Experimental and simulated grain boundary groove profiles in tungsten

Abstract

Grain-boundary grooving has been studied on polished surfaces of polycrystalline tungsten annealed at 1350 8 C. Atomic force microscopy images were taken in the same area for each groove after di erent annealing times. Secondary oscillations next to the main groove maxima (predicted for grooving by surface di usion) were observed, to our knowledge for the ® rst time. The agreement between experimental and calculated groove pro® les (using the surface di usion model of Mullins (1957, J. appl. Phys., 28, 333)) improved when grain-boundary¯uxes were introduced.The theory of grain boundary grooving by surface di usion was rigorously developed by Mullins (1957). Mullins' expressions for the width w and depth d of the grooves can be written as follows: …3 †In these equations, t is the time of annealing, m the slope of the surface at the groove root,¯D s the product of the thickness of the layer in which surface di usion occurs and the surface self-di usion coe cient, respectively, O the atomic volume of the di using species, ® s the free energy of the solid± gas interface, k the Boltzmann constant and T the absolute temperature.

Evolution of crystal morphologies to equilibrium by surface diffusion with anisotropic surface free energy in three dimensions

“…We test for different computational grids and obtained the consistent results on the occurrence of faceting, the shape and orientations of facets and the main evolution features. Hence, the hill-and-valley structure obtained in our computation is not a numerical artifact but reflects the solution behavior of the mathematical model that closely represents a phenomenon observed in physical experiments [27,30,31]. Note that in physical experiments the very initial formation of a hill-and-valley structure (faceting) is quick and complex [30].…”

“…Surface diffusion is usually faster than volume diffusion for small crystals [27,28]. Hence, it is expected that the crystal will first evolve to the curved blocks and later to curved cubes.…”

Surface Diffusion of Oxygen Transport Membrane Materials Studied by Grain‐Boundary Grooving

“…During groove formation according to Mullins's model, grain‐boundary flux is assumed to be zero. Therefore, the amount of matter that is removed from the grain boundary below the original surface is equal to the amount of matter deposited above the original surface upon groove formation . The formation of grain‐boundary groove by surface diffusion is accompanied by an increase in depth of the groove with time ( t ) 1/4 .…”

Remnant grooves on alumina surfaces

“…The theory predicts two surface maxima, one on each side of the groove. These ridges have been observed experimentally in W [11,12], Fe [13], Pd [14], NiAl [15], Al 2 O 3 [16][17][18], ZrO 2 [19], SrTiO 3 [20], and CeO 2 [21]. MullinsÕ theory describes the development of a thermal-grain-boundary groove by surface diffusion and allows surface diffusion coefficients to be deduced from the geometries of grain-boundary grooves:…”