The Oxygen Reduction Reaction in Non- aqueous Electrolytes: Li ...
Li ion diffusion mechanisms in Li PO electrolytes
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Reference [1] B. Wang et al., Journal of Solid State Chemistry 115, 313 (1995) [2] A. K. Ivanov-Shitz et al., Crystallography Reports 46, 864 (2001). [3] Y.-W.Hu et al., Journal of the Electrochemical society 124, 1240 (1977). [4] PWscf – http://www.pwscf.org. [5] A. R. West, Basic Solid State Chemistry, Second Edition (John Wiley & Sons, Inc. 2000) [6] B. N. Mavrin et al., Journal of Experimental and Theoretical Physics 96, 53 (2003). [7]F. Harbach and F. Fischer, Physica Status Solidi B 66, 237 (1974). [8] L. Popovi´ c et al., Journal of Raman Spectroscopy 34, 77 (2003). Intrinsic defects The formation energies of interstitial-vacancy pairs are found to be E f (γ )=1.7 eV and E f (β )= 2.1 eV. Estimating the intrinsic activation energy as E A = E m (interstitial) + E f /2, we obtain good agreement with experiment. 2 Crystal Net direction Experiment (eV) This work (eV) γ -Li 3 PO 4 a 1.23 1.1 b 1.14 1.1 c 1.14 1.1 β -Li 3 PO 4 b 1.6 a 1.4 c 1.4 Interstitial mechanism γ -Li 3 PO 4 2b 2c I a 2c II a 2b I 0 II* I 0 0 0.1 0.2 0.3 0.4 0.5 Energy (eV) II 0 II 0 a-axis I 0 I 0 0 0.1 0.2 0.3 0.4 0.5 Energy (eV) b c & axes β -Li 3 PO 4 2b 2b I 2a 2c 2c 2a II I 0 II 0 II 1 I 0 0 0.2 0.4 0.6 0.8 Energy (eV) b-axis I 0 I 0 0 0.2 0.4 0.6 0.8 Energy (eV) a c & axes Interstitial migration paths show the most efficient ion transport mechanism for both γ - and β -Li 3 PO 4 , with computed migration barriers of 0.3–0.5 eV, in good agreement with the measured 0.5 eV acti- vation energy of extrinsic interstitials for Li 4 SiO 4 -Li 3 PO 4 solid solutions. 3 Structural diagrams show meta-stable interstitial sites I and II located in the two distinct void channels for both crystals. Vacancy mechanism γ -Li 3 PO 4 1(d) 2(c) 3(d) 0.2 0.4 0.6 0.8 1 Energy (eV) a -axis 1(d) 2(c) 3(d) 0.2 0.4 0.6 0.8 1 Energy (eV) LDA GGA a -axis 1(d) 4(d) 5(d) 0.2 0.4 0.6 0.8 1 Energy (eV) LDA GGA b-axis 4(d) 8(d) 7(d) 0.2 0.4 0.6 0.8 1 Energy (eV) 4(d) 6(c) 7(d) 0.2 0.4 0.6 0.8 1 Energy (eV) LDA GGA c -axis β -Li 3 PO 4 4(b) 3(b) 5(b) 0.2 0.4 0.6 0.8 Energy (eV) a -axis 7(b) 5(b) 6(b) 0.2 0.4 0.6 0.8 Energy (eV) 7(b) 2(a) 6(b) 0.2 0.4 0.6 0.8 Energy (eV) c -axis 1(b) 2(a) 3(b) 0.2 0.4 0.6 0.8 Energy (eV) b-axis Energy path diagrams for various vacancy migration paths in crystalline Li 3 PO 4 , showing minimal barriers of 0.62 eV along the c-axis path for the γ form and 0.55 eV along the b-axis path for the β form. These barriers are 0.3 eV lower than the measured activation energy for vacancy-rich Li 2.88 PO 3.73 N 0.14 , 1 where oxygen-vacancies may affect the migration barrier. Raman spectra LDA calculations show better agreement with experimental spectra than GGA; simulation results in this poster are presented for the LDA functional unless otherwise specified. 200 400 600 800 1000 ν (cm -1 ) Exp. B LDA GGA Exp. C Exp. D Exp. A Raman active modes of γ -Li 3 PO 4 , comparing ex- perimental results with LDA and GGA calcula- tions. Experiment A (from Ref. 6) was measured at room temperature (RT). Experiment B and C (from Ref. 7) were measured at RT and liquid nitro- gen temperature (LNT), respectively. Experiment D (from Ref. 8) was measured at LNT. 200 400 600 800 1000 ν (cm -1 ) GGA LDA Exp. Raman active modes of β -Li 3 PO 4 , comparing ex- perimental results with LDA and GGA calcula- tions. Experimental data (from Ref. 8) were mea- sured at LNT. Crystal structures a 2b 2c 1 4 5 7 6 8 2 3 γ -Li 3 PO 4 Space group: Pnma Metastable at room temperature; experimentally measured. The Li ions are located on two crys- tallographically different sites indicated with dif- ferent shadings (gray and dark balls) in the figure. Using the Wyckoff labels, the d site accounts for 8 equivalent atomic sites and the c site accounts for 4 equivalent atomic sites per unit cell. The P and O ions are indicated by small balls and sticks (colored yellow and blue respectively). 2b 2c 2a 1 2 3 4 5 6 7 β -Li 3 PO 4 Space group: Pmn2 1 Low-temperature phase and energetically more sta- ble than γ -phase. Two crystallographically distinct Li sites are also indicated with different shadings in the figure. Using the Wyckoff labels, the b site accounts for 4 equivalent atomic sites and the a site accounts for 2 equivalent atomic sites per unit cell. Our calculations verify that the β form is en- ergetically more stable: E γ - E β =0.03(0.01) eV/Li 3 PO 4 for LDA (GGA) calculations. Introduction • Solid-state lithium ion electrolytes such as Li 3 PO 4 -based materials 1 are becoming increasingly im- portant in batteries and related technologies. • Li ion diffusion in crystalline γ -Li 3 PO 4 has been measured to be slightly anisotropic with activation energies of 1.1–1.3 eV. 2 The activation energies can be reduced to 0.97 eV by N doping 1 and to 0.5 eV by admixture with Li 4 SiO 4 . 3 • In this work, first-principles calculations 4 have been performed to model the migration energies for both vacancy and interstitial mechanisms of Li ions in γ -Li 3 PO 4 and β -Li 3 PO 4 . For extrinsic defects, activation energy E A is the same as the migration energy of the defects, E m . However, for intrinsic defects, using quasi-equilibrium statistical mechanics arguments, 5 it follows that E A = E m + E f /2, where E f is the formation energy of the vacancy-interstitial pair. Yaojun Du and N. A. W. Holzwarth Department of Physics, Wake Forest University, Winston-Salem, NC, USA Supported by NSF grants DMR-0405456 and 0427055. Li ion diffusion mechanisms in Li 3 PO 4 electrolytes
Transcript of Li ion diffusion mechanisms in Li PO electrolytes
Reference[1] B. Wang et al., Journal of Solid State Chemistry 115, 313 (1995)[2] A. K. Ivanov-Shitz et al., Crystallography Reports 46, 864 (2001).[3] Y.-W.Hu et al., Journal of the Electrochemical society 124, 1240 (1977).[4] PWscf – http://www.pwscf.org.[5] A. R. West, Basic Solid State Chemistry, Second Edition (John Wiley & Sons, Inc. 2000)[6] B. N. Mavrin et al., Journal of Experimental and Theoretical Physics 96, 53 (2003).[7] F. Harbach and F. Fischer, Physica Status Solidi B 66, 237 (1974).[8] L. Popovic et al., Journal of Raman Spectroscopy 34, 77 (2003).
Intrinsic defectsThe formation energies of interstitial-vacancy pairs are found to be Ef (γ) = 1.7 eV and Ef (β) =2.1 eV. Estimating the intrinsic activation energy as EA = Em(interstitial) + Ef/2, we obtain goodagreement with experiment.2
Crystal Net direction Experiment (eV) This work (eV)γ-Li3PO4 a 1.23 1.1
b 1.14 1.1c 1.14 1.1
β-Li3PO4 b 1.6a 1.4c 1.4
Interstitial mechanismγ-Li3PO4
2b
2cI
a2c
II
a
2b
I0 II* I00
0.10.20.30.40.5
Ener
gy (e
V)
II0 II0
a-axis
I0 I00
0.10.20.30.40.5
Ener
gy (e
V) b c & axes
β-Li3PO4
2b 2b
I2a
2c 2c
2a II
I0 II0 II1 I00
0.20.40.60.8
Ener
gy (e
V) b-axis
I0 I00
0.20.40.60.8
Ener
gy (e
V) a c & axes
Interstitial migration paths show the most efficient ion transport mechanism for both γ- and β-Li3PO4,with computed migration barriers of 0.3–0.5 eV, in good agreement with the measured 0.5 eV acti-vation energy of extrinsic interstitials for Li4SiO4-Li3PO4 solid solutions.3 Structural diagrams showmeta-stable interstitial sites I and II located in the two distinct void channels for both crystals.
Vacancy mechanismγ-Li3PO4
1(d) 2(c) 3(d)
0.20.40.60.8
1
Ener
gy (e
V) a-axis
1(d) 2(c) 3(d)
0.20.40.60.8
1
Ener
gy (e
V) LDA
GGAa-axis
1(d) 4(d) 5(d)
0.20.40.60.8
1
Ener
gy (e
V)
LDAGGA
b-axis
4(d) 8(d) 7(d)
0.20.40.60.8
1
Ener
gy (e
V)
4(d) 6(c) 7(d)
0.20.40.60.8
1
Ener
gy (e
V) LDA
GGAc-axis
β-Li3PO4
4(b) 3(b) 5(b)
0.20.40.60.8
Ener
gy (e
V) a-axis
7(b) 5(b) 6(b)
0.20.40.60.8
Ener
gy (e
V)
7(b) 2(a) 6(b)
0.20.40.60.8
Ener
gy (e
V) c-axis
1(b) 2(a) 3(b)
0.20.40.60.8
Ener
gy (e
V) b-axis
Energy path diagrams for various vacancy migration paths in crystalline Li3PO4, showing minimalbarriers of 0.62 eV along the c-axis path for the γ form and 0.55 eV along the b-axis path forthe β form. These barriers are 0.3 eV lower than the measured activation energy for vacancy-richLi2.88PO3.73N0.14,1 where oxygen-vacancies may affect the migration barrier.
Raman spectraLDA calculations show better agreement with experimental spectra than GGA;
simulation results in this poster are presented for the LDA functional unlessotherwise specified.
200 400 600 800 1000ν (cm-1)
Exp. B
LDA
GGA
Exp. C
Exp. D
Exp. A
Raman active modes of γ-Li3PO4, comparing ex-perimental results with LDA and GGA calcula-tions. Experiment A (from Ref. 6) was measured atroom temperature (RT). Experiment B and C (fromRef. 7) were measured at RT and liquid nitro-gen temperature (LNT), respectively. ExperimentD (from Ref. 8) was measured at LNT.
200 400 600 800 1000ν (cm-1)
GGA
LDA
Exp.
Raman active modes of β-Li3PO4, comparing ex-perimental results with LDA and GGA calcula-tions. Experimental data (from Ref. 8) were mea-sured at LNT.
Crystal structures
a2b
2c
145
7
68
23
γ-Li3PO4 Space group: PnmaMetastable at room temperature; experimentallymeasured. The Li ions are located on two crys-tallographically different sites indicated with dif-ferent shadings (gray and dark balls) in the figure.Using the Wyckoff labels, the d site accounts for 8equivalent atomic sites and the c site accounts for 4equivalent atomic sites per unit cell. The P and Oions are indicated by small balls and sticks (coloredyellow and blue respectively).
2b
2c
2a
1 2 345
6
7 β-Li3PO4 Space group: Pmn21Low-temperature phase and energetically more sta-ble than γ-phase. Two crystallographically distinctLi sites are also indicated with different shadingsin the figure. Using the Wyckoff labels, the b siteaccounts for 4 equivalent atomic sites and the asite accounts for 2 equivalent atomic sites per unitcell. Our calculations verify that the β form is en-ergetically more stable: Eγ − Eβ = 0.03(0.01)eV/Li3PO4 for LDA (GGA) calculations.
Introduction• Solid-state lithium ion electrolytes such as Li3PO4-based materials1 are becoming increasingly im-
portant in batteries and related technologies.• Li ion diffusion in crystalline γ-Li3PO4 has been measured to be slightly anisotropic with activation
energies of 1.1–1.3 eV.2 The activation energies can be reduced to 0.97 eV by N doping1 and to 0.5eV by admixture with Li4SiO4.3
• In this work, first-principles calculations4 have been performed to model the migration energiesfor both vacancy and interstitial mechanisms of Li ions in γ-Li3PO4 and β-Li3PO4. For extrinsicdefects, activation energy EA is the same as the migration energy of the defects, Em. However,for intrinsic defects, using quasi-equilibrium statistical mechanics arguments,5 it follows that EA =Em + Ef/2, where Ef is the formation energy of the vacancy-interstitial pair.
Yaojun Du and N. A. W. HolzwarthDepartment of Physics, Wake Forest University, Winston-Salem, NC, USA
Supported by NSF grants DMR-0405456 and 0427055.
Li ion diffusion mechanisms in Li3PO4 electrolytes
