A projection-based reformulation of the coincident site lattice Σ for arbitrary bicrystals at finite temperature

2017 ◽  
Vol 73 (2) ◽  
pp. 87-92 ◽  
Author(s):  
B. Runnels
Keyword(s):  
Grain Boundary ◽  
Closed Form ◽  
Finite Temperature ◽  
Coincident Site Lattice ◽  
Inner Product ◽  
Site Lattice ◽  
Numerical Result ◽  
Regularization Parameters ◽  
Continuous Fields

The coincident site lattice and, specifically, the `Σ value' of a grain boundary are a ubiquitous metric for experimental classification of grain boundaries. However, the mathematical nature of Σ – a pathological function taking values of either an integer or infinity – has been relatively unexplored. This work presents a framework for interpreting Σ as the inverse of a projection defined using the standardL2inner product over continuous fields that represent lattices. `Pre-mollifiers' are used to introduce thermal regularization in the context of the inner product, and a closed-form analytic result is derived. For all nonzero values of the regularization parameters, the formulation is mathematically smooth and differentiable, providing a tool for computationally determining experimental deviation from measured low-Σ boundaries at finite temperatures. It is verified that accurate Σ values are recovered for sufficiently low Σ boundaries, and that the numerical result either converges towards an integer value or diverges to infinity.

Fracture Strengths of Individual Grain Boundaries in Ni3Ai Using a Miniaturized Disk Bend Test

1991 ◽  
Vol 238 ◽  
Author(s):  
Douglas E. Meyers ◽  
Alan J. Ardell
Keyword(s):  
Plastic Deformation ◽  
Grain Boundary ◽  
Grain Boundaries ◽  
Grain Growth ◽  
Coincident Site Lattice ◽  
Bend Test ◽  
High Angle ◽  
Load Drop ◽  
Site Lattice ◽  
Special Boundaries

ABSTRACTThe results of our initial efforts at measuring the fracture strengths of grain boundaries In Ni3Al using a miniaturized disk-bend test are presented. The samples tested were 3 mm in diameter and between 150 and 300 μm thick. An Ingot of directlonally-solidlfled, boron-free Ni3Al containing 24% Al was annealed between 1300 and 1350 °C to induce grain growth, producing many grain boundaries In excess of 1.5 mm in length. Specimens were cut from these In such a way that one long grain boundary was located near a diameter of the specimen. The relative orientations of the grains on either side of the boundary were determined from electron channeling patterns. Low-angle boundaries are so strong they do not fracture; Instead the samples deform In a completely ductile manner. High-angle boundaries always fracture, but only after considerable plastic deformation of the two grains flanking them. Fracture is Indicated by a load drop in the load vs. displacement curves. A method involving extrapolation of the elastic portion of these curves to the displacement at fracture is used to estimate the fracture stresses. This procedure yields consistent values of the fracture strengths of high-angle boundaries. The measured stresses are large (∼2 to 3 GPa), but considerably smaller than those required for the fracture of special boundaries, as predicted by computer simulations. No correlation was found between the fracture stresses or loads and the geometry of the high-angle boundaries, many of which are close to, but deviate from, coincident site lattice orientations.

Clustering of coincident site lattice boundaries in polycrystals

1988 ◽  
Vol 46 ◽  
pp. 630-631
Author(s):  
Valerie fendle ◽  
Brian Ralph
Keyword(s):  
Electron Microscope ◽  
Grain Boundary ◽  
Thermomechanical Processing ◽  
Austenitic Stainless Steels ◽  
Coincident Site Lattice ◽  
Thin Foil ◽  
Texture Measurement ◽  
Bulk Specimen ◽  
Site Lattice ◽  
Special Boundaries

The distribution of coincident site lattice (CSL) and other geometrically special boundaries have been analysed in the form of “grain misorientation texture” (GMT) plots for several systems (pure nickel, a number of austenitic stainless steels and a complex superalloy, 1-5). Several heat treatment conditions have been investigated for each system. Principally, electron back scattering (EBS) in a scanning electron microscope has been used to collect the “microtexture” (i.e. grain specific) data which combines the considerable advantages of bulk specimen texture analysis, grain environment specification with semi-automatic operation. These data are currently being supplemented with thin foil transmission electron microscope (TEM) analyses which permit more detailed investigation of the grain boundary parameters (especially grain boundary planes).Conventional texture measurement shave akey role in assessing the overall changes which occur during thermomechanical processing. However, the very detailed orientation measurements give only a statistical picture and this means that neither the geometry of individual boundaries (the GMT) nor ary tendency for clustering of particular texture types or boundary types may be detected.

The texture between grains

1994 ◽  
Vol 52 ◽  
pp. 616-617
Author(s):  
V. Randle
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Boundary Surface ◽  
Coincident Site Lattice ◽  
Electron Back Scatter Diffraction ◽  
List Type ◽  
Type Number ◽  
Grain Orientations ◽  
Boundary Properties

The ‘texture between grains’, sometimes called mesotexture, refers to the distribution of geometry/crystallography at grain boundaries and grain junctions (edges). These parameters can be accessed from measurements of individual grain orientations, and the most efficient means of collecting such data is by electron back-scatter diffraction (EBSD) in a scanning electron microscope. The reason for studying the texture at grain boundaries and junctions, on an individual basis, is that the properties of these defects (e.g. energy, mobility, diffusivity, resistivity etc) is geometry-dependent. It is desirable to investigate the nature of this relationship and how improved grain boundary properties might be achieved.The following information can be obtained:1.Misorientation across grain boundaries, allowing them to be classified as low/high angle, and according to the coincident site lattice model.2.The orientation of the grain boundary surface (plane) itself with respect to the lattice of each neighbouring grain.3.Classification of grain junctions as I-lines (dislocation balance) or U-lines (dislocation imbalance).4.The connectivity between grain boundaries, or between the grain boundary/junction networks.

Role of Coincident Site Lattice Boundaries in Creep and Stress Corrosion Cracking

2004 ◽  
Vol 819 ◽  
Author(s):  
G.S. Was ◽  
B. Alexandreanu ◽  
Peter Andresen ◽  
Mukul Kumar
Keyword(s):  
Grain Boundary ◽  
Stress Corrosion ◽  
Stress Corrosion Cracking ◽  
High Purity ◽  
Coincident Site Lattice ◽  
Corrosion Cracking ◽  
304 Stainless Steel ◽  
Boundary Structure ◽  
Site Lattice

AbstractInterfaces control many properties in engineering materials, several of which are critical to the integrity of the engineering structure. In single phase, solid solution, austenitic alloys, grain boundaries are often the weak link, displaying susceptibility to creep, corrosion and stress corrosion cracking. As such, grain boundary structure control affords the opportunity to improve the overall performance of alloys in a variety of applications. The role of coincident site lattice boundary (CSLB) enhancement and grain boundary connectivity is examined for how it affects the response of an alloy to stress and the environment. Specifically, the effect of grain boundary character on creep, grain boundary sliding, intergranular stress corrosion cracking, and irradiation assisted stress corrosion cracking in austenitic nickel-base (high purity Ni-Cr-Fe and alloy 600) and iron-base (high purity Fe-Cr-Ni and 304 stainless steel) alloys and for ferritic- martensitic alloy T91 is discussed.

The orientation relationships of nanobelt-like Si2Hf precipitates in an Al–Si–Mg–Hf alloy

2016 ◽  
Vol 49 (4) ◽  
pp. 1223-1230 ◽  
Author(s):  
Xueli Wang ◽  
Huilan Huang ◽  
Xinfu Gu ◽  
Yanjun Li ◽  
Zhihong Jia ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Heat Treatment ◽  
Coincident Site Lattice ◽  
Orthorhombic Structure ◽  
Orientation Relationships ◽  
Lattice Distribution ◽  
Site Lattice ◽  
Transmission Electron ◽  
Habit Planes ◽  
Al Matrix

The orientation relationships (ORs) between the Al matrix and Si2Hf precipitates with an orthorhombic structure in an Al–Si–Mg–Hf alloy after heat treatment at 833 K for 20 h were investigated by transmission electron microscopy and electron diffraction. Four ORs are identified as (100)Al||(010)p, (0\overline {1}1)Al||(101)pand [011]Al||[\overline {1}01]p; (11\overline {1})Al||(010)pand [011]Al||[\overline {1}01]p; (12\overline {1})Al||(010)p, (101)Al||(100)pand [1\overline {11}]Al||[001]p; (\overline {11}1)Al||(010)pand [112]Al||[\overline {1}01]p. The habit planes of these four ORs are rationalized by the fraction of good atomic matching sites at the interface. In addition, the formation of Si2Hf precipitates with a nanobelt-like morphology is interpreted on the basis of the near-coincident site lattice distribution.

scholarly journals Effects of thermomechanical treatment on the occurrence of coincident site lattice boundaries in high strength low alloy steel

2013 ◽  
Vol 16 (6) ◽  
pp. 1350-1354 ◽  
Author(s):  
Renato Soares de Castro ◽  
Ricardo Artur Sanguinetti Ferreira ◽  
Igor Rafael Vilarouco Pedrosa ◽  
Yogendra Prasad Yadava
Keyword(s):  
Alloy Steel ◽  
Thermomechanical Treatment ◽  
Coincident Site Lattice ◽  
High Strength ◽  
Low Alloy Steel ◽  
Site Lattice
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