Damage by Hydroxyl Generation in Silica
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amage by Hydroxyl Generation in Silica K. G. Schella, *, T. Fetta, E. C. Bucharskya, M. J. Hoffmanna, and S. M. Wiederhornb aKarlsruhe b
Institute of Technology, Institute for Applied Materials, Karlsruhe, Germany National Institute of Standards and Technology, Gaithersburg, MD *e-mail: [email protected] Received March 5, 2020; revised May 19, 2020; accepted June 5, 2020
Abstract—When water diffuses into silica glass it reacts chemically forming nanometre sized pores that change the physical properties of the glass, for example, affect its strength. Here we discuss the effect of water on Young’s modulus, and show how it is reduced by the water reaction, whereby a proportional behaviour applies to small amounts of water involved in the reaction. The value of the elastic modulus will be not linear with the hydroxyl-quantity in the glass for very high concentrations. The relationship between hydroxyl concentration and Young’s modulus can be determined from measurements of sound wave velocity and will be represented by damage and pore models from literature. Keywords: damage, E-Module, silica, sound velocity DOI: 10.1134/S1087659620050077
MOTIVATION Water diffuses into silica glass as a molecule, reacting with the silica network according to the following equation: (1) ≡Si–O–Si ≡ + H2O ↔ ≡SiOH + HOSi ≡. The concentration of the hydroxyl water S = [≡SiOH] is usually expressed in terms of the OH-concentration, [OH], whereas the concentration of the molecular water is given by C = [H2O]. This type of diffusion, i.e., reaction-diffusion, was studied extensively by Doremus [1]. When water reacts with silica glass, clear evidence for volume swelling has been reported by Brückner [2, 3], Shackelford [4], and Shelby [5], who showed that the density of the silica glass due to reaction (1) decreased, even though the water content of the glass increased. Consequently, the volume also must have increased. In vitreous solids that have thin surface layers, expansion of the surface layer parallel to the surface of the solid is constrained by the bulk glass. This constraint results in compressive stresses parallel to the surface of the solid; these must be overcome in any strength test, resulting in an increase in the strength of the solid. On the other hand, the generation of hydroxyl groups destroys the original silica network und must reduce the intrinsic load capability of the network. A question of interest is whether any strength-increasing effect is counteracted by local damage caused by creation of hydroxyl groups.
When hydroxyl groups have been formed, silica rings are broken and the mechanical cohesion is weakened. The effect of such “defects” in the glass structure can be treated by using the damage variable D of continuum damage mechanics [6–8]. This parameter is proportional to the density of micro-defects, D(S). Their regions of influence are symbolized in Fig. 1 by the circles of radius R [9]. The number of defects intersecting the prospective crack plane is then proportional to the number of defects in the volume elem
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