Effect of elastic stresses on the morphological stability of a solid sphere growing from a supersaturated melt

Caroli, B.; Caroli, C.; Roulet, B.; Voorhees, Peter W.

doi:10.1016/0001-6160(89)90284-8

Cited by 28 publications

(11 citation statements)

References 14 publications

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“…For example, well-known phenomena like "orange peel" in Hadfield steels, Ostwald ripening and the recently-observed "precipitate doublets" in Ni-A1 alloys [49], the instability of solid-liquid interface in Mo-Ni alloy [50], grooving in stressed aluminum 1100 samples [51] can presumably be explained in this way. (See also the discussions in [25,27,28]. )…”

Section: Metallurgymentioning

confidence: 99%

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The stress driven instability in elastic crystals: Mathematical models and physical manifestations

1993

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Summary. Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the abovementioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.

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Section: Metallurgymentioning

confidence: 99%

“…Recently, the instability in question was rediscovered by different authors (see publications [25][26][27][28]). A remarkably lucid explanation of the instability was given by Nozieres [29], who also proposed the simplest physical approach to these phenomena.…”

Section: Introductionmentioning

confidence: 99%

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

1993

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“…If the inclusion is growing, a further instability becomes possible, corresponding to the one discovered by Mullins and Sekerka [192] which in the non-elastic case appears as soon as a certain critical radius (which depends on the rate of growth) is exceeded. This type of instability has been investigated using linear theory by several authors [103,115,91,65].…”

Section: A Single Non-spherical Inclusionmentioning

confidence: 99%

Untitled

Fratzl¹,

Penrose²,

Joel³

1999

Journal of Statistical Physics

233

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Elastic interactions arising from a difference of lattice spacing between two coherent phases can have a strong influence on the phase separation (coarsening) of alloys. If the elastic moduli are different in the two phases, the elastic interactions may accelerate, slow down or even stop the phase separation process. If * Dedicated to John W. Cahn, on the occasion of his 70th birthday 1 the material is elastically anisotropic, the precipitates can be shaped like plates or needles instead of spheres and can form regular precipitate superlattices.Tensions or compressions applied externally to the specimen may have a strong effect on the shapes and arrangement of the precipitates. In this paper, we review the main theoretical approaches that have been used to model these effects and we relate them to experimental observations. The theoretical approaches considered are (i) 'macroscopic' models treating the two phases as elastic media separated by a sharp interface (ii) 'mesoscopic' models in which the concentration varies continuously across the interface (iii) 'microscopic' models which use the positions of individual atoms.

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“…The 4la-bulk instability was rediscovered by Caroli et al (1989), Srolovitz (1989), and Leo and Sekerka (1989). In particular, according to the numerical evaluation of Srolovitz (1989), the 4la-bulk instability theory of the onset of instability in epitaxial films is in satisfactory quantitative agreement with the experimental data.…”

Section: The Stability Criteria Of the Trench-like Pattern Of Corrugamentioning

confidence: 92%

The Stress Driven "Rearrangement" Instability in Crystalline Films

Grinfeld

1993

Journal of Intelligent Material Systems and Structures

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It has been demonstrated that, in the absence of surface tension, a flat boundary of non-hydrostatically stressed elastic solids is always unstable with respect to "mass rearrangement". Specific mechanisms of the rearrangement can be different, for instance: (a) melting-freezing or vaporization-sublimation processes at liquid-solid or vapor-solid phase boundaries, (b) surface diffusion of particles along free or interface boundaries, and (c) adsorption-desorption of atoms in epitaxial crystal growth. In this paper, the role of this instability in the problems of epitaxy is discussed; in particular, the new opportunities delivered by this instability are considered for realistic explanation of the recently discovered phenomena of dislocation-free Stranski-Krastanow pattern of epitaxial growth. These phenomena cannot be interpreted in the framework of traditional viewpoints, since, according to the classical theory, the Stranski-Krastanow pattern develops as the result of proliferation of misfit dislocations appearing at the interface "crystalline film-substrate".

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Effect of elastic stresses on the morphological stability of a solid sphere growing from a supersaturated melt

Cited by 28 publications

References 14 publications

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Untitled

The Stress Driven "Rearrangement" Instability in Crystalline Films

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