Review of the Thermoelectric Properties in Nanostructured Fe 2 VAl

: Besides alloying, nanostructuring was implemented to improve the thermoelectric properties in Fe 2 VAl. This Heusler alloy indeed displays a thermoelectric ﬁgure of merit too small for applications ( ZT ~0.1 at 300 K) which is caused by a large lattice thermal conductivity ( λ L = 27 W · m − 1 · K − 1 at 300 K). The effect of nanostructuring on the microstructure and on the thermoelectric properties of alloyed Fe 2 VAl are therefore reviewed. By mechanical alloying followed by spark plasma sintering, the average grain size ( D ) was decreased to D ~300–400 nm in Fe 2 VAl 0.9 Si 0.1 , Fe 2 VAl 0.9 Si 0.07 Sb 0.03 , Fe 2 V 1.05 Al 0.95 , and Fe 2 V 0.9 W 0.1 Al. As expected, phonon scattering at the numerous grain boundaries lead to a strong decrease in the lattice thermal conductivity, which reached values as small as λ L = 3.3 W · m − 1 · K − 1 . However, in all the reviewed examples, the thermoelectric ﬁgure of merit ( ZT ) is only marginally or not even improved when comparing to non-nanostructured samples because the electrical resistivity also increases upon nanostructuring. A signiﬁcantly improved ZT = 0.3 at 500 K was only recently observed in severely deformed Fe 2 VAl 0.95 Ta 0.05 by high pressure torsion because the very ﬁne microstructure ( D ~100 nm) strongly enhanced the thermal conductivity reduction.


Introduction
Thermoelectric devices can be used either as refrigerators (Peltier effect) or electric power generators (Seebeck effect). Despite their relatively small conversion efficiency, they are commercialized for localized or silent refrigeration and they are considered for powering the wireless sensors required by future applications such as the "Internet of Things" [1] or the "Industry 4.0" [2].
The conversion efficiency of a thermoelectric device (power generator or cooler) is related to the dimensionless figure of merit ZT of its constituting materials. ZT is defined by the expression ZT = (α 2 /ρ)(T/λ) with α the Seebeck coefficient, ρ the electrical resistivity, λ the thermal conductivity, and T the absolute temperature. Bismuth telluride (Bi 2 Te 3 ), which is the material currently used in commercialized thermoelectric refrigerators, displays a high dimensionless figure of merit ZT = 1 at 300 K for both n-& p-type doping. Bismuth and tellurium are indeed chemical elements favorable in several ways to high thermoelectric performances. They often form small-gap semi-conducting compounds with a high electronic mobility, which arises from the non-ionic and strongly covalent character of their chemical bonds. The large atomic mass of these two elements also confer to their compounds a small thermal conductivity. However, the cost of tellurium (~150 $/kg) which arises from its scarcity in the Earth's crust prevents a broader use of Bi 2 Te 3 in applications: a mass-market based on bulk materials incorporating this element is most likely non-sustainable. Cheaper and more abundant thermoelectric materials are thus needed to replace Bi 2 Te 3 . Fe 2 VAl is the Heusler alloy [3] that could challenge Bi 2 Te 3 as a thermoelectric material. Its constituting chemical elements are inexpensive [4] and it displays a power factor equal to PF = α 2 /ρ~5 mW·m −1 ·K −2 at 300 K [5], larger than in Bi 2 Te 3 . However, Fe 2 VAl is not yet a substitute of Bi 2 Te 3 because its thermal conductivity is more than one order of magnitude larger (27 W·m −1 ·K −1 at 300 K in pristine Fe 2 VAl) than in Bi 2 Te 3 , leading to ZT~0.1. It is thus mandatory to decrease its thermal conductivity to make it competitive with Bi 2 Te 3 . The thermal conductivity is the sum of the electronic thermal conductivity (λ e ) and the lattice thermal conductivity (λ L ). Once the power factor has been maximized by controlling the charge carrier concentration, the electronic thermal conductivity which varies like the electrical conductivity (Wiedemann-Franz law) cannot be reduced and only the lattice thermal conductivity can be decreased.
Several research paths have been undertaken in the literature to decrease the lattice thermal conductivity in Fe 2 VAl. The first one relies on scattering of heat carrying phonons by the atomic mass fluctuations which arise when one of the constituting element is substituted by a heavier one [6]. A decrease in the lattice thermal conductivity in alloyed Fe 2 VAl was first published by Nishino et al. [7] who substituted Al by Si or Ge: it decreased from λ L = 27 W·m −1 ·K −1 at 300 K in Fe 2 VAl to λ L = 15 W·m −1 ·K −1 in Fe 2 VAl 0.9 Si 0.1 and λ L = 11 W·m −1 ·K −1 in Fe 2 VAl 0.9 Ge 0.1 at 300 K. Since then, many other chemical elements have been substituted and even multi-substituted Fe 2 VAl alloys have been investigated [8]. Most of the data reported in the literature on this subject are compiled in Table 1. One can easily notice in Table 1 that substitution by one or several heavy elements is an efficient way to decrease λ L in Fe 2 VAl since it leads to a −80% reduction. Nonetheless, the lowest value of lattice thermal conductivity achieved in substituted Fe 2 VAl (5 W·m −1 ·K −1 ) is still three times larger than in Bi 2 Te 3 (~1.5 W·m −1 ·K −1 ). Nanostructuring has been the other research path which was thus implemented to further decrease λ L and it is the goal of this article to review its effect on the thermoelectric properties of Fe 2 Val.

Nanostructured Fe 2 VAl
Improved performances were observed in thermoelectric materials with strongly reduced grain sizes [16,17]. In these nanostructured materials, the improvement is related to a decrease in the lattice thermal conductivity promoted by enhanced rates of phonons scattering on the numerous grain boundaries induced by their fine microstructure [18,19]. Reductions of λ L by 25%, 37%, and 90% at 300 K were for instance observed in n-type Half-Heusler (~200 nm crystals) [20], in n-type filled skutterudites (~150 nm crystals) [21] and in silicon (~20 nm crystals) [22] respectively. Methods such as ball milling (BM) combined with Spark Plasma Sintering (SPS), melt spinning (MS), and high pressure torsion (HPT) were thus implemented in alloyed Fe 2 VAl, leading to fine-grained samples and to a decrease in the lattice thermal conductivity. Nonetheless, the thermoelectric figure of merit was improved in only very few cases because upon nanostructuration, the electrical resistivity increases as well. In the next sections, a detailed examinations of these results will be presented.

Synthesis, Microstructure and Thermal Conductivity
Mikami et al. [23] published the first research work on nanostructured Fe 2 VAl 0.9 Si 0.1 . They mechanically alloyed in a planetary ball mill powders of elemental Fe, V, and Si with a Fe-Al alloy [24] and obtained a powder constituted by a face-centered cubic solid solution of these elements. This powder is a collection of micrometric particles (~7 µm) which agglomerate much smaller nanocrystallites (~20 nm). After spark plasma sintering at temperature ranging between 900 and 1000 • C, this solid solution orders in the L2 1 structure. The densified samples are polycrystals with an average grain size (D) and a relative density (d) which increase with the sintering temperature and range from D~100 nm to D~400 nm and d = 80% to d = 98% respectively. A scanning electron microscope (SEM) image of the densest sample in Ref. [23] is displayed in Figure 1. pressure torsion (HPT) were thus implemented in alloyed Fe2VAl, leading to fine-grained samples and to a decrease in the lattice thermal conductivity. Nonetheless, the thermoelectric figure of merit was improved in only very few cases because upon nanostructuration, the electrical resistivity increases as well. In the next sections, a detailed examinations of these results will be presented.

Synthesis, Microstructure and Thermal Conductivity
Mikami et al. [23] published the first research work on nanostructured Fe2VAl0.9Si0.1. They mechanically alloyed in a planetary ball mill powders of elemental Fe, V, and Si with a Fe-Al alloy [24] and obtained a powder constituted by a face-centered cubic solid solution of these elements. This powder is a collection of micrometric particles (~7 μm) which agglomerate much smaller nanocrystallites (~20 nm). After spark plasma sintering at temperature ranging between 900 and 1000 °C, this solid solution orders in the L21 structure. The densified samples are polycrystals with an average grain size (D) and a relative density (d) which increase with the sintering temperature and range from D ~ 100 nm to D ~ 400 nm and d = 80% to d = 98% respectively. A scanning electron microscope (SEM) image of the densest sample in Ref. [23] is displayed in Figure 1.  [23], with copyright permission from Elsevier, 2008.
As expected, upon reduction of the grain size, the thermal conductivity decreases in Fe2VAl0.9Si0.1. It is nonetheless also decreased by the pores which are present in the samples since their relative density is smaller than 100%. In the present review, in order to account of the porosity and to compare values of thermal conductivity only affected by the grain size reduction, the original Mikami's data were corrected by the effective medium theory expression of Odelevski [25]: where λmeas is the measured thermal conductivity, d is the relative density and λreal is the value of a 100% dense sample. For average grain sizes ranging from micron-size (arc-melted sample) to D ~ 400 nm and to D ~ 100 nm, the lattice thermal conductivity decreases from λL = 16.5 W·m −1 ·K −1 to λL = 13.4 W·m −1 ·K −1 and to λL = 7.9 W·m −1 ·K −1 . Given the large uncertainty on the average grain size, it is difficult to use a model like Nan and Birringer's [26] to assess more quantitatively the efficiency of As expected, upon reduction of the grain size, the thermal conductivity decreases in Fe 2 VAl 0.9 Si 0.1 . It is nonetheless also decreased by the pores which are present in the samples since their relative density is smaller than 100%. In the present review, in order to account of the porosity and to compare values of thermal conductivity only affected by the grain size reduction, the original Mikami's data were corrected by the effective medium theory expression of Odelevski [25]: λ real = 2λ meas.
(3d−1) where λ meas is the measured thermal conductivity, d is the relative density and λ real is the value of a 100% dense sample. For average grain sizes ranging from micron-size (arc-melted sample) to D~400 nm and to D~100 nm, the lattice thermal conductivity decreases from λ L = 16.5 W·m −1 ·K −1 to λ L = 13.4 W·m −1 ·K −1 and to λ L = 7.9 W·m −1 ·K −1 . Given the large uncertainty on the average grain size, it is difficult to use a model like Nan and Birringer's [26] to assess more quantitatively the efficiency of phonon scattering by the grain boundaries. Anyway in Mikami's work, this effect is strong enough to decrease λ L by 12% when comparing the densest nanostructured Fe 2 VAl 0.9 Si 0.1 (d = 98%, D = 400 nm) to the arc-melted (AM) one. Subsequently, by using more energetic conditions at the ball milling stage, a smaller average grain size of D~300 nm was achieved in Fe 2 VAl 0.9 Si 0.1 by Ref. [27]. This lead to λ L = 9.2 W·m −1 ·K −1 , a value even smaller which shows directly the effect of grain boundary scattering on thermal transport.
Other compositions than Si-substituted Fe 2 VAl were also nanostructured by the same techniques: for instance Fe 2 VAl 0.9 Si 0.07 Sb 0.03 [28] and Fe 2 V 1−y W y Al (0 ≤ y ≤ 0.1) [27] which displayed average grain sizes similar to the previously cited research works, D~400 nm and D~300 nm, respectively. Figure 2 shows the effect on the lattice thermal conductivity of varying the concentration of W in Fe 2 V 1−y W y Al and compares it to Fe 2 VAl 1−x Si x (0 ≤ x ≤ 0.1). It can easily be noticed that substituting W, a heavy 5d element, rather than Si leads to an extra −6 W·m −1 ·K −1 decrease in the lattice thermal conductivity which is equal to λ L = 3.3 W·m −1 ·K −1 in nanostructured (D~300 nm and d ≥ 98%) Fe 2 V 0.9 W 0.1 Al. phonon scattering by the grain boundaries. Anyway in Mikami's work, this effect is strong enough to decrease λL by 12% when comparing the densest nanostructured Fe2VAl0.9Si0.1 (d = 98%, D = 400 nm) to the arc-melted (AM) one. Subsequently, by using more energetic conditions at the ball milling stage, a smaller average grain size of D ~ 300 nm was achieved in Fe2VAl0.9Si0.1 by Ref. [27]. This lead to λL = 9.2 W·m −1 ·K −1 , a value even smaller which shows directly the effect of grain boundary scattering on thermal transport. Other compositions than Si-substituted Fe2VAl were also nanostructured by the same techniques: for instance Fe2VAl0.9Si0.07Sb0.03 [28] and Fe2V1−yWyAl (0 ≤ y ≤ 0.1) [27] which displayed average grain sizes similar to the previously cited research works, D ~ 400 nm and D ~ 300 nm, respectively. Figure 2 shows the effect on the lattice thermal conductivity of varying the concentration of W in Fe2V1−yWyAl and compares it to Fe2VAl1−xSix (0 ≤ x ≤ 0.1). It can easily be noticed that substituting W, a heavy 5d element, rather than Si leads to an extra −6 W·m −1 ·K −1 decrease in the lattice thermal conductivity which is equal to λL = 3.3 W·m −1 ·K −1 in nanostructured (D ~ 300 nm and d ≥ 98%) Fe2V0.9W0.1Al. Besides ball milling, high pressure torsion (HPT) followed by annealing was the other technique [29] recently implemented by Masuda et al. to refine the microstructure in alloyed Fe2VAl [30]. Fe2V1.05Al0.95 and Fe2VAl0.95Ta0.05 were the two investigated compositions, which indeed displayed differing properties under these severe deformations. The average grain size in the latter alloy is approximately D ~ 100 nm, a very small value for well densified Fe2VAl, whereas it is D ~ 400 nm in the former alloy. The authors ascribed this effect to a slowdown of the grain boundary migration by the excess Ta segregated at these grain boundaries. Microstrains have also been previously invoked in HPT-treated skutterudites [31] to act as phonon scatterers and to decrease the thermal conductivity. Nonetheless, the strain due to HPT deformation "almost vanished in Fe2VAl0.95Ta0.05 by annealing at 900 K" [30] and its effect on λL can be neglected. Hence, by the combined effect of the grain boundaries and the mass fluctuations arising from the substitution of heavy Ta, the lattice thermal conductivity is decreased to λL = 3.2 W·m −1 ·K −1 , a value nearly 10 times smaller than in pristine Fe2VAl.
Finally, grain boundaries are not the only interface which can scatter phonons: antiphase boundaries separating antiphase domain have newly been shown to decrease the lattice thermal conductivity in Fe2Val [32]. Rapidly quenching Fe2VAl from temperatures where its disordered B2 or A2 variants are stable, allowed stabilizing a nanostructured variant of Fe2VAl. It is constituted by L21 antiphase domains (APDs) separated by antiphase boundaries (APBs), which indeed scatter the Besides ball milling, high pressure torsion (HPT) followed by annealing was the other technique [29] recently implemented by Masuda et al. to refine the microstructure in alloyed Fe 2 VAl [30]. Fe 2 V 1.05 Al 0.95 and Fe 2 VAl 0.95 Ta 0.05 were the two investigated compositions, which indeed displayed differing properties under these severe deformations. The average grain size in the latter alloy is approximately D~100 nm, a very small value for well densified Fe 2 VAl, whereas it is D~400 nm in the former alloy. The authors ascribed this effect to a slowdown of the grain boundary migration by the excess Ta segregated at these grain boundaries. Microstrains have also been previously invoked in HPT-treated skutterudites [31] to act as phonon scatterers and to decrease the thermal conductivity. Nonetheless, the strain due to HPT deformation "almost vanished in Fe 2 VAl 0.95 Ta 0.05 by annealing at 900 K" [30] and its effect on λ L can be neglected. Hence, by the combined effect of the grain boundaries and the mass fluctuations arising from the substitution of heavy Ta, the lattice thermal conductivity is decreased to λ L = 3.2 W·m −1 ·K −1 , a value nearly 10 times smaller than in pristine Fe 2 VAl.
Finally, grain boundaries are not the only interface which can scatter phonons: antiphase boundaries separating antiphase domain have newly been shown to decrease the lattice thermal conductivity in Fe 2 Val [32]. Rapidly quenching Fe 2 VAl from temperatures where its disordered B2 or A2 variants are stable, allowed stabilizing a nanostructured variant of Fe 2 VAl. It is constituted by L2 1 antiphase domains (APDs) separated by antiphase boundaries (APBs), which indeed scatter the phonons. When domains as small as~100 nm are synthesized, the lattice thermal conductivity is decreased from 28 to 17 W·m −1 ·K −1 [32].

Electronic Transport Properties and ZT
In all the previously cited references [23,27,28,30], despite differing compositions, the Seebeck coefficient peaks as a function of temperature (200-500 K) at the same value, e.g.,~−130 µV·K −1 . This is due to the well-established fact that the Seebeck coefficient in most cases does not depend on the exact nature of the dopant but depends on the charge carrier concentrations. Since this last parameter is weakly affected by the modifications of the microstructure, the Seebeck coefficient is also hardly modified and it does not influence the figure of merit.
But the electrical resistivity is not immune to the changes of microstructure because grain boundaries also scatter electrons. In all the previously cited references, as can be noticed in Table 2 when comparing to arc melted samples displaying micrometric grain sizes, resistivity systematically increases when the grain sizes decreases. This compensates the reduction of lattice thermal conductivity previously discussed and hence ZT only marginally increases when the grain size is decreased to D~400 nm. In an attempt to circumvent this effect, Mikami et al. synthesized Fe 2 VAl 0.9 Si 0.1 + Bi nanocomposites but they did not improve ZT [33]. As can be seen in Figure 3, it is only very recently that, in severely deformed (HPT) and annealed Fe 2 VAl 0.95 Ta 0.05 , the strong decrease in λ L arising from the very small D~100 nm grain size overcomes the increase in electrical resistivity and leads to the improved value of figure of merit ZT = 0.3 (+50%) at 500 K. This last example shows that nanostructring is a promising research path, which leads to improvements of ZT in alloyed Fe 2 VAl and that it deserves to be pursued in the next future. phonons. When domains as small as ~100 nm are synthesized, the lattice thermal conductivity is decreased from 28 to 17 W·m −1 ·K −1 [32].

Electronic Transport Properties and ZT
In all the previously cited references [23,27,28,30], despite differing compositions, the Seebeck coefficient peaks as a function of temperature (200-500 K) at the same value, e.g., ~ −130 μV·K −1 . This is due to the well-established fact that the Seebeck coefficient in most cases does not depend on the exact nature of the dopant but depends on the charge carrier concentrations. Since this last parameter is weakly affected by the modifications of the microstructure, the Seebeck coefficient is also hardly modified and it does not influence the figure of merit.
But the electrical resistivity is not immune to the changes of microstructure because grain boundaries also scatter electrons. In all the previously cited references, as can be noticed in Table 2 when comparing to arc melted samples displaying micrometric grain sizes, resistivity systematically increases when the grain sizes decreases. This compensates the reduction of lattice thermal conductivity previously discussed and hence ZT only marginally increases when the grain size is decreased to D ~ 400 nm. In an attempt to circumvent this effect, Mikami et al. synthesized Fe2VAl0.9Si0.1 + Bi nanocomposites but they did not improve ZT [33]. As can be seen in Figure 3, it is only very recently that, in severely deformed (HPT) and annealed Fe2VAl0.95Ta0.05, the strong decrease in λL arising from the very small D ~ 100 nm grain size overcomes the increase in electrical resistivity and leads to the improved value of figure of merit ZT = 0.3 (+50%) at 500 K. This last example shows that nanostructring is a promising research path, which leads to improvements of ZT in alloyed Fe2VAl and that it deserves to be pursued in the next future.  Annealed" means severely deformed by HPT, followed by annealing. Reproduced from [30], with copyright permission from American Institute of Physics, 2012. Table 2. Average grain size (D), thermal, and electronic transport properties in various nanostructured and substituted Fe 2 VAl alloys at 300 K except ZT max which is the maximum value of the dimensionless thermoelectric figure of merit as a function of temperature. "AM" stands for arc melted.

Conclusions
Ball milling or high pressure torsion lead to nanometric grain size in alloyed Fe 2 VAl. The heat carrying phonons are not only scattered by the mass fluctuations provided by alloying but also by the numerous grain boundaries introduced in the microstructure. The lattice thermal conductivity is thus strongly decreased but in most of the reviewed cases, the electrical resistivity is also increased by the refined microstructure and this precludes any gain of ZT. Nonetheless, in severely deformed Fe 2 VAl 0.95 Ta 0.05 with D~100 nm [30], the strong decrease in the lattice thermal conductivity overcompensate the electrical resistivity increase and an improved ZT = 0.3 is reached at 500 K. These promising results will certainly be followed by similar research effort to improve ZT by nanostructuring Fe 2 VAl.

Conflicts of Interest:
The author declares no conflict of interest.