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First principles investigation on the elastic and electronic properties of Mn, Co, Nb, Mo doped LiFePO4
Computational Materials Science 155 (2018) 410–415
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First principles investigation on the elastic and electronic properties of Mn, Co, Nb, Mo doped LiFePO4
T
⁎
Dongxu Zhang, Jie Wang, Kangze Dong, Aimin Hao
School of Materials Science and Engineering, Northeastern University, Shenyang 110819, PR China School of Resources and Materials, Northeastern University at Qinhuangdao, Qinhuangdao 066004, PR China Key Laboratory of Dielectric and Electrolyte Functional Material Hebei Province, Qinhuangdao, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: LiFePO4 Band structure Formation energy Elastic Anisotropic
In this work, the mechanical stability and electronic property of LiFePO4 doped with Mn, Co, Nb and Mo studied using the first principles calculation. The doped LiFePO4 has low defect formation energy and meets the criterion of mechanical stability, indicating that the doping of the four 3d transition metals can be stable. Band structure calculations depict half-metallic nature of the doping system. By calculating the Debye temperature and Poisson's ratio, it is found that the dopants can improve the mechanical stability of LiFePO4. In addition, the study of the anisotropy of the material also shows that the doping of Co can make the material tend to be more isotropic. The above shows that the doping of Mn, Nb, Mo, especially Co, can improve the mechanical stability of the material and reduce the degree of anisotropy of the material, thereby reducing the risk of microcracking and shear deformation of the material.
1. Introduction The olivine-type LiFePO4 was put forward by Padhi [1] in 1997 firstly. It can be used as cathode material for Li ion second battery. It attracts much attention, because of its high theoretical capacity, good stability and safety, low cost and environmental friendly [2]. At present, this material is mainly used in Electric Vehicle (EV) and Hybrid Electric Vehicle (HEV), but the low ionic and electronic conductivity affects its cycling performance and restricts its further application on lithium batteries [3]. In order to improve its performance, many efforts have focused on particle size reduction, carbon coating and cation doping [4–8]. In these methods, the cation doping has attracted much attention as an effective method. Wang and co-workers [9], by first principles calculations and experiments, confirmed that the doping of Mo can enhance the electronic conductivity of materials. Chung et al. [10] have been observed that the electrochemical properties of LiFePO4 were improved by doping Nb. All the above studies indicate that doping can effectively improve the partial performance of materials. However, current doping studies ignore the effect of material stability on battery performance. And the stability and safety of the battery materials are the basis of its application. At the same time, it will also greatly affect the performance of the material. The unstable lattice vibration will cause phase transition of the material [11]. And external pressure may also lead to material
⁎
deformation, resulting in material instability. Wang et al. [12] found that after 60 cycles, the charging and discharging curve of LiFePO4 would have obvious slope characteristics. The polarization is increased upon cycling. In addition, flaws can be observed in some particles after 10 cycles, which should be a result from internal high strain during lithium extraction/insertion process. Maxish et al. [13] use the first principle to calculate the elastic properties of LixFePO4. It is found that LixFePO4 has a smaller shear modulus and a higher degree of anisotropy compared with other cathode materials, which leads to the decrease of the capacity of the LiFePO4 and the poor cycle performance. Because the lattice structure symmetry of LiFePO4 after doping will be changed, the structural stability of materials will also be changed. As a commercially available cathode material, LiCoO2 also suffers from the breakdown of micro-structure due to internal strain [14]. At present, many studies have shown that the doping of metal cations in Co site can effectively protect the structural stability of LiCoO2, inhibit the phase transition and improve the cycle performance of the material [15–17]. Therefore, the doping in Fe site may play a positive role in improving the structural stability of LiFePO4 and improving its cycling performance. To the best of our knowledge the change of LiFePO4 stability after doping has not been investigated. In this work, four elements of transition group Mn, Co, Nb, and Mo are selected for substitution. By calculating the formation energy, elastic properties and anisotropy, the
Corresponding author at: School of Materials Science and Engineering, Northeastern University, Shenyang 110819, PR China. E-mail address: [email protected] (A. Hao).
https://doi.org/10.1016/j.commatsci.2018.09.010 Received 1 August 2018; Received in revised form 29 August 2018; Accepted 3 September 2018 Available online 08 September 2018 0927-0256/ © 2018 Elsevier B.V. All rights reserved.
Computational Materials Science 155 (2018) 410–415
D. Zhang et al.
Fig. 2. Band structures of LiFePO4. The red and blue lines represent majorityspin states and minority-spin states, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 1. Bulk model of M-doped LiFePO4 (M = Mn, Co, Nb, Mo).
Table 1 Lattice parameters of LiFePO4 before and after doping.
influence of different doping elements on the structure stability of the material is studied. LiFePO4
2. Computational details LiFe1-1/8Mn1/8PO4 LiFe1-1/8Co1/8PO4 LiFe1-1/8Nb1/8PO4 LiFe1-1/8Mo1/8PO4
All calculations are performed using the CASTEP in the framework of the density functional theory (DFT). The general gradient approximation (GGA) by Perdew and Wang (PW91) for the exchange-correlation was used. The configulation of Li-1s2 2s1, O-2s2 2p4, P-3s2 3p3, Fe-3d6 4s2, Co-3d7 4s2, Nb-4s2 4p6 4d4 5s1 are treated as the valence electrons for the Ultrasoft Pseudopotentials (USPP). Energy cut-off for the plane waves (380 eV) and a Monkhorst-Pack mesh (3 × 4 × 5) [11] were applied to ensure the total ground state energy convergence of 1.0 × 10−5 eV per atom. For the geometry optimization, Broyden – Fletcher – Goldfarb – Shanno (BFGS) algorithm was used. For all the calculations 1 × 2 × 1 supercell were used. As shown in Fig. 1, the calculation model of LiFePO4, space group is Pnma, has an orthorhombic olivine structure. Each cell contains four formula units and 28 atoms. The doping models were obtained by replacing a Fe atom in 1 × 2 × 1 supercell. And the doping concentration of all doped models is 1/8. In the crystal structure, each FeO6 octahedron is connected by the corners shared. Meanwhile, FeO6 octahedron linked to two LiO6 octahedron and one PO4 tetrahedron by the edge shared.
Ours: Expt. [18]: Calc. [19]: Ours: Ours: Ours: Ours:
a (Å)
b (Å)
c (Å)
V (Å3)
10.35 10.33 10.49 10.36 10.32 10.43 10.39
12.06 12.02 11.83 12.1 12.04 12.11 12.11
4.72 4.69 4.75 4.73 4.72 4.73 4.73
589.16 582.34 589.46 593.48 587.62 597.41 595.09
of doped elements. It is worth noting that the changes in lattice constants are only reflected in the changes in the values of a and b, and the size of the c value remains basically unchanged. The band structure of Mn, Co, Nb, Mo doped is shown in Fig. 3. After Mn doping, the energy gap of the majority-spin is reduced from 3.29 eV to 3.04 eV, and the energy gap of minority gap is changed from 0.19 eV to 0.18 eV. It can be seen that an overlap of the minority-spin bands after the doping of Co and Nb, indicating that it’s a half metal. After Mo doping, the energy gap of the majority-spin is reduced from 3.29 eV to 2.53 eV, and the energy gap of minority gap is changed from 0.19 eV to 0.13 eV. The orbital contribution of dopants (Mn, Co, Nb and Mo) in the vicinity of the Fermi level is more clearly indicated by plotting the partial densities of states. It is not difficult to find from Fig. 4 that the dorbitals of the dopants contributes to the density of states in the vicinity of and reduces the band gap. In addition, the more the number of the d band electrons of the dopants, the higher the peak near the Fermi level. The d-orbital of Nb goes through the Fermi level and causes the band gap of LiFePO4 after doping to disappear. Therefore, the band gaps after doping of Mn, Co, Nb and Mo are decreased, which is beneficial to the transition of electrons and plays an important role in improving the electron mobility of LiFePO4. The defect formation energy Ef is an important concept used to characterize the degree of difficulty in the formation of a particular defect and the stability of its system. The smaller the energy is, the more stable it is. A formation energy greater than 0 indicates that the formation of the substance is endothermic, and less than 0 is exothermic. The formation energy of a defect or impurity M in charge state q is defined as [20]:
3. Results and discussion 3.1. Geometries, electronic property and formation energy The lattice optimization results of the undoped system are basically consistent with those measured experimentally. We have carried out spin-polarized electronic structure calculations of LiFePO4. The result is shown in Fig. 2. It can be seen an energy gap of 0.19 eV of the minorityspin bands. Our results are in good agreement with Yamada et al. [3]. It indicates that the models and parameters used in the calculation are reasonable. The variation of the side length of the doped system is less than 1% in Table 1, indicating that the doping does not destroy the original lattice structure, and the doping concentration is more reasonable. The change of lattice volume after doping is consistent with the ionic radius 411
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D. Zhang et al.
Fig. 3. Band structures of LiFePO4 after doping. The red and blue lines represent majority-spin states and minority-spin states, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Ef [X q ] = Etot [X q ]−Etot [bulk ]− ∑ ni μi + q [EF + EV + ΔV ] i
When any elastic medium is elongated in the longitudinal direction, it will contract in the lateral direction, and C12, C13, and C23 react to this property. The criteria for mechanical stability of orthorhombic are given by [21]
(1)
Etot[Xq] is the total energy with one defect or impurity M in the cell. Etot[bulk] is the total energy of pure LiFePO4. ni indicates the number of atoms of type i that have added to (ni > 0) or removed from(ni < 0) the cell. μi is the chemical potential of the i atom itself. It is worth noting that the doping system charge in this paper is zero, so the last item need not be considered. The formula for doping M (M = Mn, Co, Nb, Mo) can be simplified to:
Ef = E (LiFe1 − n Mn PO4 )−E (LiFePO4 )−nE (M) + nE (Fe)
C11 > 0, C22 > 0, C33 > 0, C44 > 0, C55 > 0, C66 > 0, C11 + C22 + C33 + 2(C12 + C13 + C23) > 0, (C11 + C22−2C12) > 0, (C11 + C33−2C13) > 0, (C22 + C33−2C23) > 0
(3)
From Table 3, it can be seen that the stiffness coefficient of LiFePO4 calculated in this paper is basically consistent with the value calculated in Ref. [13]. The stiffness coefficients before an d after doping correspond to the criterion of mechanical stability, indicating that the doped material is stable and ensures the feasibility of doping. In addition, the shear-related C44, C55, and C66 are significantly smaller than C11, C22, and C33 indicate that LiFePO4 is more susceptible to shear deformation. The values of C44, C55, and C66 after Mn, Co, Nb, and Mo doping were significantly improved. This results show that doping can improve the stability of the material by improving the shear resistance of the material. In addition to the elastic constants, there are still many properties that describe the mechanical stability of the crystal. Since the cathode materials are sintered powder after synthesis, it can be regarded as polycrystalline samples polymerized by single phase monocrystals with a random orientation. Debye temperature can reflect material stability and bond strength of materials. Besides, the physical properties of many materials, such as heat capacity, thermal expansion coefficient and melting point, are all related to Debye temperature. One of the ways to calculate the Debye temperature is to calculate the elastic constant and the average speed of sound [22].
(2)
From Table 2, it is not difficult to find that the doped materials have small formation energy in each system, which are easy to dope and can exist stably. The Mn-doped system has the smallest energy and formation energy, indicating that it is the most easily formed and most stable. Each metal particle doped from easy to difficult are Mn, Nb, Co, Mo. 3.2. Elastic properties The stability of the battery cathode material largely affects its electrochemical performance [11]. Poor stability will lead to phase transformation and degradation of cathode materials, which will affect the charge and discharge performance of batteries. Therefore, the calculation of the stability of cathode materials becomes particularly important. The stiffness coefficient (Cij) and the compliance coefficient (Sij) are calculated for calculating the elastic properties of materials. In orthorhombic, C11, C22, and C33 represent the linear compressibility along the X, Y, and Z axes, respectively, while C44, C55, and C66 are related to the shear strengths of the {1 0 0}, {0 1 0}, and {0 0 1} planes. 412
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Fig. 4. Partial densities of states calculated of the dopants (Mn, Co, Nb and Mo).
υl and υt are the transverse and longitudinal elastic wave velocities of the polycrystalline material related to the bulk modulus B and the shear modulus G.
Table 2 Energy and formation energy of the doped system. Compounds
LiFe1-1/8Mn1/ 8PO4
Energy (eV) ΔEƒ
−23725.17 −0.18
LiFe1-1/8Co1/ 8PO4 −24113.13 0.06
LiFe1-1/8Nb1/
LiFe1-1/8Mo1/
8PO4
8PO4
−24621.15 −0.01
4
−25005.16 4.65
G υt = ⎜⎛ ⎟⎞ ⎝ρ⎠
1
h 3n N ρ 3 TD = ⎡ ⎛ A ⎞ ⎤ υm k⎢ ⎣ 4π ⎝ M ⎠ ⎥ ⎦
(4)
(6)
1 2
(7)
The Debye temperature of the Co doped material is greatly improved, followed by the doping of Mn and Mo. The Debye temperature decreases slightly after Nb doping. This shows that the doping of Co can effectively improve the stability of LiFePO4, thereby improving its electrochemical performance. However, the doping of Nb has a negative effect on the structural stability of the material. There are mainly two methods for studying LiFePO4 as an orthorhombic polycrystalline material. The bulk modulus and shear modulus
where h is the Planck constant, k is the Boltzmann constant, NA is the Avogadro constant, ρ is the density, M is the molar mass, and n is the number of atoms in each molecule. The average wave speed of a polycrystalline material can be expressed as −1 3
1⎛ 2 1 ⎞⎤ υm = ⎡ ⎢ 3 ⎜ υ3 + υ 3 ⎟⎥ t l ⎠⎦ ⎝ ⎣
1
2 ⎛ B + 3G⎞ υl = ⎜ ⎟ ρ ⎝ ⎠
(5)
Table 3 Elastic constants (in GPa) and Debye temperature (in K).
LiFePO4 +Mn +Co +Nb +Mo
Ours: Ref. [13]: Ours: Ours: Ours: Ours:
C11
C22
C33
C44
C55
C66
C12
C13
C23
ρ [g/cm3]
TD [K]
153.1 133.0 160.0 172.3 153.1 153.6
195.4 203.0 205.5 215.8 182.5 199.2
164.1 172.3 199.2 195.9 168.1 176.3
33.8 34.9 57.0 60.4 36.4 43.3
53.5 47.8 62.0 69.1 57.0 61.6
54.0 42.4 47.3 62.3 50.7 54.8
73.8 74.3 74.3 72.3 68.6 71.2
60.7 54.3 58.5 53.2 56.2 62.6
37.4 55.2 42.9 39.2 39.2 41.4
3.57 3.52 3.53 3.58 3.61 3.63
564 – 599 633 555 577
413
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Table 4 Shear and bulk modulus, Young modulus (in GPa), and Poisson ratio.
LiFePO4 +Mn +Co +Nb +Mo
Ours: Ref. [13]: Ours: Ours: Ours: Ours:
GR
GV
GH
BR
BV
BH
EH
νH
B/G
47.8 44.3 57.0 65.0 49.0 53.0
51.0 46.7 59.2 66.3 51.5 55.6
49.4 45.5 58.1 65.6 50.2 54.3
94.4 94.3 101.3 100.9 92.1 97.3
95.1 97.3 101.8 101.5 92.4 97.7
94.8 95.8 101.5 101.2 92.2 97.5
126.3 125.0 146.4 161.8 127.5 137.4
0.28 0.30 0.26 0.23 0.27 0.27
1.92 2.11 1.75 1.54 1.84 1.80
10 cycles. And microcracks are suspected to be one of the factors that affect the electrochemical performance of the battery. Maxisch et al. [13] believed that this crack generation may be caused by the anisotropy of the material. The anisotropy of orthotropic materials is mainly reflected in the anisotropy of shear anisotropy and linear bulk modulus. The anisotropy of shear modulus can be expressed as follows: For the {1 0 0} shear planes in 〈0 1 0〉 and 〈0 1 1〉 directions is
of the material can be calculated separately according to the methods proposed by Voigt (BV and GV) and Reuss (BR and GR). It has been proved that the two calculation results of Voigt and Reuss are the upper limit and the lower limit of the true polycrystal constant [23]. Taking the average of the two can more accurately represent the bulk modulus and shear modulus of the material.
G=
GR + G V 2
(8)
B=
BR + B V 2
(9)
(12)
A1 = 4C44/(C11 + C33−2C13)
For the {0 1 0} shear planes in 〈0 0 1〉 and 〈1 0 0〉 directions is
A2 = 4C55/(C22 + C33−2C23)
Young's modulus and Poisson's ratio can be calculated using the following formula:
(13)
For the {0 0 1} shear planes in 〈1 1 0〉 and 〈0 1 0〉 directions is (14)
A3 = 4C66/(C11 + C22−2C12)
E=
9BG 3B + G
(10)
ν=
3B−2G 6B + 2G
(11)
The calculation results are shown in Table 5. When the values of A1, A2, and A3 are 1, the material is isotropic, and the degree of deviation from 1 indicates the degree of anisotropy. For the LiFePO4, the value of A3 approaches 1 tends to isotropy and A1 and A2 slightly less than 1 present anisotropy. The doping of Nb has little effect on the anisotropy of the material. The doping of Mo slightly increased A1 and A2. The doping of Co and Mn tends to make the {1 0 0} plane isotropic. However, the doping of Mn reduces the value of A3 while the doping of Co still keeps the {0 0 1} plane isotropic. In summary, the doping of Co can effectively reduce the shear anisotropy of the material and inhibit the generation of microcracks. The anisotropy of the bulk modulus can be estimated by calculating the bulk modulus along the crystal axis. Define the bulk modulus in the dp dp dp direction of each crystal axis as Ba = a da , Bb = b db , Bc = c dc . The bulk modulus anisotropy along the b-axis on the a and c axes can be written B B as ABa = Ba , ABc = B c . When the values are 1, the material is isotropic, b b and the degree of deviation from 1 indicates the degree of anisotropy. From the results, it can be found that there is a certain degree of anisotropy in each system, in which the doping of Nb makes the bulk modulus of the material more tend to be isotropic. Doping of Mn, Co, Mo has little effect on the bulk modulus anisotropy of LiFePO4. However, LiFePO4 itself has strong resistance to linear compression, the bulk modulus anisotropy may not be the main factor affecting the microcracks of materials. Chung and Buessem [26] proposed a more practical method to test the shear modulus and bulk modulus anisotropy of polycrystalline materials. Its formula can be defined as:
With the above formula, the calculated results are listed in Table 4. Bulk modulus refers to the ability of materials to resist fracture, indicating the incompressibility of materials. Shear modulus is used to characterize the material's ability to resist shear strain. The shear modulus of LiFePO4 is 49.4 GPa and the bulk modulus is 94.8 GPa. Compared with LiCoO2 and LiMn2O4 cathode materials, there is a big gap between them [24]. However, the doping of Mn and Co increased the BH and GH of the material, especially the shear resistance of the material. The doping effect of Co was the most obvious. The influence of Nb and Mo doping on the material is limited. The doping of Nb and Mo increased the GH value of the material, but the BH value after Nb doping decreased. Young's modulus is a physical quantity describing the ability of a solid material to resist deformation. It is similar to Debye temperature, and its result is consistent with calculation of the Debye temperature. The doping of Co greatly increases the ability of the material to resist deformation. The Poisson's ratio (νH) is the elastic constant that reflects the material's transverse deformation and indicates the material's ability to resist shear deformation. The smaller the Poisson's ratio, the more difficult it is for the material to undergo shear deformation. LiFePO4 has a large Poisson's ratio (0.28), which is prone to shear deformation. The values of Poisson's ratio after Mn, Nb and Mo doping do not change a lot, but doping of Co makes the Poisson's ratio of the material significantly reduced. This shows that doping of Co can significantly improve the ability of the material to resist shear strain. This is consistent with the previous analysis. Pugh [25] proposed that the material's plasticity and toughness can be judged by the value of B/G. When the value of B/G is greater than 1.75, the material has better toughness, whereas the material is brittle. From Table 4 it is not difficult to find that the doping of Mn, Nb, and Mo will make the material brittle. The doping of Co also becomes more brittle while greatly increasing the strength of the material.
AG = (G V−G R )/(G V + G R )
(15)
AB = (B V−BR )/(B V + BR )
(16)
Table 5 Anisotropic properties (in GPa) of LiFePO4 before and after doping.
LiFePO4 +Mn +Co +Nb +Mo
3.3. Anisotropy Wang et al. [12] found that LiFePO4 will produce microcracks after 414
A1
A2
A3
ABa
ABc
AG (%)
AB (%)
0.691 0.941 0.923 0.697 0.846
0.752 0.778 0.829 0.838 0.842
1.075 0.872 1.023 1.023 1.042
0.883 0.759 0.796 0.907 0.812
0.733 0.852 0.781 0.822 0.802
3.24 1.89 0.99 2.49 2.39
0.37 0.25 0.3 0.16 0.21
Computational Materials Science 155 (2018) 410–415
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where B and G represent the bulk modulus and shear modulus of the material. V and R represent values calculated by Voigt and Reuss. A value of 0 represents the isotropic and 100% represents the greatest degree of anisotropy. LiFePO4 has an large shear anisotropy, which is also an important reason for its easy generation of microcracks. The doping of Mn, Nb, Mo, and Co all make the shear modulus of LiFePO4 more isotropic, and the doping of Co is the most obvious. In addition, the doping of Mn, Nb, Mo, and Co also reduces the bulk modulus anisotropy of LiFePO4. In summary, the doping of Mn, Nb, Mo, especially Co, can effectively reduce the anisotropy of LiFePO4 and suppress the generation of microcracks.
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4. Conclusion Using first-principles calculations, it was found that the doping of Mn, Nb, Mo, and Co has less formation energy and meets the criterion of mechanical stability, indicating that doping can be stable. It can be seen from the band structure that the doping of the four elements can reduce the band gap to facilitate the transition of electrons, especially the doping of Co and Nb. Doping of Mn, Nb, Mo, and Co can improve the mechanical stability of LiFePO4, especially the shear resistance of the material, and the doping of Co is particularly significant. In addition, the generation of microcracks increases the polarization of the electrode and causes a fade in capacity. The study of the anisotropy of the material shows that the doping of Mn, Nb, Mo, especially Co, can suppress the generation of microcracks and improve the material properties. Author contributions D. Zhang conceived the idea, analyzed the data, and wrote the main manuscript text. D. Zhang, J. Wang and K. Dong performed the simulations. A. Hao supervised and conceived this study, and provided intellectual and technical guidance. All authors discussed the results and commented on the manuscript. Acknowledgments This work was financially supported by National Natural Science Foundation of China (Nos. 51774002, 51674068), Natural Science Foundation of Hebei Province (No. E2018501091), the Science and Technology Project of Hebei Province (No. 15271302D), the Training Foundation for Scientific Research of Talents Project, Hebei Province (No. A2016005004), the Fundamental Research Funds for the Central Universities (No. N172302001). References [1] A.K. Padhi, K.S. Nanjundawamy, J.B. Goodenough, Phospho-olivion as positive electrode materials for rechargeable lithium batteries, J. Electrochem. Soc. 144
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
First principles investigation on the elastic and electronic properties of Mn, Co, Nb, Mo doped LiFePO4
T
⁎
Dongxu Zhang, Jie Wang, Kangze Dong, Aimin Hao
School of Materials Science and Engineering, Northeastern University, Shenyang 110819, PR China School of Resources and Materials, Northeastern University at Qinhuangdao, Qinhuangdao 066004, PR China Key Laboratory of Dielectric and Electrolyte Functional Material Hebei Province, Qinhuangdao, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: LiFePO4 Band structure Formation energy Elastic Anisotropic
In this work, the mechanical stability and electronic property of LiFePO4 doped with Mn, Co, Nb and Mo studied using the first principles calculation. The doped LiFePO4 has low defect formation energy and meets the criterion of mechanical stability, indicating that the doping of the four 3d transition metals can be stable. Band structure calculations depict half-metallic nature of the doping system. By calculating the Debye temperature and Poisson's ratio, it is found that the dopants can improve the mechanical stability of LiFePO4. In addition, the study of the anisotropy of the material also shows that the doping of Co can make the material tend to be more isotropic. The above shows that the doping of Mn, Nb, Mo, especially Co, can improve the mechanical stability of the material and reduce the degree of anisotropy of the material, thereby reducing the risk of microcracking and shear deformation of the material.
1. Introduction The olivine-type LiFePO4 was put forward by Padhi [1] in 1997 firstly. It can be used as cathode material for Li ion second battery. It attracts much attention, because of its high theoretical capacity, good stability and safety, low cost and environmental friendly [2]. At present, this material is mainly used in Electric Vehicle (EV) and Hybrid Electric Vehicle (HEV), but the low ionic and electronic conductivity affects its cycling performance and restricts its further application on lithium batteries [3]. In order to improve its performance, many efforts have focused on particle size reduction, carbon coating and cation doping [4–8]. In these methods, the cation doping has attracted much attention as an effective method. Wang and co-workers [9], by first principles calculations and experiments, confirmed that the doping of Mo can enhance the electronic conductivity of materials. Chung et al. [10] have been observed that the electrochemical properties of LiFePO4 were improved by doping Nb. All the above studies indicate that doping can effectively improve the partial performance of materials. However, current doping studies ignore the effect of material stability on battery performance. And the stability and safety of the battery materials are the basis of its application. At the same time, it will also greatly affect the performance of the material. The unstable lattice vibration will cause phase transition of the material [11]. And external pressure may also lead to material
⁎
deformation, resulting in material instability. Wang et al. [12] found that after 60 cycles, the charging and discharging curve of LiFePO4 would have obvious slope characteristics. The polarization is increased upon cycling. In addition, flaws can be observed in some particles after 10 cycles, which should be a result from internal high strain during lithium extraction/insertion process. Maxish et al. [13] use the first principle to calculate the elastic properties of LixFePO4. It is found that LixFePO4 has a smaller shear modulus and a higher degree of anisotropy compared with other cathode materials, which leads to the decrease of the capacity of the LiFePO4 and the poor cycle performance. Because the lattice structure symmetry of LiFePO4 after doping will be changed, the structural stability of materials will also be changed. As a commercially available cathode material, LiCoO2 also suffers from the breakdown of micro-structure due to internal strain [14]. At present, many studies have shown that the doping of metal cations in Co site can effectively protect the structural stability of LiCoO2, inhibit the phase transition and improve the cycle performance of the material [15–17]. Therefore, the doping in Fe site may play a positive role in improving the structural stability of LiFePO4 and improving its cycling performance. To the best of our knowledge the change of LiFePO4 stability after doping has not been investigated. In this work, four elements of transition group Mn, Co, Nb, and Mo are selected for substitution. By calculating the formation energy, elastic properties and anisotropy, the
Corresponding author at: School of Materials Science and Engineering, Northeastern University, Shenyang 110819, PR China. E-mail address: [email protected] (A. Hao).
https://doi.org/10.1016/j.commatsci.2018.09.010 Received 1 August 2018; Received in revised form 29 August 2018; Accepted 3 September 2018 Available online 08 September 2018 0927-0256/ © 2018 Elsevier B.V. All rights reserved.
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Fig. 2. Band structures of LiFePO4. The red and blue lines represent majorityspin states and minority-spin states, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 1. Bulk model of M-doped LiFePO4 (M = Mn, Co, Nb, Mo).
Table 1 Lattice parameters of LiFePO4 before and after doping.
influence of different doping elements on the structure stability of the material is studied. LiFePO4
2. Computational details LiFe1-1/8Mn1/8PO4 LiFe1-1/8Co1/8PO4 LiFe1-1/8Nb1/8PO4 LiFe1-1/8Mo1/8PO4
All calculations are performed using the CASTEP in the framework of the density functional theory (DFT). The general gradient approximation (GGA) by Perdew and Wang (PW91) for the exchange-correlation was used. The configulation of Li-1s2 2s1, O-2s2 2p4, P-3s2 3p3, Fe-3d6 4s2, Co-3d7 4s2, Nb-4s2 4p6 4d4 5s1 are treated as the valence electrons for the Ultrasoft Pseudopotentials (USPP). Energy cut-off for the plane waves (380 eV) and a Monkhorst-Pack mesh (3 × 4 × 5) [11] were applied to ensure the total ground state energy convergence of 1.0 × 10−5 eV per atom. For the geometry optimization, Broyden – Fletcher – Goldfarb – Shanno (BFGS) algorithm was used. For all the calculations 1 × 2 × 1 supercell were used. As shown in Fig. 1, the calculation model of LiFePO4, space group is Pnma, has an orthorhombic olivine structure. Each cell contains four formula units and 28 atoms. The doping models were obtained by replacing a Fe atom in 1 × 2 × 1 supercell. And the doping concentration of all doped models is 1/8. In the crystal structure, each FeO6 octahedron is connected by the corners shared. Meanwhile, FeO6 octahedron linked to two LiO6 octahedron and one PO4 tetrahedron by the edge shared.
Ours: Expt. [18]: Calc. [19]: Ours: Ours: Ours: Ours:
a (Å)
b (Å)
c (Å)
V (Å3)
10.35 10.33 10.49 10.36 10.32 10.43 10.39
12.06 12.02 11.83 12.1 12.04 12.11 12.11
4.72 4.69 4.75 4.73 4.72 4.73 4.73
589.16 582.34 589.46 593.48 587.62 597.41 595.09
of doped elements. It is worth noting that the changes in lattice constants are only reflected in the changes in the values of a and b, and the size of the c value remains basically unchanged. The band structure of Mn, Co, Nb, Mo doped is shown in Fig. 3. After Mn doping, the energy gap of the majority-spin is reduced from 3.29 eV to 3.04 eV, and the energy gap of minority gap is changed from 0.19 eV to 0.18 eV. It can be seen that an overlap of the minority-spin bands after the doping of Co and Nb, indicating that it’s a half metal. After Mo doping, the energy gap of the majority-spin is reduced from 3.29 eV to 2.53 eV, and the energy gap of minority gap is changed from 0.19 eV to 0.13 eV. The orbital contribution of dopants (Mn, Co, Nb and Mo) in the vicinity of the Fermi level is more clearly indicated by plotting the partial densities of states. It is not difficult to find from Fig. 4 that the dorbitals of the dopants contributes to the density of states in the vicinity of and reduces the band gap. In addition, the more the number of the d band electrons of the dopants, the higher the peak near the Fermi level. The d-orbital of Nb goes through the Fermi level and causes the band gap of LiFePO4 after doping to disappear. Therefore, the band gaps after doping of Mn, Co, Nb and Mo are decreased, which is beneficial to the transition of electrons and plays an important role in improving the electron mobility of LiFePO4. The defect formation energy Ef is an important concept used to characterize the degree of difficulty in the formation of a particular defect and the stability of its system. The smaller the energy is, the more stable it is. A formation energy greater than 0 indicates that the formation of the substance is endothermic, and less than 0 is exothermic. The formation energy of a defect or impurity M in charge state q is defined as [20]:
3. Results and discussion 3.1. Geometries, electronic property and formation energy The lattice optimization results of the undoped system are basically consistent with those measured experimentally. We have carried out spin-polarized electronic structure calculations of LiFePO4. The result is shown in Fig. 2. It can be seen an energy gap of 0.19 eV of the minorityspin bands. Our results are in good agreement with Yamada et al. [3]. It indicates that the models and parameters used in the calculation are reasonable. The variation of the side length of the doped system is less than 1% in Table 1, indicating that the doping does not destroy the original lattice structure, and the doping concentration is more reasonable. The change of lattice volume after doping is consistent with the ionic radius 411
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Fig. 3. Band structures of LiFePO4 after doping. The red and blue lines represent majority-spin states and minority-spin states, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Ef [X q ] = Etot [X q ]−Etot [bulk ]− ∑ ni μi + q [EF + EV + ΔV ] i
When any elastic medium is elongated in the longitudinal direction, it will contract in the lateral direction, and C12, C13, and C23 react to this property. The criteria for mechanical stability of orthorhombic are given by [21]
(1)
Etot[Xq] is the total energy with one defect or impurity M in the cell. Etot[bulk] is the total energy of pure LiFePO4. ni indicates the number of atoms of type i that have added to (ni > 0) or removed from(ni < 0) the cell. μi is the chemical potential of the i atom itself. It is worth noting that the doping system charge in this paper is zero, so the last item need not be considered. The formula for doping M (M = Mn, Co, Nb, Mo) can be simplified to:
Ef = E (LiFe1 − n Mn PO4 )−E (LiFePO4 )−nE (M) + nE (Fe)
C11 > 0, C22 > 0, C33 > 0, C44 > 0, C55 > 0, C66 > 0, C11 + C22 + C33 + 2(C12 + C13 + C23) > 0, (C11 + C22−2C12) > 0, (C11 + C33−2C13) > 0, (C22 + C33−2C23) > 0
(3)
From Table 3, it can be seen that the stiffness coefficient of LiFePO4 calculated in this paper is basically consistent with the value calculated in Ref. [13]. The stiffness coefficients before an d after doping correspond to the criterion of mechanical stability, indicating that the doped material is stable and ensures the feasibility of doping. In addition, the shear-related C44, C55, and C66 are significantly smaller than C11, C22, and C33 indicate that LiFePO4 is more susceptible to shear deformation. The values of C44, C55, and C66 after Mn, Co, Nb, and Mo doping were significantly improved. This results show that doping can improve the stability of the material by improving the shear resistance of the material. In addition to the elastic constants, there are still many properties that describe the mechanical stability of the crystal. Since the cathode materials are sintered powder after synthesis, it can be regarded as polycrystalline samples polymerized by single phase monocrystals with a random orientation. Debye temperature can reflect material stability and bond strength of materials. Besides, the physical properties of many materials, such as heat capacity, thermal expansion coefficient and melting point, are all related to Debye temperature. One of the ways to calculate the Debye temperature is to calculate the elastic constant and the average speed of sound [22].
(2)
From Table 2, it is not difficult to find that the doped materials have small formation energy in each system, which are easy to dope and can exist stably. The Mn-doped system has the smallest energy and formation energy, indicating that it is the most easily formed and most stable. Each metal particle doped from easy to difficult are Mn, Nb, Co, Mo. 3.2. Elastic properties The stability of the battery cathode material largely affects its electrochemical performance [11]. Poor stability will lead to phase transformation and degradation of cathode materials, which will affect the charge and discharge performance of batteries. Therefore, the calculation of the stability of cathode materials becomes particularly important. The stiffness coefficient (Cij) and the compliance coefficient (Sij) are calculated for calculating the elastic properties of materials. In orthorhombic, C11, C22, and C33 represent the linear compressibility along the X, Y, and Z axes, respectively, while C44, C55, and C66 are related to the shear strengths of the {1 0 0}, {0 1 0}, and {0 0 1} planes. 412
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Fig. 4. Partial densities of states calculated of the dopants (Mn, Co, Nb and Mo).
υl and υt are the transverse and longitudinal elastic wave velocities of the polycrystalline material related to the bulk modulus B and the shear modulus G.
Table 2 Energy and formation energy of the doped system. Compounds
LiFe1-1/8Mn1/ 8PO4
Energy (eV) ΔEƒ
−23725.17 −0.18
LiFe1-1/8Co1/ 8PO4 −24113.13 0.06
LiFe1-1/8Nb1/
LiFe1-1/8Mo1/
8PO4
8PO4
−24621.15 −0.01
4
−25005.16 4.65
G υt = ⎜⎛ ⎟⎞ ⎝ρ⎠
1
h 3n N ρ 3 TD = ⎡ ⎛ A ⎞ ⎤ υm k⎢ ⎣ 4π ⎝ M ⎠ ⎥ ⎦
(4)
(6)
1 2
(7)
The Debye temperature of the Co doped material is greatly improved, followed by the doping of Mn and Mo. The Debye temperature decreases slightly after Nb doping. This shows that the doping of Co can effectively improve the stability of LiFePO4, thereby improving its electrochemical performance. However, the doping of Nb has a negative effect on the structural stability of the material. There are mainly two methods for studying LiFePO4 as an orthorhombic polycrystalline material. The bulk modulus and shear modulus
where h is the Planck constant, k is the Boltzmann constant, NA is the Avogadro constant, ρ is the density, M is the molar mass, and n is the number of atoms in each molecule. The average wave speed of a polycrystalline material can be expressed as −1 3
1⎛ 2 1 ⎞⎤ υm = ⎡ ⎢ 3 ⎜ υ3 + υ 3 ⎟⎥ t l ⎠⎦ ⎝ ⎣
1
2 ⎛ B + 3G⎞ υl = ⎜ ⎟ ρ ⎝ ⎠
(5)
Table 3 Elastic constants (in GPa) and Debye temperature (in K).
LiFePO4 +Mn +Co +Nb +Mo
Ours: Ref. [13]: Ours: Ours: Ours: Ours:
C11
C22
C33
C44
C55
C66
C12
C13
C23
ρ [g/cm3]
TD [K]
153.1 133.0 160.0 172.3 153.1 153.6
195.4 203.0 205.5 215.8 182.5 199.2
164.1 172.3 199.2 195.9 168.1 176.3
33.8 34.9 57.0 60.4 36.4 43.3
53.5 47.8 62.0 69.1 57.0 61.6
54.0 42.4 47.3 62.3 50.7 54.8
73.8 74.3 74.3 72.3 68.6 71.2
60.7 54.3 58.5 53.2 56.2 62.6
37.4 55.2 42.9 39.2 39.2 41.4
3.57 3.52 3.53 3.58 3.61 3.63
564 – 599 633 555 577
413
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Table 4 Shear and bulk modulus, Young modulus (in GPa), and Poisson ratio.
LiFePO4 +Mn +Co +Nb +Mo
Ours: Ref. [13]: Ours: Ours: Ours: Ours:
GR
GV
GH
BR
BV
BH
EH
νH
B/G
47.8 44.3 57.0 65.0 49.0 53.0
51.0 46.7 59.2 66.3 51.5 55.6
49.4 45.5 58.1 65.6 50.2 54.3
94.4 94.3 101.3 100.9 92.1 97.3
95.1 97.3 101.8 101.5 92.4 97.7
94.8 95.8 101.5 101.2 92.2 97.5
126.3 125.0 146.4 161.8 127.5 137.4
0.28 0.30 0.26 0.23 0.27 0.27
1.92 2.11 1.75 1.54 1.84 1.80
10 cycles. And microcracks are suspected to be one of the factors that affect the electrochemical performance of the battery. Maxisch et al. [13] believed that this crack generation may be caused by the anisotropy of the material. The anisotropy of orthotropic materials is mainly reflected in the anisotropy of shear anisotropy and linear bulk modulus. The anisotropy of shear modulus can be expressed as follows: For the {1 0 0} shear planes in 〈0 1 0〉 and 〈0 1 1〉 directions is
of the material can be calculated separately according to the methods proposed by Voigt (BV and GV) and Reuss (BR and GR). It has been proved that the two calculation results of Voigt and Reuss are the upper limit and the lower limit of the true polycrystal constant [23]. Taking the average of the two can more accurately represent the bulk modulus and shear modulus of the material.
G=
GR + G V 2
(8)
B=
BR + B V 2
(9)
(12)
A1 = 4C44/(C11 + C33−2C13)
For the {0 1 0} shear planes in 〈0 0 1〉 and 〈1 0 0〉 directions is
A2 = 4C55/(C22 + C33−2C23)
Young's modulus and Poisson's ratio can be calculated using the following formula:
(13)
For the {0 0 1} shear planes in 〈1 1 0〉 and 〈0 1 0〉 directions is (14)
A3 = 4C66/(C11 + C22−2C12)
E=
9BG 3B + G
(10)
ν=
3B−2G 6B + 2G
(11)
The calculation results are shown in Table 5. When the values of A1, A2, and A3 are 1, the material is isotropic, and the degree of deviation from 1 indicates the degree of anisotropy. For the LiFePO4, the value of A3 approaches 1 tends to isotropy and A1 and A2 slightly less than 1 present anisotropy. The doping of Nb has little effect on the anisotropy of the material. The doping of Mo slightly increased A1 and A2. The doping of Co and Mn tends to make the {1 0 0} plane isotropic. However, the doping of Mn reduces the value of A3 while the doping of Co still keeps the {0 0 1} plane isotropic. In summary, the doping of Co can effectively reduce the shear anisotropy of the material and inhibit the generation of microcracks. The anisotropy of the bulk modulus can be estimated by calculating the bulk modulus along the crystal axis. Define the bulk modulus in the dp dp dp direction of each crystal axis as Ba = a da , Bb = b db , Bc = c dc . The bulk modulus anisotropy along the b-axis on the a and c axes can be written B B as ABa = Ba , ABc = B c . When the values are 1, the material is isotropic, b b and the degree of deviation from 1 indicates the degree of anisotropy. From the results, it can be found that there is a certain degree of anisotropy in each system, in which the doping of Nb makes the bulk modulus of the material more tend to be isotropic. Doping of Mn, Co, Mo has little effect on the bulk modulus anisotropy of LiFePO4. However, LiFePO4 itself has strong resistance to linear compression, the bulk modulus anisotropy may not be the main factor affecting the microcracks of materials. Chung and Buessem [26] proposed a more practical method to test the shear modulus and bulk modulus anisotropy of polycrystalline materials. Its formula can be defined as:
With the above formula, the calculated results are listed in Table 4. Bulk modulus refers to the ability of materials to resist fracture, indicating the incompressibility of materials. Shear modulus is used to characterize the material's ability to resist shear strain. The shear modulus of LiFePO4 is 49.4 GPa and the bulk modulus is 94.8 GPa. Compared with LiCoO2 and LiMn2O4 cathode materials, there is a big gap between them [24]. However, the doping of Mn and Co increased the BH and GH of the material, especially the shear resistance of the material. The doping effect of Co was the most obvious. The influence of Nb and Mo doping on the material is limited. The doping of Nb and Mo increased the GH value of the material, but the BH value after Nb doping decreased. Young's modulus is a physical quantity describing the ability of a solid material to resist deformation. It is similar to Debye temperature, and its result is consistent with calculation of the Debye temperature. The doping of Co greatly increases the ability of the material to resist deformation. The Poisson's ratio (νH) is the elastic constant that reflects the material's transverse deformation and indicates the material's ability to resist shear deformation. The smaller the Poisson's ratio, the more difficult it is for the material to undergo shear deformation. LiFePO4 has a large Poisson's ratio (0.28), which is prone to shear deformation. The values of Poisson's ratio after Mn, Nb and Mo doping do not change a lot, but doping of Co makes the Poisson's ratio of the material significantly reduced. This shows that doping of Co can significantly improve the ability of the material to resist shear strain. This is consistent with the previous analysis. Pugh [25] proposed that the material's plasticity and toughness can be judged by the value of B/G. When the value of B/G is greater than 1.75, the material has better toughness, whereas the material is brittle. From Table 4 it is not difficult to find that the doping of Mn, Nb, and Mo will make the material brittle. The doping of Co also becomes more brittle while greatly increasing the strength of the material.
AG = (G V−G R )/(G V + G R )
(15)
AB = (B V−BR )/(B V + BR )
(16)
Table 5 Anisotropic properties (in GPa) of LiFePO4 before and after doping.
LiFePO4 +Mn +Co +Nb +Mo
3.3. Anisotropy Wang et al. [12] found that LiFePO4 will produce microcracks after 414
A1
A2
A3
ABa
ABc
AG (%)
AB (%)
0.691 0.941 0.923 0.697 0.846
0.752 0.778 0.829 0.838 0.842
1.075 0.872 1.023 1.023 1.042
0.883 0.759 0.796 0.907 0.812
0.733 0.852 0.781 0.822 0.802
3.24 1.89 0.99 2.49 2.39
0.37 0.25 0.3 0.16 0.21
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where B and G represent the bulk modulus and shear modulus of the material. V and R represent values calculated by Voigt and Reuss. A value of 0 represents the isotropic and 100% represents the greatest degree of anisotropy. LiFePO4 has an large shear anisotropy, which is also an important reason for its easy generation of microcracks. The doping of Mn, Nb, Mo, and Co all make the shear modulus of LiFePO4 more isotropic, and the doping of Co is the most obvious. In addition, the doping of Mn, Nb, Mo, and Co also reduces the bulk modulus anisotropy of LiFePO4. In summary, the doping of Mn, Nb, Mo, especially Co, can effectively reduce the anisotropy of LiFePO4 and suppress the generation of microcracks.
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4. Conclusion Using first-principles calculations, it was found that the doping of Mn, Nb, Mo, and Co has less formation energy and meets the criterion of mechanical stability, indicating that doping can be stable. It can be seen from the band structure that the doping of the four elements can reduce the band gap to facilitate the transition of electrons, especially the doping of Co and Nb. Doping of Mn, Nb, Mo, and Co can improve the mechanical stability of LiFePO4, especially the shear resistance of the material, and the doping of Co is particularly significant. In addition, the generation of microcracks increases the polarization of the electrode and causes a fade in capacity. The study of the anisotropy of the material shows that the doping of Mn, Nb, Mo, especially Co, can suppress the generation of microcracks and improve the material properties. Author contributions D. Zhang conceived the idea, analyzed the data, and wrote the main manuscript text. D. Zhang, J. Wang and K. Dong performed the simulations. A. Hao supervised and conceived this study, and provided intellectual and technical guidance. All authors discussed the results and commented on the manuscript. Acknowledgments This work was financially supported by National Natural Science Foundation of China (Nos. 51774002, 51674068), Natural Science Foundation of Hebei Province (No. E2018501091), the Science and Technology Project of Hebei Province (No. 15271302D), the Training Foundation for Scientific Research of Talents Project, Hebei Province (No. A2016005004), the Fundamental Research Funds for the Central Universities (No. N172302001). References [1] A.K. Padhi, K.S. Nanjundawamy, J.B. Goodenough, Phospho-olivion as positive electrode materials for rechargeable lithium batteries, J. Electrochem. Soc. 144
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