On the calibration of high-energy X-ray diffraction setups. II. Assessing the rotation axis and residual strains

2014 ◽  
Vol 47 (5) ◽  
pp. 1585-1595 ◽  
Author(s):  
Andras Borbély ◽  
Loïc Renversade ◽  
Peter Kenesei
Keyword(s):  
Residual Strain ◽  
Rotation Axis ◽  
Strain Tensor ◽  
High Energy ◽  
Laboratory Frame ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cell Parameters ◽  
Area Detector ◽  
Residual Strains

The calibration of high-energy X-ray diffraction setups using an area detector and a rotation axis is discussed. The characterization of the tilt and spatial distortions of an area detector was discussed in part one of this series [Borbély, Renversade, Kenesei & Wright (2014).J. Appl. Cryst.47, 1042–1053]. Part II links the detector frame to the laboratory frame comprising an additional rotation axis and introduces a general diffractometer equation accounting for all sources of misalignment. Additionally, an independent high-accuracy method for the evaluation of the crystallographic orientation and cell parameters of the undeformed reference crystal is presented. Setup misalignments are mainly described in terms of a residual strain tensor, considered as a quality label of the diffractometer. The method is exemplified using data sets acquired at beamlines ID11 (European Synchrotron Radiation Facility) and 1-ID (Advanced Photon Source) on Al and W single crystals, respectively. The results show that the residual strain tensor is mainly determined by the detector spatial distortion, and values as small as 1–2 × 10−4can be practically achieved.

On the calibration of high-energy X-ray diffraction setups. I. Assessing tilt and spatial distortion of the area detector

2014 ◽  
Vol 47 (3) ◽  
pp. 1042-1053 ◽  
Author(s):  
Andras Borbely ◽  
Loic Renversade ◽  
Peter Kenesei ◽  
Jonathan Wright
Keyword(s):  
Rotation Axis ◽  
Strain Tensor ◽  
Calibration Procedure ◽  
High Energy ◽  
European Synchrotron Radiation Facility ◽  
Data Sets ◽  
X Ray Diffraction ◽  
Spatial Distortion ◽  
X Ray ◽  
Area Detector

The geometry of high-energy X-ray diffraction setups using an area detector and a rotation axis is analysed. The present paper (part 1) describes the methodology for determining continuously varying spatial distortions and tilt of the area detector based on the reference diffraction rings of a certified powder. Analytical expressions describing the degeneration of Debye rings into ellipses are presented and a robust calibration procedure is introduced. It is emphasized that accurate detector calibration requires the introduction of spatial distortion into the equation describing the tilt. The method is applied to data sets measured at the Advanced Photon Source and at the European Synchrotron Radiation Facility using detectors with different physical characteristics, the GE 41RT flat-panel and the FReLoN4M detector, respectively. The spatial distortion of the detectors is compared with regard to their use in structural and strain tensor analysis, a subject treated in part 2 of the calibration work [Borbély, Renversade & Kenesei (2014).J. Appl. Cryst.Submitted].

scholarly journals Microstructural Evolution and Strain Development in Metal Matrix Composites

2014 ◽  
Vol 996 ◽  
pp. 936-943 ◽  
Author(s):  
Guillaume Geandier ◽  
Lilian Vautrot ◽  
Matthieu Salib ◽  
Mickael Mourot ◽  
Moukrane Dehmas ◽  
...  
Keyword(s):  
Mass Fraction ◽  
High Energy ◽  
Elastic Stiffness ◽  
Steel Matrix ◽  
Matrix Composites ◽  
Mechanical State ◽  
X Ray Diffraction ◽  
Strain Development ◽  
X Ray ◽  
Cell Parameters

Composite materials present interesting mechanical properties. The metal provides the toughness and the particles are adding elastic stiffness, strength, hardness and wear resistance. High energy X-ray diffraction has been used to characterize the microstructure evolution of two types of MMCs (titanium and steel matrix) reinforced with TiC particles.Evolutions of mass fraction and mean cell parameters shows the effect of reinforcement on the kinetics and mechanical state of the final composites.

Evaluation of grain-average stress tensor in a tensile-deformed Al–Mn polycrystal by high-energy X-ray diffraction

2017 ◽  
Vol 50 (4) ◽  
pp. 1144-1157 ◽  
Author(s):  
Loïc Renversade ◽  
András Borbély
Keyword(s):  
Rotation Axis ◽  
Three Dimensional ◽  
Calibration Method ◽  
High Energy ◽  
Normal Strain ◽  
X Ray Diffraction ◽  
Synchrotron Source ◽  
X Ray ◽  
Strain Stress ◽  
Individual Grains

Three-dimensional X-ray diffraction was applied to characterize the strain/stress evolution in individual grains of an Al–0.3 wt% Mn polycrystal deformedin situat a synchrotron source. Methodological aspects concerning the calibration of the geometrical setup and the evaluation of the strain/stress tensors are discussed. A two-step calibration method separately treating the detector and the rotation axis allows one to determine the centre-of-mass position and crystallographic orientation of grains with standard errors of about 1.5 µm and 0.02°, respectively. Numerical simulations indicate that the error of normal strain components (about 1 × 10−4) is mainly caused by calibration errors, while the error of shear components (about 0.5 × 10−4) is largely influenced by counting statistics and random spot-centre errors due to detector distortion. The importance of monitoring the beam energy is emphasized.

In Situ Structural Evolution of Steel-Based MMC by High Energy X-Ray Diffraction and Comparison with Micromechanical Approach

2013 ◽  
Vol 768-769 ◽  
pp. 313-320 ◽  
Author(s):  
Guillaume Geandier ◽  
Moukrane Dehmas ◽  
Mickael Mourot ◽  
Elisabeth Aeby-Gautier ◽  
Sabine Denis ◽  
...  
Keyword(s):  
Phase Transformation ◽  
Coefficient Of Thermal Expansion ◽  
Hydrostatic Stress ◽  
Structural Evolution ◽  
High Energy ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cell Parameters ◽  
The Matrix

In situ high energy X-ray diffraction synchrotron was used to provide direct analysis of the transformation sequences in steel-based matrix composite (MMC) reinforced with TiC particles. Evolution of the phase fractions of the matrix and TiC particles as well as the mean cell parameters of each phase were determined by Rietveld refinement from high energy X-ray diffraction (ID15B, ESRF, Grenoble, France). In addition, some peaks were further analysed in order to obtain the X-ray strain during the cooling step. Non-linear strain evolutions of each phase are evidenced, which are either associated with differences in the coefficient of thermal expansion (CTE) between matrix and TiC particle or to the occurrence of phase transformation. Micromechanical calculations were performed through the finite element method to estimate the stress state in each phase and outline the effects of differences in CTE and of volume change associated with the matrix phase transformation. The calculated results led to a final compressive hydrostatic stress in the TiC reinforcement and tensile hydrostatic stress in the matrix area around the TiC particles. Besides, the tendencies measured from in situ synchrotron diffraction (mean cell parameters) matched with the numerical estimates.

scholarly journals High energy white beam x-ray diffraction studies of residual strains in engineering components

2008 ◽  
Author(s):  
S. Y. Zhang ◽  
W. Vorster ◽  
T. S. Jun ◽  
X. Song ◽  
M. Golshan ◽  
...  
Keyword(s):  
High Energy ◽  
X Ray Diffraction ◽  
X Ray ◽  
White Beam ◽  
Residual Strains

Low Temperature Transformations in β-Metastable Ti 5553 Titanium Alloy

2013 ◽  
Vol 738-739 ◽  
pp. 97-102 ◽  
Author(s):  
A. Settefrati ◽  
E. Aeby-Gautier ◽  
B. Appolaire ◽  
M. Dehmas ◽  
G. Geandier ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Titanium Alloy ◽  
Room Temperature ◽  
Metastable Phase ◽  
High Energy ◽  
Isothermal Transformation ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cell Parameters ◽  
Direct Quenching

Precipitation decomposition in β metastable phase in TI 5553 alloy were characterized by electrical resistivity and high energy X-ray diffraction for two thermal paths, isothermal transformation at 325°C after direct quenching, or cooling to room temperature and further ageing at 325°C. Both treatments led to different transformation sequences with formation of ω and/or α''. Mean cell parameters of β and α'' were characterized all along the transformation. Results suggest a transformation with poor solute partitioning and building of large stresses in each phase.

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