Diffusion Di Research Articles

Discharge characteristic analysis of lithium-sulfur batteries considering the discontinuous deposit and transport-limited effects

The modeling research plays a crucial role in grasping the reaction mechanisms and forecasting the performance of lithium-sulfur (Li–S) batteries. A transient Li–S battery model including continuity, transportation, and reaction kinetics by simultaneously considering the discontinuous deposit of discharge product Li2S and the transport limitation in the concentrated electrolyte, is developed to reveal the discharge phenomena. The effects of operating conditions and electrolyte and electrode properties on the discharge behaviors including voltage-capacity curve, energy density, profiles of solid product (ɛLi2S) and porosity (ɛ) at the cathode are quantitatively studied. It is found that low discharge rate is beneficial to the discharge capacity and utilization of cathode sulfur. Enhancing precipitate (S8) solubility Ksp, S8 and ionic diffusivity Di improves voltage plateau and specific energy to varying degrees; the promotion of voltage plateau will be inconspicuous as electrode conductivity σ is enlarged over 0.1 S/m. With the rise of ɛ from 0.5 to 0.9, the specific capacity and the specific energy are expanded by around 5 times. When lengthening Lca from 20 μm to 60 μm, the specific capacity ascends from 944.5 to 991.5 mAh/g-S, whereas the growth rate of specific capacity and specific energy decreases gradually; the practical total energy almost increases linearly with thickness, yielding a 218.75% enhancement. With a certain period of relaxation, the recovered cell capacity after the high discharge rate is higher than that after the low discharge rate. This work may guide in designing electrodes and electrolytes and provide performance regulation strategies for Li–S batteries.

Is excess faster than deficient? A molecular-dynamics study of oxygen-interstitial and oxygen-vacancy diffusion in CeO2

The diffusivity of oxygen interstitials (Di) and of oxygen vacancies (Dv) in fluorite-structured CeO2 was studied by means of classical molecular dynamic simulation techniques. Simulations were performed on cells that were either oxygen abundant or oxygen deficient at temperatures 1500 ≤ T / K ≤ 2000 for defect site fractions 0.18% ≤ ni/v ≤ 9.1%. In general, we found that at a given temperature T and defect site fraction ni/v the vacancy diffusivity Dv was higher than the interstitial diffusivity Di. Isothermal values of Di and Dv were constant at low defect site fractions (ni/v < 0.91%), but the behaviour diverged at higher ni/v: whereas Dv decreased at higher nv, Di increased at higher ni. The analysis also yielded, as a function of ni/v, activation enthalpies (ΔHmig) and entropies (ΔSmig) of vacancy migration and of interstitial migration. A constant value of 0.6 eV was found for low nv, with increases in observed for nv > 0.91%. For low ni a constant value of 1.4 eV was found, with a surprising decrease in for ni > 0.91%. The effect of dopants on the behaviour of the defect diffusivities was also studied. Doping with Gd3+ had a detrimental effect on vacancy diffusion, with a slight decrease in Dv and an increase in being observed. Donor doping with Nb5+, in contrast, was beneficial, resulting in higher Di and a decrease in . We suggest that the migration mechanism of oxygen interstitials in CeO2, non-collinear interstitialcy, is responsible for the lower defect diffusivity and higher migration barrier.

Surface doping of TiO2 powders via a gas–melt reaction using thermal plasma as an excitation source

Surface doping is an effective method to engineer and functionalize powder materials without modulating the internal crystal structure. This study proposed a facile technique for surface doping via a gas–melt reaction using thermal plasma as an excitation source. Doping molten titania (TiO2) particles with La was preliminarily explored owing to the broad photocatalytic applications of TiO2. Scanning electron microscopy, X-ray diffraction (XRD), X-ray photoelectron spectroscopy, transmission electron microscope, diffuse reflectance spectroscopy, photoluminescence spectroscopy and Fourier transform infrared spectroscopy were adopted to characterize the morphology, phase composite, chemical state, fine structure, and optical property of the doped TiO2 powder, respectively. Results indicated that molten TiO2 doped with La solidified into spherical particles under the effect of surface tension. No modification of the internal crystal structure was indicated in the XRD patterns, except that the diffraction peak of rutile TiO2 (110) shifted to low angles after surface doping with La. The obtained TiO2 powder exhibited sensitivity to sunlight and near-infrared light, and a La/Ti atomic ratio of 19.4% was achieved. The diffusivity Di of La in molten TiO2 ranged from 10−8 m2/s to 10−7 m2/s, as determined from the gas–melt reaction.

Response to “Comment on ‘Diffusion of n-type dopants in germanium’ ” [Appl. Phys. Rev. 2, 036101 (2015)

In this reply to the comment of Cowern et al., we demonstrate on the basis of full numerical simulations of radiation enhanced dopant diffusion via the kick-out mechanism that the g/λ analysis fails to consistently describe boron (B) diffusion in germanium (Ge) under irradiation. Cowern et al. missed to perform a consistency check with results for the diffusivity DI of Ge interstitials (I) determined from Ge self-diffusion under irradiation. Data deduced for DI from the exponential B profile reported by Cowern et al. deviate several orders of magnitude from the self-diffusion study. This clearly disproves the validity of the kick-out mechanism to control radiation enhanced B diffusion in Ge. Exponential B profiles like those established in Ge under irradiation are also reported for silicon by Venezia et al. [Phys. Rev. B 69, 125215 (2004)]. The characteristic shape is not described by the kick-out mechanism but rather explained qualitatively by the complex formation and dissolution of defect clusters. Modeling of B diffusion in Ge under irradiation performed by Schneider et al. [Phys. Rev. B 87, 115202 (2013)] is fully consistent with self-diffusion under irradiation. This constraint led us to conclude that the characteristic B profiles are additionally affected by the formation of immobile B clusters. Although a direct microscopic proof of B cluster formation is still lacking, the report of Venezia et al. on B clustering in Si during irradiation with similar exponential B profiles also supports our interpretation of B diffusion in Ge under irradiation.

Ionic contribution to Rayleigh line wing under conditions of light scattering by liquid electrolytic solutions

A theoretical treatment is performed of the mechanism (suggested in N. F. Bunkin andA. V. Lobeev, Z. Phys. Chem. 214, 269 (2000)) of ionic effect on the Rayleigh line wing under conditions of light scattering by liquid electrolytic solutions. The mechanism consists essentially in that the fluctuation electric field caused by Brownian motion of ions dissolved in a liquid leads, because of the Kerr polarization effect, to fluctuations of optical anisotropy of the scattering medium. The spectral characteristics of the Rayleigh line wing are obtained using the fluctuation-dissipative theorem as applied to equilibrium thermal electromagnetic field. Expressions are derived for the integral intensity and spectral width (Δν) of the Rayleigh line wing in terms of parameters of liquid solution such as the temperature T, the viscosity η, the concentration of dissolved ions ni, and the coefficient of their diffusion Di. It is demonstrated that Δν ∝ exp(−W/2T), where W is the activation energy of ion mobility bi = Di/T. The possible region of validity of developed theoretical concepts as applied to the experimental data for the Rayleigh line wing in electrolytic solutions is discussed.

Transport parameters and solubility coefficients of polymers at their glass transition temperatures

Many parameters of polymers exhibit breaks when temperature passes through glass transition. It is also often assumed that fractional free volume (FFV) at the glass transition temperature (Tg) has a standard value (the isofree volume concept). As gas diffusion (D) and permeability (P) coefficients depend on FFV, and mechanism of sorption and permeation is different above and below Tg, a question can be asked if D and P parameters of various gases in polymers have standard values at corresponding Tg, and, if not, how the values of D(Tg) and P(Tg) vary with Tg in different polymers. To examine this problem, two approaches were used: (1) extrapolation to Tg of numerous P and D values measured at ambient temperatures; (2) an analysis of direct data obtained in different polymers at their Tg. In both cases, qualitatively similar results were obtained: the D(Tg) and P(Tg) values increase with growing Tg independently of the nature of gas. Permselectivity Pi(Tg)/Pj(Tg) and selectivity of diffusion Di(Tg)/Dj(Tg) are reduced when Tg increases. The dependence of the solubility coefficients S(Tg) = D(Tg)/P(Tg) is much weaker than those of D(Tg) and P(Tg). This conclusion was confirmed by the results of direct measurements of S in a wide range of temperature including Tg for several gas/polymer systems. An analysis of the results of positron annihilation studies of free volume in polymers led to the conclusion that the observed increases in the D(Tg) and P(Tg) values with Tg are caused mainly by thermal activation of diffusion processes at Tg. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1691–1705, 2000

Mesoscopic kinetics of nonequilibrium solidification

Disadvantages of Aziz interface partition model [J. Appl. Phys. 53, 1158 (1982)] are summarized in this article. Using transition state theory and Maxwell–Boltzmann distribution law, a mesoscopic solute partition model (MPM) including multilayer interface for dilute solution is put forward. It is shown that the static interface structure and roughening behavior have significant effects on solute partitioning. Both the partition processes of semiconductors and metals can be explained by MPM rationally. The Aziz model is just a particular case of MPM for monolayer interface without roughening before complete trapping occurs. Comparisons of MPM with experimental results in Si (As, Ge, Bi, Sn) and Al(Cu, Sn, Ge, In) show pretty good agreement, provided an educated speculation of interface roughening behavior is given. Also in MPM, it is pointed out that interface diffusivity Di correlates with the interface scale. For semiconductors with an atomic sharp solid/liquid interface, Di is close to DL, the diffusivity of bulk liquid. On the other hand, for metals with a diffuse interface, Di can be orders of magnitude lower than DL, to some extent estimated by DSDL, the geometric mean of the diffusivity of bulk solid and liquid.

Transport parameters and solubility coefficients of polymers at their glass transition temperatures

Many parameters of polymers exhibit breaks when temperature passes through glass transition. It is also often assumed that fractional free volume (FFV) at the glass transition temperature (Tg) has a standard value (the isofree volume concept). As gas diffusion (D) and permeability (P) coefficients depend on FFV, and mechanism of sorption and permeation is different above and below Tg, a question can be asked if D and P parameters of various gases in polymers have standard values at corresponding Tg, and, if not, how the values of D(Tg) and P(Tg) vary with Tg in different polymers. To examine this problem, two approaches were used: (1) extrapolation to Tg of numerous P and D values measured at ambient temperatures; (2) an analysis of direct data obtained in different polymers at their Tg. In both cases, qualitatively similar results were obtained: the D(Tg) and P(Tg) values increase with growing Tg independently of the nature of gas. Permselectivity Pi(Tg)/Pj(Tg) and selectivity of diffusion Di(Tg)/Dj(Tg) are reduced when Tg increases. The dependence of the solubility coefficients S(Tg) = D(Tg)/P(Tg) is much weaker than those of D(Tg) and P(Tg). This conclusion was confirmed by the results of direct measurements of S in a wide range of temperature including Tg for several gas/polymer systems. An analysis of the results of positron annihilation studies of free volume in polymers led to the conclusion that the observed increases in the D(Tg) and P(Tg) values with Tg are caused mainly by thermal activation of diffusion processes at Tg. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1691–1705, 2000

DIFFUSIONAL MODEL FOR INTRAPARTICLE ION EXCHANGE KINETICS IN NONLINEAR SELECTIVE SYSTEMS

ABSTRACT The diffusional model for the intraparticle ion exchange (IE) kinetics in selective ion exchangers is presented. The model develops the phenomenological formulation based on the irreversible thermodynamics and includes mass balance equations with description of ion fluxes by the Nernst-Plank relations. The model is based on the supposition that during the exchange RA+B = RB + A involving a chemical reaction of counter-ions (B and A) with the resin site R, diey can exist in the exchanger in two states, namely “free” and as the species formed by their combination with fixed groups R. Counter-ions B and A are considered to be immobile while “bound” and to move unimpeded while “free”. The mathematical formulation of the IE kinetic process in this case is described by a system of two nonlinear diffusion equations in partial derivatives where the effective self diffusion coefficients Dii and the cross interdiffusion coefficients Dij depend on the concentration of the diffusing counter-ions (B and A) and coions Y, and also on the values of equilibrium constants KRB and KRA describing the stability of RB and RA complexes in the ion exchanger phase. As the result, the ion fluxes are described within the generalized Fick formulation. Fickian diffusivities Dij compose 2×2 diffusional matrix with determining each of them through the individual diffusivity Di of the ions B, A and F. The set of diffusional equations along with the appropriate initial and boundary conditions solved by using a computer gives transient concentration profiles which compose concentration waves in the ion exchanger bead. For various combination of diffusional and selectivity factors the concentration waves in the bead have been presented in the pseudo 3dimensional space {concentration - radius - time}. This presentation simplifies the interpretation of the process and makes it visual. It is shown that the difference both in concentration waves profiles and rate between forward and reverse exchange of two counter-ions may arise not only from unequal diffusion coefficients but also from unequal dissociation constants of the complexes formed with the fixed groups.

Dissipation-theory treatment of the transition from diffusion-controlled to diffusionless solidification

The steady-state velocity of a planar liquid-solid interface is predicted by calculating the free energy dissipated by irreversible processes at the interface and equating it to the available driving free energy. A solute drag term and an intrinsic interfacial mobility term are included in the dissipation calculations for a binary alloy. The solute drag calculation employs a solute trapping model, which has been extended to concentrated alloys. The result is presented in terms of a single unknown parameter, the interfacial diffusivity Di. A transition from diffusion controlled to diffusionless solidification occurs over approximately an order of magnitude in growth velocity, as the interface speed surpasses the maximum speed with which solute atoms can diffuse across the interface to remain ahead of the growing crystal.

Crystal Growth and Solute Trapping

ABSTRACTA simple model for solute trapping during rapid solidification is presented in terms of a single unknown parameter, the interfacial diffusivity Di. A transition from equilibrium segregation to complete solute trapping occurs over roughly an order of magnitude in growth speed, as the interface speed surpasses the maximum speed with which solute atoms can diffuse across the interface to remain ahead of the growing crystal. This diffusive speed is given by Di/λ, where λ is the interatomic spacing, and is typically of the order 10 meters per second. Comparison is made with experiment. The steady–state speed of a planar interface is predicted by calculating the free energy dissipated by irreversible processes at the interface and equating it to the available driving free energy. A solute drag term and an intrinsic interfacial mobility term are included in the dissipation calculations. Steady–state solutions are presented for Bi–doped Si during pulsed laser annealing.