www.sciencemag.org/content/344/6191/1252817/suppl/DC1

Supplementary Materials for

Capturing metastable structures during high-rate cycling of LiFePO4

nanoparticle electrodes

Hao Liu, Fiona C. Strobridge, Olaf J. Borkiewicz, Kamila M. Wiaderek, Karena W.

Chapman, Peter J. Chupas, Clare P. Grey*

*Corresponding author. E-mail: cpg27@cam.ac.uk

Published 27 June 2014, Science 344, 1252817 (2014)

DOI: 10.1126/science.1252817

This PDF file includes:

Supplementary Text

Figs. S1 to S5

Full Reference List

Supplementary Text

Verification of the whole pattern fitting method

In order to verify the validity of the fitting results, we treat the peak asymmetry of

the (200) and (301) reflections by fitting the selected regions with a series of peaks to

model reflections from phases of varying lithium composition. The (200) and (301)

reflections are chosen based on the fact that reflections from the LiFePO4 and the FePO4

phases are well separated to give a better resolution of the asymmetrical profile.

Peak positions of the two end phases, LiFePO4 and FePO4, are obtained from the

whole pattern fitting of the pattern at the beginning of charge and the top of first charge,

respectively. By trial and error, we found that at least 8 intermediate phases are needed to

achieve a good fitting of the reflection profile. The 8 intermediate reflections are

distributed equally in d-spacing between the LiFePO4 and the FePO4 reflections,

therefore, a total of 10 reflections are employed to fit each of the (200) and the (301)

reflection profiles. In the fitting process, the refined parameters are the intensities of

individual peaks and a global peak width parameter for all 10 peaks; all peak positions

are fixed.

Extraction of relative phase population is based on the work by Rudman (46). The

integrated intensity of each reflection corresponding to the composition LixFePO4 is

given by

)()(),()()(2

xNLPAxFKxI (S7)

where

F(x) – structure factor of LixFePO4,

A(, ) – absorption factor,

LP() – Lorentz-polarization factor,

N(x) – the number of unit cells of LixFePO4 in the irradiated volume.

Since the reflection profile of interest spans only over a small 2 range ((2)<1°),

to a first approximation, A(, ) and LP() can be considered as constant. Hence,

)()()(2

xNxFxI (S8)

and F(x) is treated as a linear combination of the experimentally determined F(0) and

F(1) (structure factors of LiFePO4 and FePO4, respectively), )0()1()1()( FxFxxF (S9)

As a result, we are able to extract the relative phase population from the integrated

peak intensity, and the fitting results of the (200) and (301) reflections are shown in figs.

S5A and B, respectively. Fig. S5B appears to be noisier than fig. S5A because of the

lower intensity of the (301) reflections. It can be seen that fig. S5 is in very good

agreement with the result obtained from the whole pattern fitting method shown in Fig. 3.

Fig. S1

Characterizations of the pristine C/LiFePO4 composite powder. (A) Image by scanning

electron microscope (SEM). (B) Rietveld refinement of the x-ray diffraction data for the

pristine LiFePO4 measured at ID31, ESRF, Grenoble, France. The wavelength

determined by calibration was 0.39996 Å. (C) Particle size distribution based on an

analysis of 95 particles observed in the SEM images.

Fig. S2

Development of peak asymmetry for the reflections from LiFePO4 (LFP). The (200),

(211)/(020), and (301) reflections from LiFePO4 asymmetrically broaden towards higher

2θ angles, while the (101) reflection asymmetrically broadens towards lower angles. The

same reflections from FePO4 (FP) are marked by dashed lines.

Fig. S3

Typical whole powder pattern fitting results. This pattern is taken at 720 s, corresponding

to the global composition of Li0.43FePO4. (A) Only symmetrical peak profile is used. (B)

Symmetrical peak profiles convoluted with the hkl-dependent exponential function.

Fig. S4

Refinement result of the scale factors of the LiFePO4 (LFP) and FePO4 (FP) phases

during the first two cycles.

Fig. S5

Phase population distribution obtained from multi-peak fitting. (A) shows the result for

the (200) reflection and (B) for the (301) reflection.

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