scholarly journals Description of Changes in Crystal Orientations by the Elements of Logarithm of a Rotation Matrix

Scanning ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Susumu Onaka ◽  
Kunio Hayashi
Keyword(s):  
Single Crystal ◽  
Symmetric Tensor ◽  
Rotation Matrix ◽  
Euler Angles ◽  
Real Numbers ◽  
Crystal Orientations ◽  
Angle Pair

The logarithmln⁡Rof rotation matrixRis a skew symmetric tensor consisting of three independent elements of real numbers. In addition to the Euler angles and the axis/angle pair, the elements ofln⁡Rcalled the log angles are also the set of three parameters ofR. In this paper, we will show that the concept of the log angles is also useful to discuss changes in crystal orientations. The changes inRas a function of the position are given by the changes in the log angles. As an example, orientation changes caused by arrays of dislocations in a plastically deformed Cu single crystal are discussed.

scholarly journals Focused Ion Beam Milling of Single-Crystal Sapphire with A-, C-, and M-Orientations

Materials ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 2871
Author(s):  
Qiuling Wen ◽  
Xinyu Wei ◽  
Feng Jiang ◽  
Jing Lu ◽  
Xipeng Xu
Keyword(s):  
Single Crystal ◽  
Surface Quality ◽  
Material Removal ◽  
Focused Ion Beam ◽  
Removal Rate ◽  
Ion Beam ◽  
Crystal Orientations ◽  
Aluminum Ions ◽  
Single Crystal Sapphire

Sapphire substrates with different crystal orientations are widely used in optoelectronic applications. In this work, focused ion beam (FIB) milling of single-crystal sapphire with A-, C-, and M-orientations was performed. The material removal rate (MRR) and surface roughness (Sa) of sapphire with the three crystal orientations after FIB etching were derived. The experimental results show that: The MRR of A-plane sapphire is slightly higher than that of C-plane and M-plane sapphires; the Sa of A-plane sapphire after FIB treatment is the smallest among the three different crystal orientations. These results imply that A-plane sapphire allows easier material removal during FIB milling compared with C-plane and M-plane sapphires. Moreover, the surface quality of A-plane sapphire after FIB milling is better than that of C-plane and M-plane sapphires. The theoretical calculation results show that the removal energy of aluminum ions and oxygen ions per square nanometer on the outermost surface of A-plane sapphire is the smallest. This also implies that material is more easily removed from the surface of A-plane sapphire than the surface of C-plane and M-plane sapphires by FIB milling. In addition, it is also found that higher MRR leads to lower Sa and better surface quality of sapphire for FIB etching.

OrientXplot: a program to analyse and display relative crystal orientations

2015 ◽  
Vol 48 (4) ◽  
pp. 1330-1334 ◽  
Author(s):  
Ross Angel ◽  
Sula Milani ◽  
Matteo Alvaro ◽  
Fabrizio Nestola
Keyword(s):  
Single Crystals ◽  
Diffraction Pattern ◽  
Euler Angles ◽  
Electron Backscattered Diffraction ◽  
Orientation Data ◽  
User Control ◽  
Crystal Orientations ◽  
Orientation Matrix ◽  
Crystallographic Axes

Orientations of single crystals are usually determined by diffraction experiments. Indexing of a diffraction pattern from one crystal leads to the determination of its `orientation matrix', which defines the orientation of its crystallographic axes relative to a set of reference axes associated with the diffractometer. Crystal orientations can also be described in terms of Euler angles, especially from electron backscattered diffraction measurements.OrientXplotis a Windows program that reads all common types of orientation matrices, as well as orientation data such as Euler angles. The program calculates and displays the relative orientations of pairs of crystals, such as twins or inclusion crystals trapped inside host crystals.OrientXplotcan manipulate (under user control) the orientation matrices to allow for ambiguities in indexing that arise from crystal symmetries. Orientation data can be displayed on a stereogram or output in numerical form for plotting in external programs.

scholarly journals Atomic-scale characterization of occurring phenomena during hot nanometric cutting of single crystal 3C–SiC

RSC Advances ◽  
2016 ◽  
Vol 6 (75) ◽  
pp. 71409-71424 ◽  
Author(s):  
Saeed Zare Chavoshi ◽  
Xichun Luo
Keyword(s):  
Molecular Dynamics ◽  
Single Crystal ◽  
Md Simulation ◽  
Atomic Scale ◽  
Nanometric Cutting ◽  
Crystal Orientations ◽  
Scale Characterization

Nanometric cutting of single crystal 3C–SiC on the three principal crystal orientations at various cutting temperatures spanning from 300 K to 3000 K was investigated by the use of molecular dynamics (MD) simulation.

scholarly journals Effects of Crystal Orientations on the Low-Cycle Fatigue of a Single-Crystal Nickel-Based Superalloy at 980 °C

2018 ◽  
Vol 32 (3) ◽  
pp. 381-390 ◽  
Author(s):  
Liu Liu ◽  
Jie Meng ◽  
Jin-Lai Liu ◽  
Hai-Feng Zhang ◽  
Xu-Dong Sun ◽  
...  
Keyword(s):  
Single Crystal ◽  
Low Cycle Fatigue ◽  
Cycle Fatigue ◽  
Nickel Based Superalloy ◽  
Crystal Orientations

scholarly journals Effect of secondary crystal orientations on the deformation anisotropy for nickel-based single-crystal plate with notch feature

2019 ◽  
Vol 54 (1) ◽  
pp. 54-64 ◽  
Author(s):  
Yu Zhai ◽  
Muhammad Kashif Khan ◽  
José Correia ◽  
Abílio MP de Jesus ◽  
Zhiyong Huang ◽  
...  
Keyword(s):  
Single Crystal ◽  
Deformation Process ◽  
Crystal Orientation ◽  
Turbine Blades ◽  
Von Mises Stress ◽  
Slip Systems ◽  
Nickel Based Superalloy ◽  
Crystal Orientations ◽  
Single Crystal Plate ◽  
Von Mises

The effects of the secondary crystal orientations on the nickel-based single-crystal superalloy turbine blades were investigated. The stress concentration features were used for investigation of the optimal secondary crystal orientation leading to the higher strength of the single-crystal turbine blades. The crystal plastic finite element method coupled with micromechanics constitutive model is applied to study the effect of secondary crystal orientation on plastic deformation and mechanical behavior around the cooling holes and notches with the primary (load) orientation fixed at [001] direction. For nickel-based superalloy plates with holes or notches, the secondary crystal orientation effect on the strength needs to be clarified at various load levels. The maximum von Mises stress in the single-crystal alloy varies significantly with variation in the secondary crystal orientations. It was found that only two slip systems dominate the deformation process of the material owing to their favorable orientation with loading. The secondary orientation of 45° was identified with lowest resolved shear stress in the dominating slip systems and potential of producing higher strength for single-crystal turbine blades.

Sign in / Sign up

Export Citation Format

Share Document