stereographic triangle
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2021 ◽  
Vol 2144 (1) ◽  
pp. 012029
Author(s):  
S Ya Betsofen ◽  
K A Speransky ◽  
A V Bespalov ◽  
S S Alexandrova

Abstract The accuracy of determining the LTEC with respect to metals and alloys with an HCP lattice based on inverse pole figures (IPF) is analyzed depending on the number of experimental points on the IPF using three averaging options: (1) taking into account the irregular arrangement of reflections on the stereographic triangle according to Morris; (2) by the multiplicity factor and (3) with the same weight of each orientation. It is shown that when evaluating the LTEC for semi-finished products with a basal texture, 17 reflections on the IPF are sufficient to provide an error of <1% when using Morris averaging and the multiplicity factor; in the case of a prismatic texture, an error of <1% is provided by all three averaging options, while Morris averaging is minimal.


AIP Advances ◽  
2016 ◽  
Vol 6 (6) ◽  
pp. 065023 ◽  
Author(s):  
R. Méndez-Camacho ◽  
V. H. Méndez-García ◽  
M. López-López ◽  
E. Cruz-Hernández

2006 ◽  
Vol 15-17 ◽  
pp. 864-869 ◽  
Author(s):  
Kentaro Yuge ◽  
Yoshihiro Terada ◽  
Takashi Matsuo

The creep deformations of γ-single phase Ni-20mass%Cr single crystals with stress axes within standard stereographic triangle and at the three pole positions have been investigated. The most of the creep life is occupied by the transient stage, which consists of Stage I and Stage II. In Stage I, the creep rate just after loading remains constant. In Stage II, the creep rate decreases continuously. Except for the single crystals with stress axes of [001] and [1,–11] poles, the single crystals make the creep deformation using the primary slip plane of (111). As a result, the cross section of the specimens turns from circular to elliptical in shape. However, there are marked difference in deformation manner among single crystals with the stress axes within standard stereographic triangle. The single crystals whose angle between stress axis and primary slip plane of (111), θ. is more than 45° shows the heterogeneous deformation during creep. While, the homogeneous deformation will be expected in the single crystals with θ less than 45°. In this study, by using the four single crystals with θ less than 45°, the change in the stress axis with the creep deformation at 1173K-29.4MPa, is investigated and the deformation manner due to the primary slip plane of (111) is estimated by conducting the creep interrupting tests. In the two single crystals with stress axes in the standard stereographic triangle where the moving range of θ is narrow, comparing to the others, the spot of the stress axis in the inverse pole figure moves for <1,– 01> direction by using (111)<1,–01> slip system, and after arriving at the [001]-[1,–11] line, the spot turns to its direction for [1,–11] pole using (111)<1,–10> slip system. While, in the other two single crystals whose stress axes located in the area with wider moving range of θ, the spot of stress axis only move for <1,–01> direction. And, the widely spread spot of the stress axis is confirmed after subjecting the small strain.


2006 ◽  
Vol 980 ◽  
Author(s):  
Xiaohua Min ◽  
Eisaku Sakurada ◽  
Masao Takeyama ◽  
Takashi Matsuo

AbstractBased on our analysis of a lot of creep rate-strain curves of PST crystals with the different angles between the lamellar plate and the stress axis, designated as ø, it was confirmed that the creep rate and the creep deformation manner strongly depend on the ø. It was supposed that the predominant creep deformation using γ plate during the transient stage is derived by the fully suppression of the operation of another slip systems not parallel to γ plate through α2 plate. It was also confirmed that the initial stress axes of the PST crystals within the standard stereographic triangle move for the [001]-[111] line, and then turn their directions for [111] pole during the transient stage. This moving manner of the stress axis indicated that the first slip system of [101](111) continues to the area near the [001]-[111] line in the standard stereographic triangle, and then, the second slip system of [110](111) operates. By comparing this moving manner to the creep rate-strain curve, it is suggested that the first slip system of [101](111) operates during the Stage I where the light decrease in the creep rate remains, after that, the second slip system of [110](111) appears and leads to steep decrease in the creep rate. This stage was designated as the Stage II. According to this conception, it is supposed that the strain at the end of the Stage I is directly correlated with the angle from the initial stress axis to the [001]-[111] line in the standard stereographic triangle. In this study, this supposition was confirmed by conducting the creep tests at 1148 K/68.6 MPa using two PST crystals with ø of 31° and 34°. The initial stress axis of the PST crystal with ø of 31° locates nearer to the [001]-[-111] line than that of the PST crystal with ø of 34°. The strain at the end of the Stage I of the PST crystal with ø of 31° is half that of the PST crystal with ø of 34°. By analyzing the inverse pole figures of the creep interrupted PST crystals, it was confirmed that the angle from the initial stress axis to the [001]-[111] line is correlated with the strain of the transient stage.


2004 ◽  
Vol 854 ◽  
Author(s):  
Sh. Seydmohamadi ◽  
H. Wen ◽  
Zh. M. Wang ◽  
G. J. Salamo

ABSTRACTWe investigate the formation of (In, Ga)As self assembled quantum structures grown on different orientations of a GaAs substrate along one side of the stereographic triangle between (100) and (111)A surfaces. The samples were grown by Molecular Beam Epitaxy, monitored by Reflection High-Energy Electron Diffraction during the growth and characterized by in-situ Scanning Tunneling Microscopy and Atomic Force Microscopy. A systematic transition from zero dimensional (In, Ga)As quantum dots to one dimensional quantum wires was observed as the substrate was varied along the side of the triangle within 25° miscut from the (100) toward (111)A, which includes several high index surfaces. We propose an explanation for the role of the substrate in determining the type of the nanostructure that is formed.


2004 ◽  
Vol 849 ◽  
Author(s):  
Sh. Seydmohamadi ◽  
H. Wen ◽  
Zh. M. Wang ◽  
G. J. Salamo

AbstractWe investigate the formation of (In, Ga)As self assembled quantum structures grown on different orientations of a GaAs substrate along one side of the stereographic triangle between (100) and (111)A surfaces. The samples were grown by Molecular Beam Epitaxy, monitored by Reflection High-Energy Electron Diffraction during the growth and characterized by in-situ Scanning Tunneling Microscopy and Atomic Force Microscopy. A systematic transition from zero dimensional (In, Ga)As quantum dots to one dimensional quantum wires was observed as the substrate was varied along the side of the triangle within 25° miscut from the (100) toward (111)A, which includes several high index surfaces. We propose an explanation for the role of the substrate in determining the type of the nanostructure that is formed.


2004 ◽  
Vol 859 ◽  
Author(s):  
Sh. Seydmohamadi ◽  
H. Wen ◽  
Zh. M. Wang ◽  
G. J. Salamo

ABSTRACTWe investigate the formation of (In, Ga) As self assembled quantum structures grown on different orientations of a GaAs substrate along one side of the stereographic triangle between (100) and (111)A surfaces. The samples were grown by Molecular Beam Epitaxy, monitored by Reflection High-Energy Electron Diffraction during the growth and characterized by in-situ Scanning Tunneling Microscopy and Atomic Force Microscopy. A systematic transition from zero dimensional (In, Ga) As quantum dots to one dimensional quantum wires was observed as the substrate was varied along the side of the triangle within 25° miscut from the (100) toward (111)A, which includes several high index surfaces. We propose an explanation for the role of the substrate in determining the type of the nanostructure that is formed.


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