scholarly journals Textural equilibrium melt geometries around tetrakaidecahedral grains

2018 ◽  
Vol 474 (2212) ◽  
pp. 20170639 ◽  
Author(s):  
John F. Rudge
Keyword(s):  
Grain Boundaries ◽  
Cross Sections ◽  
Mean Curvature ◽  
Dihedral Angles ◽  
Total Surface Energy ◽  
Space Filling ◽  
Energy Bound ◽  
Molten Materials ◽  
Two Parameters ◽  
Equilibrium Geometries

In textural equilibrium, partially molten materials minimize the total surface energy bound up in grain boundaries and grain–melt interfaces. Here, numerical calculations of such textural equilibrium geometries are presented for a space-filling tessellation of grains with a tetrakaidecahedral (truncated octahedral) unit cell. Two parameters determine the nature of the geometries: the porosity and the dihedral angle. A variety of distinct melt topologies occur for different combinations of these two parameters, and the boundaries between different topologies have been determined. For small dihedral angles, wetting of grain boundaries occurs once the porosity has exceeded 11%. An exhaustive account is given of the main properties of the geometries: their energy, pressure, mean curvature, contiguity and areas on cross sections and faces. Their effective permeabilities have been calculated, and demonstrate a transition between a quadratic variation with porosity at low porosities to a cubic variation at high porosities.

Effect of Crystallographic Quality of Grain Boundaries on Both Mechanical and Electrical Properties of Electroplated Copper Thin Film Interconnections

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Naokazu Murata ◽  
Naoki Saito ◽  
Kinji Tamakawa ◽  
Ken Suzuki ◽  
Hideo Miura
Keyword(s):  
Electrical Properties ◽  
Grain Boundaries ◽  
Fatigue Fracture ◽  
High Crystallinity ◽  
Mechanical And Electrical Properties ◽  
Copper Interconnection ◽  
Electroplated Copper ◽  
Two Parameters ◽  
Low Crystallinity

Effects of crystallographic quality of grain boundaries on mechanical and electrical properties were investigated experimentally. A novel method using two parameters of image quality (IQ) and confidence index (CI) values based on electron back-scattering diffraction (EBSD) analysis was proposed in order to evaluate crystallographic quality of grain boundaries. IQ value was defined as an index to evaluate crystallinity in region irradiated with electron beam. CI value determined existence of grain boundaries in the region. It was found that brittle intergranular fatigue fracture occurred in the film without annealing and the film annealed at 200 °C because network of grain boundaries with low crystallinity remained in these films. On the other hand, the film annealed at 400 °C caused only ductile transgranular fatigue fracture because grain boundaries with low crystallinity almost disappeared. From results of measurement of electrical properties, electrical resistivity of copper interconnection annealed at 400 °C with high crystallinity (2.09 × 10−8 Ωm) was low and electron migration (EM) resistance was high compared with an copper interconnection without annealing with low crystallinity (3.33 × 10−8 Ωm). It was clarified that the interconnection with high crystallinity had superior electrical properties. Thus, it was clarified that the crystallographic quality of grain boundaries has a strong correlation of mechanical and electrical reliability.

Stresses and Deformations of Toroidal Shells of Elliptical Cross Section: With Applications to the Problems of Bending of Curved Tubes and of the Bourdon Gage

1952 ◽  
Vol 19 (1) ◽  
pp. 37-48
Author(s):  
R. A. Clark ◽  
T. I. Gilroy ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Closed Shell ◽  
Open Shell ◽  
Elliptical Cross Section ◽  
Axially Symmetric ◽  
Elliptical Cross ◽  
Two Parameters ◽  
Toroidal Shells

Abstract This paper is concerned with the application of the theory of thin shells to several problems for toroidal shells with elliptical cross section. These problems are as follows: (a) Closed shell subjected to uniform normal wall pressure. (b) Open shell subjected to end bending moments. (c) Combination of the results for the first and second problems in such a way as to obtain results for the stresses and deformations in Bourdon tubes. In all three problems the distribution of stresses is axially symmetric but only in the first problem are the displacements axially symmetric. The magnitude of stresses and deformations for given loads depends in all three problems on the magnitude of the two parameters bc/ah and b/c where b and c are the semiaxes of the elliptical section, a is the distance of the center of the section from the axis of revolution, and h is the thickness of the wall of the shell. For sufficiently small values of bc/ah trigonometric series solutions are obtained. For sufficiently large values of bc/ah asymptotic solutions are obtained. Numerical results are given for various quantities of practical interest as a function of bc/ah for the values 2, 1, 1/2, 1/4 of the semiaxes ratio b/c. It is suggested that the analysis be extended to still smaller values of b/c and to cross sections other than elliptical.

Grain Boundary Analysis of Crept Alloy 617

2012 ◽  
Vol 1383 ◽  
Author(s):  
Fan Zhang ◽  
David P. Field
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Electron Backscatter Diffraction ◽  
Creep Damage ◽  
Original Material ◽  
Alloy 617 ◽  
Plane Normal ◽  
Lattice Misorientation ◽  
Two Parameters ◽  
Backscatter Diffraction

ABSTRACTAlloy 617, a high-temperature creep-resistant, nickel-based alloy, is being considered for the primary heat exchanger for the next generation nuclear plant, which is highly influenced by thermal creep. The main objective of this study is to inspect the crept grain boundaries under its imitated working condition, and to determine which boundaries are susceptible to damage and which are more resistant, in order to help improve its creep resistance in future manufacturing. Electron backscatter diffraction was used to measure the proportions of each boundary by observing and analyzing these crept microstructures. The grain-boundary distribution can be expressed in terms of five parameters including three parameters of lattice misorientation and two parameters of the grain-boundary plane normal. Three conditions were analyzed: the original material, metal that was annealed without stress, and ones that were crept at 1000ºC at 19 MPa and 25 MPa for various times. Though observation, it is found that the voids seldom occur at low angle grain boundaries, and coherent twin boundaries are also resist to creep damage.

The Influence of Microstructure on the Tensile Damage of Lamellar Grey Cast Iron

1984 ◽  
Vol 34 ◽  
Author(s):  
A. Fontaine ◽  
G. Zambelli
Keyword(s):  
Cast Iron ◽  
Cross Sections ◽  
Damage Mechanics ◽  
Degradation Process ◽  
Grey Cast Iron ◽  
Heterogeneous Microstructure ◽  
The Matrix ◽  
Grey Cast ◽  
Mechanics Concepts ◽  
Two Parameters

ABSTRACTThe rupture behaviour of lamellar grey cast iron under tension depends on the overall damage suffered by the heterogeneous microstructure. In order to quantify the influence of microstructural components on the rupture behaviour of the material, it is therefore preferable to apply “Damage Mechanics” concepts rather than “Linear Fracture Mechanics”. In this preliminary study the damage process is assumed to be isotropic and two parameters are considered; firstly a damage limit σ0 and secondly, a damage rate B. Measurements made on a grey cast iron, cast in three different cross sections, show that these damage parameters may be used to separate the contributions of the graphite network and the matrix wich interact in the degradation process of the heterogeneous microstructure of lamellar grey cast iron.

The Calculation of Compressible Fluid Flow by the Use of a Generalized Entropy Chart

1948 ◽  
Vol 159 (1) ◽  
pp. 313-334 ◽  
Author(s):  
J. Kestin ◽  
A. K. Oppenheim
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Generalized Entropy ◽  
Specific Heats ◽  
Simplifying Assumptions ◽  
Isentropic Flows ◽  
Basic Equations ◽  
Two Parameters ◽  
Physical Phenomena ◽  
Velocity Pressure

Calculations of the flow of gases in pipes or ducts of varying cross-sections are important in the design of turbines and compressors, nozzles for various applications, exhaust or radiator ducts, thrust augmenting devices, etc. Provided certain simplifying assumptions are made, there is no difficulty in writing down the basic equations, but when the velocities are comparable to that of sound and compressibility effects cannot therefore be neglected, the solution of the transcendental equations present difficulties which hinder a clear discussion of the physical phenomena. Here the problem is solved by the use of a generalized entropy chart, off which results may be directly read. For example, if the conditions in the reservoir from which the gas is assumed to be discharged are known, the complete conditions at any given cross-section may be read off when two parameters at the section considered are specified. The parameters may include the velocity, pressure, density, temperature, local Mach number, local velocity of sound, area of cross-section, mass flow per unit area, momentum per second, etc. The method is not confined to isentropic flows and may be applied to such problems as the flow in straight pipes or convergent and divergent nozzles including losses by either friction or condensation shocks. The co-ordinates of the chart are: dimensionless entropy σ = ( s— s0) J/R and dimensionless enthalpy ι = h/h0 = T/T0 where the meaning of the symbols is given later. All other variables are expressed in terms of these two co-ordinates and tables for several values of the ratio of specific heats are included to facilitate the drawing of such charts. The method does not aim at presenting new facts, but its usefulness lies in the provision of a comprehensive graphical means of calculating one-dimensional flow of compressible fluids. The charts lend themselves to the construction of a mechanical device for simplifying their use, such as a portable scale with sliding curves.

The Effect of Grain Boundaries on Surface Diffusion Mediated-Planarization of Polycrystalline Cu Films

1995 ◽  
Vol 389 ◽  
Author(s):  
R.A. Brain ◽  
D.S. Gardner ◽  
D.B. Fraser ◽  
H.A. Atwater
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Surface Diffusion ◽  
Cross Sections ◽  
Boundary Surface ◽  
Surface Profile ◽  
Transmission Electron Micrograph ◽  
Cu Films ◽  
Transmission Electron

ABSTRACTIn situ, ultrahigh vacuum anneals were performed to induce Cu reflow at 500°C following deposition of Cu films and a Ta barrier layer on 1 μm wide by 1 μm deep trenches. Transmission electron micrograph cross-sections show profiles which suggest that grain boundaries and surface energy anisotropy significantly affect reflow. The extent of reflow is dependent on the structure of grain boundary-surface intersections, and the surface profile consists of regions of low curvature within grains and with sharp discontinuities in curvature at grain boundaries, a structure that inhibits surface diffusion. We present results showing how the surface diffusion mediated reflow varies with grain boundary groove angle and position, and compare these results with finite-element simulations that model surface diffusion-driven reflow.

The Influence of the Exterior Surface on Grain Boundary Mobility Measurements

2014 ◽  
Vol 95 ◽  
pp. 56-65
Author(s):  
Amy Novick-Cohen ◽  
Anna Zigelman ◽  
Arkady Vilenkin
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Mean Curvature ◽  
Boundary Energy ◽  
Polycrystalline Materials ◽  
Normal Velocity ◽  
Exterior Surface ◽  
Mean Curvature Motion ◽  
Curvature Motion ◽  
Half Loop

Polycrystalline materials typically contain a very large number of grains whose surrounding grain boundaries evolve over time to reducethe overall energy of the microstructure. The evolution of the microstructure is influencedby the motion of the exterior surface since the grain boundaries couple to the exterior surface of the specimen; these effects can be appreciable especially in thin specimens. We model these effects using the classical framework of Mullins, in whichgrain boundaries move by mean curvature motion, Vn =A κ, and the exterior surface evolves by surface diffusion, Vn = -BΔs κ. Here Vn and κ denote the normal velocity and the mean curvature of the respective evolving surfaces, and Δs is the surface Laplacian. A classical way to determine A, the ``reduced mobility," is to make measurements based on the half-loop bicrystalline geometry. In this geometry one of the two grains, which embedded within the other, recedes at a roughly constant rate which can provide an estimate for A. In this note, we report on findings concerning the effects of the exterior surface on grain boundary motion and mobility measurements in the context of the half-loop bicrystalline geometry. We assume that the ratio of grain boundary energy to the exterior surface energy is small, and suitable assumptions are made of the specimen aspect ratio.

scholarly journals Strupczewski Method for Parametric Design Hydrographs in Ungauged Cross-Sections

2017 ◽  
Vol 64 (1) ◽  
pp. 49-67 ◽  
Author(s):  
Wiesław Gądek ◽  
Beata Baziak ◽  
Tamara Tokarczyk
Keyword(s):  
Cross Sections ◽  
Parametric Design ◽  
Complex Function ◽  
River Catchment ◽  
Flood Hydrograph ◽  
Skewness Coefficient ◽  
Design Hydrographs ◽  
Flow Changes ◽  
The Times ◽  
Two Parameters

AbstractNonparametric hydrographs, constructed by the method suggested by Archer, are usually used for developing parametric design hydrographs. Flow changes in time are described by the UPO ERR Gamma complex function, which denotes a Gamma curve reformulated to have a Unit Peak at the Origin (abbreviated to UPO), supplemented by the Exponential Replacement Recession (ERR) curve. It may be observed, that this solution does not work in some areas of the upper Vistula and middle Odra catchments when the times of the rising limb of a hydrograph are higher than the times of the falling limb, i.e. when the skewness coefficient approximates 0.5 or higher values. Better results can be achieved with the function suggested by Strupczewski in 1964. It is a solution which uses two parameters of the flood hydrograph. The objective of the present paper is to assess the Strupczewski method by comparing it with a complex UPO ERR Gamma function for gauged cross-sections in the upper Vistula and middle Odra catchments. The assessment was carried out for 30 gauged cross-sections (15 in each river catchment). The parameters were optimized for width-hydrograph descriptors W75 and W50, designed by the Archer method, and for the skewness coefficient s. Optimization using only two width-hydrograph descriptors aims to test how the Strupczewski method works for cross-sections for which the values of width-hydrograph descriptors W75 and W50 are known. The assessment of both methods was carried out with reference to a nonparametric hydrograph constructed by the Archer method. The results of these assessments suggest that the Strupczewski method may be used not only for gauged cross-sections, but also for ungauged ones.

scholarly journals Preliminary geophysical study for groundwater exploration in the eastern region of Islamabad

1996 ◽  
Vol 14 ◽  
Author(s):  
K. A. Khan
Keyword(s):  
Cross Sections ◽  
Groundwater Exploration ◽  
High Resistivity ◽  
Eastern Region ◽  
Unconfined Aquifers ◽  
Electrical Resistivity Survey ◽  
True Resistivity ◽  
Geophysical Study ◽  
Two Parameters ◽  
The Relationship

Geophysical study was carried out in the area lying to the east of Islamabad to identify potential aquifers and to establish the relationship between the geoelectric and hydrogeologic parameters. Electrical resistivity survey using the Schlumberger electrode configuration was carried out at 32 stations. Data processing and interpretation were done using a PC based software. The true resistivity and thickness of various subsurface horizons were interpreted in terms of geological columns and cross-sections to reveal the presence of clay, sand, gravel and boulders as the subsurface lithology. The wide occurrence of gravels and boulders suggest that most of the regions in the project area represent the promising zone of groundwater. Both confined and unconfined aquifers have been encountered. The resistivity information was used to plot Dar-Zarrouk curves across selected profiles in order to determine the electrical behaviour of the aquifer. These curves show that the surficial layer is composed of material of high resistivity while the second layer constitutes the aquifer having high longitudinal conductance. Finally, statistical analyses involving linear regression were carried out to find out the relationship between electric and hydraulic properties of the aquifers. The results indicate that there is no significant relationship between the two parameters. All the results were compiled to demarcate promising groundwater drill sites.

scholarly journals 3D microstructure and critical current properties of ultra-fine-grain Ba(Fe,Co)2As2 bulk superconductors

2021 ◽  
Author(s):  
Yusuke Shimada ◽  
Shinnosuke Tokuta ◽  
Akinori Yamanaka ◽  
Akiyasu Yamamoto ◽  
Toyohiko. J Konno
Keyword(s):  
Grain Boundaries ◽  
Critical Current ◽  
Weak Link ◽  
Three Dimensional ◽  
High Energy ◽  
Dimensional Structure ◽  
Polycrystalline Materials ◽  
Fine Grain ◽  
Pore Length ◽  
Two Parameters

Abstract In iron-based superconductors, randomly oriented grain boundaries have a strong influence on the transport properties via intrinsic weak-link and flux pinning mechanisms. Herein we report the critical current density (Jc) and the three-dimensional microstructure of polycrystalline bulk Co-doped Ba122 superconductors, with highly dense grain boundaries (grain size smaller than 50 nm), produced by high-energy milling. Three-dimensional electron microscopy revealed that the anomalous growth of secondary particles (aggregation) and the inter-aggregation structures were significantly different in the samples with finer grains, which may have extrinsically limited Jc. These important microstructural features were quantified as two parameters—local thickness and total pore length—by reconstructing the three-dimensional structure of the superconducting phase using the adaptive thresholding method. The results obtained in this study suggest that understanding and controlling the microstructural formation process by sintering are instrumental for improving the Jc properties of 122 polycrystalline materials consisting of ultrafine grains.

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