Supporting Information Silicon Framework-based Lithium Silicides at ...
Supporting Information
Silicon Framework-based Lithium Silicides at High Pressures Shoutao Zhang1, Yanchao Wang1, Guochun Yang1,2,* and Yanming Ma1,*
1
State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China 2 Centre for Advanced Optoelectronic Functional Materials Research and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China,
*
E-mail: [email protected] and [email protected]
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Supporting Figures
Figure S1. Comparison of the fitted Birch-Murnaghan equation of states for LiSi in the Pm-3m structure by using the calculated results from the PAW pseudopotentials and the full-potential LAPW methods.
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Figure S2. Chemical stabilities of Li-Si system at ambient pressure. The formation enthalpies of Li-Si compounds are relative to the enthalpies of elemental decomposition into solidified phases of Li and Si. Dashed lines connect data points, and solid lines denote the convex hull. Fm-3m structure of elemental Li and Fd-3m structure of elemental Si were adopted to calculate the formation enthalpies. Several structures (e.g. Li3Si2, Li2Si, Li3Si, and Li4Si) predicted by minima hopping method are also included and denoted by blue triangles. The formation enthalpies of our predicted structures (e.g. Li3Si2, Li2Si, Li3Si) are equal to those of structures obtained by minima hopping method. In other words, structures predicted by minima hopping method are well reproduced by our calculations. For Li4Si composition, the formation enthalpy of our predicted P213 structure (4 formula units) is slightly lower than that of I4/m (2 formula units). This might originate from the smaller unit cells used in minima hopping simulations (i.e. Unit cell contains maximum number of 16 atoms in their simulations).
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Figure S3. Phonon spectra of LiSi4 with Cmmm symmetry at 25 GPa.
Figure S4. Phonon spectra of LiSi3 with P6/mmm symmetry at 25 GPa.
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Figure S5. Phonon spectra of LiSi2 with P2/m symmetry at 25 GPa.
Figure S6. Phonon spectra of Li2Si3 with P2/m symmetry at 25 GPa.
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Figure S7. Phonon spectra of LiSi with P4/mmm symmetry at 25 GPa.
Figure S8. Phonon spectra of Li2Si with P6/mmm symmetry at 25 GPa.
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Figure S9. Phonon spectra of Li3Si with Fm-3m symmetry at 25 GPa.
Figure S10. Phonon spectra of Li4Si with R-3m symmetry at 25 GPa.
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Figure S11. Electronic band structure and projected density of states of LiSi4 with Cmmm symmetry at 25 GPa.
Figure S12. Electronic band structure and projected density of states of LiSi3 with P6/mmm symmetry at 25 GPa.
Figure S13. Electronic band structure and projected density of states of LiSi2 with P2/m symmetry at 25 GPa.
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Figure S14. Electronic band structure and projected density of states of Li2Si3 with P2/m symmetry at 25 GPa.
Figure S15. Electronic band structure and projected density of states of LiSi with P4/mmm symmetry at 25 GPa.
Figure S16. Electronic band structure and projected density of states of Li2Si with P6/mmm symmetry at 25 GPa.
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Figure S17. Electronic band structure and projected density of states of Li3Si with Fm-3m symmetry at 25 GPa.
Figure S18. Electronic band structure and projected density of states of Li4Si with R-3m symmetry at 25 GPa.
Figure S19. Calculated ELF in the (100) plane for LiSi4 with Cmmm symmetry.
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Table S1. Detailed structural information of the predicted stable Li-Si compounds at selected pressures. Phases P Lattice Atomic coordinates (GPa) Parameters (fractional) Atoms x y z (Å, °) LiSi4-Cmmm 25 Li(2a) 0.0000 0.0000 0.0000 a = 4.2071 b = 12.0560
Si(4j)
0.5000 0.0966 0.5000
c = 2.3850
Si(4j)
1.0000 0.1954 0.5000
a = b = 5.1492
Li(2a)
0.0000 0.0000 0.0000
c = 3.2859
Si(8h)
0.7050 0.1029 0.0000
a = b = 4.7810
Li(1b)
0.0000 0.0000 0.5000
c = 2.4231
Si(3g)
0.5000 0.0000 0.0000
a = b = 3.4120
Li(1c)
0.5000 0.5000 0.0000
c = 10.7123
Li(2g)
0.0000 0.0000 0.3353
α = β = γ = 90.0000
Si(1a)
0.0000 0.0000 0.0000
Si(4i)
0.5000 0.0000 0.1670
Si(2h)
0.5000 0.5000 0.3342
Si(2e)
0.5000 0.0000 0.5000
a = b = 3.2140
Li(2b)
0.5000 0.5000 0.0000
c = 6.6560
Si(2a)
0.0000 0.0000 0.0000
α = β = γ = 90.0000
Si(4d)
0.5000 0.0000 0.2500
a = 6.1002
Li(2m)
0.3141 0.0000 0.6878
b = 2.4435
Si(1b)
0.0000 0.5000 0.0000
c = 4.6895
Si(1f)
0.0000 0.5000 0.5000
α = γ = 90.0000
Si(2n)
0.3518 0.5000 0.1958
a = 8.0690
Li(2n)
0.1038 0.5000 0.2859
b = 2.4322
Li(2n)
0.3087 0.5000 0.8673
c = 6.1309
Si(1a)
1.0000 0.0000 0.0000
α = γ = 90.0000
Si(2m)
0.1818 0.0000 0.5920
α = β = γ = 90.0000 LiSi4-I4/m
100
α = β = γ = 90.0000 LiSi3-P6/mmm 25
α = β = 90.0000 γ = 120.0000 LiSi3-P4/mmm 40
LiSi3-I4/mmm
LiSi2-P2/m
100
25
β = 82.4464 Li2Si3-P2/m
25
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Si(2m)
0.3856 0.0000 0.1858
Si(1g)
0.5000 0.0000 0.5000
a = b = 2.4107
Li(1a)
0.0000 0.0000 0.0000
c = 3.7057
Si(1d)
0.5000 0.5000 0.5000
a = b = c = 2.4878
Li(1a)
0.0000 0.0000 0.0000
α = β = γ = 90.0000
Si(1b)
0.5000 0.5000 0.5000
a = b = 3.8592
Li(2d)
0.6666 0.3333 0.5000
c = 2.3779
Si(1a)
0.0000 0.0000 0.0000
a = b = 2.4180
Li(4e)
0.5000 0.5000 0.1798
c = 7.2867
Si(2a)
0.0000 0.0000 0.0000
a = b = c = 5.4488
Li(4a)
0.0000 0.0000 0.0000
α = β = γ = 90.0000
Li(8c)
0.7500 0.7500 0.7500
Si(4b)
0.0000 0.0000 0.5000
β = 68.7800 LiSi-P4/mmm
25
α = β = γ = 90.0000 LiSi-Pm-3m
100
Li2Si-P6/mmm 25
α = β = 90.0000 γ = 120.0000 Li2Si-I4/mmm
100
α = β = γ = 90.0000 Li3Si-Fm-3m
Li3Si-Fmmm
25
100
a = 3.5431
Li(16m) 0.5000 0.8134 0.6510
b = 10.1694
Li(8i)
0.5000 0.0000 0.3343
c = 6.1197
Si(8h)
0.5000 0.8913 0.0000
a = b = 3.9295
Li(6c)
0.0000 0.0000 0.7891
c = 11.3365
Li(6c)
0.0000 0.0000 0.6009
α = β = 90.0000
Si(3a)
0.0000 0.0000 1.0000
a = b = 4.7398
Li(8h)
0.2928 0.0437 0.0000
c = 3.8116
Si(2b)
0.0000 0.0000 0.5000
a = 3.5597
Li(32h)
0.0308 0.6753 0.9261
b = 6.2592
Si(8a)
0.2500 0.7500 0.2500
α = β = γ = 90.0000 Li4Si-R-3m
25
γ = 120.0000 Li4Si-I4/m
45
α = β = γ = 90.0000 Li4Si-Fddd
100
c = 11.9973 α = β = γ = 90.0000
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Silicon Framework-based Lithium Silicides at High Pressures Shoutao Zhang1, Yanchao Wang1, Guochun Yang1,2,* and Yanming Ma1,*
1
State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China 2 Centre for Advanced Optoelectronic Functional Materials Research and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China,
*
E-mail: [email protected] and [email protected]
S-‐1
Supporting Figures
Figure S1. Comparison of the fitted Birch-Murnaghan equation of states for LiSi in the Pm-3m structure by using the calculated results from the PAW pseudopotentials and the full-potential LAPW methods.
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Figure S2. Chemical stabilities of Li-Si system at ambient pressure. The formation enthalpies of Li-Si compounds are relative to the enthalpies of elemental decomposition into solidified phases of Li and Si. Dashed lines connect data points, and solid lines denote the convex hull. Fm-3m structure of elemental Li and Fd-3m structure of elemental Si were adopted to calculate the formation enthalpies. Several structures (e.g. Li3Si2, Li2Si, Li3Si, and Li4Si) predicted by minima hopping method are also included and denoted by blue triangles. The formation enthalpies of our predicted structures (e.g. Li3Si2, Li2Si, Li3Si) are equal to those of structures obtained by minima hopping method. In other words, structures predicted by minima hopping method are well reproduced by our calculations. For Li4Si composition, the formation enthalpy of our predicted P213 structure (4 formula units) is slightly lower than that of I4/m (2 formula units). This might originate from the smaller unit cells used in minima hopping simulations (i.e. Unit cell contains maximum number of 16 atoms in their simulations).
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Figure S3. Phonon spectra of LiSi4 with Cmmm symmetry at 25 GPa.
Figure S4. Phonon spectra of LiSi3 with P6/mmm symmetry at 25 GPa.
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Figure S5. Phonon spectra of LiSi2 with P2/m symmetry at 25 GPa.
Figure S6. Phonon spectra of Li2Si3 with P2/m symmetry at 25 GPa.
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Figure S7. Phonon spectra of LiSi with P4/mmm symmetry at 25 GPa.
Figure S8. Phonon spectra of Li2Si with P6/mmm symmetry at 25 GPa.
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Figure S9. Phonon spectra of Li3Si with Fm-3m symmetry at 25 GPa.
Figure S10. Phonon spectra of Li4Si with R-3m symmetry at 25 GPa.
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Figure S11. Electronic band structure and projected density of states of LiSi4 with Cmmm symmetry at 25 GPa.
Figure S12. Electronic band structure and projected density of states of LiSi3 with P6/mmm symmetry at 25 GPa.
Figure S13. Electronic band structure and projected density of states of LiSi2 with P2/m symmetry at 25 GPa.
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Figure S14. Electronic band structure and projected density of states of Li2Si3 with P2/m symmetry at 25 GPa.
Figure S15. Electronic band structure and projected density of states of LiSi with P4/mmm symmetry at 25 GPa.
Figure S16. Electronic band structure and projected density of states of Li2Si with P6/mmm symmetry at 25 GPa.
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Figure S17. Electronic band structure and projected density of states of Li3Si with Fm-3m symmetry at 25 GPa.
Figure S18. Electronic band structure and projected density of states of Li4Si with R-3m symmetry at 25 GPa.
Figure S19. Calculated ELF in the (100) plane for LiSi4 with Cmmm symmetry.
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Table S1. Detailed structural information of the predicted stable Li-Si compounds at selected pressures. Phases P Lattice Atomic coordinates (GPa) Parameters (fractional) Atoms x y z (Å, °) LiSi4-Cmmm 25 Li(2a) 0.0000 0.0000 0.0000 a = 4.2071 b = 12.0560
Si(4j)
0.5000 0.0966 0.5000
c = 2.3850
Si(4j)
1.0000 0.1954 0.5000
a = b = 5.1492
Li(2a)
0.0000 0.0000 0.0000
c = 3.2859
Si(8h)
0.7050 0.1029 0.0000
a = b = 4.7810
Li(1b)
0.0000 0.0000 0.5000
c = 2.4231
Si(3g)
0.5000 0.0000 0.0000
a = b = 3.4120
Li(1c)
0.5000 0.5000 0.0000
c = 10.7123
Li(2g)
0.0000 0.0000 0.3353
α = β = γ = 90.0000
Si(1a)
0.0000 0.0000 0.0000
Si(4i)
0.5000 0.0000 0.1670
Si(2h)
0.5000 0.5000 0.3342
Si(2e)
0.5000 0.0000 0.5000
a = b = 3.2140
Li(2b)
0.5000 0.5000 0.0000
c = 6.6560
Si(2a)
0.0000 0.0000 0.0000
α = β = γ = 90.0000
Si(4d)
0.5000 0.0000 0.2500
a = 6.1002
Li(2m)
0.3141 0.0000 0.6878
b = 2.4435
Si(1b)
0.0000 0.5000 0.0000
c = 4.6895
Si(1f)
0.0000 0.5000 0.5000
α = γ = 90.0000
Si(2n)
0.3518 0.5000 0.1958
a = 8.0690
Li(2n)
0.1038 0.5000 0.2859
b = 2.4322
Li(2n)
0.3087 0.5000 0.8673
c = 6.1309
Si(1a)
1.0000 0.0000 0.0000
α = γ = 90.0000
Si(2m)
0.1818 0.0000 0.5920
α = β = γ = 90.0000 LiSi4-I4/m
100
α = β = γ = 90.0000 LiSi3-P6/mmm 25
α = β = 90.0000 γ = 120.0000 LiSi3-P4/mmm 40
LiSi3-I4/mmm
LiSi2-P2/m
100
25
β = 82.4464 Li2Si3-P2/m
25
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Si(2m)
0.3856 0.0000 0.1858
Si(1g)
0.5000 0.0000 0.5000
a = b = 2.4107
Li(1a)
0.0000 0.0000 0.0000
c = 3.7057
Si(1d)
0.5000 0.5000 0.5000
a = b = c = 2.4878
Li(1a)
0.0000 0.0000 0.0000
α = β = γ = 90.0000
Si(1b)
0.5000 0.5000 0.5000
a = b = 3.8592
Li(2d)
0.6666 0.3333 0.5000
c = 2.3779
Si(1a)
0.0000 0.0000 0.0000
a = b = 2.4180
Li(4e)
0.5000 0.5000 0.1798
c = 7.2867
Si(2a)
0.0000 0.0000 0.0000
a = b = c = 5.4488
Li(4a)
0.0000 0.0000 0.0000
α = β = γ = 90.0000
Li(8c)
0.7500 0.7500 0.7500
Si(4b)
0.0000 0.0000 0.5000
β = 68.7800 LiSi-P4/mmm
25
α = β = γ = 90.0000 LiSi-Pm-3m
100
Li2Si-P6/mmm 25
α = β = 90.0000 γ = 120.0000 Li2Si-I4/mmm
100
α = β = γ = 90.0000 Li3Si-Fm-3m
Li3Si-Fmmm
25
100
a = 3.5431
Li(16m) 0.5000 0.8134 0.6510
b = 10.1694
Li(8i)
0.5000 0.0000 0.3343
c = 6.1197
Si(8h)
0.5000 0.8913 0.0000
a = b = 3.9295
Li(6c)
0.0000 0.0000 0.7891
c = 11.3365
Li(6c)
0.0000 0.0000 0.6009
α = β = 90.0000
Si(3a)
0.0000 0.0000 1.0000
a = b = 4.7398
Li(8h)
0.2928 0.0437 0.0000
c = 3.8116
Si(2b)
0.0000 0.0000 0.5000
a = 3.5597
Li(32h)
0.0308 0.6753 0.9261
b = 6.2592
Si(8a)
0.2500 0.7500 0.2500
α = β = γ = 90.0000 Li4Si-R-3m
25
γ = 120.0000 Li4Si-I4/m
45
α = β = γ = 90.0000 Li4Si-Fddd
100
c = 11.9973 α = β = γ = 90.0000
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