3Si5||2001|| |
|Ca-Li-Si||B||-||Ca2Li5Si3 Ca2LiSi Ca2LiSi3 CaLi2Si CaLiSi2||2003||Unpublished|
|Ca-Sr-Zn||B||(Ca,Sr)Zn2 (Ca,Sr)Zn5 (Ca,Sr)Zn13||-||2003|||
|Cu-La-Ni||B||La(Cu,Ni) La(Cu,Ni)2 La(Cu,Ni)5 La(Cu,Ni)||-||2012|||
|Fe-Mn-Si||B||(Fe,Mn)Si (Fe,Mn)5Si3 (Fe,Mn)3Si||-||1993|||
The large number of ternary solid phases with significant solution ranges compiled in Table 2 and Table 3 highlights the necessity to go beyond simple stoichiometric binary and ternary phase descriptions. A simplified notation is used in Table 2 and Table 3 to emphasize more clearly the three possibilities for ternary solid solution phases:
(i) Those extending from binary intermetallic phases with limited, though significant, solubility of the third component of the majority component are marked in a bold font. For example, the phase denoted as Ag(Al,Mg)3 extends from the binary AgMg3 into the ternary Mg-Ag-Al systems but not throughout since there is no stable AgAl3 phase.
(ii) Complete solid solubility exists, such as in the Mg-Ca-Li system between the C14-type phases CaMg2 and CaLi2. Thus, none of the two mutually substituting components Mg and Li is denoted as majority species in the C14-Ca(Mg,Li)2 phase.
(iii) Truly ternary phases, marked by an asterisk (*), are stable over a significant solid solution range in the ternary system only, which does not extend to a binary edge system. All the phases compiled in the column “Ternary stoichiometric phases” are, of course, also truly ternary phases.
The benefit of the simplified notation presented is understood by comparison with the sublattice models actually used in the thermodynamic descriptions. For an example of case (iii) in the ternary Mg-Al-Ca system, the hexagonal ternary Laves phase C36 is modeled with a complex three-sublattice model following the crystallographic prototype for this phase in the MgNi2 structure (Pearson symbol hP24, space group P63/mmc). The stoichiometric formula used in this model is (Al)36(Al,Mg)14(Ca,Mg)25, where the major species are also highlighted by bold font . In Table 2 the simplified notation *C36-Ca(Al,Mg)2 is used for this phase in order to show at a glance that the approximate stability range occurs around 33 at.% Ca in the ternary system, but not throughout to any binary edge system, as indicated by the asterisk (*). All other more complex sublattice models and mutual phase equilibria have been digested in the same manner to produce concise information on the stable solid solution ranges and to convey this message in Table 2 more clearly. For an example of case (i) in the ternary Mg-Al-Li system, the phase denoted as Li(Al,Mg) clearly indicates that the binary “LiAl” phase extends with significant, though limited, solubility of Mg as stable phase into the ternary system. This information is not easily deduced from the actual sublattice model of this NaTl-structure-type phase including vacancies, (Li,Mg,Va)(Al,Li,Mg), which also provides the stoichiometry deviation of “LiAl” in the binary Al-Li system .
In addition, 23 thermodynamic descriptions for ternary systems have been developed and are implemented in the Mg database, classified with status B and unpublished. These are 8 Mg-systems: Mg-Al-Y, Mg-Cu-Ni, Mg-Gd-Mn, Mg-Li-Zn, Mg-Mn-Y, Mg-Mn-Zr, Mg-Ni-Si, Mg-Y-Zr; and 15 non-Mg systems: Al-Ca-Ce, Al-Ca-Li, Al-Ca-Si, Al-Ce-Gd, Al-Ce-La, Al-Ce-Y, Al-Cu-Nd, Al-Gd-La, Al-Gd-Nd, Al-Gd-Y, Al-La-Nd, Al-La-Y, Al-Li-Mn, Al-Mn-Sc, Cu-Ni-Si.
The importance of ternary non-Mg systems is analogous to the binary non-Mg system explained for the example of the compound SiC in the previous section. This is not only relevant for the secondary phases found in multicomponent Mg alloys, but also for applications that require calculations over a wide composition range, such as joining dissimilar materials, interface reactions between distinct alloys or materials compatibility of distinct alloys, and so on. For any thermodynamic calculation applied to multicomponent alloys it is thus useful to check if the major alloying components are covered by the 122 ternary systems modeled in the database (status A or B) to ensure that the calculation results are validated by underlying experimental data. For some multicomponent Mg alloy systems, the thermodynamic descriptions have been validated by experimental investigations. Those with a published reference are summarized in Table 4.
The essential work to be performed for multicomponent intermetallic solution phases requires joining of the binary or ternary sublattice models into a unique and consistent description. Quaternary interaction parameters have not been used in any solution phase. The entry “none” in Table 4 means that from the cited experimental validation, using key samples, no quaternary solubility was found. Truly multicomponent phases occur very rarely. In the database, only two stoichiometric phases are modeled: Al5Cu2Mg8Si6 and Al8FeMg3Si6.
In fact, the solution phases given in Table 4 all originate from the binary intermetallic phase: from CaMg2 into the Mg-Al-Ca-Sr and Mg-Al-Ca-Mn-Sr systems, and from Ca2Sn into the Mg-Ca-Ce-Sn and Mg-Ca-Si-Sn systems. This comprehensive and consistent solution phase modeling was also done for the intermetallic REMg and REZN phases which enables a reasonable extrapolation into multicomponent Mg-Zn-RE/Y systems (RE = Ce, La, Nd, Gd).
|Table 4. Multicomponent Mg-containing systems with verified thermodynamic descriptions and their classified modeling status. Indication details same as in Table 2.|
|System||Modeling status||Higher intermetallic solid solution phases||Higher stoichiometric phases||Year of study||Ref.|
At this point, the rule of thumb is reflected and evidenced: The more components included, the less additional information is required. This rule is proper for Mg alloy thermodynamics, on the basis of meticulous Calphad modeling of the binary and ternary systems and consistent treatment of multicomponent intermetallic solution phases.
4. Crystal Structure Guided Modeling of Multicomponent Intermetallic Solution Phases
In the previous chapter, the experimentally validated stability ranges of ternary intermetallic solution phases in the individual ternary and some multicomponent systems have been worked out. The focus of this chapter is on the proper modeling of such phases considering the information given by the crystal structure. The basic idea is that intermetallic phases occurring in different binary systems may be modeled as the same phase if they share the same crystal structure. If, in addition, the lattice parameters are similar and the components do not exhibit strong repulsive interactions, the simplest realistic description is that of a single phase with ideal substitutional solution. That is certainly a better approximation compared to the implementation as separate compound phases, which is in fact equivalent to complete demixing.
This approach is detailed in the following examples, highlighting the diversity of such unified phases. The continuous solubility or the solubility limits of such phases eventually result from the competition of phases as modeled in the database.
One example depicted in Figure 3 is the phase “REMg”, emerging from ten stable binary REMg or REZn phases with the common cP2-CsCl crystal structure. Accordingly, it is modeled with two sublattices with site ratios 1:1. On the first sublattice, the rare earths (Ce,Gd,La,Nd,Y) are majority components, denoted by bold font, whereas Mg and Zn are minority components denoted by an italic font. On the second sublattice (Mg,Zn) are majority and (Al,Mn,Li) minority components, respectively. The minority species cannot reach a complete occupancy on their sublattice in the stable region of the phase named REMg. Nevertheless, it is essential to assess a reasonable Gibbs energy function for all the metastable end member phases, such as the “CeAl” composition of the REMg phase. The REMg phase occurs as stable continuous solid solution (Ce,Nd)Mg in the Mg-Ce-Nd system, Figure 4, and as Ce(Mg,Zn) solution in the Mg-Ce-Zn system, Figure 5. In the Mg-Al-Ce system, it is a limited solid solution Ce(Mg,Al) as shown in Figure 6. In these calculated ternary isothermal phase diagram sections the ternary intermetallic solution phases are highlighted by red lines and the ternary stoichiometric phases by red dots. Three-phase regions (triangles) are shaded.
In the Mg-Ce-Nd system, Figure 4, the Mg-rich corner is “locked-in” by the continuous solid solution of the (Ce,Nd)5Mg41 phase. Therefore, only this phase is expected together with (Ce,Nd)Mg12 in Mg-rich alloys with Ce and Nd. In as-cast microstructures, the (Ce,Nd)5Mg41 phase is typically suppressed by impeded nucleation/growth. The resulting metastable phase diagram reveals a drastic extension of the primary crystallization field of (Ce,Nd)Mg12 and this phase is in fact found in as-cast samples .
The Mg-Ce-Zn system, Figure 5, looks even more complicated. Three ternary solubilities are observed, including one continuous solid solution and, additionally, three ternary stoichiometric phases. Mg-rich alloys with Ce and Zn show the secondary phase (Ce,Zn)Mg12 with large Zn content up to 40 at.% Zn and possibly the ternary phase T2, Ce2Mg53Zn45 depending on the Ce:Zn ratio .
Figure 6 shows the Mg-Al-Ce system at 400 °C with limited solubility of the third component in (Ce(Mg,Al) and Ce(Mg,Al)12 and one ternary stoichiometric phase Al13CeMg6. Apparently the phase Ce(Al,Mg)2 occurs in two separate composition ranges and might be even mistaken for a ternary phase. However, at higher temperatures, around 740 °C, a complete solution range between CeAl2 and CeMg2 is established  (see also Table 2). For Mg-rich alloys, the Al solubility of the Ce(Mg,Al)12 phase is crucial, since it blocks the way to an equilibrium of (Mg) with the mid-composition Ce(Al,Mg)2 phase during solidification and heat treatments.
In the Mg-Al-Sr system at 400 °C, Figure 7, a similar cut-off is expected due to the Al solubility of the Sr2(Mg,Al)17 phase. In this system, even the ternary Al38Mg58Sr4 can be formed in Mg-rich alloys during Scheil solidification .
The six stable binary end members of the multicomponent phase “RE2Mg17” sketched in Figure 8 crystallize in the hP38-Ni17Th2 structure type. The four RE2Zn17 phases are stable down to room temperature whereas Ce2Mg17 and La2Mg17 are stable at high temperature only. Therefore, Ce2Mg17 does not appear in the isothermal Mg-Ce-Nd section at 500 °C in Figure 4. At higher temperature, the RE2Mg17 phase becomes stable in this system and the limited Nd solubility in Ce2Mg17 is modeled, considering the Gibbs energy of the metastable end member Nd2Mg17 marked in orange in Figure 8.
Two non-Mg systems will be given as examples for reasonably calculated phase diagrams without using any ternary parameter after unification of binary intermetallics crystallizing in the same crystal structure. Figure 9 shows the Ce-La-Si system where five binary compounds were unified to ternary continuous solid solutions, since they share identical crystal structures of the corresponding binary phases:
• (Ce,La)Si2 (tI12-ThSi2 structure type)
• (Ce,La)Si (oP8-FeB structure type)
• (Ce,La)5Si4 (Zr5Si4 structure type)
• (Ce,La)3Si2 (tP10-U3Si2 structure type)
• (Ce,La)5Si3-HT (tI32-Cr5B3 structure type)
The comprehensive modeling of the phase “CaCu5” (hP6-CaCu5 structure type), which unifies five Cu- and five Ni-containing phases is illustrated in Figure 10. Focusing on the Ce-Cu-Ni system, this includes the phases CeCu5 and CeNi5, sharing the CaCu5 structure type, which are therefore modeled as one phase Ce(Cu,Ni)5. Experimental proof of this continuous solid solution of Ce(Cu,Ni)5 was given by .
However, the phases CeCu2 (CeCu2-type structure) and CeNi2 (CuMg2-type structure) crystallize in different structure types and cannot be joined. The same applies to the phases CeCu (FeB-type structure) and CeNi (CrB-type structure) which must also be modeled as separate phases. Their very limited ternary solubilities  are not considered in this first-stage description. Based on these considerations, the ternary Ce-Cu-Ni phase diagram in Figure 11 can be calculated without using any ternary interaction parameter as an extrapolation from the binary systems. This provides a reasonable estimation for this system, especially in Ce-poor regions.
Intermetallic solid solution phases extending to ternary or higher alloy systems are shown to be abundant in Mg alloys. Therefore, calculations that are not based on proper thermodynamic descriptions of at least the important ternary systems may be precarious. Describing only the binary compounds is inadequate for ternary or higher Mg alloy applications.
Thermodynamic descriptions of intermetallic solution phases should be guided by their crystal structure. Generally, such phases occurring in different binary systems may be modeled as the same phase if they share the same crystal structure. Joining such phases enables more realistic predictions of multicomponent alloy phase diagrams and phase formation calculations. The diversity of such unified phases is emphasized.
On the basis of meticulous Calphad modeling of the binary and ternary systems and consistent treatment of multicomponent intermetallic solution phases, the following rule of thumb is proper for Mg alloy thermodynamics: The more components that are included, the less additional information is required. That enables applications of truly multicomponent Mg alloys involving thermodynamic calculation of any kind of phase diagram sections or liquidus and solidus projections, solidification simulation using the limiting Scheil and equilibrium conditions and obtaining thermodynamic driving forces for kinetic processes.
Conflict of Interest
The authors declare no conflict of interest.
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