All spectra were overlaid with fits from the method of Le Ca¨er and Dubois [4]. Solid lines show the fit of the Arrhenius relationship between IS and temperature, with an activation energy of about 400 meV and a prefactor of 1.0 × 1011 Hz. were obtained from the lines between 80◦C and 200◦C. Shifts have been obtained for the lines between 80◦C and 200◦C. Crystal structure and lattice parameters were determined by Rietveld refinement, as shown by the solid line.
Overview
Cell thermodynamics
Thermodynamic parameters in cells
Gibbs phase rule in cells
Cell kinetics
- Arrhenius relation
- Nernst equation and Tafel equation on electrodes
- Marcus theory of electron transfer
- Fick’s laws
According to this principle, the nuclear coordinates must oscillate in the appropriate configuration from the reactant to the product. In the case of a strong electrolyte, the conductivity σ is the sum of the contributions of cations and anions.
Electrode materials for rechargeable Li batteries
- Anode
- Cathode
- Hexagonal TiS 2
- Olivine LiMPO 4
- Hexagonal LiMO 2
- Spinel LiMn 2 O 4
- Li-S and Li-O 2
- Rhombohedral FeF 3
- Resonant scattering
- M¨ ossbauer spectrum
- Hyperfine interactions
- Isomer shift
- Electric quadrupole splitting
- Magnetic dipole splitting
- Dynamical phenomena
- Valence fluctuation
- Superparamagnetic relaxation
The electrostatic interaction at r=0 is determined by integrating the product of nuclear charge density and electron charge density. The electric field gradient (EFG) of the surrounding electrons is the Laplacian of their total electric potential, also in the form of the 3×3 tensor, ∂V /∂ei∂ej.
Experimental techniques
Sample preparation
The physical thickness of the sample is approximately equal to the thickness of the Al plate. On the other hand, if the sample is too thick, most of the incident photons may be attenuated and the counting rate becomes low.
Experimental setup
Furnace
As a cathode material for lithium-ion batteries, LiFePO4 has several advantages over many commercial cathodes. The high-frequency peaks in the Raman spectra of LiFePO4 correspond to vibrational modes of the P-O bonds, which have no visible change at elevated temperatures up to 400◦C.
Phase composition
The cluster expansion was used to calculate formation energies of various Li/vacancy and Fe2+/Fe3+ configurations in the lattice, to reproduce the phase diagram [74]. At room temperature, a two-phase mixture of triphyllite and heterosite is thermodynamically stable and covers a wide range of composition. The phase diagram for LixFePO4 prepared as nanocrystallites was also estimated to be changed, but this is not supported by other experimental results [81, 82].
Lithium and electron transport
The solid solution behavior in the electrochemical curve was seen in nanocrystalline LiFePO4 and during rapid discharge [76, 77]. M¨ossbauer spectrometry was used to measure the frequency and activation energy of the thermally activated polaron hopping in mixed Fe2+/Fe3+ at different charge states of LixFePO4 prepared as two-phase mixtures and as solid solutions [90, 5, 2]. The coupling between Li ions and electrons was thought to be responsible for the increase of the energy barrier for polarons.
Electrochemical performance
Various methods have been adopted to synthesize lithium iron phosphate (LiFePO4), including solid-state reaction, carbothermal reduction, aqueous precipitation, hydrothermal reaction, microwave heating, and pulsed laser deposition. Among them, the most common method is solid-state reaction, grinding of precursors without a solution environment and long-term heating. More practically, conductive carbon is often added to Li, Fe, and P precursors in a solid-state reaction to prepare carbon-coated lithium iron phosphate (LiFePO4/C) in order to improve the conductivity of LiFePO4 and reduce iron impurities.
Experimental
Rietveld analysis with the software package Philips X'pert Plus was used to determine lattice parameters, strains and crystal sizes.
Results
The mass ratio of bead to powder was 5:1, and the crystal size could be controlled between 300 nm and 36 nm. Sample C, which was obtained from solution precipitation without mechanical processing, however, has a similar strain distribution to the samples prepared by ball milling.
Conclusion
The solid solution phase of LixFePO4 with different Li concentrations, x, was investigated by M¨ossbauer spectrometry at temperatures between 25◦C and 210◦C. Moreover, a eutectoid point is not expected for a disordered solid solution dominated by a configurational entropy of mixing. A study of valence fluctuations in both Li0.6FePO4 biphasic mixtures and disordered solid solutions at high temperatures by M¨ossbauer spectroscopy showed fast electronic fluctuations in the solid solution phase, but essentially no electronic dynamics in the two-phase mixture [5. ].
Experimental
Results
As discussed below, analyzes of the other solid solutions also yielded two local maxima, viz. evidence for two different local chemical environments of Fe, even at a temperature of 210◦C, although the two IS values merged at 210◦C. This correlates with the change of EIS values (Fig. 5.6), where the EIS of Fe2+ and Fe3+ has a monotonic increase or decrease with temperature, and a distinct temperature for the beginning of the temperature range of changes in EIS for each composition. Parts (a) and (b) correspond respectively to the Fe2+ and Fe3+ doublets from the two peaks in the quadrupole splitting distribution in fig.
Discussion
Because the Li+ ion does not move from the neighborhood of the Fe2+ ion, the isomer shift is not significantly altered, although dynamic distortions of the environment may alter the EIS somewhat. The EFG is sensitive to the orientation of the charge distortion, which changes as Li+ passes between adjacent sites. However, we can use this information on the Fe3+ relaxations to understand the charge transfer process.
Conclusion
A small polaron involves displacements of the positions of neighboring atoms when there is a change of valence on a central atom. M¨ossbauer spectrometry gives a picture of the electron density and electron dynamics from the point of view of the nuclei of iron atoms. In contrast to LixFePO4 with large crystals previously studied as a two-phase mixture of heterosite and triphyllite [5, 2], the thermal relaxations of EQS and IS in Li0.5FePO4 nanocryst.
Experimental
An EQS distribution can be obtained by fitting the measured spectra to sums of doublets with different splitting centroid shifts (i.e. isomer shifts). In the present study of nanocrystalline Li0.5FePO4 prepared as a mixture of heterosite and triphylite phases, the interpretation emphasized the effects of temperature on the change dynamics, and not on local environments. This indicates a much faster rate of small polaron hopping and electron dynamics in nanocrystalline material with similar phases.
Results
Solid lines show fits of the hyperfine field distribution obtained by the method of Le C¨aer and Dubois [4]. The isomer shifts for bulk Li0.6FePO4, on the other hand, are independent of temperature. The Arrhenius behavior of the isomer shifts (Fig. 6.10) gave activation energies of 400 and 420 meV, essentially the same, for Fe2+ and Fe3+.
Discussion
The activation energy for the EQS of Fe3+ is essentially the same as for the isomer shift, consistent with a common origin in small polaron hopping. Ingalls' explanation might lower the activation energy for the EQS of Fe2+, but we suggest that this lower activation energy could come from neighboring Li+ ions or vacancies. The effects are expected to be greater for Fe2+ ions, which are more likely to have Li+ ions nearby, so a lower activation energy for the EQN for Fe2+ seems reasonable [2].
Conclusion
The solid solution phase of nanocrystalline Li0.65FePO4 was fast to form above 200◦C, but did not demix at lower temperatures. Demixing below 200◦C was found after prolonged annealing of nanocrystalline Li0.35FePO4, however consistent with the equilibrium phase diagram of bulk LixFePO4. The stability of the solid solution of nanocrystalline LixFePO4 is kinetic in origin, which may arise with effects of crystal surfaces.
Introduction
On the surfaces of 40 nm carbon-free LiFePO4 crystals produced by jet milling, a thin amorphous layer was reported to help stabilize the solid solution inside [134]. In this work, we tested the stability of nanocrystalline solid solutions and two-phase mixtures of LixFePO4 (x= 0.35 and 0.65) at different temperatures. However, the results from Li0.65FePO4 suggest and the results from Li0.35FePO4 indicate that the equilibrium temperature for the immiscibility transformation is similar in bulk and nanocrystalline materials.
Experimental
The phase boundary at room temperature has been reported to change with decreasing crystal size, as indicated by electrochemical cycling and synchrotron XRD [78, 80]. Compared to LixFePO4 with large crystals, the unmixing transformation is slower in the nanocrystalline material, which makes thermodynamic equilibrium more difficult to achieve. Distributions of electric quadrupole splitting (EQ) were analyzed by the method of Le Ca¨er and Dubois [4], using a linear correlation between isomer shift and quadrupole splitting.
Results and discussion
In the case of nano-Li0.65FePO4, although the solid solution phase persisted for many days at temperatures below 200◦C (Fig. 7.4(b)), the prolonged annealing showed that the nano-Li0.35FePO4 solid solution undergoes demixing below 200◦C (Fig. The solid solution phase of nano-Li0.35FePO4 is not thermodynamically stable at low temperatures.
Conclusion
Previous work suggested that the phase diagram of LixFePO4 should change with decreasing crystal size [78]. For example, XRD patterns of annealed 25 nm LixFePO4 showed the consistent transition temperature from the two-phase to the solid solution at 200◦C [81]. In this work, we evaluated the boundaries of the two-phase mixture of heterosite and triphyllite during Li insertion and extraction in LixFePO4.
Experimental
If the open circuit voltages are measured under thermodynamically reversible conditions and plotted against the corresponding temperatures, the slopes and intercepts can give results of the entropy and enthalpy change with composition at a specific x. Structural phase transitions during lithiation in LixCoO2, for example, were accompanied by changes in the entropy profile [149].
Results and discussion
8.5, since the transition from a logarithmic curve to a constant straight line occurs at the composition x = 0.95, the entropy change can be an alternative indication of the two-phase boundary for OCV. ∆S remains around -0.7kB instead of 0kB across the plateau from x=0.05 to x=0.95. This deviation indicates a steady decrease in entropy from the charged state to the discharged state as x increases. The vibrational entropy is probably different between the two-phase heterosite and triphylite and the LiαFePO4 or Li1−βFePO4 solid solution phases.
Conclusion
The results showed that the electrical conductivity of nano-LixFePO4 is comparable to that of bulk LixFePO4 prepared as solid solutions, but both are much higher than the conductivity of the bulk LixFePO4 two-phase mixtures, which is the expected phase for electrochemical lithiation. We observed a consistent phase transition temperature around 200◦C and a change in stability in the solid solution phase for some compositions in nano-LixFePO4. Our results on nano-LixFePO4 call into question the validity of previous claims of a significant change in the phase diagram of LixFePO4 when the crystal size is 30 or 40 nm.
Future work on nano-Li x FePO 4
Further attempts to improve the kinetics of Li x FePO 4
Further study on the electrical conductivity of the olivine cathodes
However, at high cycling rates, LiFe0.9Ti0.1PO4 showed much better rate capability than LiFePO4. In situ M¨ossbauer spectrometry found a change of absorption line positions and shape when delithiated Li0.45Fe0.9Ti0.1PO4 was heated to 200◦C (Fig. 9.2). Further studies of the thermodynamics and the charge kinetics on this doped olivine LiFe0.9Ti0.1PO4 could be important for the battery community.
Further study on the phase diagram of Li x FePO 4
The red line is the raw data and the blue line is the Rietveld refinement of LiFePO4 olivine. The red line is the measurement at 25◦C, the blue line was measured at 200◦C and the dashed black line was measured after the sample was cooled back to 25◦C. A simple “simulated” multichannel analyzer (MCA) for the M¨ossbauer spectrometer was built with a 32-bit buffered counter from National Instruments and LabVIEW programming.
Signal Processing Description
Testing results
Enhancement of the electrochemical activity of LiFePO4 (olivine) by an amphiphilic Ru-Bipyridine complex anchored to a carbon nanotube. Improvement of the electronic conductivity of LiFePO4 by Cr doping and its identification through basic calculations. First principles study of surface properties of LiFePO4: surface energy, structure, Wulff shape and redox potential of the surface.
The diagram of the spectrometer
The diagram of signal processing in MCA mode
The logic flowchart in MCA mode
A M¨ ossbauer spectrum of natural iron acquired from our spectrometer
![Figure 3.1: X-ray diffraction patterns of olivine LiFePO 4 , (a) sample prepared by Argonne National Laboratory [1], (b) commercial electrode by A123 r Inc](https://thumb-ap.123doks.com/thumbv2/123dok/10415537.0/38.918.201.749.140.588/diffraction-patterns-prepared-argonne-national-laboratory-commercial-electrode.webp)
