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A mathematical model of short time leaching at fracture surfaces

Journal of Non-Crystalline Solids
Publication Date
DOI: 10.1016/0022-3093(90)90197-t
  • Mathematics


Abstract Soda-lime glass samples with fresh fracture surfaces were treated in H 2O and D 2O for 15, 30, 60, and 120 min at 60°C and 85°C. The depth profiles of sodium and calcium in the leached layers were determined by NPB-SIMS, a technique which avoids surface charging by using neutral primary particles. When the glass is subjected to irreversible deformation occurring in the ‘plastic zone’ around the crack tip, a great number of siloxane bonds are broken, and therefore rapid diffusion pathways may be created. The influence of the deformed layer on the leaching kinetics was taken into account by a simple mathematical model. Starting from the assumption that the rapid pathways may be represented by pervading pores, a simple ion exchange between the water which quickly penetrates into the pores and the surrounding network is supposed. From the model of McClintock and Irwin, the thickness of the altered layer was estimated at about 15 nm. Considering the simplest case that hydronium ions are incorporated into the network at a constant rate, the mathematical description of the diffusion process reduces to a boundary value problem which is accessible to an analytical solution by the Laplace transform method. The calculated Na 2O concentration profiles are in good agreement with the concentration profiles determined after a treatment in D 2O at 60°C. The fit was based on an interdiffusion coefficient of D = 1 × 10 −15 cm 2 s −1 which holds for the network of the porous layer as well as for the unaltered glass.

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