Understanding the Thermodynamics and Crystal Structure of Complex Fe Containing Intermetallic Phases Formed on Solidification of Aluminium Alloys

Ab initio density-functional theory calculations were carried out to investigate the energetics and structure of key Fe-containing intermetallic phases that precipitate from cast Al-Si alloys. These results were compared with published experimental information and used to provide insight into developing improved models to describe the thermodynamic properties of these phases.


INTRODUCTION
The control of harmful impurities such as Fe in cast Al-Si alloys is becoming ever more important as the demand for the use of scrap materials increases. Traditionally manganese is added to prevent the formation of the harmful b-AlFeSi phase. Therefore, an understanding of phase equilibria in the Al-Fe-Mn-Si system, the solubilities of elements in various intermetallic phases and the temperatures at which they form are prerequisites for any successful control of the microstructure and the phases formed during solidification. The calculation of phase diagrams from critically assessed thermodynamic data provides an invaluable tool for providing such an understanding.
Critically assessed thermodynamic data are derived through careful analysis of all the experimental studies of thermodynamic properties and phase diagram information for a given system. Additionally, today such assessments should also consider the results of ab initio calculations, which may provide results with an accuracy equivalent to the best experimental work. Ab initio calculations may also be used to explore composition ranges of phases that are unstable and therefore inaccessible for study by experiment. In this way they can be used not just to provide key values for the critical assessment of data, but also assist in the selection of an appropriate thermodynamic model for a particular phase.
In this article, we considered in detail certain key phases of Al 6 Mn, Al 13 Fe 4 and a-Al(Fe,Mn)Si, which may form during the solidification of commercial aluminium alloys. [1][2][3] This included a thorough survey of published information on the thermodynamic properties, phase equilibria and crystal structures for these phases coupled to the calculation of the lattice parameters and enthalpies of formation using ab initio density-functional theory (DFT). These results allowed us to make key decisions related to the thermodynamic models used for these phases. An overview of the crystal structures of these phases is given in Table I.

Thermodynamic Modelling and Structural Properties
Despite its importance technologically, the phase diagram, thermodynamic properties and crystal structure of key intermetallic phases in the Al-Fe-Mn-Si system are not completely understood. All of the published critical assessments of data for the system are largely based on the results of the COST507 European research programme. [8][9][10][11] However, most of this work was carried out before reliable software and computer power made it possible to carry out detailed calculations on complex crystal structures in multicomponent systems using ab initio DFT.
Reliable thermodynamic modelling must be based on an understanding of the known crystal structure of a phase, e.g., the number of sublattices, the occupation of elements on the crystallographic sites and the energetics associated with vacancy formation. Some simplification is however sometimes necessary to minimise the number of parameters necessary to describe the thermodynamics of a phase. Ab initio calculations now provide an invaluable tool by calculating the energetics of different crystallographic configurations to identify which features are key to guide such simplification. Furthermore, as many of the measurements of thermodynamic properties were carried out years ago, ab initio calculations provide the means to check the validity of such data. In this work such calculations have been employed to calculate the enthalpies of the formation, crystal structure and energetics associated with defect formation and the solution of additional elements onto the crystal lattice.

Ab Initio Calculations
For the calculations reported here, the plane wave method using VASP, Vienna Ab initio Simulation Package, was used. 12,13 The spin-polarized generalized gradient approximation (SP-GGA-PBE) 14 within the projector-augmented wave (PAW) method 15 was employed for the exchange and correlation energy terms because the spin-polarized generalized gradient approximation describes the 3d transition metals such as Fe better than the (spin-polarized) local density approximation (LDA). [16][17][18][19] The cut-off energy of the wave functions was set at 550 eV and the cut-off energy of the augmentation functions was 700 eV to describe the rather localized Fe 3d orbitals. The electronic wave functions were sampled on dense k grids of the Brillouin zones of the unit cells. 20 To obtain the ground state of the crystals, we performed calculations for different inputs. This avoided the possibility of our results falling into metastable solutions. [16][17][18] Different k-meshes and cut-off energies were used for the waves and augmentation waves, respectively. Tests showed good convergence (< 1 meV/atom).

Al 6 Mn
The most recent review as well as assessment of data for the Al-Fe-Mn system is from the work of Lin and Selleby. 21 There are two invariant reactions in the Al-rich corner of the Al-Fe-Mn system, a eutectic reaction: Liquid ! Al 6 Mn þ Al 13 Fe 4 þ fcc at 654°C and a probable ternary peritectic reaction at 730°C: Liquid þ Al 13 Fe 4 þ Al 4 Mn ! Al 6 Mn Figure 1 shows the calculated liquidus projection for the Al-rich corner of the system with key experimental values superimposed. The phase  is the most aluminium-rich intermetallic phase in the Al-Fe system and often can precipitate from an aluminium-rich liquid containing relatively small amounts of iron. Other elements, particularly manganese, have appreciable solubility in this phase. Al 6 Mn is the most aluminium-rich intermetallic in the Al-Mn system that is in equilibrium with the liquid phase. Of particular interest is the very high solubility of iron in this phase, which extends nearly all the way across the system to the Al-Fe system. The equivalent compound Al 6 Fe has been observed experimentally, but is considered to be metastable. Al 6 Mn has a bottom-centred orthorhombic (BCO) lattice with space group Cmcm (No. 63). There are three crystallographically different species of Al with 28 atoms per unit cell. Figure 2 shows a calculated isopleth in the Al-Fe-Mn system from Al 6 Mn to the composition of Al 6 Fe. It shows the appreciable solubility of Fe in the phase. Experimental phase equilibrium data are superimposed.
Ab initio DFT calculations have been carried out to explore the crystal structure of the Al 6 Mn in detail to identify which crystallographic site iron atoms are likely to replace aluminium and to consider the possibility of solution of silicon in the phase. Figure 3a shows that the substitution of Mn by Fe is predicted to be accompanied by a heat release of 2.8 kJ mol À1 per formula unit for substitution of half of the Mn by Fe. Figure 3b shows the excellent agreement between the calculated lattice parameters and the experimental values. 29 The potential for Si substituting for Al in the Al 6 Mn lattice was also explored and shows that this is accompanied by a large enthalpy increase, i.e., substitution is not favoured. 6 Mn is in equilibrium with Al 13 Fe 4 in the Al-Fe-Mn system. Just as Fe substitutes for Mn in the Al 6 Mn phase, the Al 13 Fe 4 phase is capable of dissolving substantial amounts of Mn. However, in the binary Al-Fe system the Al 13 Fe 4 phase exists only over a relatively narrow range of homogeneity (maximum 4 at.%) that, according to recent experimental work, 30 becomes smaller as the temperature is reduced.  The crystal structure of stoichiometric Al 13 Fe 4 is now well defined. 5,[31][32][33][34][35] It has a total of 102 atomic sites per unit cell, 78 occupied by Al and 24 by Fe. If all lattice sites are occupied, this gives the composition Al 78 Fe 24 , i.e., Al 13 Fe 4 , and this represents the most Al-rich composition of the phase according to the phase diagram. There appear to have been no detailed crystal structure determinations on compositions away from stoichiometry to indicate where defects arise (from either vacancy formation or substitution). So far, the thermodynamic models for the phase have all been based on the assumption of vacancy formation on some of the aluminium sites. This has been successful in modelling the thermodynamic properties to calculate the phase diagram for the Al-Fe system, but, because it is not based on any firm foundation, is not able to provide a good basis for representing data for ternary systems such as the Al-Fe-Mn system where substitution of Mn is complex.

Figures 1 and 2 show that Al
The enthalpy of formation of Al 13 Fe 4 has been measured calorimetrically [36][37][38] and calculated using ab initio DTF at 0 K. 39,40 The calculated values are very close but significantly more negative than the calorimetric data.
We also studied the energetics (Fig. 4) associated with defect formation on the various sites of the Al 13 Fe 4 lattice. 40 The formation of vacancies was shown to be energetically highly unfavourable, which is in contrast to the commonly used thermodynamic model for the phase, which draws on the experimental work of Grin et al. 5  where the Roman numerals IX, VII and V indicate the appropriate crystallographic site. This allows for a wider range of homogeneity than is necessary for the Al-Fe system itself but would be necessary to model the extent of the homogeneity range of the phase in the Al-Fe-Mn system. 26,27 The calculations also show that the substitution of Fe onto Al sites induces magnetism. The nature of this magnetic ordering is quite complicated depending on the nature of the site or sites in which the Fe atoms substitute. On the whole, the ordering is predicted to be ferromagnetic but certain arrangements of atoms are predicted to give rise to antiferromagnetic or ferrimagnetic ordering. Further calculations were also carried out to investigate the effect of substituting Fe by Mn (Fig. 3a).

a-Al(Fe,Mn)Si
The cubic a-Al(Fe,Mn)Si phase (also known as Al 15 (Fe,Mn) 3 Si 2 ) forms as a large crystal of the primary intermetallic phase on solidification of many commercial Al alloys. It also forms with a ''Chinese script'' morphology during a subsequent eutectic reaction. The exact nature of this phase has been the subject of much uncertainty over the years and this has not been helped by the confusing and inconsistent terminology adopted for the various intermetallic phases in the quaternary system. To this end, in this article we will refer to Al 7.4 Fe 2 Si (sometimes referred to as the a-s 5 phase and a-AlFeSi) and Al 9 Mn 2 Si (sometimes referred to as a-AlMnSi). In their pioneering work, Phillips and Varley 41 did not distinguish between Al 9 Mn 2 Si and the Al 7.4 Fe 2 Si and assumed that they formed a cubic solid solution phase across the system. Munson 42 showed that while Al 9 Mn 2 Si is cubic, Al 7.4 Fe 2 Si is hexagonal and therefore the two phases could not form a continuous solid solution. Other work 29,[43][44][45] showed that the cubic a-Al(Fe,Mn)Si emanates from Al 9 Mn 2 Si by substantial substitution of Mn by Fe but that it did not extend to the Al-Fe-Si system. They also showed that the phase had a broad range of homogeneity with respect to the Si content. On the other hand, others have identified quaternary phases. [46][47][48][49] The confusion has been partially resolved by Krendelsberger. [50][51][52] As part of a comprehensive study of the Al-Fe-Si, Al-Mn-Si and Al-Fe-Mn-Si systems, she studied the section between Al 9 Mn 2 Si and Al 7.4 Fe 2 Si at 700°C. She carried out a full structure analysis of single-phase samples corresponding to Al 9 Mn 2 Si and an a-Al(Fe,Mn)Si containing approximately equal amounts of Fe and Mn. She was able to confirm that both samples had close to an identical cubic crystal structure with 138 atoms per unit cell. However, the Al 9 Mn 2 Si sample showed a simple primitive cubic lattice while the a-Al(Fe,Mn)Si sample had a bcc structure in which some of the peaks had disappeared. It is still unclear whether this indicates that a first-or second-order phase transformation takes place on the addition of Fe to Al 9 Mn 2 Si.
Ab initio calculations have been carried out to help understand this issue. Based on our experience with the calculations on the Al 13 Fe 4 phase and the experimental crystal structure model for a-Al(Fe,Mn)Si, we built a framework for DFT calculations with 24 Fe atoms occupying the two 12j sites and the remaining nine Wyckoff sites occupied by Al. This unit cell contains 24 Fe and 114 Al atoms. As expected, the calculated formation energy is noticeably higher than that of Al 13 Fe 4 . Then, in subsequent calculations, we replaced Fe by Mn and Al by Si in a systematic way. Further calculations were carried out to examine the effect of substitution of Al by Fe or Mn.
The results clearly show that mixing of Fe and Mn on the two 12j sites is favoured although one set of sites seemed more favourable for substitution than the other. More calculations are currently underway and it is hoped, that they will shed more light on the chemical compositions and related symmetry, crystal structure, energetics and electronic properties of the a-Al(Fe,Mn)Si compound.

CONCLUSION
Experimental phase diagram, thermodynamic and crystal structure data for three key Fe-based intermetallic phases that precipitate from cast Al-Si alloys were reviewed. Ab initio DFT calculations were employed to better understand the non-stoichiometry in these phases in terms of the defects. In all of the phases studied there was a marked tendency for Fe and Mn to mix on the same crystallographic sites with a negative enthalpy of mixing relative to the pure constituent compounds (Fig. 3a). For the Al 13 Fe 4 phase it was shown that the relatively narrow range of homogeneity in the Al-Fe system is due to the substitution of Fe atoms on three specific Al sites. This is in contrast to the accepted thermodynamic description, which introduced vacancies. Our calculations show that this is highly unfavourable energetically.