Influence of temperature on multicomponent diffusion in calcium and sodium aluminosilicate melts

Abstract

The effect of temperature on multicomponent chemical diffusion in liquids of the quaternary system CaO−Na 2 O−Al 2 O 3 −SiO 2 has been studied. Diffusion-couple experiments were performed around a central composition of 64.5 wt%SiO 2 , 13.3 wt%Na 2 O, 10.8 wt%CaO, 11.4 wt%Al 2 O 3. Experiments were performed for three temperatures far above the glass transition (1200, 1280 and 1360 • C), as well as 30 • C above the glass transition. Strong multidiffusive effects were observed for all temperatures, with significant uphill diffusion of calcium, demonstrating that uphill diffusion happens close to the glass transition as well as at high temperature. For each temperature, we determined the diffusion matrix of the system and quantified its eigenvectors and eigenvalues, which correspond formally to (respectively) exchanges between ions, and associated diffusion coefficients. Little variation of the eigenvectors of the diffusion matrix was observed as a function of temperature, with a dominant eigenvector corresponding to the exchange of sodium with calcium, the two other eigenvectors corresponding to the exchange of calcium with network formers. For the temperature range 1200-1360°C, the eigenvalues of the diffusion matrix have an Arrhenian temperature dependence, with an activation energy consistent with electrical conductivity for the exchange of sodium and calcium, and an activation energy consistent with viscosity for eigenvectors involving network formers. Multicomponent diffusion close to the glass transition is characterized by the same eigenvectors as at higher temperature, but some diffusion profiles are asymmetric due to strong viscosity contrasts resulting in concentration-dependent eigenvalues. Moreover, we observe some departure from Eyring relation close to the glass transition, with diffusion eigenvalues several orders of magnitude greater than the Eyring prediction. Highlights-Multicomponent diffusion matrices were determined experimentally around a central composition of 64.5 wt%SiO 2 , 13.3 wt%Na 2 O, 10.8 wt%CaO, 11.4 wt%Al 2 O 3 , for three superliquidus temperatures and 30 degrees above the glass transition.-Eigenvalues of the diffusion matrix were found to be Arrhenian down to 30 degrees above the glass transition.-Eigenvalues of exchanges involving network formers are in good agreement with Eyring's law at superliquidus temperatures, but a departure from Eyring's law is observed close to the glass transition. 65 108 2.2. Viscosities 109 Viscosities of the 12 end-member compositions were 110 measured in the range 1100 to 1400 • C, using a 111 288 periments with a gradient of aluminum show a slight 289 uphill diffusion of sodium. Uphill diffusion of sodium 290 is only observed close to T g and not at higher tempera-291 ture. 292 3.3. Diffusion matrix 293 For each temperature of the [1200 − 1360] • C range, 294 we used all available diffusion couples to obtain the 295 least-square estimation of the diffusion matrix. Close 296 to T g , the AN/NA couple was not used for the estima-297 tion of the diff...

Interdiffusion between silica thin films and soda‐lime glass substrate during annealing at high temperature

“…We then give a quantitative analysis of our results in the light of a simple model of concentration‐dependent diffusivity. Using the framework of multi‐component diffusion, we finally identify the elementary exchange mechanisms at play in the interdiffusion process and show that they are consistent with recent results obtained in bulk sodium and calcium aluminosilicate glasses …”

“…Figure shows theoretical normalized concentration profiles ( C 1 = 0, C 2 = 1) for the same diffusion time (1 hour) and value of D 1 ( D 1 = 10 −17 m 2 .s −1 from) in the less viscous substrate, and for ratios of diffusivities (linked to β by Equation ) ranging from 10 2 to 10 10 . As the ratio of diffusivities increases, the concentration profile becomes more and more asymmetric, with a steeper and steeper interface on the more viscous side.…”

“…The diffusivity ratio is consistent with the viscosity ratio of Figure , which is estimated to be 1000 for the 4.3 wt% doped layer. As for the diffusion of silicon in the glass substrate, Claireaux et al measured a diffusivity of 10 −17 m 2 .s −1 at 650°C, for sodium and calcium aluminosilicate composition. Therefore, the fitted coefficients (reported in Table ) are consistent with existing literature data, and Equation provides a way to estimate the viscosity of the thin films.…”

“…Claireaux et al have recently determined the diffusion matrix in a sodium and calcium aluminosilicate composition at 650°C. The authors obtained the following eigenvectors (exchange reactions) and their corresponding diffusion rates: …”

“…In order to verify that the diffusion matrix of Claireaux et al can be applied to our experiments, we fit experimental profiles using the exchange reactions of Equations and . The diffusion matrix of Claireaux et al was measured for a narrow composition region, in which diffusion coefficients are constant. In order to account for the strong compositions gradients of our experiments, we need to introduce a composition dependence for each diffusion eigenvalue, of the form of Equation .…”