On the role of surface energy and surface stress in phase-transforming nanoparticles

Fischer, Franz Dieter; Waitz, Thomas; Vollath, D.; Simha, N.K.

doi:10.1016/j.pmatsci.2007.09.001

Cited by 235 publications

(161 citation statements)

References 111 publications

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“…(140) was never applied before. For a sharp interface the couple was not introduced in most of the works (see Cahn (1979);Cammarata (2009);Fischer et. al.…”

Section: Position Of the Gibbsian Dividing Surface For A Nonequilibrimentioning

confidence: 99%

“…However, with elastic interface stresses, T = γ, so this condition should not be satisfied and cannot be used for the determination of the dividing surface. In most works on the sharp interface approach (Cahn (1979);Fischer et. al.…”

Section: Position Of the Gibbsian Dividing Surface For A Nonequilibrimentioning

confidence: 99%

“…Interfaces in solids, solid-liquid, and solid-gas interfaces generate additional surface stresses due to their elastic deformations, which may be both tensile or compressive. There is extended literature devoted to the derivation of constitutive equations and balance laws for elastic interfaces (see, Cahn (1979); Gurtin and Murdoch (1975); Gurtin and Struthers (1990); Javili and Steinmann (2010); Nix and Gao (1998) ;Podstrigach and Povstenko (1985); Povstenko (1991), and review articles by Cammarata (2009) ;Duan et al (2009) ;Fischer et. al.…”

Section: Introductionmentioning

confidence: 99%

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Phase field approach to martensitic phase transformations with large strains and interface stresses

Levitas

2014

Journal of the Mechanics and Physics of Solids

117

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Thermodynamically consistent phase field theory for multivariant martensitic transformations, which includes large strains and interface stresses, is developed. Theory is formulated in a way that some geometrically nonlinear terms do not disappear in the geometrically linear limit, which in particular allowed us to introduce the expression for the interface stresses consistent with the sharp interface approach. Namely, for the propagating nonequilibrium interface, a structural part of the interface Cauchy stresses reduces to a biaxial tension with the magnitude equal to the temperature-dependent interface energy. Additional elastic and viscous contributions to the interface stresses do not require separate constitutive equations and are determined by solution of the coupled system of phase field and mechanics equations. Ginzburg-Landau equations are derived for the evolution of the order parameters and temperature evolution equation. Boundary conditions for the order parameters include variation of the surface energy during phase transformation. Because elastic energy is defined per unit volume of unloaded (intermediate) configuration, additional contributions to the Ginzburg-Landau equations and the expression for entropy appear, which are important even for small strains. A complete system of equations for fifth-and sixth-degree polynomials in terms of the order parameters is presented in the reference and actual configurations. An analytical solution for the propagating interface and critical martensitic nucleus which includes distribution of components of interface stresses has been found for the sixth-degree polynomial. This required resolving a fundamental problem in the interface and surface science: how to define the Gibbsian dividing surface, i.e., the sharp interface equivalent to the finite-width interface. An unexpected, simple solution was found utilizing the principle of static equivalence. In fact, even two equations for determination of the dividing surface follow from the equivalence of the resultant force and zero-moment condition. For the obtained analytical solution for the propagating interface, both conditions determine the same dividing surface, i.e., the theory is noncontradictory. A similar formalism can be developed for the phase field approach to diffusive phase transformations described by the Cahn-Hilliard equation, twinning, dislocations, fracture, and their interaction.Keywords dividing surface, large strains, phase field approach, phase transformation, surface stresses and energy Disciplines Aerospace EngineeringComments NOTICE: This is the author's version of a work that was accepted for publication in Journal of the Mechanics and Physics of Solids. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal ...

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“…(140) was never applied before. For a sharp interface the couple was not introduced in most of the works (see Cahn (1979);Cammarata (2009);Fischer et. al.…”

Section: Position Of the Gibbsian Dividing Surface For A Nonequilibrimentioning

confidence: 99%

Section: Position Of the Gibbsian Dividing Surface For A Nonequilibrimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase field approach to martensitic phase transformations with large strains and interface stresses

Levitas

2014

Journal of the Mechanics and Physics of Solids

117

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“…We use the formalism for growth outlined in [35,36] but assume that the growing body behaves like an ideal fluid, with a defined surface stress, g (for details, see [14]). This relies on the assumption that there are three separable timescales, that of growth, remodelling and elasticity.…”

Section: Formulation Of the Model Hypothesesmentioning

confidence: 99%

“…One important simplification that can be made to help understand this problem is based on the observation that tissues, or at least cell agglomerates, can behave like viscous fluids with measureable surface tensions when observed for sufficiently long timescales [9][10][11][12]. If one describes tissues as fluids, then the equilibrium shape of their boundaries will be determined on one hand by the wettability of any substrates upon which they are sitting [13] and on the other hand by the Laplace -Young equation giving a link between interfacial curvature and tissue pressure [14]. Interestingly, it has been shown that even simple shapes of wettable regions on flat substrates display a rich variety of equilibrium liquid droplet morphologies at constant volume when surface tension plays an important role in the energy of the system [15 -17].…”

Section: Introductionmentioning

confidence: 99%

Tissue growth controlled by geometric boundary conditions: a simple model recapitulating aspects of callus formation and bone healing

Fischer

Zickler

Dunlop

et al. 2015

J. R. Soc. Interface.

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The shape of tissues arises from a subtle interplay between biochemical driving forces, leading to cell growth, division and extracellular matrix formation, and the physical constraints of the surrounding environment, giving rise to mechanical signals for the cells. Despite the inherent complexity of such systems, much can still be learnt by treating tissues that constantly remodel as simple fluids. In this approach, remodelling relaxes all internal stresses except for the pressure which is counterbalanced by the surface stress. Our model is used to investigate how wettable substrates influence the stability of tissue nodules. It turns out for a growing tissue nodule in free space, the model predicts only two states: either the tissue shrinks and disappears, or it keeps growing indefinitely. However, as soon as the tissue wets a substrate, stable equilibrium configurations become possible. Furthermore, by investigating more complex substrate geometries, such as tissue growing at the end of a hollow cylinder, we see features reminiscent of healing processes in long bones, such as the existence of a critical gap size above which healing does not occur. Despite its simplicity, the model may be useful in describing various aspects related to tissue growth, including biofilm formation and cancer metastases.

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Diffusion‐Induced Stress within Core–Shell Structures and Implications for Robust Electrode Design and Materials Selection

Baker

Cheng

2015

Advances in Electrochemical Sciences and Engineering

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On the role of surface energy and surface stress in phase-transforming nanoparticles

Cited by 235 publications

References 111 publications

Phase field approach to martensitic phase transformations with large strains and interface stresses

Phase field approach to martensitic phase transformations with large strains and interface stresses

Tissue growth controlled by geometric boundary conditions: a simple model recapitulating aspects of callus formation and bone healing

Diffusion‐Induced Stress within Core–Shell Structures and Implications for Robust Electrode Design and Materials Selection

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