Parameters used for the calculation on the LiFePO4 and FePO4 phases:
P21ma AF space group
LiFePO4: a=10.3377 Å, b=6.0112 Å, c=4.6950 Å
FePO4: a=9.7599 Å, b=5.7519 Å, c=4.7560 Å
40 irreducible K-points for SCF (4, 7, 9) grid
252 irreducible K-points for Optic (8, 13, 17) grid
RMT×Kmax=7.5
Parameters used for the calculation on the Li0.5FePO4 phase
In order to take into account the average half filling of lithium sites for the metastable phase Li0.5FePO4,
various structural hypotheses were tested by lowering the symmetry. For the FePO4 and LiFePO4 phases, the
antiferromagnetic ordering is described with the space group P2 1ma. In the present case, the atomic arrangement
presenting the less stress corresponds to a lithium ordering in the space group P11a and a charge ordering on the
metal sites with a succession of FeII (a, c) planes and FeIII (a, c) planes. A ferrimagnetic ordering was found to be
the most stable magnetic configuration (AF coupling along the b axis). Experimental cell parameters are taken
from Delacourt et al.1. Optimized atomic positions were obtained with the VASP code2 and are given below.
Details concerning the calculations with the WIEN2k3 package are also reported.
Space group:
P11a
Experimental cell parameters:
= 90°
a = 10.1300 Å
b =5.9595 Å°
c =4.7901Å°
Optimized atomic positions:
Li
FeIII
FeII
P1
P2
O1
O2
O3
O4
O5
O6
x
0
0.2754
0.2188
0.0950
0.4021
0.1129
0.3955
0.4486
0.0433
0.1743
0.6623
y
1/4
0.9697
0.4814
0.9799
0.4717
0.9896
0.4598
0.9786
0.4716
0.7837
0.1833
Z
0.7527
0.7238
0.2182
0.1647
0.6744
0.4819
0.9917
0.9208
0.4397
0.0274
0.9940
Structural optimization (atomic position only):
VASP2 package, GGA (BPE) + U (Ueff=4.3eV)
Spin polarized calculation with an antiparallel coupling between FeIII and FeII along the b axis
Energy Cut-Off for plane waves: 600eV
Shifted (2,4,4) k-point mesh with 8 irreducible k-points
Electronic structure calculation:
WIEN2k3 package, GGA (PBE) + U (Ueff=4.3eV)
1
C. Delacourt, J. Rodríguez-Carvajal, B. Schmitt, J.-M. Tarascon, and C. Masquelier, Solid State Sciences 7,
1506 (2005).
2
G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
3
P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvaniscka, and J. Luitz, WIEN2k, An Augmented Plane Wave +
Local Orbitals Program for Calculating Crystal Properties (Schwarz K., Techn. Universität Wien, Austria,
2001).
Spin polarized calculation with an antiparallel coupling between Fe III and FeII along the b axis
Plane wave basis set defined by RMT×Kmax=7.5
Shifted (4,7,9) k-point mesh with 70 irreducible k-points for the SCF
Shifted (8,13,17) k-point mesh with 468 irreducible k-points for the Optic calculation
Total, partial and joint densities of states (DOS) for FePO4 and LiFePO4:
Total and partial Fe densities of states for FePO4 (left) and LiFePO4 (right).
The origin of the 6 eV peak in FePO4 resides in the transition (red arrow) from levels at
the top of the valence band (-5 to 0 eV range) to the first levels of the conduction band (2 to 4
eV).
In the case of LiFePO4, this same peak also exists but for a greater energy (longer red
arrow). The new transition appearing (green arrow), due to the electronic structure changes,
does not contribute significantly to the total intensity of the transitions (forbidden transition).
In order to demonstrate exactly that, the joint density of states (JDOS) corresponding to
these transitions are shown in the following figures.
Total and partial joint densities of states for FePO4 (left) and LiFePO4 (right).
The JDOS in red is simply shifted to higher energies in LFP compared to FP. These
transitions are thus hidden in the main intensity rise above 6 eV in the calculation. The new
transition (green arrow) presents a very small intensity.
Anisotropic energy-loss functions for FePO4
Calculated anisotropic energy loss functions for FePO4. Thin line: along the x direction; thick line: along the y
direction; dashed line: along the z direction.