On the energy spectrum of helium II

Марченко, В. И.; Parshin, A. Ya.

doi:10.1134/s002136400806012x

Cited by 48 publications

(93 citation statements)

References 5 publications

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“…In the stepflow model, a stepped surface changes its morphology by lateral motion of steps. 1,4,[17][18][19] For an unstrained film, the elastic effect of a step can be viewed as a distribution of force dipole on the film surface along the step. The dipole interaction force decays as 1 / r 3 for two parallel straight steps with distance r. The elastic effect of a step on the surface of a strained film ͑in heteroepitaxy͒ can be approximated by a distribution of force monopole along the step.…”

Section: Introductionmentioning

confidence: 99%

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Zhu

Xiang

2009

Phys. Rev. B

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In heteroepitaxy, the mismatch of lattice constants between the crystal film and the substrate causes misfit strain and stress in the bulk of the film, driving the surface of the film to self-organize into various nanostructures. Below the roughening transition temperature, an epitaxial surface consists of facets and steps and changes its morphology by lateral motion of steps. In this paper, we present a 2 + 1-dimensional continuum model for the long-range elastic interaction on stepped surface of a strained film. The continuum model is derived rigorously from the discrete model for the interaction between steps; thus it incorporates the discrete features of the stepped surfaces. Examples show that our continuum model is much more accurate as an approximation to the discrete model than the traditional continuum approximation. Moreover, in the linear instability of a planar surface, our continuum model gives the transition from step bunching instability to step undulation instability as the distance between adjacent steps increases, which agrees with the experimental observations and the results of discrete models and is missing using the traditional continuum approximation. Numerical simulations of the surface evolution using our model in the nonlinear regime show several different surface morphologies, including the morphology of step bunching which cannot be obtained using the traditional continuum approximation.

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Section: Introductionmentioning

confidence: 99%

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Zhu

Xiang

2009

Phys. Rev. B

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“…A proposal involving a pair of forces oriented normal to the step edge in the highsymmetry plane, as shown in figure 2, first appeared in a paper by Marchenko and Parshin [2] and has since been used as a core model. This (MP) model has one free parameter, which is related to the strength of the force dipole (see footnote 5).…”

Section: Force Dipole Step Interaction: a Reviewmentioning

confidence: 99%

“…Although the existence of a force dipole is inferred from considerations of a continuous elastic surface, such a dipole can also be justified Figure 2. Schematic of a force dipole for to a step by the MP model [2]. The dipole moment is along the step edge and normal to the cross-sectional plane.…”

Section: Force Dipole Step Interaction: a Reviewmentioning

confidence: 99%

“…A detailed exposition on force dipole interactions between steps in the context of one-dimensional (1D) geometries is given by Pimpinelli and Villain [16]. They motivate and define the respective energy per unit length for straight steps via the MP model [2]. This energy decays as w −2 where w is the terrace width.…”

Section: Introductionmentioning

confidence: 99%

“…Fundamental studies of step interactions include the model by Marchenko and Parshin (MP) [2], where each step is viewed as a distribution of force dipoles in the context of continuum elasticity (see also [3]). This model describes elastic step energies in homoepitaxy, where the last layer of the crystal has the same equilibrium structure as the bulk.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Formulas for the force dipole interaction of surface line defects in homoepitaxy

Quah¹,

Liang²,

Margetis³

2010

J. Phys. A: Math. Theor.

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Abstract. By use of asymptotics, we derive explicit, simplified formulas for integrals representing the force dipole interaction energy per unit length between curved line defects (steps) of the same sign in homoepitaxy. Our starting point is continuum linear elasticity in accordance with the classic model by Marchenko and Parshin (1981 Soviet Phys. JETP 52 129). We consider geometries that stem from perturbations of concentric circular steps (radial case). In the radial case, we define a small geometric parameter, δ 2 , expressing the smallness of interstep distance relative to the circle radii. We invoke the Mellin transform with respect to δ 2 and derive systematically an approximation for the requisite integral. This technique offers an alternative to an exact evaluation in terms of elliptic integrals. We then demonstrate the use of the Mellin transform when calculating the force dipole interaction energy between smoothly, slowly varying steps that form perturbations of circles. We discuss conditions by which the force dipole interaction may favor the modulation of closed step profiles.

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Spatial ordering and anisotropy in surface stress domains and nanostructural evolution

Gao

Meng

Goyal

et al. 2008

JOM

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On the energy spectrum of helium II

Cited by 48 publications

References 5 publications

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

Formulas for the force dipole interaction of surface line defects in homoepitaxy

Spatial ordering and anisotropy in surface stress domains and nanostructural evolution

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