Activation Energy For Hopping Research Articles

Effect of particle size on dc conductivity, activation energy and diffusion coefficient of lithium iron phosphate in Li-ion cells

Cathode materials in nano size improve the performance of batteries due to the increased reaction rate and short diffusion lengths. Lithium Iron Phosphate (LiFePO4) is a promising cathode material for Li-ion batteries. However, it has its own limitations such as low conductivity and low diffusion coefficient which lead to high impedance due to which its application is restricted in batteries. In the present work, increase of conductivity with decreasing particle size of LiFePO4/C is studied. Also, the dependence of conductivity and activation energy for hopping of small polaron in LiFePO4/C on variation of particle size is investigated. The micro sized cathode material is ball milled for different durations to reduce the particle size to nano level. The material is characterized for its structure and particle size. The resistivities/dc conductivities of the pellets are measured using four probe technique at different temperatures, up to 150 °C. The activation energies corresponding to different particle sizes are calculated using Arrhenius equation. CR2032 cells are fabricated and electrochemical characteristics, namely, ac impedance and diffusion coefficients, are studied.

Sol–gel synthesis and characterization of xCuO–(1 − x)Bi2O3 (0.15 ≤ x ≤ 0.55) glasses by magnetic and spectral studies

Binary glasses having compositions xCuO–(1−x)Bi2O3 (0.15≤x≤0.55) (A1–A5: x:: 0.15, 0.25, 0.35, 0.45, 0.55) are prepared by sol–gel method. Glassy phase is ascertained by powder X-ray diffraction (XRD) studies. Glass transition temperatures, Tg, of the glasses are observed to be ~573K. Magnetic studies on the glasses at 300K in the range ±10kG show weak ferromagnetic nature, and additionally the particular glass A3 (x=0.35) at 5 and 300K in the range 0–6500Oe also indicates weak ferromagnetic nature. Observed electron paramagnetic resonance (EPR) lineshapes of the glasses in the range 5–300K are isotropic in nature, and the corresponding giso-values ~2.1±0.001 are due to similar site symmetries around the Cu2+(3d9) ions. Thermally assisted hopping of Cu2+(3d9) small polaron modulates the EPR lineshapes which results in motionally narrowed lineshapes. Activation energy of hopping, Ea, of the small polaron, calculated from derivative EPR peak-to-peak linewidths of the glasses are observed to be ~1×10−4eV (~1011Hz). Broad optical absorption bands ~400nm and ~660–735nm in the glasses are attributed to 2B1g→2Eg and 2B1g→2B2g transitions from the ground state 2B1g (|dx2−y2>) in Cu2+(3d9) ions in tetragonally distorted octahedral environment.

Studies of Anomalous Diffusion in Composite Silicon Anodes

1. Introduction The diffusion coefficient is an important parameter of active materials for lithium ion batteries, particularly in higher rate applications like electric vehicles. It is useful to know the diffusion coefficient as a function of state of charge, and other parameters like temperature. Silicon has a very high lithiation capacity (3579 mA hr g-1), but a correspondingly large expansion when fully lithiated (> 270 %). On the first charge, crystalline silicon is converted to amorphous LixSi, and then to crystalline Li15Si4 at full lithiation. The diffusion coefficient in a-LixSi will have an important influence on the movement of these two phase boundaries, which in turn will impact upon the performance and operating life of the electrode. The two main techniques used to measure diffusion coefficients are a. c. impedance, via the Warburg coefficient, and galvanostatic intermittent titration technique (GITT). This report describes the use of both of these methods on composite silicon anodes. 2. Results Electrodes were prepared using 3 µm silicon powder, with partially neutralised poly acrylic acid as binder and conductive carbon. Following a slow formation cycle (C/20), impedance spectra were recorded in two electrode half cells, at different states of charge. Figure 1 shows typical results at lithiation capacities of 300, 600, 900 and 1200 mA hr g-1. The data was fitted to equivalent circuits, with a series resistance, two resistor // CPE parallel combinations, and a low frequency constant phase element (CPE) tail. Apart from the fully delithiated anode, the tail was always at a much steeper angle than the standard Warburg value of 45o (power term = 0.5). Figure 2 shows plots of the fitted power term {n in Z = (iw)-n C-1}, at three different states of charge, during cycling. 3. Discussion One explanation for the steeper gradient is that the diffusion is anomalous or non-Fickian [1]. This can occur for charge carrier movement in amorphous solids, like LixSi. After each hop, the charge carrier can wait “for a period drawn from a broad power law distribution” [1], reducing the overall rate of diffusion. Interestingly, a recent theoretical study has calculated a wide range of activation energies for lithium hopping in amorphous silicon (0.1 to 2.4 eV [2]). The difference in the power term at 600 mA hr g-1 during lithiation and delithiation implies a structural hysteresis, which may match the voltage hysteresis observed with silicon anodes. Further results, including GITT experimental data and analysis, will be presented at the conference.

MAGNETIC AND ELECTRICAL PROPERTIES OF ELECTRON BEAM GUN DEPOSITED [Mn/Al] MULTILAYERED FILMS

By following electron beam gun evaporation technique, the magnetic multilayers in the configuration, [Mn(60nm)/Al(20nm)]n; n =1, 2 and 9 were deposited at 473K, under high vacuum conditions. From grazing incidence X- ray diffraction (GIXRD) studies, the grain sizes were determined and they were in the order of few nanometers. Atomic force microscope (AFM) were employed to study surface structure and grain sizes. The magnetization as a function of field at 150K and 200K have been measured using the MPMS SQUID - vibrating sample magnetometer (VSM). From the hysteresis loops, coercive field, saturation magnetization, remanent magnetization and antiferromagnetic coupling were determined. All the three films hinted at the existence of at antiferromagnetic interaction between Mn layers through Al layer. Electrical resistivity in the temperature range from 5K to 300K has been measured. Films exhibited semiconducting to metallic transition. The power law variation of resistivity with temperature was established for the metallic region. Conductivity data for semiconducting region of a film has been analysed using polaran hopping models, activation energy and density of states at Fermi level were established. This is for the first time that antiferromagnetic coupling between Mn layers through interfacer layer and semiconducting to metallic transition have been noticed in the present configuration of [Mn/Al] multilayers.

Structural, electrical and magnetic phase evolution of Cr substituted GdMn1−xCrxO3 (0 ⩽ x ⩽ 0.2) manganites

A series of GdMn1−xCrxO3 (0⩽x⩽0.2) have been synthesized by the conventional solid state reaction method mainly to understand the response of Cr substitution on structural, microstructural, magnetic and electrical transport properties. The X-ray diffraction shows that all samples crystallize with orthorhombic perovskite type symmetry with Pbnm space group. The room temperature Raman spectroscopy shows the reduction of Raman shift as doping concentration increase that related to anti-symmetric Jahn Teller stretching mode and symmetric-stretching mode. The temperature dependence of electrical resistivity show the semiconducting nature of these compounds and support the small polaron hoping model (SPH) and variable range hopping conduction model (VRH). The calculated hopping distance and activation energy increased as rate of Cr content increased whereas density of state at Fermi level decreased. The temperature dependence of magnetization presents that under the zero field cooling (ZFC) mode as doping concentration increases the net magnetization reverses its nature below irreversibility temperature. The magnetization results show that all samples show weak ferromagnetic nature that can further be improved with increasing Cr ions concentration.

Molecular weight effects on the phase-change-enhanced temperature coefficient of resistance in carbon nanotube/poly(N-isopropylacrylamide) composites

We investigate the temperature coefficient of resistance (TCR), of carbon nanotube composites with the phase-change polymer poly(N-isopropylacrylamide). Our results shed light on the underlying mechanism of electron transport through networks of conductive paths in the composites and its dependence on the molecular weights (MWs) of the phase-changing polymer. Measurements of the humidity dependence of the TCR reveal the dominant conduction mechanism to be variable range hopping with an exponent of ¼, corresponding to transport in a 3D system. In a humid atmosphere, a twenty-fold change in the hopping activation energy is observed as the temperature is swept across the polymer’s hydrophilic-to-hydrophobic phase-transition, while no change is observed in low humidity atmospheres or in vacuum. The TCR was found to depend on MW but to also be affected by details of the dynamics of hydration/dehydration of the composites. For operation in dry atmospheres and in vacuum the maximum TCR observed was only .002%, while in a humid atmosphere the TCR as large as 60% were observed—an order of magnitude higher than those found in common high-TCR materials used in thermal sensing applications.

Hydrogen Dynamics in Partially Quasicrystalline Zr69.5Cu12Ni11Al7.5: A Fast Field-Cycling Relaxometric Study

We studied hydrogen dynamics in a partially quasicrystalline hydrogen storage alloy Zr69.5Cu12Ni11Al7.5 by a combination of fast field-cycling nuclear magnetic relaxometry and diffusometry in static fringe field. We demonstrate that proton spin–lattice relaxation cannot be explained using a single activation energy for proton hopping between the interstitial sites. Instead, the behavior is better explained using a Gaussian distribution of activation energies, with the average value closely matching the one obtained in independent direct diffusion measurements. Knowing the diffusion constant and the correlation times for proton jumps, we estimate the average jump length.

Effect of annealing at oxygen partial pressure on the conductivity of Ni0.5Mn2.5O4 oxides

This paper presents a study of the electrical properties of nickel manganite Ni0.5Mn2.5O4−x as a function of annealing at oxygen partial pressure. The crystalline phase of manganite ceramics during annealing at oxygen partial pressure was investigated using X-ray diffraction; the predominant phase was tetragonal spinel. The electrical properties were analyzed by measuring resistance–temperature characteristics. The activation energy for electron hopping, determined using the slope of the ln ρ–1/T plots, was higher for samples annealed at lower oxygen partial pressure. The Mn4+/Mn3+ ratio, obtained through differential thermal analysis, increased with an increase in the oxygen partial pressure during annealing. The relationship between resistivity and the Mn4+/Mn3+ ratio during annealing at oxygen partial pressure was investigated.

Conducting mechanism in the epitaxialp-type transparent conducting oxideCr2O3:Mg

Epitaxial $p$-type transparent conducting oxide (TCO) $\mathrm{C}{\mathrm{r}}_{2}{\mathrm{O}}_{3}:\mathrm{Mg}$ was grown by electron-beam evaporation in a molecular beam epitaxy system on $c$-plane sapphire. The influence of Mg dopants and the oxygen partial pressure were investigated by thermoelectric and electrical measurements. The conduction mechanism is analyzed using the small-polaron hopping model, and hopping activation energies have been determined, which vary with doping concentration in the range of 210--300 \ifmmode\pm\else\textpm\fi{} 5 meV. Films with better conductivity were obtained by postannealing. The effect of postannealing is discussed in terms of a crystallographic reordering of the Mg dopant. The highest Seebeck mobilities obtained from thermoelectric measurements are of the order of ${10}^{\ensuremath{-}4}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}{\mathrm{V}}^{\ensuremath{-}1}{\mathrm{s}}^{\ensuremath{-}1}$. We investigate the fundamental properties of a Mg dopant in a high crystalline quality epitaxial film of a binary oxide, helping us understand the role of short range crystallographic order in a $p$-type TCO in detail.

Enhancing phase stability and kinetics of lithium-rich layered oxide for an ultra-high performing cathode in Li-ion batteries

To achieve a higher capacity and rate capability, the electrochemical performance of doped Li-rich layered oxide (LLO), in which Co and O ions are substituted with various dopants (Ti, Zr, Ce, Mo, W, and F), is investigated using first-principles calculations. W and Mo are candidate dopants to enhance the phase stability but are excluded due to the decreased average cell voltage of 2.5–5.4 %, lowering the energy density of a battery. Instead, F is selected as a promising dopant because F-doped LLO can achieve high structural stability without a reduction in the average cell voltage compared with un-doped LLO. The Li slab distance in F-doped LLO expands approximately 3–8% depending on the Li concentration, and the activation energy for Li hopping is reduced about 30%, suggesting faster Li ion diffusion. The enthalpy of formation of F-doped LLO is reduced to 5.3–12.4 kJ mol−1 during de-lithiation, implying an increase in phase stability. Based on the DFT prediction, we experimentally demonstrate F-doped LLO (Li1.17Ni0.17Co0.17Mn0.50O1.96F0.04) exhibits a high capacity of 252.2 mAh g−1 at 0.33C rate in the cut-off voltage range of 3.0–4.6 V. The rate capability is enhanced, and the capacity is retained up to 83% at 3C compared with the 0.33C rate.

Structural analysis and electrochemical properties of cobalt-doped Sr0.9Ce0.1MnO3−δ cathode for IT-SOFCs

Abstract

The nature of excess electrons in anatase and rutile from hybrid DFT and RPA.

The behavior of excess electrons in undoped and defect free bulk anatase and rutile TiO2 has been investigated by state-of-the-art electronic structure methods including hybrid density functional theory (DFT) and the random phase approximation (RPA). Consistent with experiment, charge trapping and polaron formation is observed in both anatase and rutile. The difference in the anisotropic shape of the polarons is characterized, confirming for anatase the large polaron picture. For anatase, where polaron formation energies are small, charge trapping is observed also with standard hybrid functionals, provided the simulation cell is sufficiently large (864 atoms) to accommodate the lattice relaxation. Even though hybrid orbitals are required as a starting point for RPA in this system, the obtained polaron formation energies are relatively insensitive to the amount of Hartree-Fock exchange employed. The difference in trapping energy between rutile and anatase can be obtained accurately with both hybrid functionals and RPA. Computed activation energies for polaron hopping and delocalization clearly show that anatase and rutile might have different charge transport mechanisms. In rutile, only hopping is likely, whereas in anatase hopping and delocalization are competing. Delocalization will result in conduction-band-like and thus enhanced transport. Anisotropic conduction, in agreement with experimental data, is observed, and results from the tendency to delocalize in the [001] direction in rutile and the (001) plane in anatase. For future work, our calculations serve as a benchmark and suggest RPA on top on hybrid orbitals (PBE0 with 30% Hartree-Fock exchange), as a suitable method to study the rich chemistry and physics of TiO2.

Impedance spectroscopy of pellets made from yttria stabilized zirconia nanoparticles generated via CW and pulsed mode of laser vaporization method

We report impedance characteristics and ac conductivity response of ~1mm thick pellets made from yttria-stabilized zirconia (YSZ) nanoparticles. Nanoparticles of different average sizes (10–16nm) and of different yttria (6mol%, 10mol% and 16mol%) contents were obtained via CO2 laser based laser vaporization method. We employed both the continuous and the pulsed mode of CO2 laser operation and obtained smallest size nanoparticles under pulsed mode of laser vaporization. Impedance spectroscopic measurements were carried out in frequency range of 10Hz–1MHz at various temperatures ranging from room temperature to 500C. Oxygen ion conductivity response was compared with respect to laser vaporization mode and yttria content in nanoparticles of YSZ. The grain and grain boundary ionic conductivity of pellets made from large sized nanoparticles generated in continuous mode of laser vaporization was two orders of magnitude low compared to pellet made of smallest average size nanoparticles (generated with pulsed mode of laser vaporization). The activation energy of ion hopping in all the samples was estimated using Arrhenius equation and found in the range 0.95–1.34eV. Possible origin of differences between conductivity in pellets made from nanoparticles generated via pulsed mode and CW mode of vaporization is discussed on the basis of association of oxygen vacancy and Y+3 ion.

Electron transport in pure and substituted iron oxyhydroxides by small-polaron migration.

Iron oxyhydroxides (FeOOH) are common crystalline forms of iron that play a critical role in technology and the natural environment via a variety of important reduction-oxidation reactions, including electrical semiconduction as an aspect. However, a basic understanding of the electron transport properties of these systems is still lacking. We examine the electron mobility in goethite (α-FeOOH), akaganéite (β-FeOOH), and lepidocrocite (γ-FeOOH) polymorphs by means of density functional theory based (DFT+U) calculations. We show that room temperature charge transport should be dominated by the small-polaron hopping type, and that the attendant mobility should be highest for pure goethite and akaganéite. Hopping pathways through the various lattices are discussed in terms of individual electron exchange steps and rates for each. Given the usual occurrence of compositional impurities in natural iron oxyhydroxides, we also investigate the effect of common stoichiometric defects on the electron hopping activation energies such as Al and Cr substitutional cations in goethite, and Cl anions in the channels of akaganéite.

The impedance analysis for the aging mechanism of CaO excess type calcium zirconate electrolyte material comparing with 8.5YSZ

A CaO excess type calcium zirconate electrolyte with a composition of Ca 1.1 Zr 0.9 O 2.9 was prepared. Its aging behavior at 900 °C and 1100 °C was evaluated by AC impedance. The conductivity decreases more seriously at higher temperature. Combined with the aging effect of 8.5 YSZ, the formation of [ Ca Zr ″ − V O •• ] promoted by annealing operation should be responsible for the aging effect in Ca 1.1 Zr 0.9 O 2.9 . The declined mobility of V O •• is viewed as the increase in hopping activation energy and the decrease in effective concentration of V O •• . Consequently, the diffusion coefficient of V O •• decreases and results in the aging behavior. • Confirmed the aging behavior in CaO excess calcium zirconate perovskite ceramics • The aging behavior works more seriously as temperature rises. • The Ca 1.1 Zr 0.9 O 2.9 presents a much more stable conductivity than the 8.5 YSZ shows. • The annealing operation enforces the formation of association [ Ca Zr ″ − V O •• ] and makes oxygen vacancy trapped. • The lock of oxygen vacancy reduces its effective diffusion coefficient.

Graded Density Ion Exchange Polymer Films on Electrodes: Impacts on Structure and Transport

The full expression of Fick’s second law includes a distance dependent diffusion coefficient, D(x). In one dimension, for distance x and time t, the concentration is expressed as shown in Equation 1.Eyring models for transport as a function density and viscosity are predicated on an activation energy for short distance hopping of the diffusing species from one low energy site to an adjacent site of similar low energy. This results in a correlation between density and viscosity.In turn, the Stokes Einstein relationship (Equation 2) specifies diffusion coefficient and viscosity η are inversely related. Equation is for a spherical diffusion species of radius r, k is the Boltzmann constant, T is temperature. If viscosity varies in space as η(x), then D(x) varies in space proportional to 1/η.Ficoll® (GE Life Sciences) is a highly branched, water soluble, hydrophilic copolymer of sucrose and epichlorohydrin that is used to establish density gradients. On application of Ficoll films to electrodes, the density gradient is preserved. Cyclic voltammetry of outer sphere redox probes such as tetramethylphenylenediamine yields near steady state responses as scan rate slows. Modeling of the voltammetric responses establishes that the density gradient establishes a steady state flux of materials to the electrodes. Images of Ficoll films immersed in solution confirm a density gradient.Here, Ficoll is used as a template to form a graded film of the ion exchange polymer, Nafion® (DuPont). Films are formed on electrodes by cocasting Ficoll and Nafion. Alternatively, a cast film of Ficoll can serve as the template for the Nafion. Films are evaluated by imaging. When compared to a uniform Nafion film, cyclic voltammograms for outer sphere redox probes that pass through the ion exchange polymer are altered. Sigmoidal as well as Gaussian voltammograms are observed, dependent on conditions of film formation. The structural morphology changes imprinted on formation of Ficoll Nafion layers alters flux through the ion exchange polymer layer. References and Acknowledgments: Support of the National Science Foundation and the University of Iowa is gratefully acknowledged. Thanks also to Dick Buck for his example as a thoughtful scientist and mentor.[1] Krysti L. Knoche and Johna Leddy, manuscript in preparation.[2] K. L. Knoche, P. D. Moberg, C. Hettige, and J. Leddy, "Simulation of Fick's Second Law for Spatially Variant Diffusion Coefficients," ECS Trans. (2013) 53 (15) 1-6.

Relationship between the structure of carbon nanocoils and their electrical property

The electrical property of carbon nanocoils (CNCs) annealed from 300 to 2900K has been studied by a four-probe technique. It was shown that the resistivity of the CNCs decreased with the increase of the annealing temperature owing to the improvement of crystallinity and the most notable change of resistivity occurred at the initial structure change of the CNCs. Besides the measurement of room-temperature resistivity of the annealed CNCs, temperature-dependent resistance of the annealed CNCs was also measured. According to the nearest neighboring hopping mechanism, the average activation energy for electron hopping in the annealed CNCs was calculated, which indicated that the average activation energy reduced with the structural improvement of CNCs. It was also found that the variation of average activation energy was also sensitive to the initial structural change of CNCs. Finally, through studying the electrical property of the CNCs under expansion, it was found that the resistance of the CNC was not changed with elongation.

Electronic Transport Characterization of BiVO4 Using AC Field Hall Technique

ABSTRACTBismuth vanadate (BiVO4) is a photoelectrode for the oxidation of water. It is of fundamental importance to understand the electrical and photoelectrochemical properties of this material. In metal oxides, the electronic transport is described by the small polaron model, first described by Mott. In this model, the resistivity varies with temperature as $\rho \,\left( T \right)\, \propto \,Te^{({{E_a } \mathord{\left/ {\vphantom {{E_a } {(k_B T))}}} \right. \kern-\nulldelimiterspace} {(k_B T))}}} $, where Ea is the hopping activation energy, kB is the Boltzmann constant and T is the absolute temperature. Resistivity measurements confirm that small polaron hopping dominates in temperature ranges from 250 K to 300 K. In addition measurements from 175K to 250K show the variable range hopping dominates the transport. To this end, the electronic transport properties of BiVO4 single crystal were characterized using resistivity measurements and Hall effect measurements over temperatures ranging from 175 K to 300 K.

Low temperature characteristics in amorphous indium-gallium-zinc-oxide thin-film transistors down to 10 K

We report on the characteristics of amorphous indium-gallium-zinc-oxide thin-film transistors (TFTs) in the temperature range of 10–300 K. In the range of 80–300 K, the transfer characteristics are consistent with thermally activated band conduction. Below 80 K, the drain current vs. temperature behavior follows Mott's law, exp(−B/T−1/4), with constant B, indicating variable range hopping. The subthreshold swing of the TFT remains unchanged in the band conduction region, but it increases rapidly with decreasing temperature below 80 K. With decreasing temperature, the hopping activation energy decreases and hopping distance increases, and are 16.8 meV and ∼11.6 nm, respectively, at 60 K.

Electrical transport phenomena prevailing in undoped nc-Si/a-SiNx:H thin films prepared by inductively coupled plasma chemical vapor deposition

A comprehensive analysis on the electrical transport phenomena prevailing in undoped nc-Si/a-SiNx:H thin films prepared by inductively coupled plasma chemical vapor deposition and its correlation with the specific inhomogeneous structure, consisting of a mixture of different phases involving charge transfer by tunneling and thermionic emission or a connected network of aggregates of such components, has been made for deeper understanding in order to facilitate and improve the device applicability of the material. The nc-Si/a-SiNx:H films exhibit a thermally activated electrical transport above room temperature. Multi-phonon hopping (MPH), following σ∝Ty, occurs below room temperature, involving higher number of acoustic phonons in less crystalline network at higher nitrogenation. In less nitrogenated network, the MPH conduction continues up to the lowest temperature because of less localization of charge carriers within larger size of the nanocrystallites. Mott variable range hopping (Mott-VRH), following ln(σ) ∝ T−¼, is in effect below a certain temperature for highly nitrogenated network. The nature of variations of Mott parameter, T*, hopping activation energy, Wh, optimum hopping distance, rh, and the estimated density of states at the Fermi level, N(EF), identify the increased degree of disorder in the film attributing enhanced amorphous concentration at higher nitrogenation. The transition from MPH to Mott-VRH occurring at higher temperature at relatively higher nitrogenation has been interpreted as the freezing out of the acoustic phonons associated with lower grain size with higher number density at comparatively higher temperature, considering the phonon wavelength approximately of the size of nanocrystallites. The present intrinsic nc-Si/a-SiNx:H material containing nanocrystallites of average size ∼12–2 nm and number density ∼1011–1012 cm−2 providing a significantly wide range of optical band gap, Eg ∼ 1.80–2.75 eV with associated very high electrical conductivity, σD ∼ 10−2–10−6 S cm−1 along with high carrier concentration, ne ∼ 1014–1011 cm−3 and electron mobility, μe ∼ 246–105 cm2 V−1 s−1, seems to be the superior, concerning issues related to usability in device fabrication, among typical wide optical gap silicon dielectric materials available in the literature, e.g., silicon carbide, silicon oxide, and amorphous silicon films with nc-Si inclusions; while being the only comprehensive report on nanocrystalline silicon nitride (nc-Si/a-SiNx:H) thin films, in particular.