Elastic Properties of Grain Boundaries in Copper

1989 ◽  
Vol 153 ◽  
Author(s):  
James B. Adams ◽  
Wilhelm G. Wolfer ◽  
Stephen M. Foiles
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Elastic Behavior ◽  
Order Of Magnitude

AbstractThe elastic constants of a Σ5 (100) twist grain boundary are calculated on a monolayer-by-monolayer basis, and the elastic behavior is shown to differ by up to an order of magnitude from bulk-like behavior. This unusual elastic behavior is found to be similar to that of uniaxiallystrained crystals, since the grain boundaries themselves are regions which are strained (expanded) in one direction.

Elastic properties of grain boundaries in copper and their relationship to bulk elastic constants

1989 ◽  
Vol 40 (14) ◽  
pp. 9479-9484 ◽  
Author(s):  
James B. Adams ◽  
Wilhelm G. Wolfer ◽  
Stephen M. Foiles
Keyword(s):  
Grain Boundaries ◽  
Elastic Properties ◽  
Elastic Constants

A Highly Reliable Al Line with Controlled Texture and Grain Boundaries

1995 ◽  
Vol 391 ◽  
Author(s):  
M. Hasunuma ◽  
H. Toyoda ◽  
T. Kawanoue ◽  
S. Ito ◽  
H. Kaneko ◽  
...  
Keyword(s):  
Grain Boundary ◽  
Single Crystal ◽  
Grain Boundaries ◽  
Empirical Relation ◽  
Boundary Structure ◽  
Homogeneous Microstructure ◽  
Grain Boundary Structure ◽  
Dislocation Arrays ◽  
Order Of Magnitude ◽  
Individual Grains

AbstractIn order to clarify the relationship between Al line reliability and film microstructure, especially grain boundary structure and crystal texture, we have tested three kinds of highly textured Al lines, namely, single-crystal Al line, quasi-single-crystal Al line and hypertextured Al line, and two kinds of conventional Al lines deposited on TiN/Ti and on SiO2. Consequently, the empirical relation between the electromigration (EM) lifetime of Al line † and the (111) full width at half maximum (FWHM) value ω is described by † ∝ ω-2 [1]. This improvement of Al line reliability results from as following reasons; firstly, homogeneous microstructure and high activation energy of 1.28eV for the single-crystal Al line (ω=0.18°); secondly, sub-grain boundaries which consisted of dislocation arrays found in the quasi-single-crystal Al line (ω=0.26°) has turned out to be no more effective mass transport paths because dislocation lines are perpendicular to the direction of electron wind. Although there exist plural grain boundary diffusion paths in the newly developed hypertextured Al line (ω=0.5°) formed by using an amorphous Ta-Al underlayer {1], the vacancy flux along the line has been suppressed to the same order of magnitude of single crystal line. It has been clarified that the decrease of FWHM value has promoted the formation of sub-grain boundaries and low-angle boundaries with detailed orientation analysis of individual grains in the hypertextured film. The longer EM lifetime for the hypertextured Al line is considered to be due to the small grain boundary diffusivities for these stable grain boundaries, and this diffusivity reduction resulted in the suppression of void/hillock pair in the Al lines. These results have confirmed that controlling texture and/or grain boundary itself is a promising approach to develop reliable Al lines which withstand higher current densities required in future ULSIs.

The Influence of Grain Boundary Migration on the Diffusion Behaviour of Thin Films

1980 ◽  
Vol 35 (6) ◽  
pp. 613-618
Author(s):  
E. Ehrmann-Falkenau ◽  
A. Wagendristel
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Boundary Migration ◽  
Boundary Surface ◽  
Depth Profiling ◽  
Lattice Diffusion ◽  
Grain Boundary Migration ◽  
Order Of Magnitude ◽  
Diffusion Behaviour

Simultaneous grain boundary-, surface- and lattice diffusion in hypothetical thin film couples of miscible components was computer simulated. On this basis the diffusion into fixed and moving grain boundaries is discussed with respect to the determination of diffusivities by depth profiling methods. The data evaluated from the synthesised depth profiles according to Whipple-Le Claire as well as to Gilmer and Farrell were compared with the diffusivities used for the computation. Agreement was found for systems with a fixed grain boundary network. Moving grain boundaries, however, may cause errors of an order of magnitude towards lower grain boundary diffusivities

Grain boundaries as heterogeneous systems: atomic and continuum elastic properties

1992 ◽  
Vol 339 (1655) ◽  
pp. 555-586 ◽  
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Elastic Properties ◽  
Discrete Model ◽  
Continuum Model ◽  
Elastic Moduli ◽  
Atomic Level ◽  
Upper And Lower Bounds ◽  
Effective Moduli ◽  
The Continuum

The relation between atomic structure and elastic properties of grain boundaries is investigated theoretically from both atomistic and continuum points of view. A heterogeneous continuum model of the boundary is introduced where distinct phases are associated with individual atoms and possess their atomic level elastic moduli determined from the discrete model. The effective elastic moduli for sub-blocks from an infinite bicrystal are then calculated for a relatively small number of atom layers above and below the grain boundary. These effective moduli can be determined exactly for the discrete atomistic model, while estimates from upper and lower bounds are evaluated in the framework of the continuum model. The complete fourth-order elastic modulus tensor is calculated for both the local and the effective properties. Comparison between the discrete atomistic results and those for the continuum model establishes the validity of this model and leads to criteria to assess the stability of a given grain boundary structure. For stable structures the continuum estimates of the effective moduli agree well with the exact effective moduli for the discrete model. Metastable and unstable structures are associated with a significant fraction of atoms (phases) for which the atomic-level moduli lose positive definiteness or even strong ellipticity. In those cases, the agreement between the effective moduli of the discrete and continuum systems breaks down.

scholarly journals Elastic Behavior of γ-Li3N under Pressure

2011 ◽  
Vol 3 (3) ◽  
pp. 569-574
Author(s):  
M. A. Hossain ◽  
A. K. M. A. Islam
Keyword(s):  
Debye Temperature ◽  
Elastic Properties ◽  
Elastic Constants ◽  
First Principles ◽  
Elastic Moduli ◽  
Gamma Transition ◽  
Elastic Behavior ◽  
Gamma Phase ◽  
First Time ◽  
First Principles Method

The elastic properties of gamma-Li3N have been studied for the first time by first-principles method. Three independent elastic constants, aggregate elastic moduli (B, G, E), Poisson’s ratio and Debye temperature are calculated as a function of pressure from 37.12 (beta to gamma transition value)  to 200 GPa and the implications of the results are discussed.Keywords: Li3N; Gamma-phase; Elastic properties; Debye temperature.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i3.7832               J. Sci. Res. 3 (3), 579-584 (2011)

The interaction of conduction electrons with dislocations and grain boundaries in metals

1982 ◽  
Vol 60 (5) ◽  
pp. 766-778 ◽  
Author(s):  
R. A. Brown
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Dislocation Core ◽  
Electron Interaction ◽  
Resonance Model ◽  
Core Electron ◽  
The Core ◽  
Order Of Magnitude ◽  
Good Agreement ◽  
Grain Boundary Resistivity

Progress in understanding the contributions of dislocations and grain boundaries to the residual electrical resistivity in metals is reviewed. Following a summary of experimental data on dislocation and grain-boundary resistivity, it is shown that the resistivity due to the latter can be simply understood in terms of the independent scattering of electrons by individual dislocations of the ordered arrays which form the boundaries. The significance of this observation in establishing the relative dominance of dislocation core scattering over strain-field scattering, so far as charge transport is concerned, is discussed. A brief review of the multitude of dislocation–electron scattering calculations which have appeared in the literature is presented. This shows that theories which neglect the core contribution have invariably failed to account for the order of magnitude of the observed resistivity, again suggesting that core scattering dominates the issue. A simple formula derived from a resonance model of the core-electron interaction is shown to yield dislocation (and hence grain-boundary resistivity) contributions in good agreement with experiment.

Atomic-Level and Effective Elastic Moduli at Grain Boundaries

1991 ◽  
Vol 229 ◽  
Author(s):  
I. Alber ◽  
J. L. Bassani ◽  
M. Khantha ◽  
V. Vitek ◽  
G. J. Wang
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Elastic Properties ◽  
Fourth Order ◽  
Continuum Model ◽  
Elastic Moduli ◽  
Atomic Level ◽  
Upper And Lower Bounds ◽  
Atomistic Model ◽  
The Continuum

AbstractThe relationship between atomic structure and elastic properties of grain boundaries is investigated from both discrete and continuum points of view. A heterogeneous continuum model of the boundary is introduced where distinct phases are associated with individual atoms and possess their atomic level elastic moduli determined from the atomistic model. The complete fourth-order tensors of both the atomic-level and the effective elastic moduli are determined, where the latter are defined for sub-blocks from an infinite bicrystal and are calculated here for a relatively small number of atom layers above and below the grain boundary. These effective moduli are determined exactly for the discrete atomistic model, while only estimates from upper and lower bounds can be determined for the continuum model. Comparison between the atomistic results and those for the continuum model establishes the validity of this definition of elastic properties for heterogeneous structures at these scales. Furthermore, these comparisons as well as algebraic properties of the fourth-order tensor of moduli lead to criteria to assess the stability of a given grain boundary structure.

Measurement of the Displacement Across a Coincidence Grain Boundary

1977 ◽  
Vol 35 ◽  
pp. 124-125
Author(s):  
J. W. Matthews ◽  
W. M. Stobbs
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Stacking Fault ◽  
The Other ◽  
Measuring Technique ◽  
High Angle ◽  
Twin Boundaries ◽  
Rigid Displacement ◽  
Cubic Crystals ◽  
Lattice Displacement

Many high-angle grain boundaries in cubic crystals are thought to be either coincidence boundaries (1) or coincidence boundaries to which grain boundary dislocations have been added (1,2). Calculations of the arrangement of atoms inside coincidence boundaries suggest that the coincidence lattice will usually not be continuous across a coincidence boundary (3). There will usually be a rigid displacement of the lattice on one side of the boundary relative to that on the other. This displacement gives rise to a stacking fault in the coincidence lattice.Recently, Pond (4) and Smith (5) have measured the lattice displacement at coincidence boundaries in aluminum. We have developed (6) an alternative to the measuring technique used by them, and have used it to find two of the three components of the displacement at {112} lateral twin boundaries in gold. This paper describes our method and presents a brief account of the results we have obtained.

Observations of dislocation interactions with recrystallized grain boundaries

1988 ◽  
Vol 46 ◽  
pp. 628-629
Author(s):  
C. W. Price
Keyword(s):  
Dislocation Density ◽  
Grain Boundary ◽  
Strain Rate ◽  
Grain Boundaries ◽  
Dislocation Structure ◽  
Hot Deformation ◽  
Static Recrystallization ◽  
High Dislocation Density ◽  
High Angle ◽  
Dislocation Interactions

Little evidence exists on the interaction of individual dislocations with recrystallized grain boundaries, primarily because of the severely overlapping contrast of the high dislocation density usually present during recrystallization. Interesting evidence of such interaction, Fig. 1, was discovered during examination of some old work on the hot deformation of Al-4.64 Cu. The specimen was deformed in a programmable thermomechanical instrument at 527 C and a strain rate of 25 cm/cm/s to a strain of 0.7. Static recrystallization occurred during a post anneal of 23 s also at 527 C. The figure shows evidence of dissociation of a subboundary at an intersection with a recrystallized high-angle grain boundary. At least one set of dislocations appears to be out of contrast in Fig. 1, and a grainboundary precipitate also is visible. Unfortunately, only subgrain sizes were of interest at the time the micrograph was recorded, and no attempt was made to analyze the dislocation structure.

Measurement of solute segregation to grain boundaries in the AEM: A review

1988 ◽  
Vol 46 ◽  
pp. 606-607
Author(s):  
D. B. Williams ◽  
A. D. Romig
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Boundary Migration ◽  
Grain Boundary Migration ◽  
Boundary Misorientation ◽  
Collector Plate ◽  
Segregation Process ◽  
Grain Boundary Misorientation ◽  
Structure Boundary ◽  
Equilibrium Segregation

The segregation of solute or imparity elements to grain boundaries can occur by three well-defined processes. The first is Gibbsian segregation in which an element of minimal matrix solubility confines itself to a monolayer at the grain boundary. Classical examples include Bi in Cu and S or P in Fe. The second process involves the depletion of excess matrix solute by volume diffusion to the boundary. In the boundary, the solute atoms diffuse rapidly to precipitates, causing them to grow by the ‘collector-plate mechanism.’ Such grain boundary diffusion is thought to initiate “Diffusion-Induced Grain Boundary Migration,” (DIGM). This process has been proposed as the origin of eutectoid transformations or discontinuous grain boundary reactions. The third segregation process is non-equilibrium segregation which result in a solute build-up around the boundary because of solute-vacancy interactions.All of these segregation phenomena usually occur on a sub-micron scale and are often affected by the nature of the grain boundary (misorientation, defect structure, boundary plane).

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