Extensions of thermal grooving for arbitrary grain-boundary flux

Abstract

Groove profiles are computed under isotropic conditions for the intersection of a periodic array of grain boundaries with an external surface, assuming that grain boundary flux I is directed to (I≳0) or away from (I<0) the surface. When I=0, the surface assumes an equilibrium (time-independent) profile. For I≠0, in a range bounded by upper and lower limits that depend on geometry and material parameters, a global steady-state develops in which the entire surface advances (I≳0) or recedes (I<0) from its original position at constant velocity. Beyond these limits, the surface near the groove roots becomes diffusively detached from the remaining surface. A rapidly growing ridge (I≳0) or slit (I<0) then develops along each grain boundary, whose tip ultimately translates at constant velocity in a local steady state, leaving the remaining surface behind. These velocity regimes govern the ultimate stability of polycrystalline materials subjected to large electric (electromigration) or stress (creep) fields, especially in thin films where grain size approximates film thickness.

Grain boundary grooving in bi-crystal thin films induced by surface drift-diffusion driven by capillary forces and applied uniaxial tensile stresses

“…How is this morphology affected by changes in the In the present simulations, the elastic strain energy density contribution is ignored since the elastic dipole interaction term is at least a few orders of magnitude larger than the ESED term, especially for the medium stress levels [22]. This may be seen from the following calculated figures using the values tabulated in Table 1 [1][2][3][4][5][6][7][8][9][10] assigned previously for EDTI. However, as mentioned previously, the difference between these two parameters decreases as the stress levels increase.…”

“…(2) At sufficiently large magnitudes of the GBF, the GB roots break away from the remaining surface to form rapidly growing ridges or slits. Klinger et al [7] stated that the use of small slope assumption (SSA) hinders the transition between these two modes; thus, a global steady-state is always possible from the solution of linearised equation. Under the SSA, Rosenberg and Ohring [8] and Genin et al [9] treated isolated groove development with constant GBF as being due to electromigration forces and normal stress gradients, respectively, acting on the grain boundary.…”

“…Klinger et al [7] defined the following two modes of surface evolution depending on the magnitude of the constant grain boundary flux (GBF). (1) At moderate magnitudes of the GBF, the entire surface advances or recedes as material is supplied or removed by the intersecting GBs.…”

Microstructural evolution and piezoelectric properties of thick Pb(Zr,Ti)O3 films deposited by multi-sputtering method: Part I. Microstructural evolution

“…The grain size of a film is closely related to its thickness because of the influence of the substrate or other underlying layers. [12][13][14] The crystallographic orientation of the film is also highly influenced by its thickness because the total strain energy stored in the system is proportional to the thickness of the film. 9,10 In addition, the orientation as well as the microstructure of the film is strongly influenced by the characteristics of the underlying layer.…”

Mechanism-Based Design for High-Temperature, High-Performance Composites. Book 4

“…Chuang and Rice (1973) showed that a slit-like cavity may extend on a grain boundary if mass diffuses rapidly into the boundary ahead of the tip. Thouless (1993) and Klinger et al (1995) studied slit formation on parallel grain boundaries. The co-evolution of pores and grains during sintering sets the microstructure of a final product.…”