Abstract
The phase equilibria associated with Heusler-type intermetallic compounds have been reviewed for systems containing Fe, Co or Ni. Ternary alloy systems are identified in which the phase equilibria are not well established or completely unknown and which are therefore prime targets for additional experimental work. Other systems in which there is conflicting information regarding the existence of a Heusler phase are also identified. Design issues are highlighted in terms of phase combinations that may benefit functional properties or processing of bulk material containing Heusler compounds.
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Introduction
Since the discovery of the first Heusler compounds, Cu2Mn(Al, Sn, Zn, Bi, Sb or B), by Heusler in 1903 [1], a large number of intermetallic compounds of the type X2YZ have been discovered. However, not all compounds of this stoichiometry have the original prototype Cu2MnAl (L21, prototype Cu2MnAl, Pearson symbol cF16, space group Fm \( \bar{3} \) m) structure. Typically, the X and Y elements are transition elements and the Z element is from Group III–V in the periodic table, although there are exceptions, Fig. 1. On this basis, there are potentially thousands of such compounds. While for decades after their discovery, these intermetallics were little more than a scientific curiosity, studied mostly for their ferromagnetic properties, in the last 25 years there is growing interest in other functional properties [2]. These include magnetic shape memory and magneto-caloric effects, thermoelectric properties and spintronic behaviour amongst others [3–6]. For some properties, a deviation from stoichiometry can lead to property changes due to the presence of constitutional defects, or changes can be produced by fourth element substitution [7, 8]. This allows the properties to be tuned to optimum values for a specific application.
Periodic table showing typical X, Y and Z elements in Heusler compounds. Modified from blank table image: http://en.wikipedia.org/wiki/File:Periodic_table_%28polyatomic%29.svg Available under CC-BY-SA license: http://creativecommons.org/licenses/by-sa/3.0/deed.en
In order to design materials based on, or incorporating, Heusler compounds it is necessary to understand the phase equilibria in the ternary systems in which they occur. However, while many papers deal with the properties of stoichiometric Heusler phases or predictions of their stability, there is a lack of ternary phase diagram data for alloy systems containing Heusler phases. Where there are phase equilibria data they are often confined to a single isothermal section, because experimental phase diagram studies are very time consuming. In some cases, the phase diagrams available contradict the results of single composition determinations of the presence of a Heusler phase. Computational thermodynamics utilizing the Calphad approach can be used to generate phase diagrams in a more efficient way than experiments and therefore offer an efficient method to investigate phase relationships. Nevertheless, some experimental data are needed such as equilibrium phase compositions, transition temperatures and thermodynamic data such as enthalpy of formation. Over the last 5 years, a program to experimentally determine enthalpies of formation of Heusler compounds has been undertaken (see for example [9, 10]) and a large dataset now exists [11]. These data are of use in Calphad calculations as well as providing benchmarks for first principles calculations. Furthermore, the Calphad approach cannot predict the occurrence of a particular intermetallic compound, whereas first principles calculations can and it is often necessary to use a hybrid approach utilizing experiment, Calphad and first principles calculations to provide accurate descriptions of the phase equilibria in complex alloy systems [12].
Given the large number of possible compounds, the use of high throughput first principles calculations to establish stability of a compound provides a useful guide in the search for new Heusler compounds [13–18]. Nevertheless, such calculations sometimes contradict experimental observations, for example, for the compound Ni2MnSn (L21) which is predicted to be less stable than corresponding binary compounds; however, the existence of the phase is well established [19–21].
The need for phase equilibria data over a range of temperature is made more apparent by the observation that it is possible for Heusler compounds to form on cooling from either an A2 bcc solid solution phase, or a B2 primitive cubic-ordered phase. Such transformations may occur by first-order or second-order, ordering transformations. This is due to the structural relationship between these phases as shown in Fig. 2. Such transformations may also be valuable for example in processing bulk material which is usually difficult for the highly ordered Heusler compound [22]. Furthermore, some properties require constitutional defect structures introduced by compositions off-stoichiometry [23, 24] or doping of the ternary intermetallic with a fourth element to promote optimum properties, e.g. thermoelectrics [24–26]. Shape memory and magnetic properties can be strongly affected by fourth element substitution [3]. This provides us a vast composition-temperature space to explore for the design and development of Heusler containing-materials.
Unit cells of a A2, b B2, c L21 and d C1b structures
In this paper we review the current knowledge of phase equilibria in Fe, Co or Ni alloy systems containing, or potentially containing, Heusler phases. In order to keep this review manageable we have confined our discussion to systems containing transition metals and Group III–IV elements. A total of 180 ternary systems have been reviewed. We have not attempted to review the specific properties of Heusler alloys as there are several excellent reviews available on this topic [2, 27–31]. We have tried to identify systematic phase equilibria according to elemental constituents and highlight which systems may offer interesting combinations of phases for functional and structural applications. We have also identified ternary systems where additional phase equilibria work is needed and potential Heusler compounds that have yet to be discovered.
Identification of Heusler structure
The identification of the presence of a Heusler compound by X-ray diffraction can sometimes be difficult due to the similarity of the structure to the A2 (prototype W, Pearson symbol cI2, space group Im \( \bar{3} \) m) and B2 (prototype CsCl, Pearson symbol cP2, space group Pm \( \bar{3} \) m) crystal structures, less than perfect order, constitutional defects and similarities in scattering between the constituent elements. It is apparent from Fig. 2 that there are close relationships between these three crystal structures and also a fourth, C1b structure (prototype AgAsMg, Pearson symbol cF12, space group F \( \bar{4} \)3m). The related C1b structure, exhibited by half-Heusler compounds, with stoichiometry XYZ, results from the removal of four X atoms from the L21 structure. Essentially, the B2 is the result of ordering from the A2 structure, and the L21 corresponds to an ordering of 8 unit cells of B2 structure in a ternary alloy. This is most easily appreciated by shifting the origin to the X atom at 1/4, 1/4, 1/4, where it can be seen that the unit cell is composed of eight B2 type unit cells, four containing the Y element in the central position and four containing the Z element in the central position, Fig. 3c [32]. In a ternary alloy composition X2YZ with a B2 structure, one of the Wyckoff positions is shared by the Y and Z elements, Fig. 3b. The simulated XRD patterns for Co0.5Fe0.25Al0.25 in the 3 different structures are shown in Fig. 4. It is apparent that the major peaks are the same, while additional superlattice peaks appear as the ordering goes to B2 and then to L21. These simulated patterns are for perfect order and the stoichiometric composition and less intense superlattice lines will occur for non-stoichiometric compositions and lower order. Thus, considerable care must be taken in identifying the Heusler, L21, structure in an alloy.
Co2FeAl in a A2, b B2 and c L21 crystal structures. Blue atoms represent Co, red atoms are Al and green atoms are Fe
Calculated XRD patterns for A2, B2 and L21 structures at the composition Co–25 at.%Fe–25 at.%Al using Cu Kα X-ray wavelength
Phase equilibria in Fe containing systems
Table 1 provides an overview of the ternary alloy systems in which an iron-based Heusler phase has been experimentally observed and also indicates those systems for which no experimental phase diagram data exist covering the Fe-based Heusler composition. In addition, we have indicated where existing phase diagrams conflict with single composition work elsewhere in the literature.
Examination of Table 1 shows that Al, Ga, Si, Ge and Sn should be favourable to form the Heusler structure with Fe when present in the Z position, whereas no Ge-containing Heusler compounds have ever been reported experimentally. Shifting our focus to the Y element candidates, the early transition elements in Columns 4 and 5 in the Periodic Table show a tendency to form the Heusler compound with Fe. This trend continues in ab initio prediction down Columns 4 and 5 with the exception of Zr which forms no Heusler phase with Fe. This is due to the relative stability of other phases even though the Fe2ZrZ compounds are predicted to have negative formation energies. In the Fe–Zr–Si system, the presence of a more stable ternary compound Fe16Zr6Si7 with a composition close to the Heusler prevents the formation of the Heusler compound [13, 33]. Moving along the transition metal series towards the non-metals, we see a strong trend against Heusler formation with Cr, Ni, Co or Cu. The exception is when Z = Mn which forms Heusler compounds with Al and Si.
Table 2 shows the calculated enthalpies of formation (0 K) for the stable Heusler phases or the difference between the energy of formation and the hull energy, for the predicted unstable Heusler phases taken from the Open Quantum Materials Database (OQMD) [13]. The OQMD is a publicly accessible database of density functional theory (DFT) calculated thermodynamic and structural properties. The hull energy is a convex surface representing the minimum energy in the system as a function of composition. Compounds that have a negative formation energy that is above the hull energy are therefore metastable compounds. Comparing with Table 1, we see a similar story to Co and Ni. There is one compound, Fe2CrSi [34], that has been made experimentally, conflicting with 0 K stability predictions. The compound was formed by annealing epitaxially grown thin films at 773 K. The compound is predicted to be only 7 kJ/mol of atoms above the hull energy at 0 K and its stability could be affected by the non-equilibrium processing. There are several predicted compounds yet to be verified, and furthermore there are even more cases where the difference between the calculated enthalpy of formation and the hull energy is generally small, less than 5 kJ/mol of atoms, and a Heusler could exist at a non-stoichiometric composition or under non-equilibrium processing. It is worth reiterating that as in the other cases, the calculated hull energy is based on the perfect stoichiometric end members without considering defects or the solubility range, which limits its ability to correctly predict phase stability.
Table 1 hides a number of problems related to the phase equilibria of the Fe–Y–Z ternary systems. For example, the Fe2TiAl Heusler has been investigated for its thermoelectric properties [35]. However, there exist a myriad of conflicting diagrams some showing Heusler structure up to 1200 °C and others devoid of the structure completely. To illustrate how bad the situation is, Fig. 5 presents a set of 3 isothermal sections at 800 °C. The left most section shows continuous transformation as a function of composition at constant temperature from the A2 (Fe)-structured solid solution phase to an ordered B2 FeAl phase and finally an L21 Fe2TiAl structure [36]. The middle diagram has continuous ordering between A2 and B2 phases with no Heusler [37], and the right most diagram presents a 2-phase field separating the broad A2/B2 single-phase region and a narrow range of Heusler compositions [38]. Conflicting sets of equilibrium phase stability such as this make alloy design and bulk processing difficult.
Rounding out the Fe2TiZ compounds, we have even less phase information. Fe2TiGa is not reported in any phase diagrams, but has been observed as a compound [39]. Fe2TiSi is seen only as a metastable extension of the D03 phase, Fe3Si [40, 41], but has been used as a distinct phase to improve thermoelectric properties of the FeTiSi half-Heusler [42]. For the compound Fe2TiSn, the crystal structure is verified to be Heusler [32], but no ternary diagram exists. The half-Heusler is stable [43] giving the potential to build a two-phase thermoelectric with higher figure of merit (zT) due to phonon scattering on the phase boundaries reducing the thermal conductivity.
Fe2VAl is one of the thermoelectric Heusler compounds [44] with relatively advanced development in the form of a vehicle scale powder-metal processed doped bimetal device having been fabricated and tested [45, 46]. This system is not much better explored than the Fe2TiAl system with the majority of diagrams showing that no Fe2VAl phase is present. The best data for working with this alloy are confined to a set of partial isothermal sections at 650, 700 and 750 °C [47]. These diagrams do not mesh well with the other data that are also sparse.
Another thermoelectric that has been subject to alloy work is Fe2VGa. The large solubility range at 800 °C and wide two-phase field with Fe room temperature structure provide opportunities to create a two-phase material with a more ductile matrix [48]. Due to the lack of higher temperature data, equilibria information makes solution treatment and high temperature forging more guesswork than science at this time.
Fe2VSi and Fe2MnAl have been confirmed experimentally [32] with Fe2VSi, in particular, observed at 300 K with a transformation to the tetragonal structure at 120 K. Fe2MnSi was similarly reported [49]. None of these compounds appear in any of the experimental ternary diagrams currently available ranging from 1473 to 298 K.
Fe2TiGe, Fe2NbAl, Fe2NbGa, Fe2TaAl and Fe2VGe [13, 15], are all predicted as stable compounds at 0 K, but do not appear in any of the existing phase diagrams nor do they show up in other experimental work. The most unexplored frontier is that of compounds predicted stable ab initio, but for which there are no phase diagrams: Fe2TaGa, Fe2TaGe and Fe2HfSn.
Phase equilibria in Co-containing systems
Table 3 provides an overview of the ternary alloy systems in which a cobalt-based Heusler phase has been experimentally observed and also indicates those systems for which no experimental phase diagram data exist covering the Co-based Heusler composition. Only two of the 11 possible systems with In are reported to have a Heusler phase, Co2FeIn [32] and Co2CrIn [50], and no phase diagrams are available for any of these systems. The possibility exists that some of the other systems may also contain an as yet undiscovered Heusler phase. A general observation for the formation of a Heusler phase in Cobalt containing alloys is that no Heusler phase is observed when either Ni or Cu is the Y element. An ordered compound has been reported [51] for Co2NiGa which was synthesized by mechanical alloying but was not observed in arc-melted samples. However, the ordered compound is reported to have a Pt2FeCu prototype structure, rather than the Cu2MnAl structure of Heusler compounds. On the other hand, if the Y element is from the first two columns of the transition metal series, a Heusler phase is observed.
For those systems with no phase equilibria data available, we can make some observations about the likelihood of Heusler phase existence. For the systems Co2NiZ and Co2CuZ, we should not expect the presence of a Heusler phase as none have been observed in any of the known phase diagrams and there are no reports of the existence of the L21 phase in any of these systems. We can also look at predicted stability from first principles calculations. There is a general trend in the Co2NiZ and Co2CuZ compositions of a decreasing stability on going down the Group III and IV columns, and the compositions with Z = Sn or In have a positive formation energy at 0 K [13]. For the other Z elements, with small negative energies of formation, they are not predicted to be stable as a result of having energies higher than the hull energy resulting from more stable compounds at other compositions, Table 4. This trend of decreasing stability has been observed experimentally [9].
In systems containing an early transition metal series Y element, many ternary compounds form, for example, 13, 10 and 4, respectively, in the Zr, Hf and Ti containing systems with Ga [52–54]. This results in numerous two- and three-phase equilibria between the Heusler compounds and other phases. This offers the opportunity to combine functional properties of different compounds to produce multifunctional materials. The Co–Hf–Ga system contains 10 ternary compounds many of which have extended solubility at constant Hf content, that is, there is site substitution between Co and Ga. This is also exhibited by some of the binary compounds. Interestingly, the compound Co2HfGa goes against this trend by having extended solubility at constant Co content indicating Ga substitution for Hf, but not vice versa, that is the phase field does not extend to higher Hf contents than 50 at.%, Fig. 6 [53] Furthermore, this Heusler compound is in equilibrium with the B2 compound CoGa and the compound CoHfGa. In the Co–Ti–Ga system, a small composition range of Co2TiGa is in equilibrium with a large composition range of CoGa offering the possibility of tuning properties through variation of volume fraction and phase compositions.
In systems with two binary B2 phases containing Co, the possibility exists for complete solid solubility from one to the other. This in turn leads to the possibility of a first or second-order ordering transformation to the L21 phase since they are structurally related, Fig. 2. An example of this is Co–Fe–Ga [55] which has an extensive L21 single-phase field covering the compositions Co2FeGa and Fe2CoGa as well as B2 phases CoGa and CoFe, Fig. 7. In this system, continuous ordering is observed from B2 to L21 on decreasing the temperature. This also occurs in the Co–Cr–Ga [56] and the Co–Mn–Ga [57] systems.
Co–Fe–Ga isothermal sections. Reproduced from [55] with permission from Elsevier
In other cases, the Heusler phase is stable to the melting point and continuous ordering occurs from the B2 phases for off-stoichiometric compositions with phase separation occurring at lower temperatures, for example, Co–Ti–Al, Figs. 8 and 9 [58]. Through suitable choice of composition, it is then possible to have a single-phase structure at high temperature and a two-phase Heusler + B2 structure at low temperature.
The systems Co–Y–Sn with Y = Ti, Zr, Hf exhibit extension of the ternary phase at the composition Co2YSn along a constant 1:1 ratio of Y:Sn. The Hf-containing compound provides some small solubility extension on either side of the 1:1 ratio. For the Hf- and Zr-containing compounds, there is no equilibrium between the Heusler phase and Co due to the intervention of binary phases. However, for Co2TiSn, there is an equilibrium with Co and since both phases are magnetic this could provide some interesting magnetic phenomena. Indeed this has been investigated [59] and unusual coercivity versus temperature behaviour was observed. The isothermal section determined by Stadnyk et al. [60] shows that there is a continuous solid solution from the Co2TiSn (prototype Cu2MnAl) composition to CoTiSn (prototype MgAgAs). This continuous change in order occurs by substitution of Co atoms by vacancies and gives a change in properties [61], which appears not to have been fully investigated to date. The properties of the stoichiometric Co2TiSn have been extensively studied (see for example [62–65]) and show that the compound is a half-metallic ferromagnet. It has a constant Seebeck coefficient as a function of temperature and combined with the half-metallic behaviour this makes the material potentially useful for thermoelectric and spintronic applications [62]. Since there is interest in improving thermoelectric properties through the use of multi-phase alloys [24, 26, 66], the phases in equilibrium with Co2TiSn are worth noting. Unfortunately, there are discrepancies between the available isothermal sections at different temperatures 1070 K [60] and 870 and 1070 K [67]. The results by Yin et al. [67] are based on CALPHAD modelling and indicate a two-phase equilibrium between Co2TiSn and CoTiSn. However, the experimental work by Stadnyk et al. [60] indicates a continuous phase field from Co2TiSn to CoTiSn and we will assume for the purposes of discussion that this is correct. Because of the extended solubility of the Co2TiSn/CoTiSn phase at constant Ti:Sn ratio, the phase equilibria involve many different binary compounds in the Co–Ti and Co–Sn systems. There is also a two-phase equilibrium with the Co solid solution that has almost no solubility for the Sn but up to 10 at.% for Ti. The two-phase fields are quite narrow so the isothermal section at 1070 K is dominated by a large number of three-phase fields [60]. The Co–Zr–Sn is very similar to Co–Ti–Sn except that the Co2ZrSn phase does not extend all the way to CoZrSn and there is a two-phase equilibrium between the two phases at 770 K.
The systems Co–Fe–Z offer some interesting possibilities for phase equilibria involving order–disorder transformations. Also there could be equilibria between Heusler phases and ductile phases that offer the potential of bulk processing. In the Co–Fe–Al system, there are substantial solid solution regions for different phases. Both B2 and L21 structures have been reported at the stoichiometric composition Co2FeAl [68–71]. Balke et al. claimed that Co2FeAl crystallizes in the B2 structure based on an annealing treatment of their arc-melted samples at 1300 K [70]. The variation in reported structure suggests that the Heusler phase may result from an ordering of the B2 on cooling below 1300 K. This is not shown on any published isothermal section, even one calculated for 600 K [72], and a review of the phase equilibria in this system concludes that there are no ternary compounds [73]. An experimental section determined at 923 K only shows the B2 phase present at the Co2FeAl composition [74, 75]. The phase diagram as a function of composition along a 50 at.% Co isopleth was investigated by Kogachi [69] who showed there was a second-order order/disorder transition B2/L21 with a maximum temperature at about 973 K, with the Heusler phase existing over a range of composition from 19 at.% Fe to 35 at.% Fe. Due to less than perfect order in the L21 phase, it was difficult to determine the limits of the transition. Later work by Balke et al. [5] on Co2FeAl1−x Si x shows an A2 + B2 to B2 + L21 order transition at a temperature of 1190 K for the Co2FeAl composition. This is not consistent with the work by Kogachi [69] and it would be of value to reinvestigate the phase equilibria over a range of compositions to define the composition range of the L21 phase field. As can be seen in Fig. 4, ordering from A2 to B2 and then to L21 results in additional diffraction lines (superlattice lines) with relatively weak intensity, making identification of the L21 ordering difficult as the transition temperature is approached and the degree of long range order decreases. The L21 phase is predicted as stable from ab initio calculations and is predicted to have a substantial formation enthalpy at 0 K of −34.5 kJ/mol [13]. Thus, a reinvestigation of the phase equilibria in the Co–Fe–Al system is needed. No Heusler phase has been reported in either the Co–Fe–In or the Co–Fe–Sn systems. This is consistent with the decreasing stability trend observed on going down the Group III and IV columns [9, 13].
A large number of papers have been published studying the Heusler compound Co2FeSi, covering thin film and bulk synthesis as well as ab initio studies, see for example [41, 71, 76–84]. The consensus of these reports is that Co2FeSi exists as an L21-structured compound to high temperature, if not to the melting point. Partial substitution of Si by Al has been shown to disorder the compound to a B2 structure [82]. It is well established that this compound is a half-metallic ferromagnet (HMF) with a high Curie temperature of 1100 K [81, 85], and is of great interest for application as a spintronic material. The effects on the properties of quaternary additions have been investigated [86] as have the effect of disordering to the B2 phase [87]. It is predicted to be a stable phase in the Co–Fe–Si system by ab initio calculations, and the calculated formation energy of −34 kJ/mol (0 K) [88] compares well with the experimentally measured value of −38.4 kJ/mol (298 K). [9] The melting point for this composition has been measured as 1513 and 1510 K, respectively [89, 90], and both researchers determined a heat effect at 1031 K [89] and 1039 K [90] interpreted as a \(\text{B}2\Rightarrow{\text{L}2}_{1}\) order transformation. However, Wurmehl et al. [85] annealed Co2FeSi arc-melted samples at 1300 K for 20 days and obtained the L21 structure. Shreder et al. [71] melted alloys and obtained the L21 structure without further annealing. These results are insufficient to adequately understand the ordering behaviour in this material and this warrants further investigation. In many papers, the details of the preparation of the Co2FeSi do not involve determining the state of order and yet it is known that this can vary with preparation technique [41]. Surprisingly, despite the large body of work indicating the existence of the L21, Co2FeSi phase, the published phase diagrams [91, [92] do not show the presence of this phase on isothermal sections at 1073 and 1433 K, Fig. 10. This significant discrepancy along with uncertainty regarding a B2-L21 transition requires a thorough re-evaluation of the phase equilibria in this system.
In the Co–Fe–Sn system, an isothermal section at 298 K is available [93], which does not show the presence of a Heusler phase. Furthermore, experimental work on bulk alloys has not shown the existence of the Heusler phase [9, 94], although it was found to be stable in quaternary alloys Co2Mn1−x Fe x Sn when x was less than 0.5 [95]. Li et al. [96] and Duan et al. [97] reported synthesizing B2 structured nanoparticles of Co2FeSn by an electrodeposition method and a solution reduction method. However, the Heusler phase was reported by Tanaka et al. [98] based on the production of thin films by an atomically controlled alternate deposition process. Further work also indicates the existence of the L21 phase after non-equilibrium processing [99]. The Heusler phase is predicted from ab initio calculations to have a negative formation energy of −2.8 kJ/mol, but not to be stable relative to other phases by +7.3 kJ/mol [13]. The relatively small energy difference may allow the formation of the Heusler phase through non-equilibrium processing as demonstrated by Tanaka et al. [98]. Based on this observation, we have identified in Table 4 a number of other Heusler compounds that also have negative formation energies and small energy differences above the hull energy, as these may also yield a Heusler phase on non-equilibrium processing.
In the Co2MnZ compounds, half metallicity has been shown for compounds with Z = Al, Ga, Sn, Si and Ge [4]. The crystal structure, electronic structure and magnetic properties of quaternary Heusler compounds of the type Co2−x Rh x MnZ (Z = Ga, Sn, Sb) have been investigated and it was noted that the quaternary addition led to different types of anti-site disorder [100]. The compound Co2MnIn is not predicted to be stable, Table 4, nor have a negative energy of formation at 0 K according to ab initio calculations. However, the existence of the Heusler phase has been reported in annealed, melt spun ribbons of Co50Mn30In20 [101]. The phase equilibria in the Co–Mn–Ga system have recently been investigated [57]. Isothermal sections at 1000, 900 and 800 °C were determined experimentally as well as the B2/L21 ordering temperature and L21 Curie temperature along the 50 at.% Co isopleth. The B2/L21 ordering temperature shows a maximum around 900 °C at the stoichiometric Heusler composition, Co2MnGa.
Comparing ab initio calculations of stability at 0 K, Table 4, with the information in Table 3, we can see that two other compounds that are known to have Heusler phases, Co2CrIn [50] and Co2VSi [9, 49, 102] are not predicted to be stable, although Co2VSi does have a substantial energy of formation, −40.9 kJ/mol and the energy difference above the hull energy is small, +2.9 kJ/mol. On the other hand, the ab initio calculations predict stable Heusler phases for a number of potential compounds that have not yet been reported and in most cases the alloy systems do not have a phase diagram. The compounds are Co2ZrGa, Co2ZrIn, Co2TiIn, Co2HfIn and Co2VGe. These should be investigated as potentially new Heusler phases can be discovered. The Co–Zr–Ga system is predicted to have a stable Heusler phase but an isothermal section at 1073 K shows a different phase, Co11Zr4Ga5 at about the Heusler phase composition [52]. This system is therefore a good candidate for some reinvestigation around the Heusler composition.
The Co–Y–Z systems with Y = V, Nb, Ta and Z a group III–IV element exhibit a number of ternary compounds. The Co–Nb–Al system has received extensive experimental study and has been the subject of a recent Calphad type modelling [103–105]. Isothermal sections are available at 4 different temperatures [103], as well as a liquidus projection [104] and with the Calphad model this system represents a good example of the extent of phase equilibria needed for alloy development. In this system, the Heusler phase Co2NbAl [106] is in equilibrium over a large range of composition with CoNbAl which is an hexagonal Laves phase, prototype MgZn2, Pearson symbol C14, space group P63/mmc [103, 107]. Furthermore, the isothermal sections show that the Co2NbAl phase field shrinks with decreasing temperature on the Aluminium-rich side, offering the possibility of precipitation of CoAl in a matrix of the Heusler phase. The Heusler phase is not in equilibrium with the (Co) terminal solid solution. In the Co–Nb–Sn system, the single isothermal section available also shows no equilibrium between Co2NbSn and Co [108]. However, there is an equilibrium between the Heusler and half-Heusler phase, CoNbSn. The Co–V–Si isothermal section at 1373 K shows the Co2VSi phase to exist off of the stoichiometric composition [109] and it is in equilibrium with the (Co) terminal solid solution. According to ab initio calculations, the Co2VSi phase has a negative formation energy but is not predicted to be the stable phase at this composition, being +2.9 kJ/mol above the hull energy formed from CoVSi + Co3V + Co2Si. This is not found to be the case in the experimental isothermal section due to the presence of some additional ternary compounds not considered in the ab initio calculations and the experimental equilibrium at this composition is Co2VSi + Co0.56V0.3Si0.14 + Co0.3V0.5Si0.2. Co2VGa exhibits a large solubility region in equilibrium with (Co) and CoGa at 1073 K. The published phase diagram violates Schreinemaker’s rule at the Co2VGa vertex of the Co2VGa + Co3V + Co0.4V0.6 3 phase region. No phase diagrams are available for Co–Ta–Z, except for Co–Ta–Al [110] but that is incomplete and does not cover the Heusler composition. However, the Heusler compound Co2TaAl [106] has been reported in arc-melted samples annealed 24 h at 1173 K and subsequently 72 h at 1073 K. The Heusler compound Co2TaGa has also been reported [111], but no phase diagram exists.
Phase equilibria in Ni containing systems
Table 5 provides an overview of the ternary alloy systems in which a nickel-based Heusler phase has been experimentally observed and also indicates those systems for which no experimental phase diagram data exist covering the Ni-based Heusler composition.
Examination of Table 5 shows that Al, Ga, In and Sn are favourable to form the Heusler structure with Ni, while no Si- and Ge-containing Heusler compound has ever been reported experimentally so far except for Ni2MnGe [112, 113]. An Ni2MnGe film with an L21 structure was reported by Lee et al. [113] through flash evaporation of crushed alloy powders from arc melting. Marazza et al. [114] prepared Ni2MnGe Heusler structured alloy using induction melting followed by annealing at 773 K for 15 days but did not provide detailed characterization, and Cherkashin et al. [115] also reported an L21 structure in Ni2MnGe but they admitted to having an inhomogeneous sample and the observed Heusler peaks could correspond to the generally observed ternary compound Ni16Mn6Ge7 (prototype Cu16Mg6Si7, Pearson symbol cF112, space group Fm \( \bar{3} \) m) [116]. The first principles calculations by Zayak et al. [117] indicate that Ni2MnGe with an L21 structure is unfavourable due to incommensurate phonon instability. The OQMD database predicts that neither the Ni2MnGe nor the Ni16Mn6Ge7 phase is stable, even though they have negative formation energies, rather the stable equilibria should be Mn + NiMnGe + Ni3Ge [13]. The inconsistent results and lack of phase diagram for this system calls for further work to be performed to establish the phase equilibria in this system. As for the Y element, the early transition elements in Columns 4 and 5 in the Periodic Table have a tendency to form the Heusler compound with Ni, while Cr in Column 6 does not. The only reported Heusler compound that contains Cr is Ni2CrAl [118], although this is not shown in the existing Ni–Cr–Al ternary phase diagrams at 1423 or 1473 K [119, 120], which present a B2 and bcc solid solution two-phase region. More detailed work is needed to resolve the contradiction. The refractory elements, Nb and Ta, form the Heusler structure with Al or Ga as the Z element. Ni2MnZ has four assured Heusler compounds out of the six possible members, while the late transition elements Fe, Co and Cu do not form the stable Heusler structure with Ni easily. The reported Heusler structure of this type is Ni2FeAl from melt-spinning technique [121], Ni2FeGa [122, 123] and a B2 phase found in Ni2CoGa [124] alloys, while a D03 structure is observed in the Ni2CuSn [125] alloy. It should be noted that the equilibrium Al–Fe–Ni phase diagram evaluated by Zhang et al. [121] indicates a B2 structure at the Ni50Fe25Al25 composition.
The calculated enthalpies of formation (0 K) for the stable Heusler phases or the difference between the enthalpy of formation and the hull energy for the predicted unstable Heusler phases in the OQMD are compiled in Table 6. Comparing with Table 5, it is obvious that many predicted unstable Heusler phases have been verified to be stable experimentally, such as Ni2MnIn and Ni2TiSn. But it should be pointed out that in these cases, the difference between the calculated enthalpy of formation and the hull energy is generally small, less than 5 kJ/mol of atoms. While for Heusler compositions without experimental verification, the difference is often larger than 10 kJ/mol of atoms, such as “Ni2FeSn” and “Ni2VIn”. It is worth noting that the calculated hull energy is based on the perfect stoichiometric end members without considering defects or the solubility range, which could be the limitation of its ability for predicting the phase stability.
Similar to the Co-containing systems, those with early transition metals (Ti, Zr, Hf) tend to have multiple binary and ternary compounds with limited solid solubility, e.g. Ni–Zr–Ga, Ni–Zr–Al systems and the Ni–Ti–Sn system, shown as an example in Fig. 11. This is quite easy to understand considering the great difference of electronegativity of the early transition metals with the other constitutional elements. It also explains the existence of the half-Heusler compounds in these systems that contain Sn since the half-Heusler structure is favoured when the chemical bond in between is to some extent covalent to make the structure that is composed of 25 % vacancies stable. While in regards of the systems that contain Al and Ga, the equiatomic composition prefers to form a hexagonal structure (prototype AlNiZr, Pearson symbol hP9, space group P \( \bar{6} \)2m). For systems where the Z element is Si or Ge, an orthorhombic structure (prototype NiSiTi, Pearson symbol oP12, space group Pnma) is observed at the equiatomic composition.
Isothermal section of Ni–Ti–Sn at 770 K. The circles represent the alloy compositions used to experimentally determine this section. Reproduced from [179] with permission from Elsevier
Half-Heusler compounds are of considerable interest as non-toxic candidates for thermoelectric application and are observed in the NiYSn systems (Y = Ti, Zr, Hf) forming an equilibrium triangle with the Heusler compound Ni2YSn and Ni3Sn2 (ht) with almost no solubility range even at a relatively high temperature (around 1000 K) [126–128]. The equilibrium between liquid phase Sn and the half-Heusler phase calls for special attention when preparing the half-Heusler phase to avoid grain boundary weakness. It is worth mentioning that phase separation through introducing a fourth element such as Zr or Hf will further improve their thermoelectric properties through reducing the lattice thermal conductivity due to the solid solution effect [129] and boundary scattering from the nanoscale phase separation [130]. Through solid-state reaction of pre-synthesized half-Heusler alloy with elemental Ni followed by spark plasma sintering, Makongo et al. [131] prepared bulk (Zr, Hf, Ti) NiSn half-Heusler composites containing nanoscale full-Heusler inclusions, showing an increase of electronic conductivity and moderate decrease of thermal conductivity, leading to a drastic improvement of the figure of merit. Furthermore, it is possible to tune the thermodynamic properties such as standard enthalpy of formation and lattice parameters to satisfy certain requirements without degrading other properties.
Ni–Ti–Z systems are especially attractive considering the simultaneous presence of two possible shape memory phases in the same system, the Heusler phase Ni2TiZ and NiTi. Special interest is devoted to Ni–Ti–Z (Z = Al, Ga) due to the equilibrium between the B2 phase NiZ and the Heusler phase Ni2TiZ, since after proper selection of alloy composition, the Heusler phase could coherently precipitate out as the strengthening phase [132–134]. The creep strength of the structural alloy NiAl can also be enhanced to a remarkable degree arising from the high-intrinsic creep strength of the non-stoichiometric B2 and L21 phase [135]. However, the equilibrium between Ni2TiAl and NiTi is disrupted at a higher temperature of 1400 K [136] by the liquid phase. Therefore, the temperature for heat treatment should be chosen carefully.
Yield strength of Ni–Hf–Al alloys increases with the increasing percentage of Heusler phase Ni2HfAl (15–96 %) [137], but it was found that precipitation of Ni2HfAl in a NiAl–0.5–1 at.% Hf alloy was detrimental to the creep properties [138, 139]. Later work established that the precipitation of Ni2HfAl in NiAl-based alloys is heterogeneous and controlled by the interfacial energy term [140]. It is reasonable to expect that Ni2NbAl and Ni2TaAl precipitates can serve in a strengthening function in Ni-based superalloys for turbine blade applications. Limited solubility range is observed in these cases [141, 142], even at high temperature. It is desirable to have isothermal sections at different temperatures or isopleths established so that the amount of precipitate could be controlled quantitatively.
Ni–Mn–Z alloys were investigated extensively due to the special magnetic properties introduced by the unique configuration of the Mn d-orbitals [143–145]. New properties with wide potential applications can be obtained through combining the ferromagnetic property and other properties, such as the magneto-optical effect, giant magneto-resistance and magneto-caloric effect. One that draws the most attention is the magnetic shape memory effect in the off-stoichiometric composition in the Ni–Mn–Z alloys. Relatively high Curie temperature and a high efficiency of magneto-mechanical transformation make them very promising for applications as actuators, sensors and for the recording and storage of information. Substantial research has been devoted to further improve the performance. Rapid solidification using advanced synthesizing methods such as melt spinning helps avoid severe compositional inhomogeneity and the resulting metastable nanoscale or even amorphous phase can impart ductility to the brittle Heusler phase [146]. Additionally, the Curie temperature of Ni2MnSn can be tuned with the substitution of Ni at the Mn sites without a significant reduction in the magnetic entropy change [147].
In the high-temperature (1373 K) isothermal section of Ni–Mn–Al system [148], B2 phase covers more than half of the composition triangle, providing a huge space to explore and design alloys. Again, the phase equilibrium between the Heusler phase and L12, Ni3Al and Ni solid solution makes it possible to function as the strengthening precipitate phase. Recently, precipita tion of nanoscale Ni2MnAl has been designed into an Fe–Mn maraging steel to obtain significant strengthening effect [149]. It is interesting to note that in the Ni–Mn–In ternary system [150], Mn and In tend to substitute for each other very well, even better than Ni–Mn. Continuous increase of the off-stoichiometric composition will change the ferromagnetic alloy into paramagnetic. Even though very little experimental phase diagram information is currently available on Ni–Mn–Ga nor Ni–Mn–Sn systems, it is assured that a wide solubility range will be observed since a large number of off-stoichiometric alloys have been prepared successfully [151–156]. The effect of variations from the stoichiometric composition was investigated theoretically using first principles calculations [157–159]. The results indicate that the stoichiometric composition has the lowest formation energy and that anti-site defects are the favoured constitutional defect. It is reasonable to assume that the Ni2MnGa Heusler phase would go through order–disorder and merge with the B2 phases NiMn and NiGa, resembling those of Ni–Mn–Al and Ni–Mn–In.
Shape memory alloys Ni–Co–Ga [160] and Ni–Fe–Ga [122] have complete solid solubility from NiGa to CoGa and FeGa due to the similarity between Fe, Co and Ni. Also, there is a larger extent for Fe, Co, Ni to replace Ga than vice versa especially on the Co or Fe side. The off-stoichiometric L21 Heusler phase Ni0–47Fe75–27Ga27–30 was reported at temperatures below 1000 K and the B2 phase disorders and forms the A2 phase in the Fe-rich region. The martensitic phase region determined using the diffusion couple method is located in a wide composition range with 30–40 at.% Ga and 0–50 at.% of Co in the Ni–Co–Ga system and with 30–36 at.% Ga and 0–20 at.% of Fe in the Ni–Fe–Ga system, making them excellent high-temperature magnetic shape memory alloys. While for the Al analogues, less solubility range is observed with regard to the substitution between Al and Fe, Co and Ni. Significant improvement of the ductility can be achieved through introducing fcc Ni solid solution on the grain boundary [161, 162], which requires high-quality phase equilibria and phase transformation information.
Cu and Ni have a complete solubility range and the high-temperature compound Cu3Sn with a D03 structure (prototype BiF3, Pearson symbol cF16, space group Fm-3m) which is a less ordered form of the L21 Heusler structure, extends to the Ni25Cu50Sn25 composition and even to Ni50Cu25Sn25 at 973 K [125]. The Ni-based Heusler structure is predicted to be less stable than the hull energy [13] but does have a negative formation energy of −16.8 kJ/mol [13] or −14.2 kJ/mol [15]. The observed D03 structure does not order to L21 at lower temperature instead the stable phase is Cu3Sn as shown on an isotherm at 513 K [125].
Discussion
The goal of this review is to obtain an overview of the status of knowledge of phase equilibria for a selected group of alloy systems containing or potentially containing a Heusler compound. Experimental work on the ternary phase diagrams is somewhat limited and in some cases non-existent. It is therefore appropriate that we use thermodynamic and ab initio databases to provide guidance in selection of alloy systems and compositions that ultimately require the synthesis of alloys. A database is only as good as the quality of its contents, and such contents are sparse at best and contradictory at worst. If we are to reap, the benefits of computational materials design and materials genome work the source data at the foundation of that work must be robust. Given the promise of multifunctional Heusler materials, there is a need for high-quality phase equilibria data obtained either through experimentation or through the use of reliable computational tools. The absence of such data leaves alloy design work as more art than science, and continued progress reliant on serendipity. Most publications in this field are aimed at determining the properties of a single-alloy composition or in some cases a range of composition for a single compound at a single annealing temperature. Very few publications take a holistic approach of examining the phase relationships to the Heusler phase and the variations in equilibrium with temperature. Needless to say, such studies are time consuming if they rely solely on experimental techniques of phase diagram determination. The combination of microstructural characterization, thermodynamic measurements, thermodynamic computation and first principles calculations of phase stability can provide an efficient method to determine the phase diagram data needed for materials design.
In many instances, where a Heusler compound is reported a single annealing temperature was used, and in some cases arc-melted ingots were used directly. Experience shows that the processing path is important in developing the phase structure and so there is little information regarding the state of a particular composition over a range of temperature outside of the phase diagrams. Furthermore, since the Heusler phase is an ordered intermetallic compound, the state of order and precise composition relative to stoichiometry can affect both the stability of the phase and its properties. Investigators reporting work on Heusler compounds should be encouraged to determine and report the state of order and actual composition of their material. It can be expected that, for cases where the compound has a negative heat of formation which is only slightly above the hull energy, it may be possible to synthesize the metastable state by some non-equilibrium processing route such as rapid solidification or mechanical alloying.
In the case of thermoelectric materials optimization, modern alloy design is essential in taking a promising compound and transforming it into an efficient device. Heusler and half-Heusler compounds are of great interest due to their high Seebeck coefficients. This ability to generate a large potential difference over a temperature gradient is just one part of the thermoelectric problem. Creating an efficient thermoelectric device requires maximizing the dimensionless figure of merit:
where α is the Seebeck coefficient, σ is the electrical conductivity, κ is the thermal conductivity and T is the temperature. A figure of merit above 1.5 would enable sufficiently efficient generation so as to compete with conventional technologies [163]. Comparable zT have been reported, but to date, production of actual devices has not realized such efficiencies [163]. To push materials beyond the current state of the art necessitates producing a high Seebeck material with high electrical conductivity and low thermal conductivity [163].
Creating divergent conductivities relies on decreasing the lattice contribution to the thermal conductivity. In order to do this, phonon scattering sites must be created on multiple length scales through the creation of phase boundaries, mixed microstructures, refined grains, nanoscale precipitates and point defects [164]. Modern alloy design necessary to obtain each of these features is predicated upon high-fidelity thermodynamic information. Furthermore, reality complicates things with real devices having to operate under conditions dictated by the thermal environment in which it is placed. As such it is not enough simply to maximize zT, but one must tune the peak temperature to the service conditions via alloying [163]. Realizing high efficiency in a real device places an even greater demand for this phase information.
The properties of half-Heusler compounds are also of interest and because of the close relationship with the Heusler phase, these compounds are frequently in equilibrium with each other and in some cases there is a single continuous solid solution from one to the other. This offers the possibility to finely adjust the defect concentration for property optimization. It is also possible to use the two-phase equilibria to advantage in thermoelectric applications where the presence of the Heusler phase improves the thermoelectric properties of the half-Heusler phase [165]. In other cases, the formation of a Heusler/half-Heusler structure can occur by a spinodal decomposition mechanism [131] and such structures offer another design option for the improvement of thermoelectric properties.
On a broader level, microstructural control and a robust knowledge of phase stability and transformation can enable the creation of larger devices in a wider variety of geometries. Conventional forging and heat treatment practices are not possible without reliable phase stability information over a wide range of temperatures. Furthermore, more modern techniques such as sinter forging [166] and severe plastic deformation [167] could be brought to bear on multifunctional materials allowing for an even greater degree of structural and functional property tuning.
Conclusions
Of the 180 ternary alloy systems reviewed, Heusler (Cu2MnAl prototype) intermetallic compounds have been reported in 9 iron-based systems, 30 cobalt-based systems and 27 nickel-based systems. First principles calculations predict Heusler stability in 17 iron-based systems, 30 cobalt-based systems and 8 nickel-based systems. In the Ni-base systems, many more Heusler compounds have been reported than predicted, but in general, the difference from the predicted hull energy is small, often less than 1 kJ/mol. On the contrary, few iron-based systems are reported to have a Heusler compound while many more are predicted. The more commonly reported structure in the Iron-based systems is the B2 (CsCl prototype) structure. There remains the possibility that the Cu2MnAl prototype structure could exist at lower temperatures or after longer annealing times that allow the additional ordering to take place. In addition, it can be difficult to distinguish between the B2 and L21 structures in some cases.
The state of order is rarely investigated or reported in papers dealing with property investigations of Heusler compounds and yet this is important in determining the properties, as is the precise composition. It may be possible to synthesize Heusler compounds that are predicted to be metastable through the use of non-equilibrium processing techniques.
We have identified the need for additional experimental phase diagram work in the following ternary systems: Co–Fe–Si, Co–Fe–Al, Co–Ta–Z (Z = Al, Ga, In, Si, Ge, Sn), Ni–Cr–Al, Ni–Mn–Ga, Ni–Mn–Ge, Ni–Mn–Sn, Fe–Ta–Ga, Fe–Co–Ga, Fe–Cu–Ga, Fe–Mn–Al, Fe–Ta–Ge, Fe–X–Si (X = V, Cr, Mn), Fe–Hf–Sn and all of the Fe–X–In systems.
The compounds Co2ZrGa, Co2ZrIn, Co2TiIn, Co2HfIn and Co2VGe are predicted stable by ab initio calculations but have not been reported experimentally.
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Yin, M., Hasier, J. & Nash, P. A review of phase equilibria in Heusler alloy systems containing Fe, Co or Ni. J Mater Sci 51, 50–70 (2016). https://doi.org/10.1007/s10853-015-9389-y
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DOI: https://doi.org/10.1007/s10853-015-9389-y