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Cu- and Fe-hexacyanoferrate as cathode materials for Potassium ion battery: A First-principles study
Accepted Manuscript Research paper Cu- and Fe-Hexacyanoferrate as Cathode Materials for Potassium Ion battery: A First-Principles Study Ehsan Targholi, S. Morteza Mousavi-Khoshdel, Mohmmadsafi Rahmanifara, M.Z.A. Yahya PII: DOI: Reference:
S0009-2614(17)30876-X http://dx.doi.org/10.1016/j.cplett.2017.09.029 CPLETT 35109
To appear in:
Chemical Physics Letters
Received Date: Accepted Date:
28 June 2017 14 September 2017
Please cite this article as: E. Targholi, S. Morteza Mousavi-Khoshdel, M. Rahmanifara, M.Z.A. Yahya, Cu- and FeHexacyanoferrate as Cathode Materials for Potassium Ion battery: A First-Principles Study, Chemical Physics Letters (2017), doi: http://dx.doi.org/10.1016/j.cplett.2017.09.029
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Cu- and Fe-Hexacyanoferrate as Cathode Materials for Potassium Ion battery: A First-Principles Study
Ehsan Targhol
S. Morteza Mousavi-Khoshde
, Mohmmadsafi Rahmanifa , M.Z.A.
Yahy a
Department of Chemistry, Iran University of Science and Technology, Tehran, Iran U:\ES\DTD550\CPLETT\35109\S5 b
Faculty of Basic Sciences, Shahed University, Tehran, Iran
c
Faculty of Defence Science and Technology, Universiti Pertahanan Nasional Malaysia, 57000 Kuala Lumpur, Malaysia d
Ionic Materials & Devices (i-MADE) Laboratory, Institute of Science, Universiti Teknologi MARA, 40450 Shah Alam, Malaysia
*
To whom correspondence should be addressed: P.O. Box: 16846-13114. Fax: (+98) 77491204. Phone: (+98) 77240540. E-mail: [email protected]
1
Abstract In this paper, the efficiency of Iron-Hexacyanoferrate (FeHCF) and Copper-Hexacyanoferrate (CuHCF) as the cathode materials for using in the energy storage application have been investigated using Density Functional Theory. The changes of their lattice parameters due to the insertion of K+ cation were explored. It was found that these changes for CuHCF are less than FeHCF. FeHCF, KFHCF, CuHCF, KCuHCF, and K2CuHCF are found to have a half-metallic nature. In contrast, K2FeHCF is found to be a diamagnetic insulator. K+ diffusion through the FeHCF and CuHCF frameworks have the energy barrier of 1.46 eV and 1.00 eV, respectively.
Keywords: Potassium Secondary Batteries; Iron Hexacyanoferrate; Copper Hexacyanoferrate; DFT.
Introduction 2
By 2040, renewable energy (such as solar and wind energy) is projected to equal coal and natural gas electricity generation [1]. However, due to their sensitive response to local climatic conditions, the electricity from these renewable resources is not continuous and reliable [2]. For load leveling and managing peak load, large-scale electrical energy storage is required [3]. Rechargeable batteries are a viable solution to overcome the limitation of variable output of renewable energy resources as well as to meet momentary consumption [4]. Most of the recent researches and also commercial developments in the field of batteries have primarily targeted electrode materials for use in portable electronic devices and vehicles [5]. To store electrical energy in large scale, the systems with low production cost, long cycle life, high power and high energy efficiency are required [6]. Post Li-ion batteries (such as Na-ion and Kion batteries) have been considered promising candidates for this propose [7]. It should be noted that although Li-ion batteries (LIBs) are good options for portable electronic devices and electric vehicles, they are not proper for use in the large-scale applications due to the high and rising prices of lithium and limitation of its source [8]. In addition, recent studies confirm that the electrode material expansion along with insertion and de-insertion of K+ ion into PB and its analogous is less than Li+, which confirms high cycling life of K-ion +CuHCF in compared to Li-ion + CuHCF system [9]. Furthermore, Eftekhari found the redox potential of FeHCF for the K+ intercalation was even higher than LIB cathodes [10]. On the other hand, due to the sensitivity of crystalline structure of electrode materials to the inserted ion radius, the regular electrode materials used in LIBs mostly fail in post LIBs [11]. Therefore, the study of other electrode materials for post LIBs has attracted a lot of attention [12, 13]. Transition metal hexacyanoferrates (MHCF), which known as the Prussian blue (PB) and Prussian blue analogues (PBAs), have a general formula AhMk[Fe(CN)6]l.nH2; were h, k, and l refer to stoichiometric numbers, A is alkali metal cation, and M is transition metal (such as Ni, Fe, Mn, V, Zn, Cu, Co) [14]. “h” could vary from 0 to 2, which causes a change in the valence electrons of Fe and M; therefore, these materials are ion and electrical conductor. PBA are a promising candidate to use in large-scale energy storage application because of their long cycle life, high power density, high energy efficiency, and a very low production cost [15]. Along with the change of M in MHCF, some structural parameters and some key properties of PB may be 3
varied. Therefore, achieved voltage, specific energy and rate capability of the battery may be affected. In this paper, we investigate the stable interstitial sites for the insertion of a K+ ion in MHCF (M= Fe or Cu) using density functional theory (DFT) calculations. The structures of the K+ ionintercalated FeHCF and CuHCF, the K+ ion insertion voltages, energy barrier for diffusion of K+ ion in the CuHCF and FeHCF framework, and redox reaction process are examined and compared. We hope that the findings increase the insight about these materials and propose some design strategies that may be used in experimental works.
Computational Method All calculations were carried out using density functional theory employed in the Cambridge Serial Total Energy Package (CASTEP). The Generalized Gradient Approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) [16] exchange-correlation potential was used for geometry optimization and electronic structures calculations. Due to the presence of transition metals in the structure of PBA, the Hubbard correction (DFT-U) was used to treat the strong onsite Coulomb interaction of localized electrons, which is not correctly described by pure LDA or GGA. Spin polarization was applied in all calculations because Fe naturally exhibit magnetic properties [17]. DFT computations which employ conventional local exchange-correlation functionals are unable to calculate the Van der Waals (vdW) interactions appropriately and hence lead to poor predictions of equilibrium structures and consequently other parameters [18]. A vdW dispersion correction was considered using the Tkatchenko and Scheffler (DFT-TS) approaches [19]. The energy cutoff was set to 500 eV (see supporting information, Figure S1). Regarding geometry optimization and electronic properties calculations, a 4×4×4 MonkhorstPack (M-P) of k-point mesh for sampling of Brillouin zone was used (see supporting information, Figure S1). During energy minimization process, the convergence threshold of energy change, maximum force, maximum stress, maximum displacement was adjusted to 2 × l05
eV/atom, 0.05 eV/ , 0.1 GPa and 0.002 , respectively. Optimization of the atomic positions
and crystal’s unit cell parameters was completed at the space group of symmetry FM-3M [20].
4
Results and discussion Structural parameters The mixed-valence nature of PB and its immediate analogs complicates the appropriate estimation of their electronic properties and structural parameters by standard DFT exchangecorrelation functional [21]. To resolve this problem, Wojde et al. used the carefully tailored distinct ultrasoft pseudopotentials for the Fe3+ and Fe2+ centers separately [22, 23]. Another solution, used to have a proper description of these systems, is using of GGA+U numerical approach [9, 21, 24, 25]. The empirical parameters of
in GGA+U are not universal and
depend significantly on the chemical environment. So literature values are often inappropriate, unless the
value was reported in the same chemical environment. In previous studies [9,
21], It was shown that the structural and electronic properties of FeHCF can be successfully estimated using GGA+U with the
=7 for one Fe center, which octahedrally coordinated to
nitrogen end of CN- group (hereafter denoted as FeA) and
=3 for other Fe center, which
octahedrally coordinated to carbon end of CN- groups (hereafter denoted as FeB). In this work, we also used the
for high-spin and
for low spin center at FeHCF. A common
method for using DFT-U is adjusting the
parameters so that the proposed
values
generate the results which are agreement with available experimental measurements of certain properties and using the so determined values to predict other properties. The selected property for adjusting
parameter of Cu and Fe in CuHCF is lattice constant which its experimental
value was reported already. For CuHCF, different appropriate
values were examined and it find that the
are 3.0 eV and 1.0 eV, respectively.
At first, the variations of FeHCF and CuHCF lattice constant are examined along with intercalation of K+ ions into their empty spaces. Figure 1 shows the cubic open framework structure of K2MHCF (M = Fe or Cu).
5
Figure 1. The cubic open framework structure of K2MHCF
The lattice parameters of FeHCF and CuHCF along with the percentage change in their lattice parameters after insertion of first and second K+ ions are collected in Table 1. Using spinepolarized GGA+U calculations, the lattice parameter of FeHCF was obtained to be 10.26 which is larger than previously reported value, 10.14 with experimental reports, 10.178
,
[9, 21, 24], and is in good agreement
[26]. This parameter for CuHCF, generated with optimum
values, is consistent with experimentally reported value, 10.10
[5]. The obtained
percentage changes for considered MHCF are around -3.51-0.20%, which smaller than those in typical LIB cathode materials (which is around 7-10%) [27]. More specifically, for insertion of first K+ ion, the percentage changes of lattice constant in CuHCF and FeHCF were obtained 3.51%, 0.20%, respectively. For insertion of second K+ ion, the percentage changes of lattice constant in CuHCF and FeHCF were obtained -0.60%, 0.10%, respectively. Obtained results for percentage changes of lattice constant show that the cycle life of CuHCF is probably more than FeHCF. Analysis of bond distances revealed that the changes in the lattice parameter are mainly due to the changes in the Fe˗C and more especially M˗N distances, while the cyanide anion geometry
6
almost unchanged. The distances of Fe-C, M-N and C-N were collected in the supporting information, Table S2. The cubic structures of MHCF have five possible interstitial sites, which are denoted with Wyckoff notations as 8c, 24d, 32f, 32f′, and 48g [28]. Ling et al. showed that the more stable interstitial sites for the insertion of K+ cation in FeHCF is the body-centered 8c site, and they also noted that the stable interstitial sites for the intercalation of K+ cation may vary in other hexacyanoferrates compounds [9]. This issue was examined in this article and the obtained results confirmed that more stable site for the intercalation of K+ ion in FeHCF and CuHCF are the body centered 8c site. As K+ is a large cation and body-centered 8c site provides the largest free space in comparison with other sites, the K+ ions prefer this site to avoid noteworthy structural deformation.
Table 1. The lattice parameters of FeHCF and CuHCF along with the percentage change in their lattice parameters after insertion of first and second K+ ions M
K0
K1
K0
K2
K1
a
a
%
a
%
Fe
10.26
9.90
-3.51%
9.84
-0.60%
Cu
10.10 10.12
0.20%
10.13
0.10%
The main reason for the reduction of FeHCF lattice constant along with insertion of K+ ions is the change of spin configuration of ground state. As will be discussed in the next section, the FeHCF have two different Fe center, which one of them is at low-spin configuration and other is at high-spin configuration. After insertion of one K+ ion, the ground states of both Fe centers are at low-spin configuration. Our calculations showed that the low-spin configurations have a smaller lattice constant in compared with high-spin configurations. Thus, with the insertion of K+ ions into the FeHCF, its volume is reduced. Regardless of the spin variation, the lattice constant changes for FeHCF in both stage of reduction reactions were achieved positive. Intercalation voltage and electronic structures The voltage to electrochemically remove of K+ ion is obtained from Equation 1 [29].
7
(1) Where
,
are the total energy of the
MHCF, which x and x0 refer to amount of
intercalated K+ ion per unit cell of MHCF after and before insertion, EK is the energy of a K atom in metallic form. Table 2 Shows the voltages for the intercalation of K+ ion into FeHCF and CuHCF. Table 2. Voltages of K+ ion insertion into MHCF. Voltages K0 K1 K1 K2 Fe
4.02
3.57
Cu
4.16
3.99
The voltages for both first and second K+ ion intercalation are positive, which denoted that these electrochemical intercalations are thermodynamically favorable. For the intercalation of K+ in FeHCF, our calculated value is 4.02 eV, in good agreement with experimentally measured voltage, 3.92 V [30]. CuHCF show higher redox voltage Which means a higher specific energy as compared to FeHCF. The voltage drops in the second stage of intercalation of K+ ion into MHCF structure are related to repulsion between positively charged K+ ions. A summary of the changes in the electronic structures of MHCFs, due to K+ ions insertion, is shown in figure 2.
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Figure 2. A summary of the changes in the electronic structures of MHCFs during the K+ ions insertion Exploration of the energy of different spin configuration shows that the ground state of FeHCF have two different Fe site. One Fe sites, FeA, is at high spin configuration with 4.07 unpaired electrons (obtained by Hirshfeld Analysis (HA)). The other Fe site, FeB, is at low spin configuration with 1.04 unpaired spin (obtained by HA). In addition, as can be seen in Figure 3, a small amount of spin density was found on Nitrogen atoms. Thus, the four unpaired electrons were seen in FeA d orbitals instead of five unpaired electrons. Mulliken Populations Analysis (MPA) predicts net charge of +1.53e and +1.36e for FeA and FeB. The difference of obtained charge with respects to the formal charges of +3 for both Fe center in FeHCF related to strong overlap between Fe d orbitals and
system of CN ligands [24]. The bond population of FeA-N
and FeB-C bonds were obtained to be -0.20e and -0.16e, respectively. In the case of CuHCF, Cu center have 0.98 unpaired electron (obtained by HA) and Fe site have 0.01 unpaired electrons (obtained by HA). HA predicts net charge of +1.38e and +1.36e for Cu and Fe centers. The bond population in Cu-N, and Fe-C were obtained to be -0.13e, and -0.16e, respectively.
Figure 3. The spin density isosurfaces of FeHCF In the first stage of reduction, i.e. insertion of first k+ ion in FeHCF framework, the FeB reduced from Fe3+ to Fe2+. Population analysis show that after insertion of one K+ ion into FeHCF framework, FeB center has 0.07 unpaired electron, which is compatible with the +2 oxidation state and low-spin configuration. Meanwhile, FeA center has 0.89 unpaired electron, which is compatible with the +3 oxidation state and Low-spin configuration. So, both Fe site are at low spin configuration. Net charges of +0.86e and +0.61e were also obtained for FeA and FeB, respectively. The bond population of FeA-N and FeB-C bonds in KFeHCF were obtained to be 0.32e and -0.29e, respectively. These values increased in comparison with FeHCF. The growth 9
of the bond population of FeA-N and FeB-C in KFeHCF in comparison with FeHCF reflects the more significant overlap between the Fe d orbital and the
system of CN ligand.
In the case of KCuHCF, our analysis show that after the first stage of redox reaction, Cu and Fe centers have an unpaired spin of 0.84 and 0.43, respectively. Net charges of +0.72e and +0.68e were also obtained for Fe and Cu, respectively. MPA give the charge populations of 0.25e and -0.29e for Cu-N and Fe-C bonds, respectively. These bond populations show the more overlap between the Fe d or Cu d orbitals and the
system of CN ligands in KCuHCF in
compared to CuHCF. After insertion of second k+ ion in the FeHCF framework, both Fe centers reduced to Fe 2+. The Hershfield Population analysis showed that both of the Fe sites is on the low-spin configuration and have no unpaired spin. Net charges of +0.48e for FeA and +0.23e for FeB were obtained, which reduced in comparison with FeHCF and KFeHCF due to the given charge of K atoms. The MPA give the charge populations of -0.36e and -0.38e for the bonds of Fe A-N and FeB-C, respectively, which reflects the stronger d-
covalent bonding in FeHCF in compared
with KFeHCF and K2FeHCF. In K2CuHCF, after insertion of second k+ ion, the Cu center has 0.6 and Fe center has 0.01 unpaired spin, and predicted net charge on both Cu and Fe centers is +0.33e, which reduced in comparison with CuHCF and KCuHCF. The MPA give the charge populations of -0.30e and 0.36e for the bonds of Cu-N and Fe-C, respectively. Electronic density of state (DOS) for considered structures (FeHCF, KFeHCF, K2 FeHCF, CuHCF, KCuHCF, and K2CuHCF) in their ground state are shown in Figure 4. A half-metal is a solid that is a metal with a Fermi surface for electrons of one spin orientation but is an insulator or semiconductor for those of the opposite spin orientation. In the case of FeHCF, minority spin states cross the Fermi level. In contrast, the wide gap in the majority spin states is seen. Thus, the FeHCF is a half-metal compound. In the structure of KFeHCF, not only 3d states of Fe A and FeB, but also (sp) states of CN ligand are fully polarized; so that only spin-down states cross the Fermi level, which denoted the half-metallic character of KFeHCF. In contrast, K2FeHCF have symmetric DOS plots of spin-up and spin-down and it found to be a diamagnetic insulator with the wide band gap of 3.10 eV. However, it was found that there is a small energy difference between the high spin and low spin configuration of K2 FeHCF. Thus, the transition between high 10
spin and low spin configuration of K2 FeHCF may occur at relatively low temperature. It should be noted that the high spin configuration of K2FeHCF is a half metal. CuHCF and KCuHCF act as a conductor to electrons in spin-down orientation, but as an insulator to those of the opposite orientation, which denoted the half-metallic behavior. After insertion of 2nd K ion, the energy of spin-up states of Fe site decreases and polarization of d orbitals of Fe site is almost eliminated. On the other hand, the population of the spin-down state of Cu sites at the Fermi level is reduced and a new state is created above the Fermi level in the spin-down orientation. K2CuHCF show the metallic spin-down DOS and a wide gap in the spinup DOS, which denoted the half-metallic behavior.
Figure 4. Electronic density of states of FeHCF, KFeHCF, K2 FeHCF, CuHCF, KCuHCF, and K2CuHCF The DOS plots of K0-2 FeHCF confirmed that in the first stage of reduction reactions, FeB reduced from Fe3+ to Fe2+; and in the second stage of reduction reactions, Fe A reduced from Fe3+ to Fe2+. In the case of CuHCF, DOS plots revealed that in the first stage of reduction reactions, iron center has a more important role in compared to Cu. However, with insertion of second K+ ion, both of metals centers (Cu and Fe) participate in the redox reaction. Further investigation showed that there is a large overlap between C 2p and Fe B 3d, as well as N 2p and FeA 3d in
11
FeHCF. The similar large overlap is seen between C 2p and Fe 3d, as well as N 2p and Cu 3d in CuHCF. These large overlapping peaks of DOS ensure structure rigidity, which confirms a high cycle life of these type of cathode materials. The CuHCF and FeHCF in contrast with many other cathode materials don’t experience any phase transformation of major dimensional changes during insertion of the alkaline ion. In addition, the bond population analysis shows that even after fully delithiation, strong covalent bonding occurs, which is not only responsible for excellent mechanical stabilities but also very crucial for the thermodynamic stability of compounds.
Diffusion Intrinsic ionic conductivity of electrode materials is another significant important factor in the electrochemical performance. For figuring out the diffusion paths and their energy barriers, Nudged Elastic Band (NEB) method was used. In this simulation one K+ ion was considered, which moves between the two favorable sites. Figure 5 shows the calculated energy curves for FeHCF and CuHCF. The activation energy of 1.46 eV for FeHCF and 1.00 eV for CuHCF were obtained. However, these values are larger than barrier energies of conventional cathode materials. Due to the high diffusion barrier of K+ ion in the MHCF structures, electrochemical performance of these materials vigorously decreased by increasing their particle size. This finding is consistent with previous experimental report [31]. Carissa et al. found that the available capacity at high current density is considerably improved by reducing the size of hexacyanoferrate nanoparticles [31]. As evidence in Figure 5, the energy barrier of K+ ion diffusion in FeHCF framework is larger than CuHCF; so, it is expected that CuHCF have a higher power density.
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Figure 5. Energy profile for diffusion of K+ ion in interstitial sites of FeHCF and CuHCF However, in experimental papers [5], it has been claimed that copper is a high-power electrode material. This inconsistency of experimental and computational results can be explained by various reasons, such as structural defects and etc., that we do not discuss about them in this article. We believe that one of the main reasons for the huge difference between the theoretical capacity and the capacity gained in the experimental works is the high diffusion barrier of the of K+ ion in the MHCF structures, which makes some of the adsorption sites get out of reach. Conclusion In this work, using DFT calculations, some properties including the geometry structures, the +
K ion insertion voltage and its mechanism, and also energy barrier for diffusion of K + ion in the CuHCF and FeHCF framework were obtained. The results showed that the variation of lattice constant for CuHCF is less than FeHCF, which denoted the more cycle life of CuHCF in comparison with FeHCF. CuHCF shows higher redox voltage Which means a higher specific energy as compared to FeHCF. FeHCF and KFeHCF have a half-metallic behavior. In contrast, it found that the K2FeHCF is a diamagnetic insulator with the wide band gap of 3.10 eV. CuHCF, KCuHCF, and K2CuHCF show the half-metallic behavior. Due to the lower energy barrier of K+ diffusion in CuHCF framework in comparison with FeHCF, the higher power density is expected for CuHCF. Overall, our results suggest CuHCF is more appropriate than FeHCF as a cathode material for various types of aqueous and non-aqueous rechargeable batteries.
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Supporting Information Energy difference as a function of the number of k-points and energy cutoff values in the SCF calculations are depicted in Figure S1. The distances of Fe-C, M-N and C-N are shown in Table S2.
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Graphical abstract
16
Highlights
CuHCF shows higher redox voltage than FeHCF.
CuHCF has a lower energy barrier of K+ diffusion in comparison with FeHCF.
CuHCF shows higher electrical conductivity in comparison with FeHCF.
17
S0009-2614(17)30876-X http://dx.doi.org/10.1016/j.cplett.2017.09.029 CPLETT 35109
To appear in:
Chemical Physics Letters
Received Date: Accepted Date:
28 June 2017 14 September 2017
Please cite this article as: E. Targholi, S. Morteza Mousavi-Khoshdel, M. Rahmanifara, M.Z.A. Yahya, Cu- and FeHexacyanoferrate as Cathode Materials for Potassium Ion battery: A First-Principles Study, Chemical Physics Letters (2017), doi: http://dx.doi.org/10.1016/j.cplett.2017.09.029
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Cu- and Fe-Hexacyanoferrate as Cathode Materials for Potassium Ion battery: A First-Principles Study
Ehsan Targhol
S. Morteza Mousavi-Khoshde
, Mohmmadsafi Rahmanifa , M.Z.A.
Yahy a
Department of Chemistry, Iran University of Science and Technology, Tehran, Iran U:\ES\DTD550\CPLETT\35109\S5 b
Faculty of Basic Sciences, Shahed University, Tehran, Iran
c
Faculty of Defence Science and Technology, Universiti Pertahanan Nasional Malaysia, 57000 Kuala Lumpur, Malaysia d
Ionic Materials & Devices (i-MADE) Laboratory, Institute of Science, Universiti Teknologi MARA, 40450 Shah Alam, Malaysia
*
To whom correspondence should be addressed: P.O. Box: 16846-13114. Fax: (+98) 77491204. Phone: (+98) 77240540. E-mail: [email protected]
1
Abstract In this paper, the efficiency of Iron-Hexacyanoferrate (FeHCF) and Copper-Hexacyanoferrate (CuHCF) as the cathode materials for using in the energy storage application have been investigated using Density Functional Theory. The changes of their lattice parameters due to the insertion of K+ cation were explored. It was found that these changes for CuHCF are less than FeHCF. FeHCF, KFHCF, CuHCF, KCuHCF, and K2CuHCF are found to have a half-metallic nature. In contrast, K2FeHCF is found to be a diamagnetic insulator. K+ diffusion through the FeHCF and CuHCF frameworks have the energy barrier of 1.46 eV and 1.00 eV, respectively.
Keywords: Potassium Secondary Batteries; Iron Hexacyanoferrate; Copper Hexacyanoferrate; DFT.
Introduction 2
By 2040, renewable energy (such as solar and wind energy) is projected to equal coal and natural gas electricity generation [1]. However, due to their sensitive response to local climatic conditions, the electricity from these renewable resources is not continuous and reliable [2]. For load leveling and managing peak load, large-scale electrical energy storage is required [3]. Rechargeable batteries are a viable solution to overcome the limitation of variable output of renewable energy resources as well as to meet momentary consumption [4]. Most of the recent researches and also commercial developments in the field of batteries have primarily targeted electrode materials for use in portable electronic devices and vehicles [5]. To store electrical energy in large scale, the systems with low production cost, long cycle life, high power and high energy efficiency are required [6]. Post Li-ion batteries (such as Na-ion and Kion batteries) have been considered promising candidates for this propose [7]. It should be noted that although Li-ion batteries (LIBs) are good options for portable electronic devices and electric vehicles, they are not proper for use in the large-scale applications due to the high and rising prices of lithium and limitation of its source [8]. In addition, recent studies confirm that the electrode material expansion along with insertion and de-insertion of K+ ion into PB and its analogous is less than Li+, which confirms high cycling life of K-ion +CuHCF in compared to Li-ion + CuHCF system [9]. Furthermore, Eftekhari found the redox potential of FeHCF for the K+ intercalation was even higher than LIB cathodes [10]. On the other hand, due to the sensitivity of crystalline structure of electrode materials to the inserted ion radius, the regular electrode materials used in LIBs mostly fail in post LIBs [11]. Therefore, the study of other electrode materials for post LIBs has attracted a lot of attention [12, 13]. Transition metal hexacyanoferrates (MHCF), which known as the Prussian blue (PB) and Prussian blue analogues (PBAs), have a general formula AhMk[Fe(CN)6]l.nH2; were h, k, and l refer to stoichiometric numbers, A is alkali metal cation, and M is transition metal (such as Ni, Fe, Mn, V, Zn, Cu, Co) [14]. “h” could vary from 0 to 2, which causes a change in the valence electrons of Fe and M; therefore, these materials are ion and electrical conductor. PBA are a promising candidate to use in large-scale energy storage application because of their long cycle life, high power density, high energy efficiency, and a very low production cost [15]. Along with the change of M in MHCF, some structural parameters and some key properties of PB may be 3
varied. Therefore, achieved voltage, specific energy and rate capability of the battery may be affected. In this paper, we investigate the stable interstitial sites for the insertion of a K+ ion in MHCF (M= Fe or Cu) using density functional theory (DFT) calculations. The structures of the K+ ionintercalated FeHCF and CuHCF, the K+ ion insertion voltages, energy barrier for diffusion of K+ ion in the CuHCF and FeHCF framework, and redox reaction process are examined and compared. We hope that the findings increase the insight about these materials and propose some design strategies that may be used in experimental works.
Computational Method All calculations were carried out using density functional theory employed in the Cambridge Serial Total Energy Package (CASTEP). The Generalized Gradient Approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) [16] exchange-correlation potential was used for geometry optimization and electronic structures calculations. Due to the presence of transition metals in the structure of PBA, the Hubbard correction (DFT-U) was used to treat the strong onsite Coulomb interaction of localized electrons, which is not correctly described by pure LDA or GGA. Spin polarization was applied in all calculations because Fe naturally exhibit magnetic properties [17]. DFT computations which employ conventional local exchange-correlation functionals are unable to calculate the Van der Waals (vdW) interactions appropriately and hence lead to poor predictions of equilibrium structures and consequently other parameters [18]. A vdW dispersion correction was considered using the Tkatchenko and Scheffler (DFT-TS) approaches [19]. The energy cutoff was set to 500 eV (see supporting information, Figure S1). Regarding geometry optimization and electronic properties calculations, a 4×4×4 MonkhorstPack (M-P) of k-point mesh for sampling of Brillouin zone was used (see supporting information, Figure S1). During energy minimization process, the convergence threshold of energy change, maximum force, maximum stress, maximum displacement was adjusted to 2 × l05
eV/atom, 0.05 eV/ , 0.1 GPa and 0.002 , respectively. Optimization of the atomic positions
and crystal’s unit cell parameters was completed at the space group of symmetry FM-3M [20].
4
Results and discussion Structural parameters The mixed-valence nature of PB and its immediate analogs complicates the appropriate estimation of their electronic properties and structural parameters by standard DFT exchangecorrelation functional [21]. To resolve this problem, Wojde et al. used the carefully tailored distinct ultrasoft pseudopotentials for the Fe3+ and Fe2+ centers separately [22, 23]. Another solution, used to have a proper description of these systems, is using of GGA+U numerical approach [9, 21, 24, 25]. The empirical parameters of
in GGA+U are not universal and
depend significantly on the chemical environment. So literature values are often inappropriate, unless the
value was reported in the same chemical environment. In previous studies [9,
21], It was shown that the structural and electronic properties of FeHCF can be successfully estimated using GGA+U with the
=7 for one Fe center, which octahedrally coordinated to
nitrogen end of CN- group (hereafter denoted as FeA) and
=3 for other Fe center, which
octahedrally coordinated to carbon end of CN- groups (hereafter denoted as FeB). In this work, we also used the
for high-spin and
for low spin center at FeHCF. A common
method for using DFT-U is adjusting the
parameters so that the proposed
values
generate the results which are agreement with available experimental measurements of certain properties and using the so determined values to predict other properties. The selected property for adjusting
parameter of Cu and Fe in CuHCF is lattice constant which its experimental
value was reported already. For CuHCF, different appropriate
values were examined and it find that the
are 3.0 eV and 1.0 eV, respectively.
At first, the variations of FeHCF and CuHCF lattice constant are examined along with intercalation of K+ ions into their empty spaces. Figure 1 shows the cubic open framework structure of K2MHCF (M = Fe or Cu).
5
Figure 1. The cubic open framework structure of K2MHCF
The lattice parameters of FeHCF and CuHCF along with the percentage change in their lattice parameters after insertion of first and second K+ ions are collected in Table 1. Using spinepolarized GGA+U calculations, the lattice parameter of FeHCF was obtained to be 10.26 which is larger than previously reported value, 10.14 with experimental reports, 10.178
,
[9, 21, 24], and is in good agreement
[26]. This parameter for CuHCF, generated with optimum
values, is consistent with experimentally reported value, 10.10
[5]. The obtained
percentage changes for considered MHCF are around -3.51-0.20%, which smaller than those in typical LIB cathode materials (which is around 7-10%) [27]. More specifically, for insertion of first K+ ion, the percentage changes of lattice constant in CuHCF and FeHCF were obtained 3.51%, 0.20%, respectively. For insertion of second K+ ion, the percentage changes of lattice constant in CuHCF and FeHCF were obtained -0.60%, 0.10%, respectively. Obtained results for percentage changes of lattice constant show that the cycle life of CuHCF is probably more than FeHCF. Analysis of bond distances revealed that the changes in the lattice parameter are mainly due to the changes in the Fe˗C and more especially M˗N distances, while the cyanide anion geometry
6
almost unchanged. The distances of Fe-C, M-N and C-N were collected in the supporting information, Table S2. The cubic structures of MHCF have five possible interstitial sites, which are denoted with Wyckoff notations as 8c, 24d, 32f, 32f′, and 48g [28]. Ling et al. showed that the more stable interstitial sites for the insertion of K+ cation in FeHCF is the body-centered 8c site, and they also noted that the stable interstitial sites for the intercalation of K+ cation may vary in other hexacyanoferrates compounds [9]. This issue was examined in this article and the obtained results confirmed that more stable site for the intercalation of K+ ion in FeHCF and CuHCF are the body centered 8c site. As K+ is a large cation and body-centered 8c site provides the largest free space in comparison with other sites, the K+ ions prefer this site to avoid noteworthy structural deformation.
Table 1. The lattice parameters of FeHCF and CuHCF along with the percentage change in their lattice parameters after insertion of first and second K+ ions M
K0
K1
K0
K2
K1
a
a
%
a
%
Fe
10.26
9.90
-3.51%
9.84
-0.60%
Cu
10.10 10.12
0.20%
10.13
0.10%
The main reason for the reduction of FeHCF lattice constant along with insertion of K+ ions is the change of spin configuration of ground state. As will be discussed in the next section, the FeHCF have two different Fe center, which one of them is at low-spin configuration and other is at high-spin configuration. After insertion of one K+ ion, the ground states of both Fe centers are at low-spin configuration. Our calculations showed that the low-spin configurations have a smaller lattice constant in compared with high-spin configurations. Thus, with the insertion of K+ ions into the FeHCF, its volume is reduced. Regardless of the spin variation, the lattice constant changes for FeHCF in both stage of reduction reactions were achieved positive. Intercalation voltage and electronic structures The voltage to electrochemically remove of K+ ion is obtained from Equation 1 [29].
7
(1) Where
,
are the total energy of the
MHCF, which x and x0 refer to amount of
intercalated K+ ion per unit cell of MHCF after and before insertion, EK is the energy of a K atom in metallic form. Table 2 Shows the voltages for the intercalation of K+ ion into FeHCF and CuHCF. Table 2. Voltages of K+ ion insertion into MHCF. Voltages K0 K1 K1 K2 Fe
4.02
3.57
Cu
4.16
3.99
The voltages for both first and second K+ ion intercalation are positive, which denoted that these electrochemical intercalations are thermodynamically favorable. For the intercalation of K+ in FeHCF, our calculated value is 4.02 eV, in good agreement with experimentally measured voltage, 3.92 V [30]. CuHCF show higher redox voltage Which means a higher specific energy as compared to FeHCF. The voltage drops in the second stage of intercalation of K+ ion into MHCF structure are related to repulsion between positively charged K+ ions. A summary of the changes in the electronic structures of MHCFs, due to K+ ions insertion, is shown in figure 2.
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Figure 2. A summary of the changes in the electronic structures of MHCFs during the K+ ions insertion Exploration of the energy of different spin configuration shows that the ground state of FeHCF have two different Fe site. One Fe sites, FeA, is at high spin configuration with 4.07 unpaired electrons (obtained by Hirshfeld Analysis (HA)). The other Fe site, FeB, is at low spin configuration with 1.04 unpaired spin (obtained by HA). In addition, as can be seen in Figure 3, a small amount of spin density was found on Nitrogen atoms. Thus, the four unpaired electrons were seen in FeA d orbitals instead of five unpaired electrons. Mulliken Populations Analysis (MPA) predicts net charge of +1.53e and +1.36e for FeA and FeB. The difference of obtained charge with respects to the formal charges of +3 for both Fe center in FeHCF related to strong overlap between Fe d orbitals and
system of CN ligands [24]. The bond population of FeA-N
and FeB-C bonds were obtained to be -0.20e and -0.16e, respectively. In the case of CuHCF, Cu center have 0.98 unpaired electron (obtained by HA) and Fe site have 0.01 unpaired electrons (obtained by HA). HA predicts net charge of +1.38e and +1.36e for Cu and Fe centers. The bond population in Cu-N, and Fe-C were obtained to be -0.13e, and -0.16e, respectively.
Figure 3. The spin density isosurfaces of FeHCF In the first stage of reduction, i.e. insertion of first k+ ion in FeHCF framework, the FeB reduced from Fe3+ to Fe2+. Population analysis show that after insertion of one K+ ion into FeHCF framework, FeB center has 0.07 unpaired electron, which is compatible with the +2 oxidation state and low-spin configuration. Meanwhile, FeA center has 0.89 unpaired electron, which is compatible with the +3 oxidation state and Low-spin configuration. So, both Fe site are at low spin configuration. Net charges of +0.86e and +0.61e were also obtained for FeA and FeB, respectively. The bond population of FeA-N and FeB-C bonds in KFeHCF were obtained to be 0.32e and -0.29e, respectively. These values increased in comparison with FeHCF. The growth 9
of the bond population of FeA-N and FeB-C in KFeHCF in comparison with FeHCF reflects the more significant overlap between the Fe d orbital and the
system of CN ligand.
In the case of KCuHCF, our analysis show that after the first stage of redox reaction, Cu and Fe centers have an unpaired spin of 0.84 and 0.43, respectively. Net charges of +0.72e and +0.68e were also obtained for Fe and Cu, respectively. MPA give the charge populations of 0.25e and -0.29e for Cu-N and Fe-C bonds, respectively. These bond populations show the more overlap between the Fe d or Cu d orbitals and the
system of CN ligands in KCuHCF in
compared to CuHCF. After insertion of second k+ ion in the FeHCF framework, both Fe centers reduced to Fe 2+. The Hershfield Population analysis showed that both of the Fe sites is on the low-spin configuration and have no unpaired spin. Net charges of +0.48e for FeA and +0.23e for FeB were obtained, which reduced in comparison with FeHCF and KFeHCF due to the given charge of K atoms. The MPA give the charge populations of -0.36e and -0.38e for the bonds of Fe A-N and FeB-C, respectively, which reflects the stronger d-
covalent bonding in FeHCF in compared
with KFeHCF and K2FeHCF. In K2CuHCF, after insertion of second k+ ion, the Cu center has 0.6 and Fe center has 0.01 unpaired spin, and predicted net charge on both Cu and Fe centers is +0.33e, which reduced in comparison with CuHCF and KCuHCF. The MPA give the charge populations of -0.30e and 0.36e for the bonds of Cu-N and Fe-C, respectively. Electronic density of state (DOS) for considered structures (FeHCF, KFeHCF, K2 FeHCF, CuHCF, KCuHCF, and K2CuHCF) in their ground state are shown in Figure 4. A half-metal is a solid that is a metal with a Fermi surface for electrons of one spin orientation but is an insulator or semiconductor for those of the opposite spin orientation. In the case of FeHCF, minority spin states cross the Fermi level. In contrast, the wide gap in the majority spin states is seen. Thus, the FeHCF is a half-metal compound. In the structure of KFeHCF, not only 3d states of Fe A and FeB, but also (sp) states of CN ligand are fully polarized; so that only spin-down states cross the Fermi level, which denoted the half-metallic character of KFeHCF. In contrast, K2FeHCF have symmetric DOS plots of spin-up and spin-down and it found to be a diamagnetic insulator with the wide band gap of 3.10 eV. However, it was found that there is a small energy difference between the high spin and low spin configuration of K2 FeHCF. Thus, the transition between high 10
spin and low spin configuration of K2 FeHCF may occur at relatively low temperature. It should be noted that the high spin configuration of K2FeHCF is a half metal. CuHCF and KCuHCF act as a conductor to electrons in spin-down orientation, but as an insulator to those of the opposite orientation, which denoted the half-metallic behavior. After insertion of 2nd K ion, the energy of spin-up states of Fe site decreases and polarization of d orbitals of Fe site is almost eliminated. On the other hand, the population of the spin-down state of Cu sites at the Fermi level is reduced and a new state is created above the Fermi level in the spin-down orientation. K2CuHCF show the metallic spin-down DOS and a wide gap in the spinup DOS, which denoted the half-metallic behavior.
Figure 4. Electronic density of states of FeHCF, KFeHCF, K2 FeHCF, CuHCF, KCuHCF, and K2CuHCF The DOS plots of K0-2 FeHCF confirmed that in the first stage of reduction reactions, FeB reduced from Fe3+ to Fe2+; and in the second stage of reduction reactions, Fe A reduced from Fe3+ to Fe2+. In the case of CuHCF, DOS plots revealed that in the first stage of reduction reactions, iron center has a more important role in compared to Cu. However, with insertion of second K+ ion, both of metals centers (Cu and Fe) participate in the redox reaction. Further investigation showed that there is a large overlap between C 2p and Fe B 3d, as well as N 2p and FeA 3d in
11
FeHCF. The similar large overlap is seen between C 2p and Fe 3d, as well as N 2p and Cu 3d in CuHCF. These large overlapping peaks of DOS ensure structure rigidity, which confirms a high cycle life of these type of cathode materials. The CuHCF and FeHCF in contrast with many other cathode materials don’t experience any phase transformation of major dimensional changes during insertion of the alkaline ion. In addition, the bond population analysis shows that even after fully delithiation, strong covalent bonding occurs, which is not only responsible for excellent mechanical stabilities but also very crucial for the thermodynamic stability of compounds.
Diffusion Intrinsic ionic conductivity of electrode materials is another significant important factor in the electrochemical performance. For figuring out the diffusion paths and their energy barriers, Nudged Elastic Band (NEB) method was used. In this simulation one K+ ion was considered, which moves between the two favorable sites. Figure 5 shows the calculated energy curves for FeHCF and CuHCF. The activation energy of 1.46 eV for FeHCF and 1.00 eV for CuHCF were obtained. However, these values are larger than barrier energies of conventional cathode materials. Due to the high diffusion barrier of K+ ion in the MHCF structures, electrochemical performance of these materials vigorously decreased by increasing their particle size. This finding is consistent with previous experimental report [31]. Carissa et al. found that the available capacity at high current density is considerably improved by reducing the size of hexacyanoferrate nanoparticles [31]. As evidence in Figure 5, the energy barrier of K+ ion diffusion in FeHCF framework is larger than CuHCF; so, it is expected that CuHCF have a higher power density.
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Figure 5. Energy profile for diffusion of K+ ion in interstitial sites of FeHCF and CuHCF However, in experimental papers [5], it has been claimed that copper is a high-power electrode material. This inconsistency of experimental and computational results can be explained by various reasons, such as structural defects and etc., that we do not discuss about them in this article. We believe that one of the main reasons for the huge difference between the theoretical capacity and the capacity gained in the experimental works is the high diffusion barrier of the of K+ ion in the MHCF structures, which makes some of the adsorption sites get out of reach. Conclusion In this work, using DFT calculations, some properties including the geometry structures, the +
K ion insertion voltage and its mechanism, and also energy barrier for diffusion of K + ion in the CuHCF and FeHCF framework were obtained. The results showed that the variation of lattice constant for CuHCF is less than FeHCF, which denoted the more cycle life of CuHCF in comparison with FeHCF. CuHCF shows higher redox voltage Which means a higher specific energy as compared to FeHCF. FeHCF and KFeHCF have a half-metallic behavior. In contrast, it found that the K2FeHCF is a diamagnetic insulator with the wide band gap of 3.10 eV. CuHCF, KCuHCF, and K2CuHCF show the half-metallic behavior. Due to the lower energy barrier of K+ diffusion in CuHCF framework in comparison with FeHCF, the higher power density is expected for CuHCF. Overall, our results suggest CuHCF is more appropriate than FeHCF as a cathode material for various types of aqueous and non-aqueous rechargeable batteries.
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Supporting Information Energy difference as a function of the number of k-points and energy cutoff values in the SCF calculations are depicted in Figure S1. The distances of Fe-C, M-N and C-N are shown in Table S2.
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Graphical abstract
16
Highlights
CuHCF shows higher redox voltage than FeHCF.
CuHCF has a lower energy barrier of K+ diffusion in comparison with FeHCF.
CuHCF shows higher electrical conductivity in comparison with FeHCF.
17