Temperature effect on redox voltage in Li_xCo[Fe(CN)₆]_y

Thermoelectric (TE) device, which can convert heat into electricity and vice versa, is a fascinating technology for smart society. In development of TE semiconductors, Seebeck coefficient [$S\equiv \frac{\mathrm{\Delta }V}{\mathrm{\Delta }T}$; $\mathrm{\Delta }V$ ($\mathrm{\Delta }T$) is the voltage (temperature) difference between the hot and cold electrodes] is a significant material parameter. Bi₂Te₃ (S = 0.2 mV/K¹1. D. A. Wright, Nature 181, 834 (1958). https://doi.org/10.1038/181834a0 at room temperature) and PbTe ( = 0.12 mV/K²2. J. P. Heremans, V. Jovovic, E. S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, and G. J. Snyder, Science 321, 554 (2008). https://doi.org/10.1126/science.1159725 at 300 K) are prototypical TE semiconductors and exhibit high dimensionless figure-of-merit ($ZT\equiv \frac{S^2}{\rho \kappa }T$: where T, ρ, and κ represent temperature, resistivity, and thermal conductivity, respectively). Actually, they are in practical use for the Peltier cooling and power generation of space vehicles.³3. H. J. Goldsmid, Introduction to Thermoelectricity (Springer-Verlag, Berlin, 2010). These materials, however, are expensive and include toxic and rare elements. In addition, these TE devices require high-grade heat source of several hundreds Kelvin to achieve 10 % -15 % of the Carnot efficiency.⁴4. C. B. Vining, Nat. Mater. 8, 83 (2009). https://doi.org/10.1038/nmat2361

Recently, Kobayashi et al.⁵5. W. Kobayashi, A. Kinoshita, and Y. Moritomo, Appl. Phys. Lett. 107, 073906 (2015). https://doi.org/10.1063/1.4928336 proposed a battery-type thermocell, whose configuration is the same as that of a lithium-ion/sodium-ion secondary batteries (LIBs/SIBs) with the exception that the anode and cathode are the same. Contrary to the conventional TE devices made by semiconductors, the battery-type thermocell converts heat into electricity through the electrochemical TE coefficient ($S_{\text{EC}}\equiv \frac{\partial V}{\partial T}$; V and T are the redox potential and temperature, respectively). The battery-type thermocell is low-cost and easy to fabricate, because the production processes of material and device are similar to those of LIBs. There already exists a long list of electrochemical TE effects in soluble ions/molecules,⁶6. I. Quickenden and Y. Mua, J. Electrochem. Soc. 142, 3985 (1995). https://doi.org/10.1149/1.2048446 e.g., [Fe(CN)₆]³⁻/[Fe(CN)₆]⁴⁻, (S_EC = 1.5 mV/K), Fe³⁺/Fe²⁺ ( = 0.8 mV/K), and Cu²⁺/Cu ( = 0.9 mV/K). We emphasize that the battery-type thermocell extends the usage of the electrochemical TE materials from soluble ions/molecules to insoluble solids used in LIBs/SIBs. Actually, Kobayashi et al.⁵5. W. Kobayashi, A. Kinoshita, and Y. Moritomo, Appl. Phys. Lett. 107, 073906 (2015). https://doi.org/10.1063/1.4928336 fabricated CR2032-type thermocell made by layered oxides, e.g., Na_0.99CoO₂ and Na_0.52MnO₂, and observed TE behavior between the anode and cathode.

Transition metal hexacyanoferrates (M-HCF), Li${}_{x}M$[Fe(CN)₆]_y (M is transition metal), are alternative candidates of the TE materials for the battery-type thermocell, because they show good electrochemical properties in LIBs/SIBs.^7–177. T. Matsuda and Y. Moritomo, Appl. Phys. Express 4, 047101 (2011). https://doi.org/10.1143/apex.4.0471018. Y. Moritomo, M. Takachi, Y. Kurihara, and T. Matsuda, Appl. Phys. Express 5, 041801 (2012). https://doi.org/10.1143/apex.5.0418019. M. Takachi, T. Matsuda, and Y. Moritomo, Jpn. J. Appl. Phys. 52, 044301 (2013). https://doi.org/10.7567/jjap.52.04430110. T. Matsuda, M. Takachi, and Y. Moritomo, Chem. Commun. 49, 2750 (2013). https://doi.org/10.1039/c3cc38839e11. Y. Lu, L. Wang, J. Cheng, and J. B. Goodenough, Chem. Commun. 48, 6544 (2012). https://doi.org/10.1039/c2cc31777j12. M. Takachi, T. Matsuda, and Y. Moritomo, Appl. Phys. Express 6, 025802 (2013). https://doi.org/10.7567/apex.6.02580213. D. Yang, J. Xu, X. Z. Liao, Y. S. He, H. Liu, and Z. F. Ma, Chem. Commum. 50, 50 (2014).14. H. W. Lee, R. Y. Wang, M. Pasta, S. W. Lee, N. Liu, and Y. Chi, Nat. Commun. 5, 5280 (2014). https://doi.org/10.1038/ncomms628015. L. Wang, J. Song, R. Qiao, L. A. Wray, M. A. Hossain, Y. D. Chung, W. Yang, Y. Lu, D. Evans, J.-J. Lee, S. Vail, X. Ahao, M. Nishijima, S. Kakimoto, and J. B. Torrance, J. Am. Chem. Soc. 137, 2548 (2015). https://doi.org/10.1021/ja510347s16. S. Yu, Y. Li, Y. Lu, B. Xu, Q. Wang, M. Yan, and Y. A. Jing, J. Power Sources 275, 45 (2015). https://doi.org/10.1016/j.jpowsour.2014.10.19617. Y. You, X. L. Wu, Y. X. Yin, and Y. G. Guo, Energy Environ. Sci. 7, 1643 (2014). https://doi.org/10.1039/c3ee44004d For example, thin film of Li_1.6Co[Fe(CN)₆]_0.92.9H₂O show high capacity of 132 mAh/g with good cyclability.⁹9. M. Takachi, T. Matsuda, and Y. Moritomo, Jpn. J. Appl. Phys. 52, 044301 (2013). https://doi.org/10.7567/jjap.52.044301 M-HCFs have face-centered cubic structure ($Fm\underset{¯}{3}m$: Z = 4). They consist of three-dimensional (3D) jungle-gym-type host framework and guest Li⁺, which is accommodated in cubic nanopores of the framework. Importantly, the host framework, - Fe - CN - M - NC - Fe -, is robust against the Li⁺ intercalation/deintercalation and concomitant reduction/oxidization of M and Fe. Actually, the host framework of Li_1.6Co[Fe(CN)₆]_0.92.9H₂O is stable even if we remove whole Li⁺ from the framework.⁹9. M. Takachi, T. Matsuda, and Y. Moritomo, Jpn. J. Appl. Phys. 52, 044301 (2013). https://doi.org/10.7567/jjap.52.044301

In this letter, we systematically investigated the TE properties of Co-HCF, Li_xCo[Fe(CN)₆]_y, against the Li concentration (x). |S_EC| is higher than the Seebeck coefficient (= 0.2 mV/K at room temperature) of Bi₂Te₃ and distributes from 0.2 to 0.8 mV/K. We further observed a sign reversal behavior of S_EC and qualitatively explained in terms of the ionic model, which include the electrostatic energy and volume expansion effect. Our observation suggests that S_EC in solid is mainly governed by the electrostatic energy.

Thin films of Li_xNa_0.13Co[Fe(CN)₆]_0.71 (denoted as LCF71) and Li_xCo[Fe(CN)₆]_0.9 (LCF90) were synthesized by electrochemical deposition and following electrochemical ion exchange. First, thin films of Na_0.84Co[Fe(CN)₆]_0.713.6H₂O (NCF71) and Na_1.6Co[Fe(CN)₆]_0.902.9H₂O (NCF90) were electrochemically synthesized on an indium tin oxide (ITO) transparent electrode. Details of the synthesis conditions are described in literature.^18,1918. F. Nakada, H. Kamioka, Y. Moritomo, J. E. Kim, and M. Takata, Phys. Rev. B 77, 224436 (2008). https://doi.org/10.1103/physrevb.77.22443619. K. Igarashi, F. Nakada, and Y. Moritomo, Phys. Rev. B 78, 235106 (2008). https://doi.org/10.1103/physrevb.78.235106 Both the compounds shows face-centered cubic structure ($Fm\underset{¯}{3}m$: Z = 4) with lattice constant (a) of 10.3 Å (NCF71) and 10.4 Å (NCF90). The film thickness was 1.5 μm, which was determined by a profilometer (aep Technology NanoMap-LS). The ion exchange procedure was done in an Ar-filled glove box using a beaker-type cell. The cathode, anode, and electrolyte were the thin film, Li metal, and ethylene carbonate (EC)/diethyl carbonate (DEC) solution containing 1 mol/L LiClO₄, respectively. The charge/discharge rate was ≈ 1 C. The cut-off voltage was from 2.0 to 4.2 V. First, Na⁺ is removed in the charge process. Then, Li⁺ is inserted in the discharge process.

The electrochemical measurements were carried out with a potentiostat (HokutoDENKO HJ1001SD8) in an Ar-filled glove box using a beaker-type cell. The cathode, anode, and electrolyte were the thin film, Li metal, and EC/DEC containing 1 mol/L LiClO₄, respectively. The charge/discharge rate was ≈ 1 C. The cut-off voltage was from 2.0 to 4.2 V. The mass of each film was evaluated from thickness, area, and ideal density. x in LCF71 (LCF90) was evaluated from the total current under the assumption that x = 0.84 (1.6) is in the discharged state and 0.13 (0.0) is in the charged state.

Figure 1 shows prototypical example of the discharge curve of the LCF71 [(a)] and LCF90 [(b)] films. In LCF71 [Fig. 1(a)], the discharge capacity is 78 mAh/g, which is close to the ideal value (= 72 mAh/g). The curve shows a single plateau (plateau I) at ≈ 3.4 V, which is ascribed to the reduction reaction:⁸8. Y. Moritomo, M. Takachi, Y. Kurihara, and T. Matsuda, Appl. Phys. Express 5, 041801 (2012). https://doi.org/10.1143/apex.5.041801 Na_0.13Co²⁺[${\text{Fe}}_{0.71}^{3+}$${\text{Fe}}_2^{+0.29}$(CN)₆]_0.71 + 0.71Li⁺ → Li_0.71Na_0.13Co²⁺[Fe²⁺(CN)₆]_0.71. In the discharge process, Li⁺ is inserted into the framework, which causes the reduction of Fe³⁺ to keep the charge neutrality. In LCF90 [Fig. 1(b)], the discharge capacity is 139 mAh/g, which is close to the ideal value (= 132 mAh/g). The curve shows two plateaus (plateaus II and III) at ≈ 4.0 and ≈ 3.2 V. Plateau II ($x\le$ 0.6) at ≈ 4.0 V is ascribed to the reaction:⁹9. M. Takachi, T. Matsuda, and Y. Moritomo, Jpn. J. Appl. Phys. 52, 044301 (2013). https://doi.org/10.7567/jjap.52.044301 Co³⁺[${\text{Fe}}_3^{+0.6}$ ${\text{Fe}}_2^{+0.4}$(CN)₆]_0.9 + 0.6Li⁺ → Li_0.6Co³⁺[Fe²⁺(CN)₆]_0.9. Plateau III ($x\ge$ 0.6) at ≈ 4.0 V is ascribed to the reaction:^8,208. Y. Moritomo, M. Takachi, Y. Kurihara, and T. Matsuda, Appl. Phys. Express 5, 041801 (2012). https://doi.org/10.1143/apex.5.04180120. M. Takachi and Y. Moritomo, Sci. Rep. 7, 42694 (2017). https://doi.org/10.1038/srep42694 Li_0.6Co³⁺[Fe²⁺(CN)₆]_0.9 + Li⁺ → Li_1.6Co²⁺[Fe²⁺(CN)₆]_0.9. The redox potential (V) for Fe³⁺/Fe²⁺ is much higher in LCF90 (≈ 4.0 V; plateau II) than in LCF71 (≈ 3.4 V; plateau I). The high-V is ascribed to the volume effect:⁹9. M. Takachi, T. Matsuda, and Y. Moritomo, Jpn. J. Appl. Phys. 52, 044301 (2013). https://doi.org/10.7567/jjap.52.044301 a (≈ 9.9 Å at $x\le$ 1) of LCF90 is much smaller than a (≈ 10.2 - 10.3 Å) of LCF71.⁸8. Y. Moritomo, M. Takachi, Y. Kurihara, and T. Matsuda, Appl. Phys. Express 5, 041801 (2012). https://doi.org/10.1143/apex.5.041801

Next, we carefully measured V against the temperature (T) of the electrolyte of the battery cell. T was monitored with a platinum resistance thermometer. In order to stabilize the respective x state, T-dependent measurement was performed after the waiting time of 10 minutes. We continuously sweep the electrolyte temperature at a slow rate of ≈ 0.01 K/s. In order to minimize the temperature gradient within the cell, temperature range is set to be narrower than 7 K. Actually, $\mathrm{\Delta }V$ [≡ V(T_max)-V(T_min), where T_max and T_min is the maximum and minimum temperature, respectively], slightly changes with time (≤ 1 mV) but approaches to a finite value. So, $\mathrm{\Delta }V$ cannot be ascribed to the temperature gradient effect within the cell. The measurements was performed at every five second. Figures 2 show temperature effect on V in LCF71. Red and blue marks represent data obtained in the heating and cooling runs, respectively. We evaluated S_EC in the respective runs by least-squares fittings, as indicated by solid straight lines. Precisely speaking, we measured the temperature dependence of the difference in the potential between anode (Li) and cathode. With assuming that S_EC of the anode (Li) is zero, we obtained S_EC of the cathode. We observed slight drift of V, probably due to leak current in the battery cell, between the heating and cooling runs. At x =0.16 [Fig. 2(a)], S_EC is negative for both the heating (S_EC = - 0.36 mV/K) and cooling (= - 0.31 mV/K) runs. Similar negative S_EC is observed at x = 0.25, 0.41, and 0.49[(b) - (d)]. Thus, we observed negative S_EC in plateau I. Figures 3 show temperature effect on V in LCF90. In plateau II ($x\le$ 0.6) region, S_EC is negative as exemplified at x = 0.21 [Fig. 3(a)]. On the other hand, in plateau III ($x\ge$ 0.6) region, S_EC is positive as exemplified at x = 0.74, 0.85, and 0.96 [(b) - (d)].

We plotted in Figs. 4 the average S_EC between the heating and cooling runs against x. S_EC is negative in plateaus I and II and positive in plateau III. We note that the redox site is Fe in plateaus I and II and Co in plateau III. Thus, we observed a sign reversal behavior of S_EC among the plateaus. In addition, |S_EC| distributes from 0.2 mV/K to 0.8 mV/K, which are higher than the Seebeck coefficient (= 0.2 mV/K¹ at room temperature) of Bi₂Te₃.

Let us discuss the x-dependence of S_EC in terms of a statistical thermodynamic model. In a mean-field approximation, ionic potential [ϕ(x)] is easily calculated from the number of the Li⁺ configurations against x,

$$\varphi (x)={\varphi }_{\text{0}}+k_{\text{B}}T\text{ln}(\frac{x}{2-x}),$$

(1)

where ${\varphi }_{\text{0}}$ and k_B represent the site potential and the Boltzmann constant, respectively. Here, we note that number of the crystallographic Li⁺ site is 2 per Li_xCo[Fe(CN)₆]_y. Taking partial differentiation with T, S_EC is obtained as

$$S_{\text{EC}}=\frac{\partial V}{\partial T}=-\frac{1}{e}\frac{\partial \varphi }{\partial T}=-\frac{k_{\text{B}}}{e}\text{ln}(\frac{x}{2-x}).$$

(2)

In Figs. 4, we plotted eq. (2) as broken curves. In LCF71 [Fig. 4(b)], the occupation effect of Na⁺ (= 0.13) is included by replacing x with x + 0.13. It is obvious that the statistical thermodynamic model fails to reproduce the experiment.

The ionic model,²¹21. J. B. Torrance, P. Lacorre, C. Asavaroengchai, and R. M. Metzger, Physica C 182, 351 (1991). https://doi.org/10.1016/0921-4534(91)90534-6 which includes only n-th ionization energy [I_n(M)] of M, electron affinity [A(O⁻)] of oxygen, and electrostatic energy, is known to be a good starting point to comprehend the electronic structure of transition metal compounds. Actually, Torrance et al.²¹21. J. B. Torrance, P. Lacorre, C. Asavaroengchai, and R. M. Metzger, Physica C 182, 351 (1991). https://doi.org/10.1016/0921-4534(91)90534-6 have applied the model to the ground state of the transition metal oxides, and successfully reproduced the metal/insulator behavior of them. The model further quantitatively reproduced the M-dependences of the optical gaps in (La,Y)MO₃²²22. T. Arima, Y. Tokura, and J. B. Torrance, Phys. Rev. B 48, 17006 (1993). https://doi.org/10.1103/physrevb.48.17006 and LaSrMO₄²³23. Y. Moritomo, T. Arima, and Y. Tokura, J. Phys. Soc. Jpn. 64, 4117 (1995). https://doi.org/10.1143/jpsj.64.4117 with subtracting a constant energy of ∼ 11 eV. Recently, Kobayashi et al.²⁴24. W. Kobayashi and Y. Moritomo, J. Phys. Soc. Jpn. 83, 104702 (2014). https://doi.org/10.7566/jpsj.83.104702 applied the model to the redox potential (V) of NaMO₂ with the O3-type structure, and successfully reproduced the M-dependence of V with subtracting a constant voltage of ∼ 16.5 V.

In the ionic model, the redox potential (V)²⁴24. W. Kobayashi and Y. Moritomo, J. Phys. Soc. Jpn. 83, 104702 (2014). https://doi.org/10.7566/jpsj.83.104702 is expressed as

$$V=\frac{1}{e}[I_3(M_{\text{r}})-I_1(\text{Li})]+(V_{\text{M}}^{M_{\text{r}}}-V_{\text{M}}^{\text{Li}})-\frac{e}{d_{M_{\text{r}}-\text{Li}}},$$

(3)

where $V_{\text{M}}^{M_{\text{r}}}$ ($V_{\text{M}}^{\text{Li}}$), and $d_{M_{\text{r}}-\text{Li}}$ are the Madelung potential at the redox (Li) site and the nearest-neighbor distance between the redox site and Li, respectively. Among the three terms, the first term ($\frac{1}{e}[I_3(M_{\text{M}})-I_1(\text{Li})]$) is essentially independent of T. On the other hand, the second ($V_{\text{M}}^{M_{\text{M}}}-V_{\text{M}}^{\text{Li}}$) and third ($\frac{e}{d_{M_{\text{M}}}-\text{Li}}$) terms should depend on T through the thermal expansion effect. With putting point charges at the Co [(1/2,0,0)], Fe [(0,0,0)] and Li [(1/4,1/4,1/4)] sites (Fig. 5), we evaluated the Madelung potentials ($V_{\text{M}}^{\text{Co}}$, $V_{\text{M}}^{\text{Fe}}$, $V_{\text{M}}^{\text{Li}}$) in plateaus I, II, and III. Details of the point charges (q_Co, q_Fe, q_Li) and x are listed in Table I. The Madelung potentials were calculated by the Fourier method (VESTA program²⁵25. K. Momma and F. Izumi, J. Appl. Crystallogr. 44, 1272 (2011). https://doi.org/10.1107/s0021889811038970) at a = 10.00 Å and 10.01 Å. In Table I, we also listed the Madelung potentials, the second, and third terms of eq. (3). With use of the coefficient (α) of thermal expansion, S_EC is expressed as $S_{\text{EC}}=\alpha \frac{\mathrm{\Delta }V}{\mathrm{\Delta }a/a}$. We tentatively used α (= 2.8 × 10⁻⁵ K⁻¹) of Na_1.32Mn[Fe(CN)₆]_0.833.5H₂O, which was evaluated from Fig. 4 of Ref. 2626. Y. Moritomo, T. Matsuda, Y. Kurihara, and J. Kim, J. Phys. Soc. Jpn. 80, 074608 (2011). https://doi.org/10.1143/jpsj.80.074608. Then, S_EC is evaluated as -0.30 mV/K (plateau I), -0.36 mV/K (plateau II), and 0.34 mV/K (plateau III). We emphasize that the sign of the calculated S_EC in each plateau is consistent with the experiment (Fig. 4). In addition, the magnitude (= 0.3 - 0.4 mV/K) of |S_EC| is comparable to the experimental values (= 0.2 - 0.8 mV/K). Thus, the ionic model semi-qualitatively reproduces the sign reversal behavior of S_EC.

In conclusion, we systematically investigated the TE properties of Co-HCF against x. |S_EC| is higher than the Seebeck coefficient (= 0.2 mV/K at room temperature) of Bi₂Te₃ and distributes from 0.2 to 0.8 mV/K. We further observed a sign reversal behavior of S_EC and qualitatively explained in terms of the ionic model, which includes the electrostatic energy and volume expansion effect. Our phenomenological approach of S_EC is easily applicable to the other materials, such as LiMO₂, LiMn₂O₄, and LiFePO₄, and will accelerate the material search.