Phosphates as Lithium-Ion Battery Cathodes: An
Evaluation Based on High-Throughput Ab Initio
Calculations: Supplementary information
Stability of the ICSD lithium phosphate containing phases
Table 2 shows the stability data for the ICSD entries containing at least Li, P, O and a redox
active element and without partial occupancies. It is surprising to see so few hydrated phases
(only Li2 Mn2 (P6 O18 )(H2 O)10 ) but the 9 other Li-M-P-O-H phases in the ICSD, with M as a redox
active element, have missing H or partial occupancies.
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ICSD number
formula
space group
energy above the hull (meV/at)
240269
Li2 V2 (PO4 )3
Pbcn(60)
0
25834
LiMnPO4
Pnma(62)
0
2808
LiCu(PO3 )3
P 21 21 21 (19)
0
39534
LiTiO(PO4 )
Pnma(62)
0
50588
Li2Ni(PO4 )F
Pnma(62)
0
56291
LiFePO4
Pnma(62)
0
63509
LiFeP2 O7
P 21 (4)
0
68522
LiMoP2 O7
P 21 (4)
0
80613
LiVO(PO4 )
Pnma(62)
0
81074
LiMo(PO4 )2
P 21 /c(14)
0
83662
Li2 Ni3 (P2 O7 )2
P 21 /c(14)
0
83832
Li1 Sn2 (PO4 )3
R3̄(148)
0
84703
Li2 Na(MoO)2 (PO4 )3
C2/c(15)
0
84943
Li3 (Mo3 O5 (PO4 )3 )
P21 /c(14)
0
93021
LiVP2 O7
P 21 (4)
0
94538
LiCa9 Mn(PO4 )7
R3c(161)
0
95979
Li1 Ti2 (PO4 )3
R3̄c(167)
0
98362
Li3 V2 (PO4 )3
P21 /c(14)
0
402760
LiNiPO4
Pnma(62)
1
51212
Li2 Ba3 Cl2 (MoO)4 (PO4 )6
P 21 21 21 (19)
1
62244
Li3 Fe2 (PO4 )3
P21 /c(14)
1
82383
LiNi2 (P3 O10 )
P21 /m(11)
1
50958
Li9 Fe3 (P2 O7 )3 (PO4 )2
P3̄c1(165)
2
51632
LiMn(PO3 )3
P 21 21 21 (19)
2
72485
Li2 CuP2 O7
C2/c(15)
2
82205
LiMo2 P2 O11
P21 /m(11)
2
69346
Li3 Fe2 (PO4 )3
Pbcn(60)
4
20610
LiFeP3 O9
P 21 21 21 (19)
5
83582
LiCo2 P3 O10
P21 /m(11)
5
95973
Li3 Fe2 (PO4 )3
R3̄(148)
6
79018
Li(Mo2 MoP3 O16 )
P1(2)
8
20537
LiVO(PO4 )
P1(2)
9
97767
LiNiPO4
Cmcm(63)
9
96964
Li1 V2 (PO4 )3
P21 /c(14)
11
97766
LiFePO4
Cmcm(63)
15
73868
Li2 VP2 O6
Pna21 (33)
17
400625
LiCoPO4
Pnma(62)
37
2149
LiCuP3 O9
P1(2)
52
65761
Li2 Mn2 (P6 O18 )(H2 O)10
P1(2)
419
Table 2: Computed Stability at 0K for the known ICSD compounds containing lithium, a redox
active metal, phosphorus and oxygen. An energy above the hull indicates thermodynamic stability
at 0K. A positive number indicates a driving force to transform to other phase(s).
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Relative stability of LiCoPO4 phases with different functionals
Table 3 shows the calculated differences in the energy per atom between the olivine and LISICON
phases of LiCoPO4 for various functionals. Regardless of the functional, the calculated energy per
atom of the olivine phase is significantly higher than that of the LISICON phase. Hence, DFT
in the GGA, GGA+U and HSE06 approximations predict the LISICON phase to be the ground
state, rather than olivine. All computations present in the table are in ferromagnetic states. Antiferromagnetic states have been computed for the olivine structure for GGA+U (U=3.4 eV) and
found to be 3 meV/at higher in energy than the ferromagnetic state. For U=5.7 eV, the AFM
state is 1 meV/at lower than the FM state for olivine.
Functional
Difference in energy olivine versus LISICON (Eolivine -ELISICON )
GGA
38 meV/at
GGA+U (U =3.4 eV)
34 meV/at
GGA+U (U =5.7 eV)
24 meV/at
HSE06
25 meV/at
Table 3: difference in energies per atom for the LiCoPO4 olivine and LISICON structures and for
different functionals.
ANOVA analysis of the factors determining the voltage
All the analysis were run using Matlab 7.11.0584 and the “anovan” function.
Redox couple and prototype ANOVA
The prototype variable was modeled as a random effect. Results for the 2+/3+, 3+/4+ and
5+/6+ couples are res[ectively presented in table 4, table 5, and table 6. The 1+/2+ and 4+/5+
couples present too few data points to be used to draw relevant conclusions.
Source
redox couple
prototype
error
total
Sum Square
111.78
36.82
8.96
167.57
d.f. Mean Square
7
15.97
78
0.47
157
0.057
242
F
Prob>F η 2
279.85 <0.0001 0.66
8.27 <0.0001 0.21
Table 4: results for the two variables ANOVA analysis on the 2+/3+ couples: redox couple and
prototype
3
Source
redox couple
prototype
error
total
Sum Square
148.42
67.09
8.53
234.36
d.f. Mean Square
11
13.49
69
0.97
238
0.036
318
F
Prob>F η 2
376.69 <0.0001 0.63
27.15 <0.0001 0.29
Table 5: results for the two variables ANOVA analysis on the 3+/4+ couples: redox couple and
prototype
Source
redox couple
prototype
error
total
Sum Square
29.18
20.42
0.91
62.05
d.f.
6
31
29
66
Mean Square
4.86
0.66
0.031
F
Prob>F η 2
154.62 <0.0001 0.47
20.94 <0.0001 0.33
Table 6: results for the two variables ANOVA analysis on the 5+/6+ couples: redox couple and
prototype
The η 2 value estimates the amount of variance that can be explained by the factor.
Effect of the number of links to a phosphate group
Figure 1 plots the z-score for the voltage versus the number of PO4 groups linked to the redox
active element. The figure does not indicate any clear dependence between the voltage and the
number of linked PO4 groups.
Figure 1: voltage z-score versus number of PO4 groups linked to the redox active element.
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An ANOVA analysis has been run using the redox couple and two continuous variables: the
electrostatic voltage and the number of PO4 groups linked to the redox active element. Results
are in table 7.
Source
redox couple
electrostatic
linked PO4
error
total
Sum Square
410.211
63.06
2.561
96.299
550.705
d.f. Mean Square
34
12.065
1
63.0601
1
2.5613
641
0.1502
677
F
80.31
419.75
17.05
Prob>F
η2
<0.0001 0.74
<0.0001 0.11
<0.0001 0.005
Table 7: results for the three variables ANOVA analysis: redox couple, electrostatic and number
of linked PO4 groups.
Effect of the P-O bond length on the voltage
Figure 1 plots the z-score for the voltage versus the P-O bond length linked to the redox active
element. The figure indicates some dependence of this factor with lower P-O bond length associated
with higher voltage.
Figure 2: voltage z-score versus P-O bond length for oxygens connected also to a redox active
element. The blue dashed line is drawn for helping the eye.
An ANOVA analysis has been run using the redox couple and two continuous variables: the
electrostatic voltage and the average P-O bond length for oxygen linked to the redox active element.
Results are in table 8.
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Source
redox couple
electrostatic
P-O length
error
total
Sum Square
407.58
51.729
12.076
73.547
517.251
d.f. Mean Square
34
11.9876
1
51.7291
1
12.0763
592
0.1242
628
F
96.49
416.38
97.21
Prob>F η 2
<0.0001 0.79
<0.0001 0.10
<0.0001 0.02
Table 8: results for the three variables ANOVA analysis: redox couple, electrostatic and P-O bond
length.
Effect of the Phosphorus to Oxygen ratio on the voltage
Results are presented in table 9.
Source
redox couple
electrostatic
P/O
error
total
Sum Square
420.23
34.749
24.274
74.586
550.705
d.f. Mean Square
34
12.3597
1
34.7487
1
24.2741
641
0.1164
677
F
106.22
298.63
208.61
Prob>F η 2
<0.0001 0.76
<0.0001 0.06
<0.0001 0.04
Table 9: results for the three variables ANOVA analysis: redox couple, electrostatic and number
of linked PO4 groups.
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