Effect of Vacancies on Magnetism, Electrical Transport, and

Article pubs.acs.org/cm

Effect of Vacancies on Magnetism, Electrical Transport, and Thermoelectric Performance of Marcasite FeSe2−δ (δ = 0.05) Guowei Li,# Baomin Zhang,§ Jiancun Rao,‡ Daniel Herranz Gonzalez,# Graeme R. Blake,# Robert A. de Groot,#,† and Thomas T. M. Palstra*,# #

Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, Groningen, The Netherlands School of Physics and Technology, University of Jinan, 336 West Road of Nan Xinzhuang, 250022 Jinan, Shandong, P. R. China ‡ School of Materials Science and Engineering, Harbin Institute of Technology, 150001 Harbin, Heilongjiang, P. R. China † Institute for Molecules and Materials, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, Gelderland, The Netherlands §

S Supporting Information *

ABSTRACT: The marcasite structure FeSe2−δ was synthesized using a simple solvothermal method. Systematic study of the electrical transport properties shows that the transport is dominated by variable-range hopping (VRH), with a changeover from Mott VRH at higher temperature to Efros-Shklovskii VRH for temperatures lower than the width of the Coulomb gap. This also confirms the presence of a Coulomb gap in the density of states at the Fermi energy. We observe that Yttrium doping increases the electrical conductivity dramatically without significantly reducing the Seebeck coefficient. This results in remarkably high power factors for thermoelectric performance in the regime where the mean hopping energy shifts from defect dominated to Coulomb repulsion dominated. High resolution transmission electron microscopy, in combination with theoretical calculations, proves the narrowing of the band gap by introducing Se vacancies. This leads to a good conductivity and is responsible for the excellent thermoelectric performance. The formation of nanoclusters, resulting from Se vacancies, is responsible for a dense system of stacking faults and the generally reported weak ferrimagnetism. This also determines the transition between the different electrical transport mechanisms and contributes to the improved thermoelectric performance. transport.3 Mott suggested that in the case of hopping between levels of different energy, the electrical conductivity and Seebeck coefficient can be expressed as4

1. INTRODUCTION Thermoelectric materials convert low quality waste heat to electricity, and diverse materials with different mechanisms are presently being explored. In most inorganic materials, where the semiclassical conduction theory describes the electrical transport, the Seebeck coefficient S and the electrical conductivity σ have opposing trends with respect to temperature, band gap, and carrier concentration. Thus, searching for a material that meets the conflicting requirement of a high Seebeck coefficient, like an insulator, and a good conductivity, like a metal, remains as a challenge. The conversion efficiency of thermoelectric materials is evaluated by the dimensionless thermoelectric figure of merit ZT (= S2σT/κ), where T and κ are the absolute temperature and thermal conductivity, respectively. The power factor P is defined by S2σ. We note that ZT values of 2−3 make thermoelectric refrigeration competitive with commercial vapor compression refrigeration systems.1 This value is difficult to achieve using semiclassical models, and a number of novel approaches have been explored, including narrow bands near the Fermi level.2 However, in some organic or disordered inorganic materials, not the semiclassical theory but hopping transport dominates the © 2015 American Chemical Society

⎡⎛ T ⎞ γ ⎤ σH = σ0 exp⎢⎜ − Mott ⎟ ⎥ ⎣⎝ T ⎠ ⎦

and SH =

∂ ln[g (E)] kB2 |E = μ (TMottT )1/2 2e dE

where σ0 is the conductivity prefactor, TMott is the characteristic hopping temperature, γ is the hopping exponent that depends on the hopping mechanism, kB is the Boltzmann’s constant, T is the absolute temperature, and g(E) is the “noninteracting” density of states. Apparently, σH and SH also have an opposing temperature dependence. However, when nonenergy dependent scattering dominates in either transport regime, the Received: July 15, 2015 Revised: November 23, 2015 Published: November 23, 2015 8220

DOI: 10.1021/acs.chemmater.5b03562 Chem. Mater. 2015, 27, 8220−8229

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Chemistry of Materials

Figure 1. (a) Fitted XRD pattern of as-prepared FeSe2−δ. (b) Illustration of the FeSe2 unit cell. The Fe atom is octahedrally coordinated by six Se atoms. Fe is in the low spin state with the t2g band fully occupied. (c) SEM image of the as-prepared sample. (d) HRTEM image shows the single crystalline nature of the sample; the inset shows the corresponding Selected Area Electron Diffraction (SAED) pattern.

conductivity could be controlled by tuning σ0 without influencing SH.5 Examples have been reported with simultaneous increase in electrical conductivity and Seebeck coefficient by doping or changing the carrier concentration.6 More importantly, the hopping regime is also ideal for thermoelectric conversion though two simple physical mechanisms: on the one hand, the Fermi level lying close to the band edge would result in a strong broken particle-hole symmetry. On the other hand, transport assisted by phonons is available because of the wide energy window near the Fermi level. This means that the carriers can obtain enough energy from the phonons to hop in the system.7 Earlier studies found that in the hopping regime where the carriers are strongly localized, the soft gap in the density of states has a profound influence on the thermopower and makes it more sensitive in the single density of states than the conductivity.8 This has been confirmed in many reports where it was concluded that the thermoelectric power obeys a dependence A√T + BT in the variable range hopping regime or A/T + BT in the case of hopping between the empty sites.9,10 Thus, the understanding of electrical transport mechanisms is critical for the design of new thermoelectric material for next-generation applications. In fact, many efforts have been made aiming to control the transport mechanism, especially in semiconductors. At sufficiently high temperatures, the electrical transport is dominated by the thermal activation of electrons from the valence band to the conduction band. In this regime, conduction always occurs through interactions between neighboring sites, and hence the activation energy is independent of temperature. However, in a disordered material at low temperature, the possibility to find an available nearby site with a suitable energy level decreases rapidly. In this case, the charge carriers will hop between sites beyond the nearest

neighbors with smaller energy differences. The quantum tunneling of charge carriers between localized states is generally assisted by thermally driven phonons or an applied field.11,12 The hopping length and the hopping energy are temperature dependent. This is the origin of the term “variable-range hopping” (VRH). Mott was the first to predict this hopping mechanism by assuming a constant density of states at the Fermi energy, and the temperature dependence of the resistivity follows T−1/4, which is now called Mott VRH.13 Later, Shklovskii and Efros predicted that at sufficient low temperature, the Coulomb interaction should be taken into consideration, and a “Coulomb-gap” could be present. The appearance of such a gap in the density of states at the Fermi level would result in an exponential temperature dependence of the resistivity, which is called ES VRH.14 For both the Mott and ES VRH models to be valid, the electrons should hop a mean distance that is longer than the localization length. The hopping between the initial and final sites can be achieved directly or by involving an additional third site.15 Thus, the crossover from the Mott VRH model at higher temperature to the ES VRH model at lower temperature could be observed when the hopping energy is of the order of or smaller than the Coulombgap energy. Indeed, by carefully controlling the synthesis, one can observe this crossover in several systems but only limited to (doped) thin films at extremely low temperature.15,16 As a common selenide mineral, ferroselite (FeSe2) was first reported in 1955 in the Ust’-Uyuk uranium deposit in Tuva, Siberia. Under ambient conditions, FeSe2 adopts the marcasite structure, while high temperature/high pressure synthesis leads to the pyrite structure.17 In the pyrite phase the Fe cations form a face-centered cubic sublattice. As in the marcasite phase, the Fe atoms in pyrite are octahedrally coordinated, but the octahedra share corners.18 The pyrite phase has received little 8221


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Figure 2. (a) Magnetization loops measured at 5 and 300 K; the inset shows the low-field region. (b) Fitting of loops with the LAS model. (c) Fieldcooled susceptibility shows a sharp transition at around 100 K. (d) HRTEM image of a microrod showing Se vacancies; the image in the lower left inset was obtained from the selected area outlined in red after Fourier filtering in order to highlight the axial stacking faults.

ray diffraction indicates high purity samples containing only the marcasite phase. We observe WFM in agreement with previous reports. This can be attributed to the formation of Fe7Se8 nanoclusters due to the existence of Se-rich defects. The VRH mechanism dominates the electrical transport over a wide temperature regime due to Anderson localization. A crossover from the Mott model to the ES VRH model is observed for the first time in a polycrystalline bulk material, which indicates the existence of a Coulomb gap at low temperatures. As a thermoelectric material, FeSe2−δ has an estimated figure of merit ZT = 0.23 at 554 K, which can be improved to 0.32 by doping with 2% Y. There is also a temperature-induced n-p-n switching of the conduction type caused by the inherent Se vacancies. The interesting properties and favorable toxicological properties make marcasite FeSe2 an attractive material for optical, electronic, thermoelectric, and photovoltaic applications.

attention due to the difficult synthesis, which needs more extreme conditions compared with the marcasite phase. In the orthorhombic marcasite structure, each Fe atom is coordinated to six Se atoms forming an octahedron, as illustrated in Figure 1(b). Two neighboring octahedra share edges and form a linear chain parallel to the orthorhombic c-axis. FeSe2 has attracted interest mainly due to its semiconductor and optical absorption properties. It is a good candidate as a solar cell absorption material since it has an appropriate band gap (∼1 eV) and a high absorption coefficient (>105 cm−1).19,20 Recent research found that FeSe2 nanoparticles with a diameter of ∼30 nm display strong photoluminescence with a quantum yield of 16%, comparable to that of II−VI semiconductors.21 Unfortunately, some fundamental properties of marcasite FeSe2 still remain unclear. For example, a Mössbauer study of marcasite in an external magnetic field confirmed the absence of a magnetic moment at the iron atom, together with the presence of a negative electric field gradient, suggesting that Fe2+ in FeSe2 has a low spin configuration, with the lower t2g electronic state completely filled and the upper eg electronic state completely empty (S = 0).22 However, all the reported synthetic samples show a similar weak ferrimagnetism (WFM). Most authors have simply attributed this to the existence of ferrimagnetic impurities, surface oxidation, or spin canting.23,24 Electrical transport properties are also controversial with only a few papers reporting the resistivity data above liquid nitrogen temperatures. An explanation in terms of simple thermally activated transport does not concur with the available experimental data.25 Recently, the natural mineral tetrahedrites such as Cu12‑xMxSb4S13, where M is Zn or Fe, have been shown to be good candidates for thermoelectric applications due to their low lattice thermal conductivity.26 Similar results were also confirmed in marcasite phase FeSe2.27 Thus, it is important to understand the charge carrier transport mechanism by exploring the band structure and electron and hole asymmetries at the Fermi level of marcasite FeSe2.28 In this work, 3-dimensional (3D) FeSe2−δ hierarchical structures are synthesized by a facile solvothermal method. X-

2. METHOD 2.1. Synthesis. Two mmol of FeCl2 and 3.6 mmol of Se powder were mixed in a Teflon lined autoclave of volume 50 mL. Ethylamine (30 mL) was added, and the solution was stirred for 10 min. The autoclave was placed in an oven and heated at 180 °C for 18 h. After cooling down to room temperature after the oven was switched off, a black product was collected, washed with 2 M of HCl for 8 h, and then washed with distilled water and ethanol several times. Finally, the product was dried in vacuum at 60 °C overnight. 2.2. Characterization. X-ray powder diffraction (XRD) at room temperature was performed using a Bruker D8 Advance diffractometer equipped with a Cu Kα source (λ = 0.15406 nm). The morphology and crystal structure were probed using a Philips XL 30 scanning electron microscope (SEM). High-resolution TEM (HRTEM) and TEM-EDX were performed using a Tecnai G2 F30 S-Twin at an acceleration voltage of 300 kV. The magnetization was measured using a Quantum Design MPMS-XL7 SQUID magnetometer. For measurement of the electrical properties, a circular shaped polycrystalline sample was prepared by pressing the powder under 500 MPa (1 Ton) for 15 min. The electrical contacts were made using Pt wire of 0.05 mm diameter connected to the sample by silver paint. The electrical measurements were performed using a Quantum Design Physical 8222


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Chemistry of Materials Properties Measurement System (PPMS) and an Agilent 3458a multimeter. Electronic band structure calculations are described in the Supporting Information. For high temperature resistivity and Seebeck coefficient measurements, bar shaped samples were prepared by pressing the powder under 500 MPa (1 Ton) for 15 min. The samples were transferred to a quartz tube, which was sealed under vacuum and heated at 700 °C for 1 day. The relative density of the sintered sample was determined to be 96.8%. The measurements were performed using a Linseis LSR-3 system.

In addition, for single domain noninteracting particles, the coercivity is a direct consequence of the ratio KE/Ms, and the theoretical coercivity can be described as HC = γ KE/Ms, where γ = 0.64 for cubic anisotropy. Excellent fits are obtained with the LAS model for both loops at 5 and 300 K, as shown in Figure 2(b), indicating that the WFM originates from ferromagnetic regions within the sample. We further plot the magnetization versus H−1: a good linear relation is observed as shown in Figure S2(a). We conclude that microstructural inhomogeneities act as stress centers on the spin alignment around them.32 Field-cooled magnetization measurement at 100 Oe was carried out: a distinct change in magnetization is observed at around 100 K, as shown in Figure 2(c). We ascribe this to another uncommon iron selenide, Fe7Se8. Previous research found that a spin rotation occurs abruptly in the hexagonal 3c structure of Fe7Se8 between 110 and 130 K, depending on the detailed synthesis procedure.33 Thus, we think that ferromagnetic Fe7Se8 nanoclusters are responsible for the WFM in diamagnetic FeSe2−δ. To validate this assumption, we synthesized high purity 3c Fe7Se8, and the same abrupt magnetization change is observed at the same temperature, 100 K (Figure S2(b)). Below this temperature, the direction of the moments is in the (001) plane and changes to the [001] direction when the temperature is above 100 K. The ordering temperature is far higher than this transition temperature, up to 393 K. With the fitting parameters from the LAS model, we calculate the coercivities at 5 and 300 K, respectively, as listed in Table 1. The excellent agreement between the theoretical

3. RESULTS AND DISCUSSION 3.1. Phase and Morphology. The X-ray diffraction pattern for the as-prepared sample is displayed in Figure 1(a), which is consistent with the orthorhombic FeSe2 structure (JCPDS no. 65-2570). Rietveld refinement was performed based on the reported Pnnm structural model, and the final agreement factors converged to Rp = 0.0134 and wRp = 0.0205. The refined unit cell parameters are as follows: a = 4.8031(6) Å, b = 5.7849(2) Å, and c = 3.5840(4) Å. The iron atoms occupy positions (0 0 0) and (1/2 1/2 1/2), while the refined fractional coordinates of the Se atom was x = 0.2127(2), y = 0.3691(7), and z = 0, in perfect agreement with the measurement on a single crystal sample.29 No extra peaks belonging to iron oxide or iron selenide were observed within the instrumental resolution. The morphology of the asprepared samples was observed by scanning electron microscopy (SEM), from which we can see that the product consists of well-defined three-dimensional (3D) flower-like structures with a homogeneous size and shape distribution (Figure 1(c)). Interestingly, the flower structure was still retained after a 30 min ultrasonic process, indicating strong interactions between the rods upon organization of the flowershaped structure (Figure S1). HRTEM reveals that the microrods are single-crystalline (Figure 1(d)). Lattice fringes with spacings of 0.378 and 0.247 nm correspond to the (110) and (120) planes, respectively, consistent with the SAED pattern, as illustrated in the inset to Figure 2(d). 3.2. Magnetic Properties. Magnetization measurements for the as-prepared sample were performed and are displayed in Figure 2(a). Magnetic hysteresis loops are clearly detected both at 5 and 300 K. The coercive field (Hc) is 245 Oe at 5 K and decreases to 85 Oe at 300 K. The magnetization curve at 5 K shows a significant paramagnetic component in applied fields up to 6 T. However, the loop measured at 300 K reaches saturation in a field of only 250 Oe. This lack of magnetic saturation at low temperature indicates the existence of particles or regions of the sample in which magnetically disordered spins become ordered with increasing field. It results in the increase of magnetization at sufficiently low temperature.30 The small spontaneous magnetization indicates that only a small fraction of atoms holds a permanent magnetic moment and contributes to ferrimagnetism. For polycrystalline magnetic materials, the hysteresis loops can be modeled with the Law of Approaching to Saturation (LAS) in the form of

Table 1. Parameters Obtained by Fitting Magnetization versus Field with the LAS Modela

a

R2

B

Ms (emu/g)

KE (105 Jm‑3)

Hc (Cal.)

Hc (Exp.)

5 300

0.9981 0.9994

3.911 × 10−4 3.181 × 10−5

13.64 9.68

0.5233 0.1059

245.5 70.0

245 85

The Ms data for 3c Fe7Se8 are taken from our own work.

and experimental values confirms the existence of noninteracting Fe7Se8 nanoclusters. In fact, the discovery of magnetism in nonmagnetic materials has been reported in many systems, and the origin of ferri/ferromagnetism in these materials is generally assumed to be intrinsic defects such as vacancies, stacking faults, or twin boundaries.34−37 For the marcasite phase FeSe2, stacking faults are a common type of vacancy cluster due to their low energy. Thus, a number of stacking faults is expected and experimentally confirmed by HRTEM, as shown in Figure 2(d) and the left lower inset. One can clearly see a contrast change in the HRTEM image because the faults occur in bunches. These planar defects are generally located at the center, rather than at the surface as in the single crystalline pyrite (FeS2). No dangling bonds are expected in the stacking fault areas but rather a rearrangement of atoms due to the displacement vector and leading to the formation of a different phase as shown later.38 The removal of these stacking faults is very difficult and generally requires annealing at high temperatures.39 The vacancies created in the selenium layers not only induce an increased lattice constant but also alter the atomic arrangement. This will lead to local deviations from the symmetry of the bulk material in the stacking fault areas.40 We expect that Fe3+ is generated in these areas, and the lowest energy distributions of the Fe2+ vacancies and Fe3+ ions favor the formation of clusters consisting of four octahedral vacancies

M(H ) = Ms(1 − aH −1 − bH −2) + cH

where M is the magnetization in a field of H, Ms is saturation magnetization, a is a constant that describes structural inhomogeneity within the sample, c is related to para-effect caused by the external field, and b is related to effective magnetic anisotropy (KE) by31

T (K)

the the the the

b = 4KE 2/15Ms 2 8223


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Figure 3. (a) Temperature dependence of the electrical resistivity of FeSe2−δ. The inset shows the plot in terms of a thermal activation model. ρ(T) fitted using the Mott (b) and ES VRH models (c). (d) Dependence of hopping distance and hopping energy on temperature in the ES VRH regime.

surrounding a tetrahedrally coordinated Fe3+.41 This corresponds to a 3c Fe7Se8 ferrimagnetic cluster, as illustrated in Figure S3. The weight percentage of Fe7Se8 is calculated to be 1.14% based on the saturation magnetization data at 5 K. This corresponds to a Se/Fe mole ratio of 1.98, very close to the data from TEM measurement, which is 1.95 according to the Energy Dispersive X-ray Spectroscopy (EDX). For comparison, we synthesized a stoichiometric FeSe2 sample by changing the ratio of FeCl2:Se from 1.8 to 2. The corresponding XRD pattern, shown in Figure S4(a), proves the high purity of the obtained sample. The magnetization versus applied field curve measured at 300 K shows typical paramagnetic behavior (Figure S4(b)). The temperature dependent magnetic susceptibility of the stoichiometric FeSe2 sample could be well fitted (Figure S4(c)) using the Curie−Weiss Law: χ = χm + C/(T−θ), where χm represents the Pauli paramagnetic contribution from conduction electrons, C is the Curie constant, and θ is the Weiss temperature. The difference in magnetic properties of the two samples provides further evidence that Se vacancies are responsible for the weak ferromagnetism in FeSe2−δ. 3.3. Electrical Transport Properties. Temperature dependent electrical transport was investigated using the fourprobe technique. As shown in Figure 3(a), the value of the resistivity decreases as the temperature is raised, indicating semiconductor behavior. This is not unexpected when we consider that marcasite FeSe2 is actually comprised of a deformed hexagonal close-packing of anions with each Fe atom coordinated by six Se atoms forming an octahedron. Only half of the octahedra are filled by metal atoms. An anion−anion bond is formed due to the approach of two opposite vertices of the empty octahedra, which is caused by the enlargement of the cation-occupied octahedra. Thus, it is expected that part of the marcasite phase should be nonmetallic.42 Semiconductor behavior has also been confirmed in other marcasite structures such as FeP2, OsP2, and OsAs2.42,43 However, in contradiction

with other reports, no Arrhenius behavior is observed in the measured temperature range in our FeSe2−δ sample (inset to Figure 3(a)).25 This means that thermal activation is not the mechanism that determines the electrical transport. An excellent linear relationship of ln(ρ) with T−1/4 is observed in the temperature range of 65−290 K. This is evidence for Mott VRH conductivity behavior. This behavior suggests the existence of localized states in the band gap and a finite density of states at the Fermi level (Figure 3(b)). The persistence of VRH up to 300 K indicates that hierarchical FeSe2−δ is a defect-rich system, similar to single-crystalline FeS2 nanostructures.38 It is worth noting that VRH conductivity is present in two different temperature intervals, the low temperature range between 70 and 120 K, and the high temperature range between 150 and 300 K, characterized by two different slopes. The characteristic temperatures TMott are determined to be 1.92(2) × 105 and 3.76(1) × 106 K for the low and high Mott VRH temperature range, respectively. The mean hopping distance and the average hopping energy between sites are given by Rhop,Mott = 3/8(TMott/T)1/4 and Δhopping = 3/8(TMott/T)1/4, respectively.13 The corresponding values are calculated and plotted in Figure S5. Both conditions, Rhop,Mott > ξ (localization length) and Δhopping > kBT, are fulfilled, proving that the VRH dominates the electron transport in the present system. We also note that the hopping distance decreases and the hopping energy increases with increasing temperature in both the low and high temperature Mott VRH regime. This indicates that disorder plays an important role in the Mott VRH temperature regime, consistent with the large number of vacancies and defects as indicated previously. It has been proved that the TMott here is related to the localization length as well as the density of states near the Fermi level according to TMott = 18/kBN(EF)ξ3. From the above fitting, the N(EF) is determined to be 4.8 × 1019 (eV· cm3)−1. As further evidence, we carried out DFT (density functional theory) calculations on both FeSe2 (Fe24Se48) and 8224


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Figure 4. (a) Total DOS (density of states) of both FeSe2 and FeSe1.92 in the marcasite structure as a function of energy. The dotted green curve stands for the total DOS of FeSe2 (Fe24Se48), and the solid black curve is for the total DOS of FeSe1.92 (Fe24Se46). The inset shows an enlarged view of the total DOS of FeSe1.92 (Fe24Se46) with energy very near to the Fermi energy. (b) The marcasite phase can be viewed as chains of Fe octahedra along the c-axis. (c) TEM image showing the existence of many stacking faults in the sample.

FeSe1.92 (Fe24Se46) with the marcasite structure. The total DOS (density of states) of FeSe2 (the dotted green curve) is shown in Figure 4(a); the region from −2.0 eV to −0.5 eV is characterized by hybridized Fe-3d and Se-4p orbitals. A band gap of 1.01 eV is obtained, which agrees excellently with the experimental value. 24 However, for Se-deficient FeSe 2 (FeSe1.92), where one vacancy is created by removing one Se−Se dimer in a supercell (Fe24Se46) with the marcasite structure, a clear band gap narrowing is observed with a value of 0.29 eV from the total DOS (the solid black curve), and localized states (resulting from the first and next-nearest neighboring Fe atoms to the vacancy) appear in the energy range from −0.4 to 0.6 eV, as shown in Figure 4a. In the energy range of 6 meV below the Fermi energy, the averaged total DOS is 3.1 × 1019 states (eV·cm3)−1 (equivalent to 3.8 × 10−2 states (eV·supercell)−1; details are shown in the inset of Figure 4a), which agrees well with our fitting result and provides firm evidence for the Mott VRH dominated transportation. At temperatures lower than 65 K, we find that the temperature dependence of the resistivity deviates from the Mott VRH model and that the behavior is governed by the ES VRH of carriers expressed by ρ(T) = A0 exp(TES/T)1/2, as shown in Figure 3(c). In 1, 2, and 3 dimensions, the characteristic temperature TES is given by TES = βe2/εξkB, where ε is the dielectric constant of the material, and β is a numerical constant of the order of unity (for 3D, β = 2.8).44,45 A localization length (ξ) of 2.84 nm can be obtained from the fitting results. The mean hopping distance and the average hopping energy between sites are given by Rhop,Mott = ξ/4(TES/T)1/2 and Δhopping = kBT/2(TES/T)1/2, all of these values being consistent with the criteria for the ES VRH theory to be applicable, as shown in Figure 3(d) (see Table 2). Apparently, the localization caused by the random potential distribution of impurities and defect states (individual or planar Se vacancies) is responsible for the VRH conduction

mechanism. The stacking faults (as illustrated in Figure 4(c)) and vacancies (Figure 2(d)) in the FeSe2−δ structure not only induce the formation of ferromagnetic nanoclusters but also the localization of charge carriers. In this case, the carriers hop beyond the nearest empty sites, over a longer distance to find a state with a lower energy difference, assisted by atomic displacement in the lattice (phonons), according to Schnakenberg’s theory.46,47 The calculated localization length (ξ) of 2.84 nm is assumed to be of the same order as the Bohr radii of FeSe2, which is almost eight times the hopping distance between nearest neighbor Fe ions (0.358 nm). However, it is much smaller than the crystal size, which is ∼54.2(5) nm according to the XRD data. Namely, the localization length is the characteristic length scale of the overlap of the wave functions between different hopping sites, and this does not need to be the same as the crystal.44 Another interesting point is the large hopping distance, 7.46 nm at 80 K and 6.39 nm at 290 K, which is also within the range of crystalline domain diameters of ∼6 nm. Such a long hopping distance at relatively high temperature is unexpected. Longer hopping distances of the order of micrometers have been previously reported but were only observed in two-dimensional electron gas systems at ultralow temperatures (generally below 0.5 K).48,49 We still lack a satisfactory explanation for this phenomenon. We consider that the present FeSe2−δ system has a larger percentage of grain boundaries compared with the 2D films, and we expect that the electrons are transported via tunneling across the interface of two adjacent grains, which would result in a large distance between the hopping sites. Here, two crossovers are observed. The first happens in the Mott VRH range where the two regimes cross in the temperature range between 120 and 160 K. The two regimes are characterized by different values of TMott. TMott is related to the localization length, and the value is a reflection of the probability for hopping.50 Previous research found that the change of TMott is associated with the disorder present in the system and could be attributed to the ferromagnetic (FM) transition and well-defined FM properties below the crossover temperature.51,52 The crossover temperature of 120 K reminds us of the existence of Fe7Se8 nanoclusters in Se-deficient areas of the FeSe2−δ system, where a spin rotation happens at this temperature. As supporting evidence, the electrical transport properties of pure 3c-Fe7Se8 were also measured and are shown in Figure S6. A metal−insulator transition is observed over a wide temperature range, and Mott VRH starts to dominate the transport at temperatures above 110 K (a detailed analysis on the pure Fe7Se8 phase will be given in a separate paper). A second

Table 2. Fitting Parameters for the Mott and ES VRH Models VRH model

T range

TMott/ES (K)

ξ (nm)

ES

20−65

915.0

2.84

Mott

65−120

1.92 × 105

2.84

Mott

160−300

3.76 × 105

2.84

Rhopping (nm) 3.92 @ 30 K 7.46 @ 80 K 7.02 @ 200 K

Δhopping (meV) 7.13(8) 12.06(4) 28.37(4)

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Figure 5. (a) Electrical resistivity and Seebeck coefficient of FeSe2−δ and 2% Y-doped samples. (b) The fitting of resistivity data at high temperature range with different models, thermally activated (TA), the Mott VRH model, and mix of TA + Mott VRH. (c) Power factors (PF) of pure FeSe2−δ and 2% Y-doped samples as a function of temperature.

3.4. Thermoelectric Performance. Finally, we evaluate the thermoelectric performance of the as-prepared FeSe2−δ hierarchical structures. The electrical resistivity data for pure FeSe2−δ is shown in Figure 5(a). The resistivity decreases from 129.8 mΩ·cm at 300 K to 6.94 mΩ·cm at 554 K, indicating semiconducting behavior. Two % Y doping reduces the resistivity of FeSe2−δ dramatically to 2.88 mΩ·cm at 554 K, nearly a factor 2.5 over the entire temperature range. This indicates a shift of the Fermi level toward the valence band as a result of an increasing carrier concentration. This is supported by the XRD data. Generally, one expects an increase in lattice constants for Y-doped FeSe2−δ because Y3+ has the larger ionic radius than Fe2+. However, our XRD refinements showed that the lattice constants for the Y-doped sample are a = 4.8027 (1) Å, b = 5.7779(8) Å, and c = 3.5757(1) Å, respectively. This smaller unit cell results in larger overlap and stronger interactions between the Fe(3d)-Se(4p) orbitals and decreases the electrical resistivity. In fact, some papers report that the carrier concentration can be increased by an order of magnitude by Y-doping.56 We modeled the high temperature resistivity data of Y doped marcasite between 350 and 554 K. Surprisingly, neither thermally activated behavior nor the Mott VRH model could give a satisfying fit, as shown in Figure 5(b). Thus, we suggest the presence of two components in the conductivity, as in the case of crystalline boron.57 More specifically, a p-type conductivity of holes in the valence band (σH) and an n-type conductivity of electron hopping in the localized conduction band (σe). The total conductivity can be expressed as σ = σH + σe. The full line in red shows the fit resulting from the above model, in excellent agreement with the experiments. This reminds us of the band structure calculations in Figure 4(a). Slight Se vacancies decrease the band gap from 1.0 to 0.29 eV for marcasite FeSe2−δ. On the one hand, it makes the localization weaker and results in easier hopping of electrons, which results in an increasing conductivity. On the other hand, it enables the coexistence of covalent bonds and metallic bonds in one sample. This indicates a high conductivity as that of a metal along with a good Seebeck coefficient as that of a semiconductor.58 The corresponding Seebeck coefficients S for undoped and doped FeSe2−δ are shown in Figure 5(a). The positive values at low temperatures indicate p-type defects. Values of 167 and −229 μV/K are observed at 300 and 554 K, respectively, for the undoped sample. The Seebeck coefficient for the doped sample is smaller than for the undoped one because of the increase in carrier concentration. Interestingly, the Seebeck coefficient changes sign from positive to negative with increasing temperature in both samples, suggesting that

crossover happens near 65 K, where ES-VRH starts to dominate the electrical transport at lower temperatures. In the VRH hopping theory, the Mott and ES hopping energy should be same at the crossover temperature, thus the exact crossover temperature can be written as Tcross = 16TES2/TM. The crossover temperature is determined to be 69 K from the fits, nearly the same as our experimental value. The small difference can be understood by considering that the crossover is a gradual process, rather than a sharp transition.16 In addition, in the ES VRH model, the width of the Coulomb gap is determined by the unperturbed DOS N(EF) in the form of ΔCG= e3√N(EF)/ε3/2. Combining the above eqs, it can be written as 0.9KB(TES3/TM)1/2 = 4.89 meV. For the crossover from ES-Mott type VRH, the criterion of ΔHopping > 2 ΔCG should be used. From Figure S5(a), one can see that at temperatures higher than 65 K, the criterion for Mott VRH conduction is fully satisfied, where the electrons will be affected by a smooth DOS despite the existence of the Coulomb gap. The arguments mentioned above prove the crossover between a Mott and an ES-type VRH transport mechanism in the present FeSe2−δ system. The same crossover has previously been reported occasionally but only for thin films.16,44,49 This is the first case for a polycrystalline sample, to the best of our knowledge. We assign this to the unique crystal structure of FeSe2−δ. As shown in Figure 4(b), the marcasite phase FeSe2 can be viewed as a stacking of one-dimensional FeSe2 chains along the ⟨001⟩ directions, where each Fe atom is coordinated by six Se atoms, to form an octahedron. The electrons are localized due to the strong disorder in our sample. At low temperatures, the resistivity is high, and the electron hops in the background of frozen charges as the surrounding charges cannot relax sufficiently. In this case, the Coulomb interactions between the hopping sites cannot be neglected. This results in the ES VRH transport of electrons between the FeSe2 chains.53 However, at higher temperatures, the charge around the hopping sites can relax and results in a larger density of states for small excitation energies. The Coulomb gap can be neglected, and the Mott VRH starts to dominate the electrical transport. We conclude that the spins are also localized, and antiferromagnetic ordering is expected. This is because the hopping electrons need extra kinetic energy to hop to the neighboring sites as a result of partial delocalization. Indeed, recent work by Kovnir et al. shows that FeSe2 chains, which can be stabilized in a new crystal structure of a mixed-valent compound, exhibit strong antiferromagnetic interactions within the chains.54 Similar 1D antiferromagnetic chains were also reported in marcasite CrSb2.55 8226


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prepared sample was explored using a combination of techniques. XRD measurement of the pellet sintered at 700 °C in vacuum indicated that the sample remained pure. No decomposition or oxidation reactions occurred during sintering (Figure S8(a)). The sample maintains the same structure after two cycles of thermoelectric measurements, as shown in Figure S8(b). More information can be obtained from thermogravimetric analysis (TGA). The sample is stable on heating to 570 K in argon and only exhibits a small weight loss that can be attributed to the desorption and evaporation of water. The first peak located at 659 K in the derivative curve of the TGA trace represents the evaporation of Se from the bulk FeSe2 and the transformation to Fe7Se8 with a weight loss of 66% at 822 K (Figure S8(c)). The excellent thermal stability is also confirmed by the fact that the power factor is maintained on cycling, as shown in Figure S8(d). Here we also note that the morphology of the FeSe2−δ changes a great deal after high temperature sintering in pellet form, as shown in Figure S7(e) and (f). This is unsurprising because 700 °C is high enough to induce further reaction to make the final product more homogeneous. This is a commonly used strategy in solid state synthesis. Thus, we show experimentally that the marcasite phase FeSe2 could be an excellent material for thermoelectric applications. Considering the natural abundance and low cost of the FeSe2 mineral, more investigations need to be done to optimize the conductivity, Seebeck coefficient, and thermal conductivity.

the electrons become the predominant charge carriers. Previous research shows that the sign changes to negative values when the temperature decreases below 81 K.25 This n-p-n switching of the semiconducting behavior just by a simple change of temperature is very unusual in a single compound and makes it a potential candidate for semiconductor switches or sensors.59 However, the reason for the sign change is still unclear. Xie et al. found a similar p-n-p switching in another metal chalcogenide, AgBeSe2.60 They attributed these reversals to the exchange of Ag and Bi atoms during the phase transition, which results in excellent thermoelectric performance. Obviously, this is not the case for our system. We notice that some recent publications have reported that the Seebeck coefficient can be controlled by choosing different doping elements and that the sign of S is sensitive to the doping level.61−63 Thus, our FeSe2−δ structure can be viewed as a system that is self-doped by selenium vacancies, since the holes in the selenium bands have an intrinsic origin (generally, Se vacancies are inevitable in the synthesis). With a suitable doping level, the Fermi surface of FeSe2−δ may contain an electron pocket and lead to Fermi surface reconstruction. A very small deficiency or change of doping level would change the sign and the temperature dependence of S. This would not occur for too high or too low doping levels.61 Hence, we studied the Sc-doped and Sc−Yb codoped systems, and the Seebeck coefficient data are shown in Figure S7. We can see that the sign changes at different temperatures: 440 K for the Sc−Yb codoped sample, 400 K for the pure sample, 380 K for the Y-doped sample, and 365 K for the Sc-doped sample. The value of S also changes significantly, from 3 μV/K for the Scdoped sample to 570.3 μV/K for the Sc−Yb doped sample, an increase of 2 orders of magnitude. Figure 5(c) shows the temperature dependence of the thermoelectric power factor (PF). The PF of both the doped and undoped samples is small and stable at low temperature. After the transition to an n-type semiconductor at ∼400 K, the PF increases continuously with temperature and reaches 11.7 mW/cmK2 at 554 K for the Y-doped sample, an improvement by a factor of ∼1.5 compared with the undoped sample. This is mainly attributed to the dramatic decrease of the resistivity in the Y-doped sample. Using the reported thermal conductivity of the marcasite phase or the pyrite phase of iron chalcogenides, ∼2 Wm−1 K−1,64,65 the thermoelectric figure of merit (ZT) values are estimated to be 0.32 and 0.23 for the doped and undoped samples at 545 K, respectively. This value is the same as that previously reported for the FeS2 pyrite phase at 700 K, but it can be further improved by nanostructure engineering according to the authors.66 The performance might be even better according to recent theoretical calculations, where it was found that the marcasite phase of FeSe2 has the lowest relaxation time among pyrite and marcasite phases of FeS2, FeSe2, and FeTe2.27 Obviously, the excellent performance for the marcasite based phases arises mainly from the low electrical conductivity at high temperatures, in the order of mΩ· cm even without doping. This good conductivity is the result of the narrowed band gap, which favors the hopping of charge carriers. As indicated by our DFT calculations (Figure 4(a)), the band gap can be controlled by the number of Se vacancies and is reduced to only 0.29 eV in this case. It might be possible to lower the band gap between the unoccupied conduction band and the partially filled valence band even further by metal doping.67 However, the dopant should be chosen carefully as shown in Figure S7. Finally, the thermal stability of the as-

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CONCLUSIONS We have synthesized 3D FeSe2−δ samples with the pure marcasite phase using a simple solvothermal method. Weak FM behavior is found as observed in previous literature reports, and we attribute this to the formation of ferromagnetic nanoclusters due to the inherent Se vacancies. Electrical transport measurement shows that VRH mechanisms dominate the electron transport over a very wide temperature regime. A crossover from Mott to ES VRH type transport is observed at 65 K, indicating the existence of a Coulomb gap in the density of states at the Fermi energy. Moreover, the resistivity and Seebeck coefficient can be easily controlled by doping; a 2% Yttrium doping results in an estimated thermoelectric figure of merit (ZT) values of 0.32 at 545 K. The mechanism behind the observed improvement in the thermoelectric performance is attributed to the unique conducting nature of marcasite FeSe2−δ with a suitable level of Se vacancies. The band gap can be decreased by introducing vacancies, which favor electron transport without influencing the Seebeck coefficient significantly. This mechanism provides an efficient way to improve the thermoelectric performance through a combination of doping and defect structures.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.5b03562. Calculations of band structures, TEM and SAED images of the sample, magnetization versus H−1 for FeSe2 at 5 and 300 K, FC magnetization for 3c Fe7Se8, view of part of the 3c Fe7Se8 unit cell, temperature dependence of hopping energy and hopping distance in the temperature ranges 65−120 K and 155−295 K, change of resistivity as a function of temperature for 3c Fe7Se8, dominance of 8227


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Mott VRH for transport in the temperature range 81− 176 K, measured Seebeck coefficients for 2% Sc, Y, and Sc−Yb doped FeSe2−δ, and thermal stability of the marcasite phase in thermoelectric application (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This work is funded by The Netherlands Organization for Scientific Research (NWO-CW: 712.011.003). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Jacob Baas for technical support and also thank Anil Kumar and Laaya Shaabani for assistance with high temperature thermoelectric characterization.

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REFERENCES

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