Thermally-Activated Electron Exchange In Cu12-xFe

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Thermally-Activated Electron Exchange In Cu FeSbS (x = 1.3, 1.5) Tetrahedrites: A Mössbauer Study

Alexey V Sobolev, Igor A. Presniakov, Daria I. Nasonova, Valeriy Yu Verchenko, and Andrei V. Shevelkov J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12779 • Publication Date (Web): 10 Feb 2017 Downloaded from http://pubs.acs.org on February 14, 2017

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The Journal of Physical Chemistry

THERMALLY-ACTIVATED ELECTRON EXCHANGE in Cu12-xFexSb4S13 (x = 1.3, 1.5) TETRAHEDRITES: a MÖSSBAUER STUDY

Alexey V Sobolev*, Igor. A Presniakov, Daria I Nasonova, Valeriy Yu Verchenko, and Andrei V Shevelkov Department of Chemistry, Lomonosov Moscow State University, 119991 Moscow, Russia

* corresponding author, e-mail: [email protected]

Abstract Mixed-valence iron Fe(III/II) tetrahedrites Cu10.7Fe1.3Sb4S13 and Cu10.5Fe1.5Sb4S13 have been prepared, characterized, and studied by Mössbauer spectroscopy. The low-temperature Mössbauer spectra (T ≤ 13 K) of all samples confirm the valence-localized nature of the ground state for the distinct Fe2+ and Fe3+ sites. At elevated temperatures the spectral transformations are characterized by a coexistence of valence-localized states Fe3+/Fe2+ (iron surrounded only by copper ions in the second coordination sphere) and valence-averaged spectral components corresponding to the electron hopping (FeA2+ FeB3+) ↔ (FeA3+ FeB2+). Our experiments suggest that these tetrahedrites belong to Robin-Day Class II mixed-valence systems that display thermally activated charge transfer. Hopping frequencies (Ωhop) have been determined from spectral simulations using the stochastic line shape theory. Analysis of the (T) temperature dependences reveals the existence of thermally activated process between (quasi) degenerate iron sites. The activation energies for Cu10.7Fe1.3Sb4S13 (EA ≈ 5.3 meV) and Cu10.5Fe1.5Sb4S13 (EA ≈ 6.6 meV) differ and suggest an important influence of the local crystal surrounding of iron ions on electron hopping. The isomer shift and quadrupole splitting values for the Fe3+ sites reveal a relatively strong and nonmonotonic change with temperature that suggests the occurrence of intrinsic charge delocalization in addition to the intersite electron hopping.

Introduction Synthetic tetrahedrites are a family of compounds structurally related to natural tetrahedrite that has a basic formula Cu12Sb4S13. This mineral had been investigated by mineralogists and crystal chemists for decades1-4 until year 2013 when its outstanding ACS Paragon Plus1Environment


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thermoelectric properties were reported for synthetic tetrahedrites of a general formula Cu12xMxSb4S13,

where M = Mn, Fe, Co, Ni, or Zn5,6. Since then an extensive research of

tetrahedrites as potential thermoelectric materials has bloomed and resulted in reaching high values of the thermoelectric figure-of-merit, ZT > 17,8. Although many aspects of chemistry and physics of tetrahedrites were already summarized in a review, the origin of high thermoelectric performance is still a matter of debate9. In particular, it was shown that the transport of charge carriers depends on spin polarization and that d-orbitals of a doping metal form the states inside the band gap for minority spins but not for majority ones, leading to different positions of Eg for different spin channels10. To this end, iron behaves differently compared to all other substituting M atoms. Whereas other d-metals form M2+ cations, iron is known to exist in tetrahedrites in both Fe2+ and Fe3+ states depending on iron concentration3,4,11. Recently we have shown that for low concentration of iron only Fe3+ cations are present but for higher iron concentration the electron hopping between Fe3+ and Fe2+ cations takes place at room temperature but freezes out at 77 K11. However, our experiments were carried out over a limited temperature range and no detailed interpretation of the resulting spectral changes was advanced11. Mössbauer spectroscopy is sensitive to dynamics on time scales comparable to the precession time (τQ) of the 57Fe nucleus in electric field gradient (EFG) to which it is exposed. If the time scale of the electron hopping (τhop) is much longer than τQ, then two static patterns (Fe3+ and Fe2+), one corresponding to each of the two environments are observed. At the other extreme, where τhop is much shorter than τQ, the

57

Fe nucleus experiences an averaged

environment and a single "motion-narrowed" component is observed in the spectrum. For an intermediate relaxation time, the spectra are more complex, showing broadened lines and greatly modified spectral line shapes12. Quantitative information on dynamics can only be obtained within this window. Relaxation rates increase with temperature, and this temperature dependence can be used to determine the activation energy for the relaxation process. In this paper we present a detailed

57

Fe Mössbauer study of the electron exchange in iron-bearing

tetrahedrites Cu12-xFexSb4S13 with x = 1.3 and 1.5. The temperature dependence of the Mössbauer spectra of these compounds, which we report here, provides a unique opportunity to obtain information on the energetics and dynamics of electron transfer in mixed valence systems. In particular, we show that there exists temperature-induced crossover from localization of Fe2+ and Fe3+ states to thermally activated delocalization of the charge due to two-center electron hopping.

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Experimental Starting materials and synthesis. All syntheses were performed using metallic iron enriched in

57

Fe isotope to enhance the Mössbauer spectra accumulation rate. Other starting

materials were CuO (99.9%), Sb (pieces, 99.999%), and S (powder, 99.9%). Copper was obtained by heating CuO under hydrogen flow and sulfur was purified by vacuum-melting as described elsewhere11. The purity of all reagents was controlled by powder X-ray diffraction. Cu10.7Fe1.3Sb4S13 and Cu10.5Fe1.5Sb4S13 samples were prepared by a standard ampule technique. Stoichiometric mixtures of starting materials were sealed in evacuated quartz ampules under vacuum, 2 × 10-2 Torr, and put into a furnace. The ampules were heated to 973 K, annealed at this temperature for 3 h, slowly cooled down to 823 K in 30 h, and finally cooled down to room temperature in a switched-off furnace. The reaction products were finely ground in an agate mortar and pressed into pellets at a pressure of 80-100 bar at room temperature. These pellets were sealed in evacuated quartz ampoules and annealed at 773 K for 25 h, followed by switching off the furnace and cooling down to room temperature5. The resulting samples were finely ground and used for further investigations. X-ray Powder Diffraction and Energy-Dispersive X-ray Spectroscopy. The phase composition and crystal structure were investigated by the standard X-ray technique using a BRUKER D8 Advance diffractometer, Cu Kα radiation. For the phase composition analysis, the program package STOE WinXPOW was used. The crystal structure refinement was performed using the Rietveld method implemented in JANA 2006 software13. Elemental composition was determined using a JSM JEOL scanning electron microscope operated at 30 kV and equipped with an EDX detection system INCA x-Sight. Elemental Fe and Sb as well as FeS2 compound, provided by MAC Analytical Standards, were used as external standards. For the determination of elemental composition of each sample, the data were collected for 10 points and then averaged. Distribution of elements across the sample was investigated by mapping. Mössbauer spectroscopy.

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Fe Mössbauer spectra for both compounds were recorded

in the temperature range of 13 – 300 K in closed-cycled SHI-850-1 JANIS RESEARCH Co. cryostat using a conventional constant-acceleration spectrometer MS-1104Em in the transmission geometry with the "sawtooth" shape of the drive and registration in 2048 channels with further presentation in 512 channels by folding and summation of neighbor channels. A radiation source

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Co(Rh) was kept at room temperature. All isomer shifts are

referred to α-Fe at 298 K. Experimental spectra were processed and analyzed using methods of spectral simulations implemented in the SpectrRelax program14.



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Results and discussion Phase composition and crystal structure refinement. Phase composition and crystal structure of two obtained samples with the Cu10.7Fe1.3Sb4S13 and Cu10.5Fe1.5Sb4S13 nominal compositions were investigated by powder X-ray diffraction and EDX spectroscopy. According to Rietveld refinement of the room temperature powder diffraction data tetrahedrite was the main phase in both samples. Minor quantities of the tetragonal (I–42d) CuFeS2 secondary phase were detected for both samples. Its content was refined as 1.8(1) mass.% in the case of the Cu10.5Fe1.5Sb4S13 sample but was too low to be correctly evaluated for the Cu10.7Fe1.3Sb4S13 sample (Figure 1). EDX analysis (Figure 2) shows that the experimental composition of the main phase agrees well with the nominal composition; the iron content, in at.%, was found to be 4.4(1) and 5.1(4)% whereas the calculated values are 4.5 and 5.2% for Cu10.7Fe1.3Sb4S13 and Cu10.5Fe1.5Sb4S13, respectively. However, small inclusions of the CuFeS2 secondary phase are clearly seen on the mapping images of selected portions of the samples, confirming the results of the X-ray diffraction study. The crystal structure of the main phase in both samples was successfully refined to low residuals using the initial model for Cu12Sb4S13, unsubstituted tetrahedrite reported previously1. According to this model, five independent positions, Cu(1) in 12d, Cu(2) in 24g, Sb(1) in 8c, S(1) in 24g and S(2) in 2a, are present in the cubic unit cell, space group I–43m, the Cu(2) site being 50% occupied (Figure 3). It is known from the literature that Fe partially substitutes copper only in the Cu(1) position that has a tetrahedral environment of four sulfur atoms11,15. Therefore, this position was set as mixed occupied by Fe and Cu in accordance with the initial composition of the sample. The Fe/Cu ratio was fixed and the obtained model was refined in an isotropic approximation. The summary of the data collection and refinement parameters for the crystal structures of Cu10.7Fe1.3Sb4S13 and Cu10.5Fe1.5Sb4S13 is given in Table 1 and the atomic parameters are listed in Table 2.

Mössbauer spectroscopy The 57Fe Mössbauer spectra of Cu10.5Fe1.5Sb4S13 and Cu10.7Fe1.3Sb4S13 samples recorded at the lowest temperature T = 13 K are shown in Figure 4. Both spectra can be described as a superposition of two Fe1 and Fe2 quadrupole doublets and magnetic Zeeman sextet Fe3 with hyperfine parameters (Table 3) corresponding to the impurity CuFeS2 phase16. The partial contributions (I) of the Zeeman sextets are in agreement with XRD data. In what follows, for clarity of presentation, the partial Zeeman components are subtracted from the experimental spectra. ACS Paragon Plus4Environment

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The quadrupole doublets Fe1 and Fe2 (Figure 4) are characterized by different values of isomer shifts (δ) and quadrupole splitting (∆) (Table 3) thus underlining that the iron ions are stabilized in two valence states. For both samples, the Fe1 subspectrum is characterized by the δ1 ≈ 0.44 mm/s and ∆1 ≈ 0.33 mm/s values that correspond to the high-spin Fe3+ ions in the slightly distorted tetrahedral sulfur environment16. The second quadrupole doublet Fe2 has noticeably larger values of δ2 ≈ 0.74 mm/s and ∆2 ≈ 2.99 mm/s (Table 3) corresponding to the Fe2+ ions in sulfides16. The relative intensities, I1/I2 ≈ [Fe3+]/[Fe2+], of the Fe1 and Fe2 subspectra are in good agreement with compositions Cu10.57(Fe2+)0.86(Fe3+)0.57Sb4S13, I1/I2 = 0.66(4) and Cu10.75(Fe2+)0.50(Fe3+)0.76Sb4S13, I1/I2 = 1.53(3), that have been determined taking into account the content of the impurity CuFeS2 phase (Table 3). Both Fe1 and Fe2 doublets are broadened with linewidth at half height (W ≈ 0.36 mm/s), which can be connected with the disordered distribution of Cu+ and iron (Fe3+ and Fe2+) ions within tetrahedrites structures. Assuming a normal distribution, we evaluated the relative probability p(m,n) ∝ (m + n)/m!n! of the local configurations {mCu+, nFe3+/2+} in the nearest local surrounding of the iron ions (Fe3+/Fe2+) (Figure 5). Each of these configurations will induce a small variation in the local surrounding (bond length or valence angles) of iron ions thus giving the observed distribution of hyperfine parameters. As temperature increases, drastic changes in experimental spectra are observed (Figure 6), despite the fact that no phase transition occurs in Fe-substituted tetrahedrites in contrast with the parent ternary compound17. The lines of the both Fe1 and Fe2 doublets are much broadened and the line broadening increases with increasing temperature, demonstrating relax-like behavior. This can be related to the electronic exchange between neighboring Fe3+ and Fe2+ ions in tetrahedra (FeS4) connected by common corners18. Therefore, both isomer shift and quadrupole interactions fluctuate simultaneously between the characteristic values for Fe3+ and Fe2+ ions [16]. Based on our earlier study11, we used a stochastic Tjon and Blume model to analyze such spectra19. We assume two-level relaxation processes between (FeA2+FeB3+)1 ↔ (FeA3+-FeB2+)2 nuclear energy levels with the relaxation time τ = (Ωhop)–1 given by τ = (τ12τ21)/(τ12 + τ21), where τ12 and τ21 stand for the relaxation times for (...)1 to (...)2 and for (...)2 to (...)1 states, respectively. The probability for the (FeA2+-FeB3+)1 state is given by n1 = τ/τ21, and the ratio of probabilities n1/n2 is roughly equal to [Fe2+]/[Fe3+] value depending on the tetrahedrites composition. This one-electron exchange process is schematically represented in Figure 7. According to Robin and Day model20, three classes of systems may be distinguished based on the magnitude of the electronic coupling ("mixing") of the "acceptor" (Fe3+) and "donor" (Fe2+) sites. The amount of such "mixing" is defined by the resonance integral H12 ACS Paragon Plus5Environment


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which is basically determined by the square of an overlap integral between neighboring iron ions and relative energies of iron states involved in the exchange. In Class I systems the coupling is very weak (i.e., the adiabatic energy curves are very close to the diabatic curves, see dashed lines in Figure 7) and activated electron transfer either does not occur at all or occurs only very slowly. For Class II systems, the resonance integral falls in the range of 0 < H12 ≤ 1/2E0, where E0 is optical absorption energy. Such systems are described by a doublewell potential (DWP). Vibronic trapping forces in combination with elastic forces give rise to the

DWP

with

minima

(±Q0)

corresponding

to

the

valence-localized

(FeA2+ -

FeB3+)1 and (FeA3+ - FeB2+)2 states (Figure 7). The activation energy EA separating the potential minima determines the frequency (Ωhop) of thermally activated electron hopping between them. The EA barrier diminishes when the resonance integral H12 is enhanced (H12 → 1/2E0) and vanishes in the Class III regime where electron delocalization is complete. Based on the relative probability p(m,n) of the local configurations {mCu+, nFe3+/2+} in the nearest local surrounding of the iron ions (Figure 5) we described the spectra in the whole temperature range using a “discrete model”, i.e., as a superposition of six quadrupole patterns corresponding to iron cations in the different local environments. Taking into account that the hyperfine fluctuations due to the electronic hopping between Fe3+ and Fe2+ sites occur at a time scale 107 - 108 s-1 (Class II, see Fig. 7) this makes necessary the data evaluation for the four local configurations {mCu+, nFe3+/2+} with m + n = 4 (where 0 ≤ m ≤ 3, 1 ≤ n ≤ 4) using the above two-level relaxation model. It should be noted that the Cu+/2+ ions cannot be involved into the fast electron transfer processes with Fe2+/3+ ions due to a very high difference in the energy levels εCu(I/II) 2σ(I))

0.0315/0.0272

0.0701/0.0579

GoF

1.29

1.50

V, Ǻ

3

Table 2. Atomic parameters in the crystal structure of Cu10.5Fe1.5Sb4S13 and Cu10.7Fe1.3Sb4S13 at room temperature. The Cu(2) position is half-occupied. The occupancy of the Cu(1)/Fe(1) position is fixed and corresponds to the Cu/Fe ratio in the nominal composition of the respective sample. Atom

Cu10.5Fe1.5Sb4S13

Wyckoff

Cu10.7Fe1.3Sb4S13

position

g

Sb(1)

8c

1

Cu(1)

12d

0.875

1/4

Fe(1)

12d

0.125*

1/4

Cu(2)

24g

0.5

0.0199(4) x 0.7833(5) 0.027(2)

S(1)

24g

1

0.3862(4) x 0.8648(5)0.0157(1)

S(2)

2a

1

y

z

Ueq, Ǻ2

g

0.2315(1) x

–x

0.028(7)

1

1/2

0

0.032(2) 0.892

1/4

1/2

0

0.032(2) 0.108*

1/4

x

0

0

0

0.019(5)

y

z

Ueq, Ǻ2

0.2311(2) x

–x

0.042(1)

1/2

0

0.046(3)

1/2

0

0.046(3)

x

0.5 0.0205(8) x 0.7836(8)0.053(4) 1 1

0.3812(6) x 0.8611(8)0.029(2) 0

0

0

* The Fe/Cu ratio was fixed in accordance with the initial composition of the samples.


0.05(1)

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Table 3. Hyperfine parameters of the

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Fe Mössbauer spectra of Cu12-xFexSb4S13

tetrahedrites at 13K. Sample

Cu10.5Fe1.5Sb4S13

Cu10.7Fe1.3Sb4S13

Sites

δ (mm/s)

ε* (mm/s)

Hhf (kOe)

W (mm/s)

A (%)

Fe1

0.45(1)

0.159(1)

-

0.35(1)

35.0(4)

Fe2

0.73(1)

1.508(1)

-

0.35(1)

53.3(4)

CuFeS2

0.36(1)

-0.01(1)

371.2(4)

0.29(2)

11.7(6)

Fe1

0.45(1)

0.175(1)

-

0.32(1)

53.8(3)

Fe2

0.74(2)

1.486(2)

-

0.32(1)

35.2(3)

CuFeS2

0.37(1)

0.00(1)

370.4(7)

0.32(1)

11.0(5)

δ is an isomer shift for 57Fe related to α-Fe at room temperature; *ε is a half of the absolute values of quadrupole splitting (∆) for paramagnetic subspectra; Hhf is hyperfine field at nuclei; W is a half-width of resonant lines; A is relative subspectra areas.


57

Fe


TOC Graphic

Fe2

Fe1

100

Absorption (%)

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eeCu10.5Fe1.5Sb4S13

-2

0 v (mm/s)

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Thermally-Activated Electron Exchange In Cu12-xFe

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