Dependence of the surface energy on the size and shape of a nanocrystal

2004 ◽  
Vol 46 (5) ◽  
pp. 954-968 ◽  
Author(s):  
M. N. Magomedov
Keyword(s):  
Surface Energy ◽  
Size And Shape

Size and shape dependency of the surface energy of metallic nanoparticles: unifying the atomic and thermodynamic approaches

2018 ◽  
Vol 20 (31) ◽  
pp. 20575-20587 ◽  
Author(s):  
Bastiaan Molleman ◽  
Tjisse Hiemstra
Keyword(s):  
Surface Energy ◽  
Metallic Nanoparticles ◽  
Size Dependency ◽  
Size And Shape ◽  
Surface Of Tension

We identify the surface of tension for faceted, metallic nanoparticles, revealing the thermodynamically consistent size dependency of the surface energy.

The Habit Plate Shift and the Morphology of ∝" Nitride Precipitate in ∝-Fe*

1982 ◽  
Vol 40 ◽  
pp. 728-729
Author(s):  
Y. C. Shih ◽  
J. W. Morris
Keyword(s):  
Surface Energy ◽  
Habit Plane ◽  
Elastic Strain ◽  
Strain Energy ◽  
Lattice Mismatch ◽  
Parent Phase ◽  
Elastic Strain Energy ◽  
Size And Shape ◽  
Linear Elastic ◽  
New Phase

A new phase which precipitates from a parent matrix has a size and shape which reflects its difference from parent phase. If the lattice mismatch is significant, the elastic strain energy is more important than the surface energy in determining the morphology and the preferred habit plane. The preferred habit of a tetragonal inclusion in a cubic matrix has been predicted by minimizing the elastic strain energy as from the Ktachaturyan linear elastic formula.

scholarly journals Surface Energy of Au Nanoparticles Depending on Their Size and Shape

Nanomaterials ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 484 ◽  
Author(s):  
David Holec ◽  
Phillip Dumitraschkewitz ◽  
Dieter Vollath ◽  
Franz Dieter Fischer
Keyword(s):  
Surface Energy ◽  
Surface Area ◽  
Complex Structure ◽  
Characteristic Size ◽  
Bulk Crystals ◽  
Size And Shape ◽  
Nanoparticle Shape ◽  
Universal Power Law ◽  
Atomistic Study ◽  
Surface Facet

Motivated by often contradictory literature reports on the dependence of the surface energy of gold nanoparticles on the variety of its size and shape, we performed an atomistic study combining molecular mechanics and ab initio calculations. We show that, in the case of Au nanocubes, their surface energy converges to the value for ( 0 0 1 ) facets of bulk crystals. A fast convergence to a single valued surface energy is predicted also for nanospheres. However, the value of the surface energy is larger in this case than that of any low-index surface facet of bulk Au crystal. This fact can be explained by the complex structure of the surface with an extensive number of broken bonds due to edge and corner atoms. A similar trend was obtained also for the case of cuboctahedrons. Since the exact surface area of the nanoparticles is an ill-defined quantity, we have introduced the surface-induced excess energy and discuss this quantity as a function of (i) number of atoms forming the nano-object or (ii) characteristic size of the nano-object. In case (i), a universal power-law behaviour was obtained independent of the nanoparticle shape. Importantly, we show that the size-dependence of the surface energy is hugely reduced, if the surface area correction is considered due to its expansion by the electronic cloud, a phenomenon specifically important for small nanoparticles.

scholarly journals Размерная зависимость упругих свойств нанокристалла аргона

2019 ◽  
Vol 61 (1) ◽  
pp. 148
Author(s):  
М.Н. Магомедов
Keyword(s):  
Elastic Modulus ◽  
Surface Energy ◽  
Specific Surface ◽  
Debye Temperature ◽  
State Equation ◽  
Optimal Shape ◽  
Nanocrystal Size ◽  
Specific Surface Energy ◽  
Size And Shape ◽  
Gruneisen Parameters

AbstractThe state equation ( P ) and isothermal elastic modulus ( B ) are calculated for argon macro- and nanocrystals at T = 10 K using in the framework the RP(vac)-model of nanocrystal. The isochoric and isobaric (at P = 0) dependences of the Debye temperature (Θ), of the first (γ) and second ( q ) Grüneisen parameters, as well as the specific surface energy (σ), B and B '( P ) = (∂ B /∂ P )_ T , are studied as the functions of size and shape of the nanocrystal. As shown, the isothermally isobaric decrease in nanocrystal size is accompanied by a decrease in functions Θ, q , σ, B and B '( P ) and by an increase in the γ parameter. However, the elastic modulus rises in the case of the isothermally isochoric decrease in the nanocrystal size. When the nanocrystal deviates from its most energetically optimal shape (a cube for the RP(vac)-model), the size dependences of these functions become more noticeable.

Unbiased estimation of particle number and sizes using the new stereological tools: the disector, the fractionator, the selector, and the nucleator — or just point-sampled intercepts

1988 ◽  
Vol 46 ◽  
pp. 428-429
Author(s):  
H.J.G. Gundersen
Keyword(s):  
Particle Number ◽  
Small Distance ◽  
Parallel Plane ◽  
Unbiased Estimation ◽  
Severe Problem ◽  
New Era ◽  
Size And Shape ◽  
Distinct Property ◽  
Sectioned Tissue

Previously, all stereological estimation of particle number and sizes were based on models and notoriously gave biased results, were very inefficient to use and difficult to justify. For all references to old methods and a direct comparison with unbiased methods see recent reviews.The publication in 1984 of the DISECTOR, the first unbiased stereological probe for sampling and counting 3—D objects irrespective of their size and shape, signalled the new era in stereology — and give rise to a number of remarkably simple and efficient techniques based on its distinct property: It is the only known way to obtain an unbiased sample of 3-D objects (cells, organelles, etc). The principle is simple: within a 2-D unbiased frame count or sample only cells which are not hit by a parallel plane at a known, small distance h.The area of the frame and h must be known, which might sometimes in itself be a problem, albeit usually a small one. A more severe problem may arise because these constants are known at the scale of the fixed, embedded and sectioned tissue which is often shrunken considerably.

The annealed (0001) α-alumina surface and its influence on thin-film growth

1995 ◽  
Vol 53 ◽  
pp. 336-337
Author(s):  
Michael W. Bench ◽  
Paul G. Kotula ◽  
C. Barry Carter
Keyword(s):  
Electron Microscopy ◽  
Surface Energy ◽  
Film Growth ◽  
Thin Film Growth ◽  
Energy Calculations ◽  
Transmission Electron ◽  
Reflection Electron Microscopy ◽  
Low Energy Electron ◽  
Surface Nature

The growth of semiconductors, superconductors, metals, and other insulators has been investigated using alumina substrates in a variety of orientations. The surface state of the alumina (for example surface reconstruction and step nature) can be expected to affect the growth nature and quality of the epilayers. As such, the surface nature has been studied using a number of techniques including low energy electron diffraction (LEED), reflection electron microscopy (REM), transmission electron microscopy (TEM), molecular dynamics computer simulations, and also by theoretical surface energy calculations. In the (0001) orientation, the bulk alumina lattice can be thought of as a layered structure with A1-A1-O stacking. This gives three possible terminations of the bulk alumina lattice, with theoretical surface energy calculations suggesting that termination should occur between the Al layers. Thus, the lattice often has been described as being made up of layers of (Al-O-Al) unit stacking sequences. There is a 180° rotation in the surface symmetry of successive layers and a total of six layers are required to form the alumina unit cell.

The nucleation of cavities at grain boundaries

1987 ◽  
Vol 45 ◽  
pp. 288-291
Author(s):  
P. J. Goodhew
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Grain Boundaries ◽  
Radiation Damage ◽  
Impurity Concentration ◽  
Driving Force ◽  
Nucleation And Growth ◽  
Phase Boundaries ◽  
Cavity Nucleation ◽  
Spherical Bubble

Cavity nucleation and growth at grain and phase boundaries is of concern because it can lead to failure during creep and can lead to embrittlement as a result of radiation damage. Two major types of cavity are usually distinguished: The term bubble is applied to a cavity which contains gas at a pressure which is at least sufficient to support the surface tension (2g/r for a spherical bubble of radius r and surface energy g). The term void is generally applied to any cavity which contains less gas than this, but is not necessarily empty of gas. A void would therefore tend to shrink in the absence of any imposed driving force for growth, whereas a bubble would be stable or would tend to grow. It is widely considered that cavity nucleation always requires the presence of one or more gas atoms. However since it is extremely difficult to prepare experimental materials with a gas impurity concentration lower than their eventual cavity concentration there is little to be gained by debating this point.

The influence of confocal microscope design on imaging performance

1993 ◽  
Vol 51 ◽  
pp. 144-145
Author(s):  
C J R Sheppard
Keyword(s):  
Image Quality ◽  
Fluorescence Imaging ◽  
Confocal Microscope ◽  
Industrial Applications ◽  
Three Dimensions ◽  
Design Parameters ◽  
Weak Signals ◽  
Size And Shape ◽  
Imaging Performance ◽  
Fundamental Limitation

The confocal microscope is now widely used in both biomedical and industrial applications for imaging, in three dimensions, objects with appreciable depth. There are now a range of different microscopes on the market, which have adopted a variety of different designs. The aim of this paper is to explore the effects on imaging performance of design parameters including the method of scanning, the type of detector, and the size and shape of the confocal aperture.It is becoming apparent that there is no such thing as an ideal confocal microscope: all systems have limitations and the best compromise depends on what the microscope is used for and how it is used. The most important compromise at present is between image quality and speed of scanning, which is particularly apparent when imaging with very weak signals. If great speed is not of importance, then the fundamental limitation for fluorescence imaging is the detection of sufficient numbers of photons before the fluorochrome bleaches.

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