Surface melting of strained and unstrained layers: Kr, Ar, and Ne

Pengra, David B.; Zhu, Da‐Ming; Dash, J. G.

doi:10.1016/0039-6028(91)90473-6

Cited by 22 publications

(24 citation statements)

References 28 publications

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“…From these resulted several scientific discoveries as the effect of strain on surface morphology [9][10][11][12][13]. Such by technology stimulated studies may they be qualified as too academic ?In this paper therefore we deliberately revisited the 100 years-old academic Wulf-theorem [14,22] [17][18][19][20][21]) or in case of coherent epitaxy but with zero misfit. For 3D coherent epitaxies on a lattice-mismatched substrate the deposited crystal is strained as well as a part of the underlying substrate [10,11,29,31] .…”

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confidence: 99%

Equilibrium nano-shape changes induced by epitaxial stress (generalised Wulf–Kaishew theorem)

Müller¹,

Kern²

2000

Surface Science

147

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A generalised Wulf-Kaishew theorem is given describing the equilibrium shape (ES) of an isolated 3D crystal A deposited coherently onto a lattice mismatched planar substrate. For this purpose a free polyhedral crystal is formed then homogeneously strained to be accommodated onto the lattice mismatched substrate. During its elastic inhomogeneous relaxation the epitaxial contact remains coherent so that the 3D crystal drags the atoms of the contact area and produces a strain field in the substrate. The ES of the deposit is obtained by minimising at constant volume the total energy (bulk and surface energies) taking into account the bulk elastic relaxation. Our main results are: (1) Epitaxial strain acts against wetting (adhesion) so that globally it leads to a thickening of the ES. (2) Owing to strain the ES changes with size.More precisely the various facets extension changes, some facets decreasing, some others increasing. (3) Each dislocation entrance, necessary for relaxing plastically too large crystals abruptly modifies the ES and thus the different facets extension in a jerky way. (4) In all cases the usual self-similarity with size is lost when misfit is considered. We illustrate these points in case of box shaped and truncated pyramidal crystals. Some experimental evidences are discussed.1 Associé aux Universités Aix-Marseille II et III. I/ Introduction:Macroscopic crystal shape studies founded crystal physic. Genuine crystal growers consider them however as an academic game in spite of the fact they do not ignore that such studies reveal essential growth mechanisms they need [1][2][3][4]. Thin film epitaxial growth, also based on geometry [5], quickly took great advantage of shape studies but on nanoscale whose impact became vital for high integration circuitry. The different epitaxial growth modes (shapes) [6,7] influence defect entrance, segregation [8] bringing with them either deleterious or benefic physical effects depending what applications are set as a goal. Coupled morphologygrowth mechanism studies combined with in-situ surface physics techniques developed in the last decade with intense technological activities on Si, Ge or III-V semi-conductors. From these resulted several scientific discoveries as the effect of strain on surface morphology [9][10][11][12][13]. Such by technology stimulated studies may they be qualified as too academic ?In this paper therefore we deliberately revisited the 100 years-old academic Wulf-theorem [14,22] [17][18][19][20][21]) or in case of coherent epitaxy but with zero misfit. For 3D coherent epitaxies on a lattice-mismatched substrate the deposited crystal is strained as well as a part of the underlying substrate [10,11,29,31] . Thus since the mechanical equilibrium of the supported crystal is reached when its free surfaces have vanishing normal stress components [23], the elastic energy density changes with the shape of the crystal and thus can be minimal for a specific shape at a given volume. In other words the ES must depend on epitaxial strain, as i...

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confidence: 99%

Equilibrium nano-shape changes induced by epitaxial stress (generalised Wulf–Kaishew theorem)

Müller¹,

Kern²

2000

Surface Science

147

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“…While the first and second terms are familiar from previous considerations for smooth walls, the third term is essential for nonideal substrates. In detail, the thermodynamic part is [1,12] …”

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Triple-Point Wetting on Rough Substrates

et al. 2002

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The influence of substrate roughness on the wetting scenario of adsorbed van der Waals films is investigated by theory and experiment. Calculating the bending free energy penalty of a solid sheet picking up the substrate roughness, we show that a finite roughness always leads to triple-point wetting reducing the widths of the adsorbed solid films considerably as compared to that of smooth substrates. Testing the theory against our experimental data for molecular hydrogen adsorbed on gold, we find quantitative agreement. DOI: 10.1103/PhysRevLett.88.055702 PACS numbers: 64.70.Hz, 67.70. +n, 68.08.Bc, 68.35.Rh Wetting of a solid substrate, exposed to a gas in thermodynamic equilibrium, is an ubiquitous phenomenon, with both fundamental aspects [1,2] and important applications [3 -5]. Microscopically, substrate wetting by a liquid film is caused by a strong substrate-particle attraction mediated by van der Waals forces. At present, an almost complete microscopic understanding of wetting on flat solid substrates is available [1,2,6] predicting the thickness of the liquid film as a function of the substrate-particle and interparticle interactions for given thermodynamic parameters such as temperature and pressure. The following basic theoretical predictions were confirmed by experiments using, e.g., noble gases [1] on different substrates: (i) For fixed thermodynamic conditions, the thickness of the wetting layer grows for increasing substrate-particle attraction. (ii) Complete wetting (i.e., a diverging thickness of the liquid layer) occurs if the substrate-particle attraction is stronger than the interparticle interaction and the thermodynamic conditions approach liquid-gas coexistence. The latter condition can be achieved only if the system temperature T is above the triple temperature T 3 . For T , T 3 , on the other hand, a solid film shows up near the sublimation line. Various experiments have shown [7][8][9][10] that the width of the solid layer always remains finite when approaching gas-solid coexistence. It is only near the triple point that a liquid layer on top of the solid sheet is formed, with a diverging width as the triple point is approached. This universal behavior is called "triple-point wetting."One major difference between a liquid and solid wetting layer is that a solid cannot relax the elastic compression caused by the substrate attraction as embodied in the (reduced) wall-particle Hamaker constant R. This fact is the basic ingredient in the traditional Gittes-Schick theory [11] of solid adsorption on flat substrates. It predicts that, for a particular value R R 0 of the substrate attraction, complete wetting is possible, while for R . R 0 , in contrast to liquid wetting, the thickness of the solid film ᐉ s decreases with increasing R. In this Letter we show that the key parameter governing adsorption of solid films is the substrate roughness rather than the elastic deformation caused by the substrate attraction. As a result of our theoretical analysis, a finite substrate roughness leads inev...

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“…This assumption is substantiated, for example, by recent experimental and theoretical studies on surface premelting [26,27], the investigation of negative thermal expansion coefficients at surfaces [28] and the observation of surface charge density waves (sCDW) [29].…”

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confidence: 93%

Development of an Ultrafast Low-Energy Electron Diffraction Setup

Gulde

2015

Springer Theses

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Surface melting of strained and unstrained layers: Kr, Ar, and Ne

Cited by 22 publications

References 28 publications

Equilibrium nano-shape changes induced by epitaxial stress (generalised Wulf–Kaishew theorem)

Equilibrium nano-shape changes induced by epitaxial stress (generalised Wulf–Kaishew theorem)

Triple-Point Wetting on Rough Substrates

Development of an Ultrafast Low-Energy Electron Diffraction Setup

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