Existing models for the diffusive growth of voids on grain interfaces, at elevated temperature, are for the most part based on quasi-equilibrium assumptions: surface diffusion is assumed to be sufficiently rapid that the cavity has a rounded, equilibrium shape, and hence cavity growth is assumed to be rate-limited only by grain boundary diffusion. However, creep rupture cavities sometimes have narrow, crack like shapes and it is appropriate to investigate non-equilibrium models for diffusive rupture. This is done here by comparing the quasi-equilibrium model to another limiting case based on a narrow, crack-like cavity shape. Criteria for choosing between the models are given on the basis of representative relaxation times for the surface diffusion process, and also by examining the properties of a ''self similar'' solution for cavity shape. By a suitable choice of parameters which measure the growth rate, this solution can be made to give results corresponding to either limiting case, and aids the interpolation between them. The results suggest that if s is the ratio of the applied stress to that which just equilibrates cavities against sintering, then for circular cavities on a grain boundary with diameter equal to a quarter of their average center-to-center spacing, the quasi-equilibrium mode applies when s < 1 + 6..delta.. and the crack-like mode when s > 2 + 9..delta... Here ..delta.. is the ratio of surface to grain boundary diffusivity. Also, the stress dependence of the growth rate and rupture lifetime is established in each case, and the results are discussed in relation to the interpretation of experimental data.
Technical Briefs Starting Transients in the Response of Linear Systems to Stationary Random Excitation J. R. Rice J. R. Rice Division of Engineering, Brown University, Providence, R. I. Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information J. R. Rice Division of Engineering, Brown University, Providence, R. I. J. Appl. Mech. Mar 1965, 32(1): 200-201 (2 pages) https://doi.org/10.1115/1.3625723 Published Online: March 1, 1965 Article history Received: September 9, 1964 Online: September 15, 2011
Magnetic feedback chemical force microscopy (MF-CFM) was used to map the complete force profile between hydroxyl- and carboxyl-terminated self-assembled monolayers (SAMs) in aqueous solution. The snap-to-contact and snap-out instabilities intrinsic to force-displacement measurements made with weak spring constant cantilevers were eliminated by using a cantilever with an attached magnetic particle and a solenoid in a servo loop to balance the tip−sample interactions. The interaction between hydroxyl-terminated surfaces in deionized water was well fit by a van der Waals model to short distances. The Hamaker constant that was determined from experiment, 1.0 × 10-19 J, is similar to that expected for a gold−gold interaction and shows that the underlying gold support dominates the attractive interaction over a large range of separations. The interaction between a carboxyl-terminated tip and a sample in 0.010 M phosphate buffer at pH 7.0 was fit with a model that includes both van der Waals and electrostatic terms. The Hamaker constant, 1.2 × 10-19 J, which is similar to that obtained for hydroxyl-terminated surfaces, confirms that the gold−gold interaction dominates the attractive part of the interaction. In addition, the Debye length, 2.9 nm, surface potential, −1.5 × 102 mV, and charge regulation parameter, −0.71, obtained from analysis of the data are consistent with previous work (Vezenov et al. J. Am. Chem. Soc. 1997, 119, 2006−2015. Hu; Bard. Langmuir 1997, 13, 5114−5119). The implications of these results and applications of MF-CFM are discussed.
