Thermal Grooving in Single versus Multilayer Thin Films
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Thermal Grooving in Single versus Multilayer Thin Films Peter M. Anderson, Jue Wang, Sridhar Narayanaswamy* Dept of Materials Science and Engineering, Ohio State University, 2041 College Rd., Columbus, OH 43210; *Rockwell Science Center, 1049 Camino Dos Rios, Thousand Oaks, CA 91360 ABSTRACT A 2D analytic result is presented for the penetration distance P of grain boundary grooves as a function of time t during heating and straining of polycrystalline multilayer thin films with immiscible phases. These grooves can ultimately pinch off individual layers. The result shows that P ~ t0.25 initially and P ~ t at longer time. This new analysis contrasts single- versus multilayer thin film response. INTRODUCTION Grain boundary grooving is driven by a tendency to reduce system grain boundary energy and it serves as an important mechanism for morphological breakdown of multilayer thin films at elevated temperature. For example, γ-Ni(Al)/γ'-Ni3Al multilayer thin films with bilayer period Λ = 40 nm to 240 nm have been observed to break down via thermal grooving along grain boundaries, after exposure to T > 800 ºC for less than 100 hours [1, 2]. In contrast, Cu/Nb multilayers with Λ = 150 nm groove in a stable manner, forming a series of triple junctions that balance Cu/Ni interfacial energy with either Cu/Cu or Ni/Ni grain boundary energies [3]. Mullins [4] provides a 2D grooving analysis of an isolated grain boundary terminating at a free surface and shows that penetration depth P increases as t0.25. Thouless [5] considers grooving in single layer polycrystalline thin films on immiscible substrates subjected to an in-plane creep rate ε˙ . A critical time scale τ is identified below which P ~ t0.25 and above which P ~ t. Two recent complementary analyses consider the stability of multilayer thin films with immiscible phases. Josell et al. [6] shows that for a given multilayer thin film system, a needle-like columnar grain morphology is more stable to pinch-off via grooving than a pancake-like one. Sridhar et al. [7] highlights that stored elastic energy in epitaxial and externally stressed multilayer thin films can promote pinch-off, but only single crystal layers are considered. This paper extends the framework of the single layer Thouless analysis to study grain boundary grooving in a 2D, free-standing multilayer thin film geometry subjected to an in-plane strain rate ε˙ . Similar to the Thouless analysis, P ~ t0.25 initially and P ~ t at longer time. Similar to the Josell analysis, films with needle-like grains are predicted to be more stable than those with pancake-like grains. The analytic expressions highlight the kinetics of the grooving process that are not available in either the Josell or Sridhar analyses. MODEL DEVELOPMENT Figures 1 and 2 highlight aligned versus staggered geometries assumed in the analysis, as well as transport processes and field variables. Phases α and β alternate layer-by-layer with bilayer period Λ. However, the aligned case has α/α and β/β grain boundaries that are aligned vertically w
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