Solid-state diffusion coefficient

YURIA, s., STEPHAN, A.M., KATAOKA, H., louic conduction mechanisms of hthium gel polymer electrolytes investigated by the conductivity and diffusion coefficient, Solid State Ionics, 2003,160(122), 149-53. 

Diffusion in solid state materials when the activities of diffusing species are not concentration independent does not follow Fick s law. The diffusion coefficient has... 

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

An important result of this study is the conclusion of a particle-size-dependent COads surface mobility. The value obtained for large Ft particles is significantly smaller than Deo at a solid/gas interface. However, Kobayashi and co-workers, using solid state NMR, performed measurements of the tracer diffusion coefficient Deo at the solid/electrolyte interface and for Ft-black particles (about 5nm grain... 

One possibility for increasing the minimum porosity needed to generate disequilibria involves control of element extraction by solid-state diffusion (diffusion control models). If solid diffusion slows the rate that an incompatible element is transported to the melt-mineral interface, then the element will behave as if it has a higher partition coefficient than its equilibrium partition coefficient. This in turn would allow higher melt porosities to achieve the same amount of disequilibria as in pure equilibrium models. Iwamori (1992, 1993) presented a model of this process applicable to all elements that suggested that diffusion control would be important for all elements having diffusivities less than... 

Diffusion is one of the most important natural processes. The varying rate of diffusion yields an excellent characteristic of individual states of aggregation. While diffusion coefficients in gases are of the order of 10-1 cm2 s-1, those in solutions are of the order of 10 5cm2 s 1 and, in solids, of 10 10 cm2 s 1. 

Fig. 7. Predicted diffusion coefficients for hydrogen (H) and deuterium (D) in niobium, as calculated by Schober and Stoneham (1988) from a model taking account of tunneling between various states of vibrational excitation and comparison with experimental measurements (solid lines). Theoretical curves are shown both for a model using harmonic vibrational wave functions (dashed lines) and for a model with anharmonic corrections (dashed-dotted lines).

Kleinfeld, M. Wiemhofer, H.-D. 1988. Chemical diffusion coefficients and stabihty of CuInS2 and CuInSe2 from polarization measurements with point electrodes. Solid State Ionics. 28-30 1111-1115. 

Diffusion coefficients in amorphous solids such as oxide glasses and glasslike amorphous metals can be measured using any of the methods applicable to crystals. In this way it is possible to obtain the diffusion coefficients of, say, alkah and alkaline earth metals in silicate glasses or the diffusion of metal impurities in amorphous alloys. Unlike diffusion in crystals, diffusion coefficients in amorphous solids tend to alter over time, due to relaxation of the amorphous state at the temperature of the diffusion experiment. 

The normal state of affairs during a diffusion experiment is one in which the concentration at any point in the solid changes over time. This situation is called non-steady-state diffusion, and diffusion coefficients are found by solving the diffusion equation [Eq. (S5.2)] ... 

Yasuda I and Hishinuma M. Electrical conductivity and chemical diffusion coefficient of Sr-doped lanthanum chromites. Solid State Ionics 1995 80 141-150. 

This is the first instance in which solid-state-like diffusion coefficients have been estimated from STM images. Thus, it seems likely that room temperature diffusion coefficients might be obtained with STM for well characterized systems in the future (87). 

The previous paper (63) also studied the disintegration of solid solutions and for that purpose samples were heated for 300 hours at 250°C, but no signs of disintegration were detected in an X-ray diffractogram. This might be due to the fact that solid state diffusion is still too slow at that temperature. This is supported by the low diffusion coefficient calculated if one extrapolates from the experimental values determined at high temperature (60). 

The preceding data, though limited in nature, represent one of the first attempts to measure solid state diffusion rates of alkali elements into the near-surface region of feldspars and natural glasses at low temperature. As such, interesting comparisons can be made with diffusion coefficients and activation energies calculated from numerous high temperature isotope and tracer diffusion studies f 11-181. 

The papers of Mallon and Ray [98, 123] can be regarded as the state of the art in understanding and modelling solid-state polycondensation. They assumed that chain ends, catalysts and by-products exist solely in the amorphous phase of the polymer. Because of the very low mobility of functional groups in the crystalline phase, the chemical reactions are modelled as occurring only in the amorphous phase. Additionally, the diffusion of by-products is hindered by the presence of crystallites. The diffusivity of small molecules was assumed to be proportional to the amorphous fraction. Figure 2.32 shows the diffusion coefficients for the diffusion of EG and water in solid PET. 

For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

Moller, K. and Gevert, T. 1994, An FTIR solid-state analysis of the diffusion of hindered phenols in low-density polyethylene (LDPE) the effect of molecular size on the diffusion coefficient. J. Appl. Polym. Sci. 51 895-903. 

The following compilation is restricted to the transport coefficients of protonic charge carriers, water, and methanol. These may be represented by a 3 X 3 matrix with six independent elements if it is assumed that there is just one mechanism for the transport of each species and their couplings. However, as discussed in Sections 3.1.2.1 and 3.2.1, different types of transport occur, i.e., diffusive transport as usually observed in the solid state and additional hydrodynamic transport (viscous flow), especially at high degrees of solvation. Assuming that the total fluxes are simply the sum of diffusive and hydrodynamic components, the transport matrix may... 

Figure 18.2. Diffusion coefficient of carbon in iron as a function of the inverse of temperature. (From C. Kittel, Introduction to Solid State Physics, 7th ed., Wiley, New York, 1996, with permission from Wiley.)...

In this equation, aua represents the product of the coefficient of electron transfer (a) by the number of electrons (na) involved in the rate-determining step, n the total number of electrons involved in the electrochemical reaction, k the heterogeneous electrochemical rate constant at the zero potential, D the coefficient of diffusion of the electroactive species, and c the concentration of the same in the bulk of the solution. The initial potential is E/ and G represents a numerical constant. This equation predicts a linear variation of the logarithm of the current. In/, on the applied potential, E, which can easily be compared with experimental current-potential curves in linear potential scan and cyclic voltammetries. This type of dependence between current and potential does not apply to electron transfer processes with coupled chemical reactions [186]. In several cases, however, linear In/ vs. E plots can be approached in the rising portion of voltammetric curves for the solid-state electron transfer processes involving species immobilized on the electrode surface [131, 187-191], reductive/oxidative dissolution of metallic deposits [79], and reductive/oxidative dissolution of insulating compounds [147,148]. Thus, linear potential scan voltammograms for surface-confined electroactive species verify [79]... 

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