Synthesis, microstructure, and thermoelectric properties of Sb-Based high entropy alloys

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Introduction
Thermoelectric (TE) technology serves to directly transform a heat flux into useful electric power.The efficiency of a TE material is specified by its dimensionless figure of merit (zT), which can be expressed as zT = S 2 σ/κT, where S represents the Seebeck coefficient, σ is the electrical conductivity, κ is the total thermal conductivity, and T is the absolute temperature [1,2].To obtain a high zT value the material must have high values of S and σ combined with a low value for κ.The κ has contributions from electrons and phonons and is written as κ = κ e + κ L .
Here κ e and κ L are the electronic thermal conductivity and the lattice thermal conductivity, respectively.To optimize for a high zT, the ratio σ/(κ e +κ L ) should be maximized, while σ and κ e are dependent through the Wiedemann-Franz law κ e = LσT, where L is the Lorenz number/function [3][4][5][6].For low values of σ, zT will increase with increasing σ but will decrease for high values of σ since κ e then increase with σ.So, careful optimization is needed to improve the zT value.Many efforts have been made in zT enhancements through κ L reduction using nanostructuring [7], nanocomposites [8], and inclusions [9], while for the best performing TE materials, the value of κ L is at the phonon-glass limit [2], which is a fundamental lower limit.
Over the past decades, there has been a large interest in intermetallic compounds belonging to the family of Heusler compounds having simple crystal structures [10,11].The attractive features are: diverse electrical properties, thermal stability, and mechanical robustness.Heusler compounds are promising functional materials for many application areas including spintronics [12,13], thermoelectrics [14][15][16][17][18][19], topological insulators [20,21], optoelectronics [22,23], and solar cells [24,25].A bottleneck for TE applications of the simple half-Heusler compounds has been their large κ L and there are many reports on attempts to minimize it [26][27][28].Among the approaches has been substituting atoms to increase the disorder to approach the phonon glass limit, and introducing precipitates and grain boundaries to increase phonon scattering.
HEA are multi-element (⪆5) alloys with near equiatomic composition.They have been given large attention due to their vast potential within many fields [29,30].One driving force behind the vastly increasing volume of research reports on HEA-materials has been to investigate the unexplored central region of the multi-component alloy phase space.A simple explanation for the structure of HEAs is that high configurational entropy may thermodynamically favor the single solid solution phases over alloys with intermetallic (IM) phases [31].The high configurational entropy may in general extend the phase space that is available for exploring new materials, which may lead to the discovery of the materials that are needed for a sustainable future.The concepts for HEA alloys can be transferred to research on compounds, which are not necessarily metallic.Here, we call it HEA-based compounds, which have also been suggested to have many interesting structural and functional properties [29][30][31][32][33][34].In addition, the complex phase of these alloys can be a success factor for the cases where inharmonicity and nanostructuring are beneficial [35,36].The high degree of disorder on some of the sublattices of HEAs may increase the phonon scattering and is thus conceptually similar to thermal conductivity reduction strategies in research on thermoelectric materials, as mentioned above.Thus, it is rational to speculate that the extreme chemical disorder in HEAs could possibly retain low lattice thermal conductivity resulting from their strong inharmonicity, and thus may open the door for new and unexplored avenues of HEAs as next-generation materials.High TE performance has been reported in PbSe and SnSe 3 based HEAs [37,38].However, the use of toxic and expensive elements restricts its use for practical applications.Thus it is important to search for the compounds that are composed of earth-abundant elements and have an environmentally friendly nature.Amongst them, antimonides based intermetallic compounds are considered the best due to their environmentally friendly, earth-abundant, excellent stability, and potential for applications in various fields e.g., thermoelectrics [39,40], batteries [41,42], electrocatalytic activity in hydrogen evolution reaction [43], catalytic activity in hydrogenation [44], etc.For TE applications, much of the attention has been drawn to Sb-based compounds like half-Heusler [45,46], clathrates [47], zintl-antimonides [48], and skutterudites [49,50].However, the concept of realizing HEA in Sb-based compounds is largely ignored and needs special attention to explore this avenue for TE applications.
We tackle the challenge of employing Sb-based HEAs as nextgeneration materials by using the conventional flame melting technique for preparing antimonide-based compounds starting by replacing the binary promising TE (ZnSb) [51] with an alloy having 5 elements at the Zn site, i.e., Zn 1-a-b-c-d-e Sb, where a = Zn, b = Fe, c = Co, d = Ni, and e = Mn.After melting the compound, it is segregated into a mixture of different phases.The compositions of each phase in a multiphase alloy were observed by scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS) capabilities.An alloy having large volume fraction composition that satisfies the conditions of HEAs both by compositions-based and by calculated configurational entropy was selected and synthesized for further investigations.Fortunately, the resulting single-phase materials adopt a Heusler type structure, which is an interesting material for TE applications.Heusler-like alloys are flexible to adapt their physical properties by simply changing the number of Valence Electron Counts (VEC) present.For example, the known semiconductors are alloys with VEC = 8 or 18 [12].Therefore, we calculate the VEC of the crystallized alloy by assuming a solid solution of (MnNiSb) 1-x (ZnFe 1-y Co y Sb) x , where x = 0.33 and y = 0.55 and found that the final skimmed Zn  18) and Zn 25.4 Fe 14 Co 11.5 Ni 7.9 Mn 7.9 Sb 33.33 (VEC = 17) were synthe-sized1 and their thermoelectric properties were examined.The subsequent samples were denoted with the prefix VEC = 18.72,VEC = 18, and VEC = 17 respectively.

Experimental methods
First, for the synthesis of Zn 10 Fe 10 Co 10 Ni 10 Mn 10 Sb 50 alloy, highpurity elemental Zn (99.99%) shot, Fe (99.99%) wire, Co (99.95%) granule, Ni (99.95%) wire, Mn (99.95%) flake, and Sb (99.99%) ingots were used as a starting material.The nominal compositions were weighed according to the stoichiometry and sealed in an evacuated thick-walled quartz ampule.The evacuated quartz ampoule was then heated using the flame melting technique and cooled in water before annealing.Care was taken to ensure complete melting and the homogeneity of the alloys.Individual phase compositions in a multiphase alloy were examined by scanning electron microscopy (SEM) coupled with energy dispersion spectroscopy (EDS) capabilities.Based on the results of the EDS, alloys with the new compositions were prepared.Since the overall composition was confirmed as an effective additional standard within the expected error limits, the individual phase compositions in multi-phase alloys could be determined with confidence.The structural characterization of the selected alloys was done by X-ray diffraction (XRD), using Bruker D8 discover with Cu Kα.For thermoelectric properties measurement selected alloys were ground into powder and then hot-pressed into pellets at 973 K for 30 min.The temperature dependence electrical properties were measured using the custom-designed setup [52].The room temperature Hall mobility and carrier concentration was measured with the sample in the van der Pauw pattern.The thermal conductivity was measured by the laser flash method using a Netzsch LFA457.

Results and discussions
The equilibrated microstructure of the as-cast Zn 10 Fe 10 Co 10- Ni 10 Mn 10 Sb 50 alloy is shown in Fig. 1(a), which exhibits the co-existence of three different phases having different shades of grey (bright-medium-dark).The phase distribution in the as-cast alloys is relatively fine and with diffuse phase boundaries.To verify the compositions of each phase, elemental analysis was performed with energy-dispersive X-ray spectroscopy (EDS).According to EDS analysis, the first phase, with a medium grey appearance in the SEM and a large volume fraction has an approximate composition of Zn 4 Fe 15 Co 15 Ni 13 Mn 5 Sb 48 .The second phase, with a dark grey color and a small volume fraction, has a composition of Zn 14 Fe 6 Co 10 Ni 14 Mn 16 Sb 40 .The third phase, with bright grey color, has an approximate composition of Zn 4 Fe 14 Co 12- Ni 10 Mn 5 Sb 56 .However, after the heat treatment at 550 • C for 20 h, there are still three different regions, each with the same shade of grey as before, but the volume proportions have changed as seen in Fig. 1(b).The first phase (medium grey) has changed the composition marginally to approximately Zn 4 Fe 14 Co 15 Ni 14 Mn 4 Sb 47 but its volume fraction was reduced.Moreover, the second phase (dark grey) has changed composition marginally to Zn 16 Fe 10 Co 8 Ni 13 Mn 15 Sb 39 and its volume fraction has increased.The third phase (bright grey) has also increased its volume fraction and changed composition marginally to Zn 2 Fe 12 Co 17- Ni 5 Mn 4 Sb 60 .It can be seen that the amount of the first phase (medium grey) with a large volume fraction in the as-cast state is reduced significantly after the heat treatments and some of it transforms into the second phase (dark grey) as shown in Fig. 1(b).This suggests that this medium grey phase is metastable and retained only when quenched with water.Fig. 1(c) is the EDS elemental mapping of the heat-treated surface showing a clear distribution of the two major phases.
Boltzmann's equation for a system can realize its state with equal probability if the atoms are interchanged will have a configurational entropy of mixing per mole given by equation (1): where R is the universal gas constant (8.314J/K mol) and W is the number of different ways of arranging the atoms in the system/solution.The total mixing entropy ΔS mix , can be divided into four contributions as shown in equation ( 2): Here ΔS vib mix is the vibrational entropy, ΔS mag mix is the magnetic dipole entropy, ΔS elec mix is the electronic randomness entropy, and ΔS conf mix is the configurational entropy.Here we only consider the configurational entropy, as the relative difference in this term will be the satisfactory yardstick for comparing the potential complexity of various alloy compositions, and the other terms cannot presently be calculated with confidence [53].For an ideal random n-component solid solution, its configurational entropy of mixing per mole is given by equation (3) [29]: where The separation into different phases is seen more clearly by the elemental mapping with EDS as shown in Fig. 2(c).It can be seen that Zn, Mn, and Sb segregate towards the minor phases, while Ni, Fe, and Co have an almost homogenous distribution.The corresponding XRD pattern also tells that the selected alloy stabilizes in a three-phase region.Following the calculation of configurational entropy approaches, as described above equation ( 4), the ΔS conf of the new compositions were calculated and presented in Fig. 2(d).One of the three phases has the compositions of HEA and the calculated ΔS conf is in the HEA regions.Interestingly, the stoichiometry of this HEA indicates a Heusler type structure.Therefore, an alloy with a composition close to Zn 16.67 Fe 9.17 Co 7.5 Ni 16.67 Mn 16.67 Sb 33.33 , which was considered as a hypothetic solid solution in a Heusler structure, was synthesized and the microstructure is shown in Fig. 2(b).This alloy is a single-phase and its crystal structure matches a Heusler type [18].The EDS element mapping confirmed a uniform distribution of all elements (Not shown here).We consider the phase to have an XYZ half-Heusler type composition, where Sb occupies the Z site in a NaCl sublattice, which is reasonable since Sb is the most electronegative element in the phase and occupies 1/3 of the sites.The other five elements would then substitute for X and Y in the Heusler composition.We may consider this as a "high entropy version".It can be viewed as a solid solution consisting of (MnNiSb) 1-x (ZnFe 1-y- Co y Sb) x where x = 0.33 and y = 0.55.Likewise, it can be viewed as a solid solution of three ternary compounds: MnNiSb, ZnFeSb, and ZnCoSb.Here, MnNiSb is a half-metallic ferromagnet [56][57][58] with the half-Heusler-structure (C1 b, F43m, #216) having a bandgap for minority spins, while no gap for majority spins.ZnFeSb has been reported to be a stable compound with a half-Heusler crystal structure (C1 b , F43m, # .This is in agreement with Xiong et al. [60], who in addition report a structure with a 2 × 2 × 2 supercell of a normal half-Heusler structure with a composition Fe 0.98 Zn 0.84 Sb.On the other hand, Persson [61] reports calculations indicating that this structure has an energy of 0.4 eV above the convex hull in the phase diagram (at 0 K) and would not be stable at equilibrium at low temperatures.For the ZnCoSb system Xiong et al. [62] list a 2 × 2 × 2 supercell of half-Heusler structure, yielding symmetry of (Fm3m) and having a composition of Co 8 Zn 8 Sb 8.This indicates that the observation of a Heusler type structure for Zn 16.67 Fe 9.17 Co 7.5 Ni 16.67 Mn 16.67 Sb 33.33 is reasonable, but not obvious.
It should be noted that most of the known semiconductor-like Half-Heusler (HH) alloys have a VEC of 18 [63].The calculated VEC for the Zn 16.67 Fe 9.17 Co 7.5 Ni 16.67 Mn 16.67 Sb 33.33 alloy is 18.72.To probe the effect of adjusting the VEC and its impact on the TE properties new alloys with VEC 18 and 17 have been prepared as shown in Fig. 3(a) and (b).The as-casted alloy with different VEC also shows a single-phase region without any agglomerations.The configurational entropy of alloys with different VEC was also calculated.As the stoichiometry and XRD indicate a HH type structure, therefore, we comment briefly on the configurational entropy of the compounds knowing that they are Heusler type alloys with a stoichiometry that is HH-like.We look at three simple possibilities.One is that we have sub-lattices XYZ, where Sb is occupying the Z lattice and does not contribute to configurational entropy, while the other elements are occupying randomly X and Y sites.Base on this assumption, the calculated configurational entropy is shown in Fig. 3(c).It is interesting to see that upon moving away from VEC 18.72 to 17, these alloys remain single-phase HEAs in the sense of containing 5 to 40 at.% of each element.But the alloy with VEC 17 lies at the boundary line between HEAs and MEAs.Another possibility is that we have the sublattices X 1 X 2 YZ and that we have as many vacancies as we have Sb atoms.If all the vacancies were positioned on the X 1 sublattice then we would have the first case.But if we make a case where the vacancies occupy X 1 , X 2 , and Y with equal probability, as do the other elements except Sb, which occupies the Z sublattice then, the configurational entropy of all VEC alloys is 2.0 R. While for the third possibility, we get an entropy of mixing equal to 1.9 R by considering the Co 8 Mn 8 Sb 8 structure, which consists of 8 layers of "Mn-Sb" and 8 layers of "Co & Vacancy" layers.We let the Mn site vary randomly with Mn and Zn while the "Co & Vacancy" layer varies with Co, Fe, and vacancies.The elemental mapping (Fig. 3(d)) confirmed that all elements reveal a homogenous distribution.The five elements in the X(X 1 X 2 ) and Y sublattice have large configurational entropy that could contribute to the formation of a single-phase, and the enhanced synthesizability compared to simple HH compounds.To check the homogeneity of the compositions, 5 EDS point measurements were carried out in different places and the results are presented in Table 1.It is interesting to see that the variation in the stoichiometry at different locations is almost the same and close to the nominal compositions.We also calculate the VEC of the actual compounds, based upon the observed EDS results.It suggests that the VEC of the actual compounds deviate from the nominal VEC, which was calculated.This is connected to the evaporation of elements with high vapor pressure during the alloying of the compound.Fig. 4 shows the X-ray diffraction patterns of samples containing various nominal VEC (18.72, 18, and 17).All peaks correspond to the Heusler-type structure Co 8 Mn 8 Sb 8 [64][65][66], which has the regular HH peaks and additional peaks (indicated by arrows) from the symmetry breaking of the 2 × 2 × 2 supercell.This proposes that all samples crystallize in a structure of 2 × 2 × 2 supercell of normal Heusler type  cells similar to Co 8 Mn 8 Sb 8 , where every two layers are shifted relative to the previous layer.The precise crystal structure determination using high-resolution TEM and first-principles calculations of these alloys would be reported elsewhere.
Fig. 5(a) represents the temperature-dependent electrical conductivity for samples having various VEC (18.72, 18, and 17).The value of the conductivity for all three samples is small compared to that for    1 for their actual concentration.All peaks agree with the Co8Mn8Sb8 pattern, which shares the pattern with NiMnSb, but has the 2 × 2 × 2 superstructure peaks in addition which are marked with an arrow.common metals.A substantial part of the resistivity comes from alloy scattering due to the atomic element substitutions.Alloy scattering is essentially temperature-independent.It will be different for the three samples with different VEC, due to their different disorder.The supercell structure may also have varying degrees of disorder, which will be studied further.The different VEC for the samples will also shift the Fermi level among the density of states and the effective carrier concentration will be different for the different samples.Hall measurements gave a carrier concentration of 1.57 × 10 22 , 1.75 × 10 21 , and 1.15 × 10 21 for VEC = 18.72, 18, and 17 respectively.We see that the measured conductivity follows the same trend with VEC as that of carrier concentration, but there is probably also an influence of different transport properties among the samples with different VEC.The temperature dependence of the conductivity is different for different VEC seen in Fig. 5(a).For the sample with VEC = 18.72, the slope is negative (up to 450 • C), which is usually considered as metallic behavior.Above this transition region; a slight increase in the electrical conductivity is observed with temperature, considered as semiconducting-like behavior.For the sample with VEC = 18 and 17, the electrical conductivity is lower than that for VEC = 18.72 and the temperature derivative has a positive slope.Fig. 5(b) represents the temperature dependence of the Seebeck coefficient.The negative values indicate that electrons dominate electrical transport properties.The absolute value of the Seebeck coefficient increases with increasing temperature irrespective of VEC, which is typical and results from more electrons around the Fermi level contributing to the transport at higher temperatures [67].For semiconductors, it can be related to the effective density of states of the conduction band increasing with temperature.While the absolute value of the Seebeck coefficient is low, it increases slightly upon moving away from VEC = 18.72 to 18 and then decreases for VEC = 17, this point can be attributed due to a modification in the shape of the band structure near the Fermi level.
The power factor (PF) is one of the main indicators to evaluate TE performance and can be calculated from the Seebeck coefficient and electrical conductivity by PF = σ⋅S 2 and is presented in Fig. 5(d).The value of PF increases with increasing temperature because the Seebeck coefficient increase.Thus, the resulting FP reaches a maximum value of 1.07 × 10 − 4 W/mK 2 at 630 K.
Given the TE performance of the compounds, not only PF but also figure-of-merit (zT) is important.To assess the zT of the compounds, we need to obtain the temperature dependence of the total thermal conductivity (κ tot ), which is presented in Fig. 6(a).It continuously decreases by moving the VEC from 18.72 to 17 and increases as the temperature increases.To understand the continuous decreases in κ tot by moving the VEC from 18.72 to 17, we estimated the influence of κ e and κ L to κ tot by using Wiedemann-Franz law to figure out the dominant factors [3,68].The Lorenz number was calculated by assuming a single parabolic band and acoustic phonon scattering [9].The calculated Lorenz numbers were in between 2.43 × 10 − 8 WΩK − 2 to 2.42 × 10 − 8 WΩK − 2 in the whole temperature range.The estimated κ e and κ L are presented in Fig. 6 (b) and (c).We can see that κ e is about half as high as κ tot , while the rest is ascribed κ L = κ tot -κ e .Here, it should be noted that the decrease in κ tot with decreasing VEC is due to the decrease in electrical conductivity observed in Fig. 5(a).Using the PF and κ tot data, we calculated the temperature-dependent zT to predict the performance for TE application and as shown in Fig. 6(d).The sample with VEC = 17 enables zT = 0.008 at 630 K.The observed increasing trend with temperature indicating that higher zT is achievable at higher temperatures.Based on these results, it can be anticipated that optimizing the phonon contribution and the Seebeck coefficients left considerable room for further improvements.Consequently, all antimonides studied in this work may be considered promising materials for future exploration, especially if their electronic transport properties are optimized for TE applications.

Conclusion
A family of new high entropy alloys based on antimonides with Heusler-like compositions was synthesized and their thermoelectric properties explored.Due to specific structural order, these alloys exhibit a correlation between the electrical properties and the VEC of the system.By changing the VEC from 18.72 to 17 the temperature-dependent electrical conductivity changes from metal to semiconducting-like behavior.Furthermore, this decrease in VEC also decreases the total thermal conductivity, which is ascribed due to a decrease in electronic thermal conductivity.It is interesting to note that all samples have relatively low thermal conductivity compared to the state-of-the-art Half-Heusler TE alloys.These findings suggest that carefully adjusting the electrical properties could enhance the TE i is the mole fraction of the i-th element, and n is the number of the components.Configurational entropy values have been used to classify materials as high-entropy alloys (>1.5 R), medium entropy alloys (MEAs) (1-1.5 R), and low entropy alloys (LEAs) (<1 R)[54].Considering the starting composition, Zn 10 Fe 10 Co 10 Ni 10 Mn 10 Sb 50 , the calculated configurational for a solid solution entropy is 1.5 R, which is the boundary line between HEAs and MEAs.As seen from the EDS data, after the melting and annealing the alloy exhibits the co-existence of three different phases.We calculated the configurational entropy for each composition and the results are presented in Fig.1(d).The composition Zn 16 Fe 10 Co 8 Ni 13 Mn 15 Sb 39 has a configurational entropy of 1.61 R. It is the composition of the dark grey phase in Fig.1(b) having increased volume fraction with annealing and therefore indicating stability.This composition satisfies the conditions of HEAs both by compositions-based and by calculated configurational entropy.Hence, further investigations were concentrated on exploring the Zn 16 Fe 10- Co 8 Ni 13 Mn 15 Sb 39 phase.Even if one can assign a value to a composition, it should be clear that one could not determine the entropy of the phase before knowing the ordering of the atoms.For compounds with other parameter combinations are suggested as descriptors indicating the stability of compounds[55], but the configurational entropy is important.To explore the selected HEAs composition, Zn 16 Fe 10 Co 8- Ni 13 Mn 15 Sb 39 was synthesized, and Fig.2(a) shows the as-cast microstructures of the selected alloys.Here, we considered the as-casted alloys because there was not much difference between the as-casted and the heat-treated alloy (550 • C 20 h).To characterize the compositions of the different phases, at least 10 EDS points at different places were used and the variations in the compositions were equal within the uncertainty.The chemical composition (in at.%) of the three phases is characterized by EDS and is shown in Fig.2(a).The solidification of Zn 16 Fe 10 Co 8- Ni 13 Mn 15 Sb 39 yields segregation into a phase with the composition, Zn 16 Fe 10 Co 8 Ni 15 Mn 17 Sb 35 , and a small volume fraction of other phases.

Fig. 2 .
Fig. 2. (a) SEM image of starting composition Zn 16 Fe 10 Co 8 Ni 13 Mn 15 Sb 39 yielding three annotated compositions (which did not change by heat treatment) (b) SEM image of starting composition Zn 16.67 Fe 9.17 Co 7.5 Ni 16.67 Mn 16.67 Sb 33.33 (c) EDS mapping of elements for the starting composition Zn 15.50 Fe 10.19 Co 7.70- Ni 12.57 Mn 14.74 Sb 39.29 and (d) Entropy of mixing "yard sticks" for selected compositions.
Fig. 2. (a) SEM image of starting composition Zn 16 Fe 10 Co 8 Ni 13 Mn 15 Sb 39 yielding three annotated compositions (which did not change by heat treatment) (b) SEM image of starting composition Zn 16.67 Fe 9.17 Co 7.5 Ni 16.67 Mn 16.67 Sb 33.33 (c) EDS mapping of elements for the starting composition Zn 15.50 Fe 10.19 Co 7.70- Ni 12.57 Mn 14.74 Sb 39.29 and (d) Entropy of mixing "yard sticks" for selected compositions.

Fig. 4 .
Fig. 4. XRD patterns of high entropy alloys synthesized with different nominal valence electron counts, VEC.See Table1for their actual concentration.All peaks agree with the Co8Mn8Sb8 pattern, which shares the pattern with NiMnSb, but has the 2 × 2 × 2 superstructure peaks in addition which are marked with an arrow.
performance and the possibility to exploit antimonides-based High Entropy alloys with Heusler-type compositions as a new class of future TE materials.This new development in alloys could also open a new door to new alloying systems, which could be applied to various energy harvesting applications and basic research.Author statements J.U.R. and P.A.C initiated the concepts and designed the experiments; N.S. carried out detailed data analysis and performed calculations; M.S. measured the transport properties; A.E.G. contributed with discussion and commented on the manuscript.T.G.F.analyzed the data and lead the research work.All the authors shared ideas and contributed to the interpretation of the results.