www.sciencemag.org/cgi/content/full/science.1241882/DC1
Supplementary Materials for
Visualization and Quantification of Electrochemical and Mechanical
Degradation in Li Ion Batteries
Martin Ebner, Federica Marone, Marco Stampanoni, Vanessa Wood*
*Corresponding author. E-mail: [email protected]
Published 17 October 2013 on Science Express
DOI: 10.1126/science.1241882
This PDF file includes:
Materials and Methods
Supplementary Text
Figs. S1 to S3
Table S1
Full Reference List
Captions for Movies S1 to S4
Other Supplementary Material for this manuscript includes the following:
(available at www.sciencemag.org/cgi/content/full/science.1241882/DC1)
Movies S1 to S4
Materials and Methods
Material Synthesis
The synthesis of SnO particles closely followed the report of Wang et al. (33):
18 mmol tin chloride dihydrate (SnCl2 2.H2O) and 24 mmol tri-sodium citrate dihydrate
(Na3C6H5O7 2.H2O) were dissolved in 25 ml DI water, and, after complete dissolution,
10 ml of potassium hydroxide solution (64.3 mmol KOH) was added drop wise during
150 s under continuous ultrasonic agitation in an ultrasonic bath with a power of 25 W.
The resulting milky white suspension was then rested for about 2 h until a black
precipitate formed and the supernatant turned clear. The reaction product was then
centrifuged and washed with DI water and ethanol several times before it was dried in a
vacuum oven at 60 °C overnight. A scanning electron micrograph (Fig. S1A) of the SnO
particles shows tetragonal particles with good uniformity in shape and size (~30 µm). As
indicated by the red arrows, multiple defects in the (001) plane are observed in the
synthesized material. Particle cross-sections (Fig. S1B and C), prepared by focused-ionbeam milling, reveal the existence of grain boundaries in the (001) planes as well as
singular voids and cracks. An X-ray diffractogram, shown in Fig. S1D, was recorded
with a Brucker D8 diffractometer using Cu Kα radiation at 40 kV and 40 mA, and
indicates the purity of tetragonal SnO.
Cell preparation & electrochemical test procedure
An electrochemical cell (Fig 1. B) was fabricated as described below. Electrode
slurries with 25 wt.% solid content were prepared by dispersing 80 wt.% SnO, 10 wt.%
carbon black (TIMCAL) and 10 wt.% PVDF (Arkema) in N-methyl-pyrrolidone (NMP,
Sigma Aldrich) using a ULTRA-TURRAX high shear mixer for 10 min, followed by
ultra-sonication for 10 min. Electrodes were prepared by coating the tip of one current
collector pin with the slurry, followed by drying at 80 °C under vacuum over night.
Active mass was estimated by weighing the current collector before and after electrode
deposition. Current collectors were then transferred into an argon-filled glovebox (O2 and
H2O <1 ppm). Finally, half-cells with metallic lithium as a combined counter and
reference electrode, a glass fiber separator, and electrolyte (1 M LiPF6 in 1:1 ethylene
carbonate:dimethyl carbonate, LP30 from Merck) were assembled. Galvanostatic
reduction and oxidation was performed at 110 mAg-1 to 10 mV vs. Li/Li+ and 167 mAg-1
rate to 2.5 V vs Li/Li+, respectively, using a Bio-logic SP-150 potentiostat with low
current module. The electrochemically active mass was determined from the measured
lithiation capacity and a theoretical capacity of 1273 mAhg-1, and is in good agreement
with the mass estimation determined by weighing. The potential during galvanostatic
reduction and oxidation at 127.3 mAhg-1 in a 1.3 cm2 coin-type half-cell with ~20 mg
active material is shown in Fig. S1C. We note that this electrochemistry recorded without
radiation exposure is comparable to the electrochemistry recorded during the SRXTM
experiment as the sample undergoes radiation exposure. This indicates that no beaminduced degradation of the sample relevant to electrochemistry occurs during the
SRXTM experiment. Furthermore, we can estimate the absorbed x-ray dosage and
determine that it should induce at most in what is classified as “some damage” (37). In
particular, for a 28 keV beam energy, 1 mm of PVDF (density 1.78 g cm-3) absorbs 3.4 %
of the incident photon flux of 1011 mm-2 s-1, resulting in an absorbed does of about 5*105
J kg-1 over 15 h of permanent radiation exposure.
2
The design of a stable electrochemical cell is critical to the success of the
experiment. As the technical drawing of our cell shows (Fig. S1D), we customize a
polymeric tube fitting (Swagelock PFA-220-6). The electrochemical cell remains
functional for weeks, due to the excellent seal provided by the commercial fitting and the
custom machined stainless steel current collectors. The gap between the two current
collectors after cell assembly is precisely controlled by the stable positioning and
accurate machining of the stainless steel pins. To improve x-ray transmission through the
cell, we machine a groove around the entire circumference of the tube fitting, leaving a
2 mm PFA sidewall thickness.
Supplementary Text
Tomography settings & reconstruction
SRXTM radiographs were recorded at the TOMCAT beamline of the Swiss Light
Source (25) at Paul Scherrer Institut in Villigen, Switzerland, using parallel,
monochromatic synchrotron radiation at 28 keV (selected using a [W/Si]100 multi-layer
monochromator), a 20 µm LAG:Ce scintillator, and an optical 10 x objective in
conjunction with a PCO.edge sCMOS camera with a chip size of 2560(h) x 2160(v)
pixel. 700 radiographs during 180 ° sample rotation with 700 ms exposure time were
recorded. The radiographs were flat- and darkfield-corrected and rearranged into
sinograms. A highly optimized routine based on the Fourier transform method and a
gridding procedure was employed to reconstruct the full tomographic dataset (26). A
Hamming window in conjunction with the standard ramp filter was used in the
reconstruction process to minimize noise contamination. The resulting voxel size of the
dataset was 0.65x0.65x0.65 µm3.
Histogram calculation and normalization of attenuation coefficients
Histograms were calculated by selecting 106 voxels from a central region of the
reconstructed tomograms that contains only electrochemically active particles and the
electrolyte, carbon black, and binder mixture. The numerical gray-scale value of each
voxel in a tomogram is linearly related to the attenuation coefficient of the sample at the
position of the voxel. In order to yield absolute values, the numbers have to be
normalized. Here, the SnO and the background peaks were utilized as internal standards
for this normalization. Based on known elemental mass attenuation coefficients (38),
densities, and molar masses, the theoretical attenuation coefficients of SnO and the
background can be calculated (Tbl. S1). The background results from low absorbing,
carbon-containing materials. For normalization, the attenuation of elemental carbon is
chosen, which is an acceptable approximation since, at two orders of magnitude smaller
than the attenuation coefficient for SnO, the exact value used is not significant. A sum of
two normal distributions is fitted to the histogram calculated from the tomogram acquired
before electrochemical reduction to determine the gray-scale values (w) of the pure SnO
and the background. Associating the theoretical attenuation coefficients with the grayscale values determined for the SnO and the background phase, determines the
normalization function Equ. S1 with a = 149.4 cm-1 and b = -46.2 cm-1.
! ! =!∙!+!
Equ. S1
3
Microstructure preprocessing
The 74 reconstructed tomograms (2650x2650x250 voxel) were partitioned into
regions of 512x512x250 voxels to enable numerical processing of the >1011 16-bit values
on a 600 core linux cluster. Each region was subjected to 3D median filtering with a 5
voxel cubic kernel. Subsequently, the regions were binarized with a variable threshold.
The threshold value for each tomogram was calculated as the arithmetic mean of the
attenuation coefficient of the carbon black, electrolyte, and binder background and the
LixSn + Li2O mixed phase. For the first 13 tomograms, a constant attenuation coefficient
equal to the attenuation coefficient of the mixed phase in the 14th tomogram was taken.
The mixed phase peak does not shift in value as it emerges from the noise, but fitting the
broad peak near the noise floor is fault-prone. The evolution of the attenuation
coefficients of the identified phases, determined by fitting the peak in the histogram, as
well as the calculated threshold values are depicted in Fig. S2A. In Fig. S2B, close-ups of
the histograms of the LixSn + Li2O and SnO peaks are shown.
The resulting datasets after binarization represent the microstructure of the sample
constituents with absorption coefficients higher than the electrolyte, carbon black, and
binder background: the SnO particles, the current collector, and the glass fiber separator.
To facilitate quantification of the volume-change of the SnO particles alone, the currentcollector and the glass fiber separator have to be removed from the datasets. This was
achieved in two steps: First, region masks that exclude the separator were calculated
based on the separators fiber shape by applying the morphological hole-filling operator
imfill() in Matlab, followed by the morphological opening operator imopen() with
spherical structure element of radius 5 voxel to copies of the thresholded datasets.
Applying voxel-by-voxel Boolean AND operations between the original thresholded
datasets and these region masks retained the shape of the SnO particles while efficiently
removing the glass fiber separator. In a second step, the planar current-collector, which
was slightly tilted with respect to the coordinate system of the tomograms, was removed
by determining the offset and inclination of the current collector-electrode interface plane
and removing all voxels on the current-collector side of this plane.
Calculation of volume expansion
To calculate the volume expansion of the active material, the entire dataset,
including all particles in the cell, was considered. The considered volume was selected
such that no particle leaves or enters the volume; otherwise the calculated volume change
would be incorrect. To compute the volume change, the volume of particles in the
electrode Vi was calculated for every tomogram by counting the number of voxels
associated with particles. The volume expansion was then calculated with Equ. S2.
!
!! = !! − 1 ∙ 100%
Equ. S2
!
The theoretical volume expansions can be calculated with Equ. S3 from the molar
volumes of the phases in relation to SnO.
! !
!! = ! ! ! !"# − 1 ∙ 100%
Equ. S3
!
!"#
They are 252 % for Li4.4Sn + Li2O and 49 % for Sn + Li2O. From the molar volumes of
the LixSn and Li2O + LixSn phases reported in Tbl. S1, the change in molar volume with
lithium content (x) can be estimated with Equ. S4 (6).
4
! ! = !! + !"
Equ. S4
3
-1
3
-1
In agreement with Ref. 6, we find k = 9.73 cm mol and k = 9.74 cm mol for the LixSn
and Li2O + LixSn phases, respectively.
Estimation of lost capacity
We estimated the state of charge, parameterized by the mean lithium content, !,
from the attenuation coefficient histograms, f(µ). We estimated the relation between
lithium content for each attenuation coefficient, x(µ), by linear interpolation between the
values of equilibrium phases reported in Tbl. S1.
!=
!!!"!"!!
! !
!!!"!"!!
!!!"!"!!
!
!!!"!"!!
∙! ! ! !"
! ! !"
Equ. S5
Equ. S5 calculates the state of charge, which is plotted as a function of oxidation
capacity in Fig. S3. The mean lithium content at 550mAhg-1 is found to be ! = 1.9,
resulting in a lost capacity of 1.9/4.4 = 43%.
5
Fig. S1.
(A) Close-up scanning electron micrograph of active particles highlighting the tetragonal
particle shape and grain boundaries in the (001) plane. (B) Particle cross-section prepared
by focused-ion-beam milling with grain boundaries indicated by dotted line and (C) close
up of grain boundaries. (D) X-ray diffractogram showing the purity of the SnO.
Reference diffractogram for the tetragonal phase is indicated in red. (E) Potential during
galvanostatic reduction and oxidation of SnO in coin-type half-cell recorded at 127 mAg1
. (F) Technical drawing of the electrochemical cell.
6
Fig. S2.
(A) Evolution of the attenuation coefficients of materials determined by fitting normal
distributions to the attenuation coefficient distributions shown in close up in (B).
7
Fig. S3.
(A) Evolution of attenuation coefficient distribution and (B) quantification of peak
broadening during oxidation. (C) Average lithium content, !, estimated from integrating
the attenuation coefficient distribution as a function of oxidation capacity.
8
Table S1.
Symbol
Unit
Li
O
C
Li2O
SnO
SnO2
SnO2 + Sn
Sn
Li0.4Sn
LiSn
Li2.33Sn
Li2.5Sn
Li2.6Sn
Li3.5Sn
Li4.4Sn
Li2O + Sn
Li2O + Li0.4Sn
Li2O + LiSn
Li2O + Li2.33Sn
Li2O + Li2.5Sn
Li2O + Li2.6Sn
Li2O + Li3.5Sn
Li2O + Li4.4Sn
Mass
attenuation
coefficient
µ/ρ
cm2g-1
0.16
0.38
0.26
0.28
6.88
6.19
6.88
7.76
7.61
7.40
6.97
6.92
6.89
6.63
6.39
6.26
6.16
6.02
5.74
5.70
5.68
5.51
5.35
Density
Molar
mass
Molar
Volume
ρ
gcm-3
0.53
0.00
1.70
2.01
6.45
6.95
7.10
7.31
6.09
5.04
3.59
2.99
2.95
2.89
2.49
4.78
4.35
3.90
3.14
2.75
2.72
2.68
2.39
M
gmol-1
6.94
16.00
12.01
29.88
134.70
150.71
269.42
118.71
121.09
124.65
132.57
133.56
134.16
139.50
144.85
148.59
150.97
154.53
162.45
163.44
164.04
169.38
174.73
Vm
cm3mol-1
13.00
12011.58
7.07
14.84
20.88
21.68
37.92
16.24
19.88
24.75
36.95
44.64
45.45
48.31
58.14
31.08
34.72
39.59
51.79
59.48
60.29
63.15
72.98
Molar
attenuation
coefficient
µ/ρ*M
cm2mol-1
1.14
6.05
3.08
8.33
927.24
933.29
1854.48
921.20
921.65
922.34
923.86
924.05
924.16
925.19
926.22
929.52
929.98
930.66
932.19
932.38
932.49
933.52
934.54
Attenuation
coefficient
µ
cm-1
0.09
0.00
0.44
0.56
44.40
43.04
48.90
56.73
46.36
37.27
25.00
20.70
20.33
19.15
15.93
29.90
26.78
23.51
18.00
15.67
15.47
14.78
12.80
Grayscale
value
w
0.31
0.31
0.31
0.31
0.61
0.60
0.64
0.69
0.62
0.56
0.48
0.45
0.45
0.44
0.42
0.51
0.49
0.47
0.43
0.41
0.41
0.41
0.39
Attenuation coefficients of all constituents of the electrode can be calculated (shaded
cells) from literature values (unshaded cells). The values for SnO and the electrolyte,
carbon black, and binder matrix are used to calculate the linear scaling transformation
Equ. S1 between the attenuation coefficients and the recorded grey-scale values (bold).
9
Movie S1.
Electrode cross-section parallel to current collector. Sequence of 74 unprocessed
tomograms show individual SnO particles in the electrode against low attuenuating
carbon black, binder, and electrolyte phase as they undergo core-shell lithiation, volume
expansion and fracture during reduction followed by volume contraction during
oxidation.
Movie S2.
Evolution of particle fracture: cross-sections. Coronal (left) and transverse (right)
cross-sections through a particle during electrochemical reduction and oxidation showing
the growth of multiple cracks in parallel (001) planes leading to zig-zag particle
morphology.
Movie S3.
Evolution of particle fracture: 3D rendering. Preferential crack initiation and growth
in the (001) planes leading to zig-zag morphology is shown for multiple particles.
Movie S4.
Evolution of an electrode subvolume: 3D rendering. During reduction, particle volume
expansion leads to expansion of the entire electrode and particle fracture. During
oxidation, the particles contract, but the electrode is permanently distorted.
10
References and Notes
1. J. Cabana, L. Monconduit, D. Larcher, M. R. Palacín, Beyond intercalation-based Li-ion
batteries: The state of the art and challenges of electrode materials reacting through
conversion reactions. Adv. Mater. 22, E170–E192 (2010). Medline
doi:10.1002/adma.201000717
2. W.-J. Zhang, Lithium insertion/extraction mechanism in alloy anodes for lithium-ion batteries.
J. Power Sources 196, 877–885 (2011). doi:10.1016/j.jpowsour.2010.08.114
3. Y. Oumellal, A. Rougier, G. A. Nazri, J.-M. Tarascon, L. Aymard, Metal hydrides for lithiumion batteries. Nat. Mater. 7, 916–921 (2008). Medline doi:10.1038/nmat2288
4. A. S. Aricò, P. Bruce, B. Scrosati, J.-M. Tarascon, W. van Schalkwijk, Nanostructured
materials for advanced energy conversion and storage devices. Nat. Mater. 4, 366–377
(2005). Medline doi:10.1038/nmat1368
5. P. Poizot, S. Laruelle, S. Grugeon, L. Dupont, J.-M. Tarascon, Nano-sized transition-metal
oxides as negative-electrode materials for lithium-ion batteries. Nature 407, 496–499
(2000). Medline doi:10.1038/35035045
6. M. N. Obrovac, L. Christensen, D. B. Le, J. R. Dahn, Alloy design for lithium-ion battery
anodes. J. Electrochem. Soc. 154, A849–A855 (2007). doi:10.1149/1.2752985
7. J. Y. Huang, L. Zhong, C. M. Wang, J. P. Sullivan, W. Xu, L. Q. Zhang, S. X. Mao, N. S.
Hudak, X. H. Liu, A. Subramanian, H. Fan, L. Qi, A. Kushima, J. Li, In situ observation
of the electrochemical lithiation of a single SnO2 nanowire electrode. Science 330, 1515–
1520 (2010). doi:10.1126/science.1195628
8. N. Balke, S. Jesse, Y. Kim, L. Adamczyk, A. Tselev, I. N. Ivanov, N. J. Dudney, S. V.
Kalinin, Real space mapping of Li-ion transport in amorphous Si anodes with nanometer
resolution. Nano Lett. 10, 3420–3425 (2010). Medline doi:10.1021/nl101439x
9. S.-C. Chao, Y.-C. Yen, Y.-F. Song, Y.-M. Chen, H.-C. Wu, N.-L. Wu, A study on the interior
microstructures of working Sn particle electrode of Li-ion batteries by in situ x-ray
transmission microscopy. Electrochem. Commun. 12, 234–237 (2010).
doi:10.1016/j.elecom.2009.12.002
10. S.-C. Chao, Y.-F. Song, C.-C. Wang, H.-S. Sheu, H.-C. Wu, N.-L. Wu, Study on
microstructural deformation of working Sn and SnSb anode particles for Li-ion batteries
by in situ transmission x-ray microscopy. J. Phys. Chem. C 115, 22040–22047 (2011).
doi:10.1021/jp206829q
11. S.-C. Chao, Y.-C. Yen, Y.-F. Song, H.-S. Sheu, H.-C. Wu, N.-L. Wu, In situ transmission xray microscopy study on working SnO anode particle of Li-ion batteries. J. Electrochem.
Soc. 158, A1335–A1339 (2011). doi:10.1149/2.043112jes
12. J. Wang, Y. C. Chen-Wiegart, J. Wang, In situ chemical mapping of a lithium-ion battery
using full-field hard x-ray spectroscopic imaging. Chem. Commun. 49, 6480–6482
(2013). Medline doi:10.1039/c3cc42667j
13. M. K. Y. Chan, C. Wolverton, J. P. Greeley, First principles simulations of the
electrochemical lithiation and delithiation of faceted crystalline silicon. J. Am. Chem.
Soc. 134, 14362–14374 (2012). Medline doi:10.1021/ja301766z
14. M. E. Stournara, P. R. Guduru, V. B. Shenoy, Elastic behavior of crystalline Li–Sn phases
with increasing Li concentration. J. Power Sources 208, 165–169 (2012).
doi:10.1016/j.jpowsour.2012.02.022
15. K. Zhao, M. Pharr, Q. Wan, W. L. Wang, E. Kaxiras, J. J. Vlassak, Z. Suo, Concurrent
reaction and plasticity during initial lithiation of crystalline silicon in lithium-ion
batteries. J. Electrochem. Soc. 159, A238–A243 (2012). doi:10.1149/2.020203jes
16. V. A. Sethuraman, V. Srinivasan, J. Newman, Analysis of electrochemical lithiation and
delithiation kinetics in silicon. J. Electrochem. Soc. 160, A394–A403 (2013).
doi:10.1149/2.008303jes
17. V. A. Sethuraman, V. Srinivasan, A. F. Bower, P. R. Guduru, In situ measurements of stresspotential coupling in lithiated silicon. J. Electrochem. Soc. 157, A1253–A1261 (2010).
doi:10.1149/1.3489378
18. S. W. Lee, M. T. McDowell, L. A. Berla, W. D. Nix, Y. Cui, Fracture of crystalline silicon
nanopillars during electrochemical lithium insertion. Proc. Natl. Acad. Sci. U.S.A. 109,
4080–4085 (2012). Medline
19. J. L. Goldman, B. R. Long, A. A. Gewirth, R. G. Nuzzo, Strain anisotropies and self-limiting
capacities in single-crystalline 3D silicon microstructures: Models for high energy
density lithium-ion battery anodes. Adv. Funct. Mater. 21, 2412–2422 (2011).
doi:10.1002/adfm.201002487
20. J. Chouvin, J. Olivier-Fourcade, J. C. Jumas, B. Simon, P. Biensan, F. J. Fernández Madrigal,
J. L. Tirado, C. Pérez Vicente, SnO reduction in lithium cells: Study by x-ray absorption,
119
Sn Mössbauer spectroscopy and x-ray diffraction. J. Electroanal. Chem. 494, 136–146
(2000). doi:10.1016/S0022-0728(00)00357-0
21. T. Ohzuku, Monitoring of particle fracture by acoustic emission during charge and discharge
of Li/MnO2 cells. J. Electrochem. Soc. 144, 3496–3500 (1997). doi:10.1149/1.1838039
22. J. O. Besenhard, M. Winter, J. Yang, W. Biberacher, Filming mechanism of lithium-carbon
anodes in organic and inorganic electrolytes. J. Power Sources 54, 228–231 (1995).
doi:10.1016/0378-7753(94)02073-C
23. P. Baudry, M. Armand, M. Gauthier, J. Masounave, In situ observation by SEM of positive
composite electrodes during discharge of polymer lithium batteries. Solid State Ion. 28,
1567–1571 (1988). doi:10.1016/0167-2738(88)90421-3
24. L. Y. Beaulieu, K. W. Eberman, R. L. Turner, L. J. Krause, J. R. Dahn, Colossal reversible
volume changes in lithium alloys. Electrochem. Solid-State Lett. 4, A137–A140 (2001).
doi:10.1149/1.1388178
25. M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R.
Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, R. Abela, Trends in
synchrotron-based tomographic imaging: The SLS experience. Proc. SPIE 6318, M1–
M14 (2006). doi:10.1117/12.679497
26. F. Marone, M. Stampanoni, Regridding reconstruction algorithm for real-time tomographic
imaging. J. Synchrotron Radiat. 19, 1029–1037 (2012). Medline
doi:10.1107/S0909049512032864
27. P. R. Shearing, N. P. Brandon, J. Gelb, R. Bradley, P. J. Withers, A. J. Marquis, S. Cooper,
S. J. Harris, Multi length scale microstructural investigations of a commercially available
Li-ion battery electrode. J. Electrochem. Soc. 159, A1023–A1027 (2012).
doi:10.1149/2.053207jes
28. M. Ebner, F. Geldmacher, F. Marone, M. Stampanoni, V. Wood, X-ray tomography of
porous, transition metal oxide based lithium ion battery electrodes. Adv. Energy Mater. 3,
845–850 (2013). doi:10.1002/aenm.201200932
29. Materials and methods are available as supplementary materials on Science Online.
30. I. A. Courtney, J. R. Dahn, Electrochemical and in situ x-ray diffraction studies of the
reaction of lithium with tin oxide composites. J. Electrochem. Soc. 144, 2045–2052
(1997). doi:10.1149/1.1837740
31. I. A. Courtney, J. R. Dahn, Key factors controlling the reversibility of the reaction of lithium
with SnO2 and Sn2BPO6 glass. J. Electrochem. Soc. 144, 2943–2948 (1997).
doi:10.1149/1.1837941
32. I. A. Courtney, W. R. McKinnon, J. R. Dahn, On the aggregation of tin in SnO composite
glasses caused by the teversible reaction with lithium. J. Electrochem. Soc. 146, 59–68
(1999). doi:10.1149/1.1391565
33. S. Wang, S. Xie, H. Li, S. Yan, K. Fan, M. Qiao, Solution route to single crystalline SnO
platelets with tunable shapes. Chem. Commun. 2005, 507–509 (2005). Medline
doi:10.1039/b414913k
34. Z. Chen, L. Christensen, J. R. Dahn, Comparison of PVDF and PVDF-TFE-P as binders for
electrode materials showing large volume changes in lithium-ion batteries. J.
Electrochem. Soc. 150, A1073–A1078 (2003). doi:10.1149/1.1586922
35. I. A. Courtney, R. A. Dunlap, J. R. Dahn, In-situ 119Sn Mössbauer effect studies of the
reaction of lithium with SnO and SnO:0.25 B2O3:0.25 P2O5 glass. Electrochim. Acta 45,
51–58 (1999). doi:10.1016/S0013-4686(99)00192-9
36. M. N. Obrovac, L. Christensen, Structural changes in silicon anodes during lithium
insertion/extraction. Electrochem. Solid-State Lett. 7, A93–A96 (2004).
doi:10.1149/1.1652421
37. D. C. Phillips, S. G. Burnay, in Irradiation Effects on Polymers, D. W. Clegg, A. A. Collyer,
Eds. (Elservier, London, 1991), p. 353.
38. J. H. Hubbell, S. M. Seltzer, Tables of x-ray mass attenuation coefficients and mass energyabsorption coefficients 1 keV to 20 meV for elements z = 1 to 92 and 48 additional
substances of dosimetric interest. (available at http://physics.nist.gov/xaamdi).