Phonons and Local Elastic Moduli in Symmetrical Tilt Boundaries
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PHONONS AND LOCAL ELASTIC MODULI IN SYMMETRICAL TILT BOUNDARIES Gui Jin Wang*, V. Vitek*, I. Alber** and J. Bassani** * Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104 "**Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104 ABSTRACT Lattice vibrations and atomic level elastic moduli have been studied for a bicrystal containing a fully relaxed symmetrical tilt boundary in Au. Central force many body potentials have been employed to describe atomic interactions. In the long-wavelength limit the phonons localized at grain boundaries can be identified with Stoneley waves known from continuum analyses. These waves are localized at the grain boundary and their velocity agrees well with that evaluated using the local effective elastic moduli of the interfacial region. However, the usually used continuum model assuming an ideal match across the interface is not sufficient to analyze these waves fully and an explicit description of interfacial properties need to be included into the continuum models of interfaces. INTRODUCTION Interfaces are regions controlling a wide variety of material properties and their studies are of principal importance in materials research. Considering numerous applications of acoustic surface waves [1], we foresee an analogous potential for employment of acoustic interfacial waves. On the continuum level Stoneley [2] was first to demonstrate the possibility of existence of generalized Rayleigh and Love waves propagating along an interface between two infinite isotropic elastic media. For anisotropic media these waves, called Stoneley waves, were extensively studied by Johnson [3]. At the same time Masri et al. [4] and Djafari-Rouhani and co-workers [51 carried out atomistic studies of waves in unrelaxed (100) interfaces between two simple cubic lattices using a Green's function method. In this study they found the Stoneley waves as well as other interfacial vibrational modes. Furthermore, Earmme et al. [6] performed similar calculations for relaxed structures of X5 (210)/[001] symmetrical tilt boundaries in Al, and discussed instabilities of some of the structures studied in terms of imaginary frequency modes. However, no definitive relationship between continuum and atomistic analyses of interfacial waves has been established. In our previous studies of the response of grain boundaries to externally applied strains we have introduced the concept of local atomic level elastic constants and developed a method of evaluating the effective local interfacial elastic moduli [7, 8]. In this paper we first present the calculations of the phonon spectra for relaxed grain boundaries in gold. We then identify in these spectra the localized acoustic interfacial modes and analyze them in terms of Stoneley waves using the concept of interfacial moduli. COMPUTING PROCEDURES All the atomistic calculations presented here have been made using empirical many-body potentials of the Finnis-Sinclair type for go
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