Capillary-based micro-battery cell for in situ X-ray powder diffraction studies of working batteries: a study of the initial intercalation and deintercalation of lithium into graphite
A novel capillary-based micro-battery cell for in situ X-ray powder diffraction (XRPD) has been developed and used to study the initial intercalation and deintercalation of lithium into graphite in a working battery. The electrochemical cell works in transmission mode and makes it possible to obtain diffraction from a single electrode at a time, which facilitates detailed structural and microstructural studies of the electrode materials. The micro-battery cell is potentially also applicable for in situ X-ray absorption spectroscopy and small-angle X-ray scattering experiments. The in situ XRPD study of the initial intercalation and deintercalation process revealed marked changes in the diffraction pattern of the graphitic electrode material. After the formation of the solid electrolyte interphase layer, the d spacing of the diffraction peak corresponding to the 002 diffraction peak of graphite 2H changes nearly linearly in two regions with slightly different slopes, while the apparent half-width of the diffraction peak displays a few minima and maxima during charging/discharging. DIFFaX+ refinements based on the initial XRPD pattern and the one after the initial discharging–charging cycle show that the structure of the graphite changes from an intergrown structure of graphite 2H and graphite 3R to a nearly ideal graphite 2H structure. DIFFaX+ was also used to refine a model of the stacking disorder in an apparent stage III compound with AαAB- and AαAC-type slabs.
Lithium-ion and lithium-ion polymer batteries have a great potential for large scale use, for example in electrical vehicles, but several challenges must be tackled in order to increase the energy and power densities, improve safety, and reduce the price of the batteries. Improved materials and an increased fundamental understanding of the electrochemical reactions and structural and microstructural changes taking place during operation are needed. In situ X-ray powder diffraction (XRPD) is a very strong tool for studying structural and microstructural changes occurring in crystalline materials during, for example, electrochemical reactions.
Conventional ex situ XRPD has been used for decades to study battery materials. A variety of different battery materials incorporated in various battery designs have historically been studied using in situ XRPD. In 1978, Chianelli et al. (1978) reported the first in situ XRPD study of a working electrochemical cell, where they investigated the crystallographic effect of lithium intercalation in TiS2 during discharging. The in situ cell was designed to be used in a conventional X-ray powder diffractometer in Bragg–Brentano geometry (in reflection mode). The cell was built up by two electrodes (positive and negative) and a separator in an electrolyte inside a Teflon/aluminium body. A beryllium window made it possible to obtain X-ray diffraction from the backside of the positive electrode. Variations over such reflection-mode in situ cells have since been used to study different batteries (Dahn & Haering, 1981; Dahn et al., 1982; Ikeshoji & Iwasaki, 1988; Mondoloni et al., 1992; Amatucci et al., 1996; Jisrawi et al., 2011). In 1992, Gustafsson et al. (1992) reported the first in situ XRPD study of a working battery in transmission mode, where they investigated the electrochemical reactions occurring in an Li–V6O13 battery during discharging, using a conventional X-ray diffractometer. The electrochemical cell used for their transmission experiments was a so-called `coffee-bag' battery built up by a thin layer of metallic lithium separated from a V6O13 electrode coated on a nickel foil in a polymer-coated aluminium-foil bag with two current collectors. Transmission-mode in situ cells, in different versions, have since been widely used to study battery materials, especially at synchrotron X-ray sources (Morcrette et al., 2002; Rosciano et al., 2007; Ruch et al., 2007; Marco & Veder, 2010; Misra et al., 2012). Baehtz et al. (2005), Nikolowski et al. (2005) and Leriche et al. (2010) have also reported electrochemical in situ cells applicable for both reflection and transmission XRPD experiments as well as for X-ray absorption spectroscopy (XAS) experiments. The reported in situ XRPD cells all have their advantages and disadvantages. The reflection-mode in situ cells are mainly used at conventional X-ray diffractometers, where the penetration depth of the X-rays is limited. Thus, depending on the thickness of the used electrode, one may only obtain diffraction from the upper part of the electrode, on the opposite side of the electrode–electrolyte interphase. The advantage is on the other hand that one potentially can obtain diffraction from only one of the crystalline phases in the electrochemical cell. The transmission-mode cells are often used at synchrotron X-ray sources for in situ studies with high time resolution. The drawback in the design of the reported transmission-mode cells is that one gets diffraction from all crystalline as well as amorphous components in the battery cell, which makes detailed studies of structural changes in the electrode materials very difficult. This is especially true for XRPD studies of graphite electrodes, where dominating diffraction from the other phases present in the battery makes detailed structural studies of the weakly scattering graphite electrode impossible. In order to overcome this issue, we have developed a transmission-mode capillary-based in situ cell that makes it possible to obtain diffraction from a single electrode at a time. Herein, we report the use of the novel capillary-based micro-battery cell in a study of the initial intercalation and deintercalation of lithium into graphite in an Li–C battery.
Graphite is used as the negative electrode material in most commercial lithium-ion and lithium-ion polymer batteries. It has been known for a long time that lithium intercalates into the graphite structure during charging, which causes an expansion of the basal spacing between the graphene sheets in the graphite structure (Ohzuku et al., 1993; Billaud et al., 1996; Flandrois & Simon, 1999). The maximum amount of lithium it is possible to intercalate into graphite electrochemically is one lithium atom per six carbon atoms, forming LiC6 (Migge et al., 2004). However, several phases are formed as intermediates during the charging and discharging processes. LiC6 is besides graphite the most well defined phase in the intercalation process. A series of other somewhat less well defined intermediate phases, for example LiC12, LiC18, LiC24, LiC27, LiC30 and LiC36, have also been reported (Dahn et al., 1990; Billaud & Henry, 2002; Yao et al., 2004; Etacheri et al., 2011). These phases are sometimes grouped and referred to as part of the non-stoichiometric Li1−xC12, LixC6 or LixC phase. The intercalation process is also referred to as staging, where LiC6 is stage I and LiC12 is stage II. The stage number refers to the number of graphene layers in the unit cell along the c axis. The chemical composition of the remaining stages in the intercalation process has been debated. LiC18 is sometimes referred to as a stage III compound (Jiang et al., 1995), whereas others call it a dilute stage II or stage 2L compound with an in-plane ordering of one lithium atom per nine carbon atoms, and not one lithium per six carbon atoms as for LiC6 and LiC12 (DiVincenzo et al., 1984; Billaud et al., 1996; Flandrois & Simon, 1999). The chemical composition of stage III is also reported to be in the range of LiC25–LiC30 (Flandrois & Simon, 1999; Yao et al., 2004). Stage IV is suggested to have a chemical composition in the range from LiC24 to LiC44–LiC50 (Ohzuku et al., 1993; Flandrois & Simon, 1999). The crystal structures of the pure graphite phases are well described, whereas those of the lithiated graphite phases in general are not well described. Two polymorphs of graphite are known, graphite 2H and graphite 3R, with hexagonal ABAB- (space group P63/mmc) and rhombohedral ABCABC-type (space group Rm) stacking, respectively. Graphite 2H is the thermodynamically most stable polymorph, but the energy difference is very small. Thus, most naturally occurring graphites have a disordered or intergrown structure with 2H and 3R stacking sequences along the common c axis (Shi, 1993; Shi et al., 1996; Dittrich & Wohlfahrt-Mehrens, 2001; Herstedt et al., 2003). LiC6 is reported to crystallize in space group P6/mmm, with a stacking sequence of AαAα (α denotes the position of the plane composed of the lithium atoms) (Guerard & Herold, 1975; Kganyago & Ngoepe, 2003). The space group of LiC12 is also suggested to be P6/mmm, with AAαAAα-type stacking (Guerard & Herold, 1975; Woo & Kamitakahara, 1983; Billaud et al., 1996; Imai & Watanabe, 2007). The stacking sequence of the diluted stage II compound, LiC18, is reported to be ABβBAα (β denotes the position of the plane composed of the lithium atoms) (Woo & Kamitakahara, 1983; Billaud et al., 1996). As for the stage III compound, the stacking sequence was suggested to be ABAαACAα or ABAαABAα (Billaud et al., 1996; Billaud & Henry, 2002). However, most of these structural studies of intercalation of lithium into graphite were based on X-ray diffraction experiments of oriented graphite samples, and not powdered ones with random oriented graphite particles, as used in commercial batteries.
Fig. 1 shows a principle sketch of the capillary-based micro-battery cell. A droplet of graphite was coated on the tip of a copper wire with a diameter of 0.15 mm. The wire was coated by dip coating in a slurry of 350 mg of graphite (Formula BT SLC 1520P from Carbo Tech Nordic ApS) and 40 mg of binder (polyvinylidene fluoride) in 1 ml of N-methylpyrrolidone. The graphite-coated wire was heated overnight at 353 K in a vacuum oven inside a glove box. The wire was placed in a glass capillary with an inner diameter of 1.05 mm and wall thickness of 0.225 mm, fixed by epoxy adhesive (Loctite 9492), and dried overnight at room temperature. A droplet of lithium metal was placed on the tip of another copper wire. The capillary was filled with liquid LiPF6 electrolyte (in a 1:1 ratio of ethylene carbonate and dimethyl carbonate) and the wire with lithium was inserted into the capillary. A small amount of silicone grease was placed at the top of the capillary before it was sealed by epoxy in order to protect the electrolyte from the gasses evolved during the drying of the epoxy.
In situ XRPD was used to study the intercalation of lithium into graphite during charging and discharging. The XRPD experiments were performed at beamline I711 at MAX-lab in Lund, Sweden. The micro-battery cell was mounted on a goniometer head using an insulating sample holder frame. The battery was connected to a potentiostat (PARSTAT 2273 from Princeton Applied Research), which was used to charge and discharge the battery with a constant current (the voltage was set to have a lower limit at 0.005 V for the discharging and an upper limit at 1.500 V for the charging). Powder diffraction data were collected during charging and discharging using a Titan CCD detector from Oxford Diffraction (2048 × 2048 pixels) with a diameter of 165 mm, a sample-to-detector distance of 73.69 mm, a wavelength of 1.002 Å, a slit size of 0.2 × 0.2 mm and an exposure time of 60 s. The data were converted to conventional one-dimensional powder patterns using the program Fit2D (Hammersley et al., 1996; Hammersley, 2005).
TOPAS Academic 4.1 (Coelho Software, Brisbane, Australia; http://www.topas-academic.net/ ) was used to extract peak information such as positions and half-width parameters. A pseudo-Voigt function was used to describe the peaks. DIFFaX+ (version 2.500 beta 10, 7 June 2010; Leoni et al., 2004), which is based on the DIFFaX code (Treacy et al., 1991), was used to model and refine the structure of the pure graphite as well as that of the lithiated graphite.
The capillary-based micro-battery cell was assembled in its charged state, where graphite is the positive electrode and lithium metal is the negative electrode. In the in situ X-ray powder diffraction experiment, the micro-battery cell was first partially discharged, charged and discharged with a constant current of 2 µA, and subsequently partially charged and discharged with a constant current of 5 µA. The relatively low charging current was chosen to minimize the risk of formation of chemical gradients in the graphite electrode material during charging and discharging. A similar micro-battery was scanned for potential long-range chemical inhomogeneity in the graphite electrode during discharging, and it did not show signs of such. Fig. 2 shows a three-dimensional plot of XRPD patterns collected during the last charging–discharging cycle. The figure reveals noticeable changes in the diffraction patterns of the graphitic electrode material during charging and discharging of the battery.
The changes in the diffraction patterns were investigated using both single-peak and whole-pattern fitting of the data. Fig. 3(a) shows the changes in the full width at half-maximum (FWHM) and d spacing of the diffraction peak corresponding to the 002 diffraction peak of graphite 2H (at 2θ ≃ 17°) as a function of time. The diffraction peak will from now on be referred to as the `0022H' one even though it strictly speaking has different indices for the different lithiated graphite phases. The `0022H' diffraction peak was treated as a single peak in the fitting process. The quotations marks around FWHM and d spacing in the figure legend indicate that this assumption may not be entirely true in parts of the charging–discharging process, as will be discussed later. Fig. 3(b) shows the corresponding charging and discharging curve of the micro-battery. The gaps in the curves in Fig. 3(a) are due to beam dumps in the synchrotron ring. Thus, information about the first discharge curve is unfortunately lost because of these beam dumps. However, if one takes a closer look at the slope of the d-spacing curve in the first discharging cycle in Fig. 3(a) and draws a line with this slope, it will intersect the d spacing of pure graphite at ∼250 min. The delay in the increment of the d spacing is caused by the formation of a solid electrolyte interphase (SEI) layer. SEI layers are known to be formed at the graphite electrode during the first discharging (or charging if graphite acts as negative electrode) process (Peled, 1979, 1998; Aurbach, 1995; Yamaguchi et al., 1998). The effect of the SEI formation can also be observed in Fig. 3(b), where the first discharging curve is markedly different from the second one. The delay in the increment of the d spacing during the first discharging was also observed for another micro-battery cell (Fig. S11). The capacity of that battery was very low compared to its theoretical capacity, but it showed the same trend. The d spacing did not increase significantly during the formation of the SEI layer.
After the first discharging and charging cycle (at t = 1030 min), the d spacing of the `0022H' diffraction peak virtually reverts to that of the initial graphite phase. However, a closer look at the diffraction patterns reveals that they are significantly different at higher angles (Figs. 4a and 4b). The XRPD pattern of the graphite phase present after the first discharging and charging cycles displays the apparent peaks of graphite 2H, whereas the graphite in the initial battery seems to be a mixture of graphite 2H and 3R.
A detailed study of the structural differences in the two graphite materials was performed using DIFFaX+. A cell containing two graphene sheets was used for the DIFFaX+ refinements (Table 1). The second sheet in the cell was stacked (2/3, 1/3) in the ab plane with respect to the first one, giving AB-type stacking of the graphene sheets in the cell. The cell is hexagonal (a = b = 2.466, c = 6.727 Å, α = β = 90, γ = 120°) but described in the triclinic space group P1. A two-layer model was used to refine the structure of the graphite phases. The two layers are identical to the cell defined in Table 1. A two-layer model gives four potential layer transitions: layer 1 → layer 1 (1–1), layer 1 → layer 2 (1–2), layer 2 → layer 1 (2–1) and layer 2 → layer 2 (2–2). The corresponding translation vectors are given in Table 2. A stacking sequence with only 1–1-type stacking forms graphite 2H, whereas 1–2-type stacking followed by 2–2-type stacking generates graphite 3R. A pseudo-Voigt function was used for the refinements over a 2θ range of 14.5–42.25° using one refined half-width parameter (W) and one fixed peak-shape parameter (the mixing parameter). The scale factor and 13 Chebyshev background parameters were also refined, together with the four stacking probabilities. The refined stacking probabilities are given in Table 2. Fig. 4 shows the DIFFaX+ refinement plots. The DIFFaX+ refinements gave the following agreement factors: Rp = 0.605%, Rwp = 0.824%, Rp (background) = 1.26% and GOF = 1.02 for the initial graphite (t = 0 min), and Rp = 0.606%, Rwp = 0.919%, Rp (background) = 1.41% and GOF = 1.12 for the phase after the first discharging and charging cycle (t = 1030 min).
The DIFFaX+ refinements show clearly that the initial discharging and charging of the battery changes the stacking sequence in the graphite phase. The initial graphite is an intergrown structure with a large domain of graphite 2H, but also significant amounts of graphite 3R. The high probability of 2–2-type stacking indicates that also the graphite 3R domains are relatively large, but they are not as abundant as the graphite 2H ones. The intercalation and deintercalation of lithium increases the probability of 1–1-type stacking significantly, whereas it decreases the probability of 2–2-type stacking. Thus, the initial discharging and charging cycle changes the structure of the graphite to a nearly pure graphite 2H structure, with only small domains of the less thermodynamically stable graphite 3R (IUPAC, 1997). The XRPD patterns collected during the initial discharging of another micro-battery cell (Fig. S2) show that the intensity of the 1013R and 0123R reflections has already decreased during the initial intercalation of lithium.
The in situ XRPD study also reveals significant changes in the apparent FWHM of the `0022H' diffraction peak (Fig. 3) during the charging and discharging of the micro-battery. These changes may be related to inhomogeneity in the stacking sequence of the graphene sheets caused by the intercalation and deintercalation of lithium into the structure during discharging and charging, respectively. Thus, one can discuss if the graphite electrode material can be seen as a single phase with various degrees of disorder during the entire intercalation process or if it rather should be regarded as a mixture of two disordered phases during the initial intercalation where the apparent FWHM increases to ∼0.36° 2θ (e.g. at t = 1255 min). A comparative fit of the region around the apparent `0022H' diffraction peak in the XRPD pattern collected at 1255 min reveals that a two-peak model fits the apparent `0022H' diffraction peak significantly better than a one-peak one, which supports the idea of a two-phase mixture of disordered phases during the initial intercalation process. However, it is a question of definition; is it a single disorder phase with predominant features along the `0022H' stacking direction or is it a mixture of two disordered (and somewhat comparable) phases? A closer look at the changes in the curve of the apparent FWHM (Fig. 3a) during the second discharge reveals that it has two major local minima after the initial major increase in the apparent FWHM. The first of these minima could also be considered as two local sub-minima. The minima may be associated with the stoichiometric lithiated graphite phases in the staging process. Peak fitting of the basal `0022H' diffraction peaks in the three corresponding XRPD patterns (from the two sub-minima and the other major minimum) shows that they can be modelled by single peaks. Thus, DIFFaX+ was used to attempt to refine the structure of the `stage III' compound based on the diffraction pattern at the second major minimum (t = 1611 min). A two-layer model (AαAB and AαAC) was used for the refinement. Each of the two layers is built up by three layers of graphene stacked AAB and AAC, respectively. α denotes the position of the plane composed of the Li atoms. An AA-type stacking sequence of graphene sheets forms hexagonal prisms where lithium may occupy up to one-third of the prisms. The repulsive forces are too high for lithium to occupy neighbouring prisms (Persson et al., 2010). However, in this case, we use a simplified model with statistically distributed lithium (within the ab plane) based on an LiC9 stoichiometry, with lithium occupying two-ninths of the prisms, giving an overall chemical composition of LiC27 for each of the three-layer slabs. The two cells are hexagonal (a = b = 2.466, c = 10.451 Å, α = β = 90, γ = 120°) but described in the triclinic space group P1. The four layer transition vectors (1–1, 1–2, 2–1 and 2–2) are all (0, 0, 1). The refined probabilities of the four layer transitions are p(1–1) ≃ 0.28, p(1–2) ≃ 0.72, p(2–1) ≃ 0.76 and p(2–2) ≃ 0.24. The agreement factors of the refinement are Rp = 1.18%, Rwp = 2.11%, Rp (background) = 2.34% and GOF = 2.57.
The DIFFaX+ refinement plot (Fig. 5) shows that all the diffraction peaks in the pattern are described by the applied model. However, it also shows that the calculated pattern does not match the intensity and broadening of all the diffraction peaks. Thus, the disorder in the structure is more complex than that described by the model. The model only allows disorder introduced by AαABAαAB and AαACAαAC slabs in a general alternating stacking sequence of three-graphene-layer AαAB and AαAC slabs. However, the structure probably also contains four- and two-layer slabs in the stacking sequences, possibly also with different amounts of lithium intercalated in the AA stacking sequence of the graphene sheets. A closer look at Fig. 5 also reveals that the `0022H' diffraction peaks are modelled at 2θ values that are too high, which suggests that at least stage II layer domains are needed in the disorder model for the structure at t = 1611 min. Unfortunately, the current version of DIFFaX+ is not capable of modelling and refining structures with layer slabs of different heights. Thus, the additional disorder cannot be included in the model in the current state. Nevertheless, the DIFFaX+ refinement clearly shows that the `stage III' compound at t = 1611 min is not the ideal defect-free LiC27 phase. Its structure contains significant amounts of stacking disorder.2
This paper reports the design of a novel capillary-based micro-battery cell for in situ X-ray powder diffraction studies of working batteries. The electrochemical cell is designed for transmission-mode experiments, mainly at synchrotron X-ray sources. The in situ cell makes it possible to obtain X-ray diffraction from a single electrode at a time, which facilitates detailed structural and microstructural studies of all types of crystalline electrode materials. The presented micro-battery cell is potentially also applicable for in situ X-ray absorption spectroscopy and small-angle X-ray scattering experiments.
The micro-battery cell was used to study the initial intercalation and deintercalation of lithium into graphite in a working Li–C battery. The d spacing of the `0022H' diffraction peak changed nearly linearly in two regions with slightly different slopes after the formation of the solid electrolyte interphase layer, whereas the apparent half-width of the `0022H' diffraction peak had a few minima and maxima during the charging–discharging process.
DIFFaX+ refinements showed that the structure of the graphite electrode changed from an intergrown structure with large domains of graphite 2H and graphite 3R to a nearly ideal graphite 2H structure with only a few and smaller graphite 3R domains. The DIFFaX+ refinement based on the diffraction pattern collected at t = 1611 min showed that the compound had a structure with stacking disorder in a generally alternating AαAB- and AαAC-type stacking sequence. This indicated that it was close to the stage III compound. However, the refinement also showed that the structure had an even more complex stacking disorder than that described by the DIFFaX+ model.
2After this article was submitted, a paper by Senyshyn et al. (2013) was published where ordering models of LixC6 phases are discussed.
The authors would like to acknowledge the staff of beamline I711 (Dörthe Haase and Carsten Gundlach) at MAX-lab for experimental assistance. Mike Wichmann is gratefully acknowledged for drawing the sketch of the capillary-based micro-battery cell (Fig. 1). Matteo Leoni is gratefully acknowledged for collaboration in optimizing/debugging of the DIFFaX+ program. The Danish Research Council is acknowledged for covering travel expenses in relation to the synchrotron experiment (via DanScatt).
Amatucci, G. G., Tarascon, T. M. & Klein, L. C. (1996). J. Electrochem. Soc. 143, 1114–1123. CrossRef CAS Web of Science
Aurbach, D. (1995). J. Electrochem. Soc. 142, 2882–2890. CrossRef CAS Web of Science
Baehtz, C., Buhrmester, T., Bramnik, N., Nikolowski, K. & Ehrenberg, H. (2005). Solid State Ionics, 176, 1647–1652. Web of Science CrossRef CAS
Billaud, D. & Henry, F. (2002). Solid State Commun. 124, 299–304. Web of Science CrossRef CAS
Billaud, D., Henry, F., Lelaurain, M. & Willmann, P. (1996). J. Phys. Chem. Solids, 57, 775–781. CrossRef CAS Web of Science
Chianelli, R. R., Scanlon, J. C. & Rao, B. M. L. (1978). J. Electrochem. Soc. 125, 1563–1566. CrossRef CAS Web of Science
Dahn, J., Fong, R. & Spoon, M. (1990). Phys. Rev. B, 42, 6424–6432. CrossRef CAS Web of Science
Dahn, J. & Haering, R. (1981). Solid State Commun. 40, 245–248. CrossRef CAS Web of Science
Dahn, J. R., Py, M. A. & Haering, R. R. (1982). Can. J. Phys. 60, 307–313. CrossRef CAS
Dittrich, H. & Wohlfahrt-Mehrens, M. (2001). Int. J. Inorg. Mater. 3, 1137–1142. Web of Science CrossRef CAS
DiVincenzo, D., Fuerst, C. & Fischer, J. (1984). Phys. Rev. B, 29, 2–4.
Etacheri, V., Marom, R., Elazari, R., Salitra, G. & Aurbach, D. (2011). Energy Environ. Sci. 4, 3243–3262. Web of Science CrossRef CAS
Flandrois, S. & Simon, B. (1999). Carbon, 37, 165–180. Web of Science CrossRef CAS
Guerard, D. & Herold, A. (1975). Carbon, 13, 337–345. CrossRef CAS Web of Science
Gustafsson, T., Thomas, J., Koksbang, R. & Farrington, G. (1992). Electrochim. Acta, 37, 1639–1643. CrossRef CAS Web of Science
Hammersley, A. P. (2005). The Fit2D Home Page, http://www.esrf.eu/computing/scientific/FIT2D/ .
Hammersley, A. P., Svensson, S. O., Hanfland, M., Fitch, A. N. & Hausermann, D. (1996). High Pressure Res. 14, 235–248. CrossRef Web of Science
Herstedt, M., Fransson, L. & Edström, K. (2003). J. Power Sources, 124, 191–196. Web of Science CrossRef CAS
Ikeshoji, T. & Iwasaki, T. (1988). Inorg. Chem. pp. 1123–1124. CrossRef Web of Science
Imai, Y. & Watanabe, A. (2007). J. Alloys Compd. 439, 258–267. Web of Science CrossRef CAS
IUPAC (1997). Compendium of Chemical Terminology, 2nd ed., compiled by A. D. McNaught & A. Wilkinson. Oxford: Blackwell Scientific Publications. http://dx.doi.org/10.1351/goldbook.R05385 .
Jiang, Z., Alamgir, M. & Abraham, K. (1995). J. Electrochem. Soc. 142, 333–340. CrossRef CAS Web of Science
Jisrawi, N. M., Wiesmann, H., Ruckman, M. W., Thurston, T. R., Reisfeld, G., Ocko, B. M. & Strongin, M. (2011). J. Mater. Res. 12, 2091–2098. CrossRef Web of Science
Kganyago, K. & Ngoepe, P. (2003). Phys. Rev. B, 68, 205111. Web of Science CrossRef
Leoni, M., Gualtieri, A. F. & Roveri, N. (2004). J. Appl. Cryst. 37, 166–173. Web of Science CrossRef CAS IUCr Journals
Leriche, J. B., Hamelet, S., Shu, J., Morcrette, M., Masquelier, C., Ouvrard, G., Zerrouki, M., Soudan, P., Belin, S. & Elkaim, E. (2010). J. Electrochem. Soc. 157, A606–A610. Web of Science CrossRef CAS
Marco, R. D. & Veder, J. (2010). Trends Anal. Chem. 29, 528–537. Web of Science CrossRef
Migge, S., Sandmann, G., Rahner, D., Dietz, H. & Plieth, W. (2004). J. Solid State Electrochem. 9, 132–137. Web of Science CrossRef
Misra, S., Liu, N., Nelson, J., Hong, S. S., Cui, Y. & Toney, M. F. (2012). ACS Nano, 6, 5465–5473. Web of Science CrossRef CAS PubMed
Mondoloni, C., Laborde, M., Rioux, J., Andoni, E. & Lévy-Clément, C. (1992). J. Electrochem. Soc. 139, 954–959. CrossRef CAS Web of Science
Morcrette, M., Chabre, Y., Vaughan, G., Amatucci, G., Leriche, J., Patoux, S., Masquelier, C. & Tarascon, J. (2002). Electrochim. Acta, 47, 3137–3149. Web of Science CrossRef CAS
Nikolowski, K., Baehtz, C., Bramnik, N. N. & Ehrenberg, H. (2005). J. Appl. Cryst. 38, 851–853. Web of Science CrossRef CAS IUCr Journals
Ohzuku, T., Iwakoshi, Y. & Sawai, K. (1993). J. Electrochem. Soc. 140, 2490–2498. CrossRef CAS Web of Science
Peled, E. (1979). J. Electrochem. Soc. 126, 2047–2051. CrossRef CAS Web of Science
Peled, E. (1998). J. Electrochem. Soc. 145, 3482–3486. Web of Science CrossRef CAS
Persson, K., Hinuma, Y., Meng, Y. S., Van der Ven, A. & Ceder, G. (2010). Phys. Rev. B, 82, 125416. Web of Science CrossRef
Rosciano, F., Holzapfel, M., Kaiser, H., Scheifele, W., Ruch, P., Hahn, M., Kötz, R. & Novák, P. (2007). J. Synchrotron Rad. 14, 487–491. Web of Science CrossRef CAS IUCr Journals
Ruch, P. W., Hahn, M., Rosciano, F., Holzapfel, M., Kaiser, H., Scheifele, W., Schmitt, B., Novák, P., Kötz, R. & Wokaun, A. (2007). Electrochim. Acta, 53, 1074–1082. Web of Science CrossRef CAS
Senyshyn, A., Dolotko, O., Muhlbauer, M. J., Nikolowski, K., Fuess, H. & Ehrenberg, H. (2013). J. Electrochem. Soc. 160, A3198–A3205. Web of Science CrossRef CAS
Shi, H. (1993). PhD thesis, Simon Fraser University, Canada.
Shi, H., Barker, J., Saïdi, M. Y. & Koksbang, R. (1996). J. Electrochem. Soc. 143, 3466–3472. CrossRef CAS Web of Science
Treacy, M. M. J., Newsam, J. M. & Deem, M. W. (1991). Proc. R. Soc. London Ser. A. 433, 499–520. CrossRef
Woo, K. & Kamitakahara, W. (1983). Phys. Rev. Lett. 50, 182–185. CrossRef CAS Web of Science
Yamaguchi, S., Asahina, H., Hirasawa, K. A., Sato, T. & Mori, S. (1998). Mol. Cryst. Liq. Cryst. 322, 239–244. CrossRef CAS
Yao, T., Ozawa, N., Aikawa, T. & Yoshinaga, S. (2004). Solid State Ionics, 175, 199–202. Web of Science CrossRef CAS
© International Union of Crystallography. Prior permission is not required to reproduce short quotations, tables and figures from this article, provided the original authors and source are cited. For more information, click here.