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  • 1
    Electronic Resource
    Electronic Resource
    On the thermodynamics of crystalline solids (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 82 (1985), S. 5192-5202 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A formalism for the analysis of thermodynamic equilibrium in an arbitrarily stressed multicomponent crystal is developed. We assume that the energy per unit cell is a function of the following per-unit-cell quantities: the entropy, the mole number of each chemical species, and six independent dot products of the three vectors that define the cell. Body forces specific to each species are included, but chemical reactions and capillarity are excluded. We use a Gibbsian variational method but refer all quantities to the unvaried state which may be one of large strain. We obtain the familiar equations of thermal and mechanical equilibrium and the uniformity of generalized potentials μi +φi for each species; the φi are associated with the body forces and the μi are identified as chemical potentials since we show them to be equal locally to the chemical potentials of components present in a fluid with which the crystal is in equilibrium. The equations of equilibrium are then rederived under the assumption that certain equations of constraint hold among the variables that specify the mole numbers per unit cell of chemical species. This allows the treatment of a system composed of both mobile and immobile species, considered by Li, Oriani, and Darken, as well as a famous example of Gibbs in which a single component solid may be in equilibrium with three fluids having different chemical potentials of that component. We then introduce an extended set of variables in order to give an explicit description of point defects and to allow comparison of our treatment with those of Herring and of Larché and Cahn. Equations are obtained that allow the determination of equilibrium defect populations; when defects are in equilibrium, our previous equations are recovered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.448644
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  • 2
    Electronic Resource
    Electronic Resource
    A Markov treatment of the self-diffusion dyadic in homogeneous crystals (1988)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 64 (1988), S. 3918-3927 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Expressions are derived for the drift velocity V and the self-diffusion dyadic D(two down arrows) of a particle in a macroscopically homogeneous multicomponent crystal based on two related finite Markov descriptions. In the first or system state description, the Markov states, αβγ⋅⋅⋅, correspond to configurational states of a crystal with periodic boundary conditions. To each Markov transition α→β is assigned the vector rαβ equal to the displacement, if any, of the particle during that transition. In the second or jump description, the Markov states ijk⋅⋅⋅ correspond to the type of jump executed by the particle. To each Markov state i is assigned the vector ri equal to the displacement of the particle executing the ith type of jump. The parameters of the second description are derived in terms of those of the first. The treatment extends previous ones in the following ways: (1) It is three dimensional; (2) it gives a rigorous derivation of D(two down arrows) when correlation and bias (i.e., nonzero V) effects are simultaneously present; (3) new expressions for D(two down arrows) are given that are equivalent to but formally simpler than previous results; (4) the general form of the results is independent of the geometrical details of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.341347
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  • 3
    Electronic Resource
    Electronic Resource
    Extensions of thermal grooving for arbitrary grain-boundary flux (1995)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 78 (1995), S. 3833-3838 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: 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(approximately-greater-than)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(approximately-greater-than)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(approximately-greater-than)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. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.359898
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  • 4
    Electronic Resource
    Electronic Resource
    Grain-boundary slit propagation in an electric field (1996)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 80 (1996), S. 6670-6676 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Advancement of a fine slit along a planar grain boundary in an electric field E0, applied parallel to the slit, is investigated by considering electromigration along both the grain boundary and the slit surface. Electrically induced flux in the grain boundary Igb (+ toward the slit tip) and both electrically and curvature-induced fluxes on the slit surfaces are considered assuming 2Is〉Igb, where Is is the flux (+ away from the slit tip) on each of the parallel slit surfaces far removed from the tip. Steady-state solutions of the transport equations are classified according to the value of a parameter β=tan−1 (2Is/Igb) which, under reasonable assumptions, depends on material parameters only. For 5π/4≥β≥β2, unique steady-state solutions exist; for β2〉β〉β1, multiple steady-state solutions occur; below β1≥π/4, no steady-state solution is possible. Since β1〈π/2, Igb〉0 (flux exiting the grain boundary into the slit) for all cases in which no steady-state solution is possible. In the case of multiple solutions, those corresponding to smallest width (and hence largest velocity) are determined. For all steady-state solutions, slit width and tip velocity scale as E−1/20 and E3/20, respectively. Results also apply to the propagation of a slit within a grain or along a passivation layer. Generally, tip velocities can approach 1 nm/s (3.6 μm/h), thereby representing a likely failure mechanism in fine-line (near bamboo structure) interconnects. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.363792
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  • 5
    Electronic Resource
    Electronic Resource
    The statistical self-similarity hypothesis in grain growth and particle coarsening (1986)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 59 (1986), S. 1341-1349 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The time dependence of particle size (e.g., mean volume) in normal grain growth, bubble growth, and late-stage coarsening is deduced from a statistical self-similarity (SSS) hypothesis, according to which consecutive configurations of the system in the self-similar mode are geometrically similar in a statistical sense, and from the scaling characteristic of v(overdot), the rate of change of the volume of a given particle. It is shown that if v(overdot) scales as v¯α under uniform magnification, where v¯ is the mean particle volume and α a constant depending on the controlling kinetics and geometry of the system, then v¯1−α is a linear function of the time. Values of α are obtained for a number of cases. The treatment is free of many of the approximations and geometrical simplifications used in most theories. Evidence for the SSS hypothesis is discussed. Special new results are obtained for two-dimensional bubble and idealized grain growth that should be testable by computer simulation or by observation of a well-behaved soap-bubble array.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.336528
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  • 6
    Electronic Resource
    Electronic Resource
    On the theory of steady-state electromigration in thin films (1992)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 61 (1992), S. 2987-2989 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Steady-state electromigration along grain boundaries in a monatomic polycrystalline thin film has been analyzed in a two-dimensional model by balancing the (applied) electric and (induced) stress driving forces to achieve a zero flux divergence. The continuity of chemical potential requires a unique stress normal to each of the three boundaries terminating at a given triple point. These stresses and the steady-state fluxes are determined by a set of linear equations subject to boundary conditions at the intersection of grain boundaries with the film edge (edge points). When the normal stress is assumed zero at all edge points, the stress typically attains maxima and minima at triple points, whereas, when the flux is assumed zero at all edge points, the stress typically builds up monotonically in the field direction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.108011
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  • 7
    Electronic Resource
    Electronic Resource
    Spreading of a void along a singular surface during electromigration: A failure mode (1997)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 70 (1997), S. 194-196 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Previous treatments of void shape evolution during electromigration have been restricted to nonsingular void surfaces. We consider the lateral spreading of a void when its leading surface is a singular facet. The facet may nucleate at the leading surface of a void migrating within one grain or may develop when a singular surface is exposed by impingement of the void at a (transverse) grain boundary. Advance of the facet requires a source of steps that we assume to be absent; void spreading results. A stationary void shape is possible when a dimensionless parameter is less than a critical value (estimated), whereas above this value the void spreads indefinitely. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.118353
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