The dislocations contrast factors of cubic crystals in the Zener constant range between zero and unity

2002 ◽  
Vol 17 (2) ◽  
pp. 104-111 ◽  
Author(s):  
I. C. Dragomir ◽  
T. Ungár
Keyword(s):  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Profile Analysis ◽  
Anisotropy Constant ◽  
Diffraction Peak ◽  
Polycrystalline Materials ◽  
Ionic Crystals ◽  
Strain Anisotropy ◽  
Cubic Crystals ◽  
Lattice Distortions

Diffraction peak profiles broaden due to the smallness of crystallites and the presence of lattice defects. Strain broadening of powders of polycrystalline materials is often anisotropic in terms of the hkl indices. This kind of strain anisotropy has been shown to be well interpreted assuming dislocations as one of the major sources of lattice distortions. The knowledge of the dislocation contrast factors are inevitable for this interoperation. In a previous work the theoretical contrast factors were evaluated for cubic crystals for elastic constants in the Zener constant range 0.5≤Az≤8. A large number of ionic crystals and many refractory metals have elastic anisotropy, Az, well below 0.5. In the present work the contrast factors for this lower anisotropy-constant range are investigated. The calculations and the corresponding peak profile analysis are tested on ball milled PbS and Nb and nanocrystalline CeO2.

Stress determination through diffraction: establishing the link between Kröner and Voigt/Reuss limits

2015 ◽  
Vol 30 (2) ◽  
pp. 99-103 ◽  
Author(s):  
Conal E. Murray ◽  
Jean L. Jordan-Sweet ◽  
Stephen W. Bedell ◽  
E. Todd Ryan
Keyword(s):  
Elastic Constants ◽  
Mechanical Response ◽  
Elastic Anisotropy ◽  
Polycrystalline Materials ◽  
X Rays ◽  
Least Squares Regression ◽  
Multiple Reflections ◽  
Cubic Symmetry ◽  
Grain Interaction ◽  
Eshelby Inclusion

The quantification of stress in polycrystalline materials by diffraction-based methods relies on the proper choice of grain interaction model that links the observed strain to the elastic stress state in the aggregate. X-ray elastic constants (XEC) relate the strain as measured using X-rays to the state of stress in a quasi-isotropic ensemble of grains. However, the corresponding interaction models (e.g., Voigt and Reuss limits) often possess unlikely assumptions as to mechanical response of the individual grains. The Kröner limit, which employs a self-consistent scheme based on the Eshelby inclusion method, is based on a more physical representation of isotropic grain interaction. For polycrystalline aggregates composed of crystals with cubic symmetry, Kröner limit XEC are equal to those calculated from a linear combination of Reuss and Voigt XEC, where the weighting fraction, xKr, is solely a function of the single-crystal elastic constants and scales with the material's elastic anisotropy. This weighting fraction can also be experimentally determined using a linear, least-squares regression of diffraction data from multiple reflections. Data on metallic thin films reveals that this optimal experimental weighting fraction, x*, can vary significantly from xKr, as well as that of the Neerfeld limit (x = 0.5).

scholarly journals Determining elastic anisotropy of textured polycrystals using resonant ultrasound spectroscopy

2021 ◽  
Vol 56 (16) ◽  
pp. 10053-10073
Author(s):  
Jordan A. Evans ◽  
Blake T. Sturtevant ◽  
Bjørn Clausen ◽  
Sven C. Vogel ◽  
Fedor F. Balakirev ◽  
...  
Keyword(s):  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Ultrasonic Pulse ◽  
Polycrystalline Materials ◽  
Induced Anisotropy ◽  
Resonant Ultrasound Spectroscopy ◽  
Aluminum Single Crystal ◽  
Resonant Ultrasound ◽  
Pulse Echo

AbstractPolycrystalline materials can have complex anisotropic properties depending on their crystallographic texture and crystal structure. In this study, we use resonant ultrasound spectroscopy (RUS) to nondestructively quantify the elastic anisotropy in extruded aluminum alloy 1100-O, an inherently low-anisotropy material. Further, we show that RUS can be used to indirectly provide a description of the material’s texture, which in the present case is found to be transversely isotropic. By determining the entire elastic tensor, we can identify the level and orientation of the anisotropy originated during extrusion. The relative anisotropy of the compressive (c11/c33) and shear (c44/c66) elastic constants is 1.5% ± 0.5% and 5.7% ± 0.5%, respectively, where the elastic constants (five independent elastic constants for transversely isotropic) are those associated with the extrusion axis that defines the symmetry of the texture. These results indicate that the texture is expected to have transversely isotropic symmetry. This finding is confirmed by two additional approaches. First, we confirm elastic constants and the degree of elastic anisotropy by direct sound velocity measurements using ultrasonic pulse echo. Second, neutron diffraction (ND) data confirm the symmetry of the bulk texture consistent with extrusion-induced anisotropy, and polycrystal elasticity simulations using the elastic self-consistent model with input from ND textures and aluminum single-crystal elastic constants render similar levels of polycrystal elastic anisotropy to those measured by RUS. We demonstrate the ability of RUS to detect texture-induced anisotropy in inherently low-anisotropy materials. Therefore, as many other common materials have intrinsically higher elastic anisotropy, this technique should be applicable for similar levels of texture, providing an efficient general diagnostic and characterization tool.

Different Grain Interaction Models Used for Interpretation of Lattice Strain Data Collected Using Grazing Incidence X-Ray Diffraction

2013 ◽  
Vol 768-769 ◽  
pp. 26-30
Author(s):  
Marianna Marciszko ◽  
Andrzej Baczmański ◽  
Mirosław Wróbel ◽  
Wilfrid Seiler ◽  
Chedly Braham ◽  
...  
Keyword(s):  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Grazing Incidence ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
Surface Layers ◽  
X Ray ◽  
Grain Interaction ◽  
Ni Alloy ◽  
Strain Data

Multireflection grazing incidence X-ray diffraction (MGIXD) was applied to measure residual stresses in thin surface layers and the problem of X-ray elastic constants (XEC) used for the interpretation of results was studied. To show the influence of the X-ray elastic constants on the interpretation of MGIDX results, polycrystalline materials having low (Ti alloy) and high elastic anisotropy of crystallites (Ni alloy) were investigated.

Structural, Electronic, and Mechanical Properties of CoN and NiN: An Ab Initio Study

2017 ◽  
Vol 72 (4) ◽  
pp. 321-330 ◽  
Author(s):  
A. Amudhavalli ◽  
M. Manikandan ◽  
A. Jemmy Cinthia ◽  
R. Rajeswarapalanichamy ◽  
K. Iyakutti
Keyword(s):  
Elastic Constants ◽  
Electronic Structures ◽  
Elastic Anisotropy ◽  
Structural Phase ◽  
Lattice Parameter ◽  
Stable Phase ◽  
Ab Initio Study ◽  
Zinc Blende ◽  
Experimental Values ◽  
Parameter Values

AbstractThe structural stabilities of cobalt mononitride (CoN) and nickel mono-nitride (NiN) were investigated among the crystal structures, namely, NaCl (B1), CsCl (B2), and zinc blende (B3). It was found that the zinc blende (B3) phase was the most stable phase for both nitrides. A pressure-induced structural phase transition from B3 to B1 phase was predicted in these nitrides. The computed lattice parameter values were in agreement with the experimental values and other theoretical values. The electronic structures reveal that these nitrides are metallic at zero pressure. The computed elastic constants indicate that CoN and NiN are mechanically stable in the B1 and B3 phases. The variations of the elastic constants, bulk modulus, shear modulus, Poisson’s ratio, and elastic anisotropy factor with pressure were investigated. The Debye temperature θD values are reported for both the nitrides in their B1 and B3 phases. The high-pressure NaCl phase of both CoN and NiN were found to be ferromagnetic.

scholarly journals The Elastic Constants of the Single Crystal of the Mg-Zn-Zr-REM Alloy from the Data of the Elastic Anisotropy and the Texture of the Polycrystalline Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
S. V. San’kova ◽  
N. M. Shkatulyak ◽  
V. V. Usov ◽  
N. A. Volchok
Keyword(s):  
Single Crystals ◽  
Young’S Modulus ◽  
Elastic Constants ◽  
Elastic Anisotropy ◽  
Young's Modulus ◽  
Rare Earth Metals ◽  
Alloy Sheet ◽  
Pole Figures ◽  
Integral Characteristics ◽  
Experimental Values

The measuring of the constants of single-crystals requires the availability of crystals of relatively big size. In this paper the elastic constants of the single crystals of magnesium alloy with zinc, zirconium, and rare earth metals (REM) were determined by means of the experimental anisotropy of Young’s modulus and integral characteristics of texture (ICT), which were found from pole figures. Using these constants the anisotropy of Young’s modulus of alloy sheet ZE10 was calculated. Deviation of calculated values from experimental values did not exceed 2%.

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