Elastic Surfaces

2019 ◽  
pp. 30-50
Author(s):  
Troy Shinbrot
Keyword(s):  
Dimensional Analysis ◽  
Laplace Equation ◽  
Rayleigh Instability ◽  
Elastic Surfaces

In this chapter, the effects of elasticity are overviewed, the Young–Laplace equation is introduced, and the importance of nondimensionalization is emphasized. Topics covered include the Plateau–Rayleigh instability and dimensional analysis.

In situ investigation of the primary recrystallization of alpha titanium in HVEM

1978 ◽  
Vol 36 (1) ◽  
pp. 634-635
Author(s):  
S. Naka ◽  
R. Penelle ◽  
R. Valle
Keyword(s):  
Dimensional Analysis ◽  
Texture Evolution ◽  
Cold Work ◽  
Three Dimensional ◽  
Primary Recrystallization ◽  
Thin Foils ◽  
In Situ Investigation ◽  
Grain Growth Model ◽  
Alpha Titanium

The in situ experimentation technique in HVEM seems to be particularly suitable to clarify the processes involved in recrystallization. The material under investigation was unidirectionally cold-rolled titanium of commercial purity. The problem was approached in two different ways. The three-dimensional analysis of textures was used to describe the texture evolution during the primary recrystallization. Observations of bulk-annealed specimens or thin foils annealed in the microscope were also made in order to provide information concerning the mechanisms involved in the formation of new grains. In contrast to the already published work on titanium, this investigation takes into consideration different values of the cold-work ratio, the temperature and the annealing time.Two different models are commonly used to explain the recrystallization textures i.e. the selective grain growth model (Beck) or the oriented nucleation model (Burgers). The three-dimensional analysis of both the rolling and recrystallization textures was performed to identify the mechanismsl involved in the recrystallization of titanium.

In situ TEM Studies of agglomeration of sub-nanometer Ru layers in Ru/C multilayers

1992 ◽  
Vol 50 (1) ◽  
pp. 256-257
Author(s):  
Tai D. Nguyen ◽  
Ronald Gronsky ◽  
Jeffrey B. Kortright
Keyword(s):  
Layered Structure ◽  
Driving Force ◽  
High Energy ◽  
Superior Performance ◽  
In Situ Tem ◽  
Rayleigh Instability ◽  
Practical Applications ◽  
Transmission Electron ◽  
Diffraction Patterns

Nanometer period Ru/C multilayers are one of the prime candidates for normal incident reflecting mirrors at wavelengths < 10 nm. Superior performance, which requires uniform layers and smooth interfaces, and high stability of the layered structure under thermal loadings are some of the demands in practical applications. Previous studies however show that the Ru layers in the 2 nm period Ru/C multilayer agglomerate upon moderate annealing, and the layered structure is no longer retained. This agglomeration and crystallization of the Ru layers upon annealing to form almost spherical crystallites is a result of the reduction of surface or interfacial energy from die amorphous high energy non-equilibrium state of the as-prepared sample dirough diffusive arrangements of the atoms. Proposed models for mechanism of thin film agglomeration include one analogous to Rayleigh instability, and grain boundary grooving in polycrystalline films. These models however are not necessarily appropriate to explain for the agglomeration in the sub-nanometer amorphous Ru layers in Ru/C multilayers. The Ru-C phase diagram shows a wide miscible gap, which indicates the preference of phase separation between these two materials and provides an additional driving force for agglomeration. In this paper, we study the evolution of the microstructures and layered structure via in-situ Transmission Electron Microscopy (TEM), and attempt to determine the order of occurence of agglomeration and crystallization in the Ru layers by observing the diffraction patterns.

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