Effective energy integral functionals for thin films in the Orlicz–Sobolev space setting

We introduce the notion of a distributional $k$-Hessian ($k=2,\ldots ,n$) associated with fractional Sobolev functions on $\unicode[STIX]{x1D6FA}$, a smooth bounded open subset in $\mathbb{R}^{n}$. We show that the distributional $k$-Hessian is weakly continuous on the fractional Sobolev space $W^{2-2/k,k}(\unicode[STIX]{x1D6FA})$ and that the weak continuity result is optimal, that is, the distributional $k$-Hessian is well defined in $W^{s,p}(\unicode[STIX]{x1D6FA})$ if and only if $W^{s,p}(\unicode[STIX]{x1D6FA})\subseteq W^{2-2/k,k}(\unicode[STIX]{x1D6FA})$.

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Studies on Water in the Hydration Chamber of a Modified Electron Microscope

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100069715 ◽

1970 ◽

Vol 28 ◽

pp. 544-545

Author(s):

R. C. Moretz ◽

G. G. Hausner ◽

D. F. Parsons

Keyword(s):

Thin Film ◽

Thin Films ◽

Electron Microscope ◽

Steady State ◽

Room Temperature ◽

Small Mass ◽

Equilibrium Pressure ◽

Biological Objects ◽

Mechanical Pump ◽

Differential Pumping

Use of the electron microscope to examine wet objects is possible due to the small mass thickness of the equilibrium pressure of water vapor at room temperature. Previous attempts to examine hydrated biological objects and water itself used a chamber consisting of two small apertures sealed by two thin films. Extensive work in our laboratory showed that such films have an 80% failure rate when wet. Using the principle of differential pumping of the microscope column, we can use open apertures in place of thin film windows.Fig. 1 shows the modified Siemens la specimen chamber with the connections to the water supply and the auxiliary pumping station. A mechanical pump is connected to the vapor supply via a 100μ aperture to maintain steady-state conditions.

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Observations on the growth of YBa2Cu3O7-δ thin films on MgO by pulsed-laser ablation

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100089652 ◽

1991 ◽

Vol 49 ◽

pp. 1068-1069

Author(s):

M. Grant Norton ◽

C. Barry Carter

Keyword(s):

Thin Film ◽

Thin Films ◽

Laser Ablation ◽

Substrate Surface ◽

Pulsed Laser ◽

Pulsed Laser Ablation ◽

Thin Film Deposition ◽

Film Deposition ◽

Laser Ablation Process ◽

Deposition Parameters

Pulsed-laser ablation has been widely used to produce high-quality thin films of YBa2Cu3O7-δ on a range of substrate materials. The nonequilibrium nature of the process allows congruent deposition of oxides with complex stoichiometrics. In the high power density regime produced by the UV excimer lasers the ablated species includes a mixture of neutral atoms, molecules and ions. All these species play an important role in thin-film deposition. However, changes in the deposition parameters have been shown to affect the microstructure of thin YBa2Cu3O7-δ films. The formation of metastable configurations is possible because at the low substrate temperatures used, only shortrange rearrangement on the substrate surface can occur. The parameters associated directly with the laser ablation process, those determining the nature of the process, e g. thermal or nonthermal volatilization, have been classified as ‘primary parameters'. Other parameters may also affect the microstructure of the thin film. In this paper, the effects of these ‘secondary parameters' on the microstructure of YBa2Cu3O7-δ films will be discussed. Examples of 'secondary parameters' include the substrate temperature and the oxygen partial pressure during deposition.

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Microstructural characterization of YBa2Cu3O7-x thin films formed by metalorganic CVD

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100089718 ◽

1991 ◽

Vol 49 ◽

pp. 1080-1081

Author(s):

P. Lu ◽

W. Huang ◽

C.S. Chern ◽

Y.Q. Li ◽

J. Zhao ◽

...

Keyword(s):

Thin Film ◽

Thin Films ◽

Critical Current Density ◽

Critical Current ◽

Current Density ◽

Film Growth ◽

Chemical Vapor ◽

Microstructural Characterization ◽

Ion Milling ◽

Conventional Grinding

The YBa2Cu3O7-x thin films formed by metalorganic chemical vapor deposition(MOCVD) have been reported to have excellent superconducting properties including a sharp zero resistance transition temperature (Tc) of 89 K and a high critical current density of 2.3x106 A/cm2 or higher. The origin of the high critical current in the thin film compared to bulk materials is attributed to its structural properties such as orientation, grain boundaries and defects on the scale of the coherent length. In this report, we present microstructural aspects of the thin films deposited on the (100) LaAlO3 substrate, which process the highest critical current density.Details of the thin film growth process have been reported elsewhere. The thin films were examined in both planar and cross-section view by electron microscopy. TEM sample preparation was carried out using conventional grinding, dimpling and ion milling techniques. Special care was taken to avoid exposure of the thin films to water during the preparation processes.

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Determination of Stoichiometry of GaAs Component in (Gaas)Ge Epitaxially Grown Thin Films by Electron Microprobe X-Ray Analysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100134922 ◽

1990 ◽

Vol 48 (2) ◽

pp. 264-265

Author(s):

D. R. Liu ◽

S. S. Shinozaki ◽

R. J. Baird

Keyword(s):

Thin Film ◽

Thin Films ◽

Monte Carlo Simulation ◽

Monte Carlo ◽

Compound Semiconductors ◽

Energy Dispersive Analysis ◽

X Ray ◽

Metastable Alloys ◽

Lower Voltage

The epitaxially grown (GaAs)Ge thin film has been arousing much interest because it is one of metastable alloys of III-V compound semiconductors with germanium and a possible candidate in optoelectronic applications. It is important to be able to accurately determine the composition of the film, particularly whether or not the GaAs component is in stoichiometry, but x-ray energy dispersive analysis (EDS) cannot meet this need. The thickness of the film is usually about 0.5-1.5 μm. If Kα peaks are used for quantification, the accelerating voltage must be more than 10 kV in order for these peaks to be excited. Under this voltage, the generation depth of x-ray photons approaches 1 μm, as evidenced by a Monte Carlo simulation and actual x-ray intensity measurement as discussed below. If a lower voltage is used to reduce the generation depth, their L peaks have to be used. But these L peaks actually are merged as one big hump simply because the atomic numbers of these three elements are relatively small and close together, and the EDS energy resolution is limited.

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Scanning-probe microscope analysis of optical thin films: A new analytical tool in a manufacturing environment

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173078 ◽

1994 ◽

Vol 52 ◽

pp. 1068-1069

Author(s):

S. P. Sapers ◽

R. Clark ◽

P. Somerville

Keyword(s):

Thin Film ◽

Thin Films ◽

Thermal Control ◽

Scanning Probe Microscope ◽

Scanning Probe ◽

List Type ◽

Manufacturing Environment ◽

Physical Measurements ◽

Probe Microscope

OCLI is a leading manufacturer of thin films for optical and thermal control applications. The determination of thin film and substrate topography can be a powerful way to obtain information for deposition process design and control, and about the final thin film device properties. At OCLI we use a scanning probe microscope (SPM) in the analytical lab to obtain qualitative and quantitative data about thin film and substrate surfaces for applications in production and research and development. This manufacturing environment requires a rapid response, and a large degree of flexibility, which poses special challenges for this emerging technology. The types of information the SPM provides can be broken into three categories:(1)Imaging of surface topography for visualization purposes, especially for samples that are not SEM compatible due to size or material constraints;(2)Examination of sample surface features to make physical measurements such as surface roughness, lateral feature spacing, grain size, and surface area;(3)Determination of physical properties such as surface compliance, i.e. “hardness”, surface frictional forces, surface electrical properties.

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The use of transmission and analytical electron microscopy in studying reactions and phase transformations in thin film

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100150046 ◽

1993 ◽

Vol 51 ◽

pp. 842-843

Author(s):

K. Barmak

Keyword(s):

Thin Film ◽

Thin Films ◽

Phase Transformations ◽

Analytical Electron Microscopy ◽

Ex Situ ◽

Multilayer Thin Films ◽

Absolute Concentration ◽

Analytical Electron ◽

Deposition Step

Generally, processing of thin films involves several annealing steps in addition to the deposition step. During the annealing steps, diffusion, transformations and reactions take place. In this paper, examples of the use of TEM and AEM for ex situ and in situ studies of reactions and phase transformations in thin films will be presented.The ex situ studies were carried out on Nb/Al multilayer thin films annealed to different stages of reaction. Figure 1 shows a multilayer with dNb = 383 and dAl = 117 nm annealed at 750°C for 4 hours. As can be seen in the micrograph, there are four phases, Nb/Nb3-xAl/Nb2-xAl/NbAl3, present in the film at this stage of the reaction. The composition of each of the four regions marked 1-4 was obtained by EDX analysis. The absolute concentration in each region could not be determined due to the lack of thickness and geometry parameters that were required to make the necessary absorption and fluorescence corrections.

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