Degradation of Functional Materials in Temperature Gradients - Thermodiffusion and the Soret Effect

Abstract

Functional materials are often exposed to high temperatures and inherent temperature gradients. These temperature gradients act as thermodynamic driving forces for the diffusion of mobile components. The detailed consequences of thermodiffusion depend on the boundary conditions of the non-isothermal sample: Once the boundaries of the sample are inert and closed for exchange of the mobile components, thermodiffusion leads to their pile-up in the stationary state (the so called Soret effect). Once the system is open for an exchange of the mobile component, chemical diffusion adds to the Soret effect, and stationary non-zero component fluxes are additionally observed in the stationary state. In this review, the essential aspects of thermodiffusion and Soret effect in inorganic functional materials are briefly summarized and our current practical knowledge is reviewed. Major examples include nonstoichiometric binary compounds (oxides and other chalcogenides) and ternary solid solutions. The potential influence of the Soret effect on the long term stability of high temperature thermoelectrics is briefly discussed. Typical Soret coefficients for nonstoichiometric compounds are found to be of the order of (dδ/dT) ≈ 1%/K.

Formation of Corrosion‐Resistant Thermal Diffusion Boride Coatings

“…In the empirical description of transport by thermal diffusion, because of the complexity of this process when the temperature gradient (▽ T ) creates an additional driving force to the concentration gradients (▽ C ), the Ludwig–Soret effect can be taken into account. In this case, the formulae can be used to express the flux linking to thermal diffusion: i.e., two temperature gradient‐driven phenomena can be outlined: D ▽ C – flux of depositing and diffusing atoms caused by their non‐uniform spatially distributed concentration due to temperature spatial non‐uniformity; DC ( Q/kT )(▽ T/T ) – clear expression of the Ludwig–Soret effect in crystalline solids. where D ( C , T , t ) is the diffusivity, s ( T , t ) is the solubility, k s ( C , T , t ) is the “Soret effect” factor providing diffusion because of temperature gradient, and k p ( c , T , t ) is the pressure stress factor. The temperature gradient can be created at thermal treatment resulting in the independent driving force for the concentration gradient.…”

Combined effect of temperature difference across interface and finite size of the ions on interdiffusion in SOFC

“…The initial concentration profiles of the cations and the value of gradient energy coefficient, W * 0 (to solve Allen-Cahn equation) are taken same as mentioned in Hu et al 35 The values of tracer diffusion coefficients ðD * i Þ at 1673 K (1400°C) for all ions taken in the present study are listed in Table S1 in the supplemental materials of Hu et al 35 There is no data available for heat of transport of the ions present in the YSZ and LSM. Therefore, in the present study, the activation energy of an ion is assumed as its heat of transport (Q i ) as suggested by Janek et al 81 The values of activation energy of ions at 1000°C are listed in Table S2 in the supplemental materials of Hu et al 35 The nondimensional value of heat of transport (Q * i ) in both phases for each ion at 1400°C is given in Table 1.…”

“…There is no data available for heat of transport of the ions present in the YSZ and LSM. Therefore, in the present study, the activation energy of an ion is assumed as its heat of transport ( Q i ) as suggested by Janek et al 81 The values of activation energy of ions at 1000°C are listed in Table S2 in the supplemental materials of Hu et al 35 The non-dimensional value of heat of transport (Qi*) in both phases for each ion at 1400°C is given in Table 1.…”

An Essay on the Heat of Transport in Solids and a Partial Guide to the Literature

“…Faupel, 1992). One of the limitations to finding clear patterns is the absence of systematic experimental studies, although the work of Sugisaki et al (1985) on the hydrogen isotopes (H, D, and T) in various metal hosts and the work of Christy (1961) and Janek et al (2002Janek et al ( , 2012 on ionic compounds provide good examples of systematic studies. Some data for ionic crystals are given in Table 1 at the end of this section and show that the values of Q*' for the defects in these compounds are generally negative.…”

“…β-Ag 2 S, β-Ag 2 Se and various oxides) and also from the possibility of using ion probes and electron probes, and the sensitivity of electrical thermopower measurements. Some of the most elegant studies are those of Janek et al (2002Janek et al ( , 2012. For consistent results with strongly ionic crystals it is necessary to have thermodynamically reversible electrodes, whilst for oxides of variable stoichiometry the boundary conditions of the thermocells are important as discussed in the papers of Gerdanian (1982 and1983) and of Timm and Janek (2005): only in closed systems will the measured effects relate directly to the heats of transport.…”