scholarly journals Influence of Microstructure on Synchrotron X-ray Diffraction Lattice Strain Measurement Uncertainty

Metals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 774
Author(s):  
Chris A. Simpson ◽  
David M. Knowles ◽  
Mahmoud Mostafavi
Keyword(s):  
Measurement Uncertainty ◽  
Strain Measurement ◽  
Lattice Strain ◽  
Strain Tensor ◽  
Measurement Data ◽  
Diffraction Peak ◽  
X Ray Diffraction ◽  
X Ray ◽  
Lattice Planes ◽  
Sampling Statistics

Accurate residual lattice strain measurements are highly dependent upon the precision of the diffraction peak location and the underlying microstructure suitability. The suitability of the microstructure is related to the requirement for valid powder diffraction sampling statistics and the associated number of appropriately orientated illuminated. In this work, these two sources of uncertainty are separated, and a method given for both the quantification of errors associated with insufficient grain sampling statistics and minimization of the total lattice strain measurement uncertainty. It is possible to reduce the total lattice strain measurement uncertainty by leveraging diffraction peak measurements made at multiple azimuthal angles. Lattice strain measurement data acquired during eight synchrotron X-ray diffraction experiments, monochromatic and energy dispersive, has been assessed as per this approach, with microstructural suitability being seen to dominate total measurement uncertainty when the number of illuminated grains was <106. More than half of the studied experimental data fell into this category, with a severe underestimation of total strain measurement uncertainty being possible when microstructural suitability is not considered. To achieve a strain measurement uncertainty under 10−4, approximately 3×105 grains must be within the sampled gauge volume, with this value varying with the multiplicity of the family of lattice planes under study. Where additional azimuthally arrayed data are available an in-plane lattice strain tensor can be extracted. This improves overall strain measurement accuracy and an uncertainty under 10−4 can then be achieved with just 4×104 grains.

Crystallite size and lattice strain of lithiated spinel material for rechargeable battery by X-ray diffraction peak-broadening analysis

2019 ◽  
Vol 43 (5) ◽  
pp. 1903-1911 ◽  
Author(s):  
Ahmed A. Al-Tabbakh ◽  
Nilgun Karatepe ◽  
Aseel B. Al-Zubaidi ◽  
Aida Benchaabane ◽  
Natheer B. Mahmood
Keyword(s):  
Crystallite Size ◽  
Lattice Strain ◽  
Diffraction Peak ◽  
Rechargeable Battery ◽  
X Ray Diffraction ◽  
X Ray ◽  
Peak Broadening

Characterizations of Mg Implanted GaN

1997 ◽  
Vol 482 ◽  
Author(s):  
Gou-Chung Chi ◽  
B. J. Pong ◽  
C. J. Pan ◽  
Y. C. Teng ◽  
C. H. Lee
Keyword(s):  
Small Angle ◽  
Lattice Strain ◽  
Structural Characteristics ◽  
Diffraction Method ◽  
Diffraction Peak ◽  
X Ray Diffraction ◽  
Green Band ◽  
Structure Defects ◽  
X Ray ◽  
Shoulder Peak

AbstractWith 150KeV Mg+ ion implantation, the optical and structural characteristics of GaN films were studied. Post-implant annealing up to 1000°C was performed in N2 ambient with a rapid thermal annealing (RTA) system, without an encapsulation layer. We observed a green band photoluminescence from Mg-implanted GaN. This green band photoluminescence should be associated with Mg induced defect-clustering in GaN. We also use the x-ray diffraction method to study the correlation between structure defects and implantation. We observed an extra shoulder peak at the small angle side of the GaN[0004] diffraction peak. The origin of this shoulder may be attributed to implanted magnesium induced GaN lattice strain.

scholarly journals Lattice strain and tilt mapping in stressed Ge microstructures using X-ray Laue micro-diffraction and rainbow filtering

2016 ◽  
Vol 49 (5) ◽  
pp. 1402-1411 ◽  
Author(s):  
Samuel Tardif ◽  
Alban Gassenq ◽  
Kevin Guilloy ◽  
Nicolas Pauc ◽  
Guilherme Osvaldo Dias ◽  
...  
Keyword(s):  
Strain Measurement ◽  
Lattice Strain ◽  
Strain Tensor ◽  
Orientation Distribution ◽  
Numerical Approach ◽  
Biaxial Stress ◽  
Lattice Orientation ◽  
Strain Mapping ◽  
X Ray ◽  
Highly Strained

Laue micro-diffraction and simultaneous rainbow-filtered micro-diffraction were used to measure accurately the full strain tensor and the lattice orientation distribution at the sub-micrometre scale in highly strained, suspended Ge micro-devices. A numerical approach to obtain the full strain tensor from the deviatoric strain measurement alone is also demonstrated and used for faster full strain mapping. The measurements were performed in a series of micro-devices under either uniaxial or biaxial stress and an excellent agreement with numerical simulations was found. This shows the superior potential of Laue micro-diffraction for the investigation of highly strained micro-devices.

scholarly journals Micro-beam Laue alignment of multi-reflection Bragg coherent diffraction imaging measurements

2017 ◽  
Vol 24 (5) ◽  
pp. 1048-1055 ◽  
Author(s):  
Felix Hofmann ◽  
Nicholas W. Phillips ◽  
Ross J. Harder ◽  
Wenjun Liu ◽  
Jesse N. Clark ◽  
...  
Keyword(s):  
Focused Ion Beam ◽  
Lattice Strain ◽  
Ion Beam ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Stress Fields ◽  
X Ray Diffraction ◽  
X Ray ◽  
Coherent Diffraction Imaging ◽  
Diffraction Imaging

Multi-reflection Bragg coherent diffraction imaging has the potential to allow three-dimensional (3D) resolved measurements of the full lattice strain tensor in specific micro-crystals. Until now such measurements were hampered by the need for laborious, time-intensive alignment procedures. Here a different approach is demonstrated, using micro-beam Laue X-ray diffraction to first determine the lattice orientation of the micro-crystal. This information is then used to rapidly align coherent diffraction measurements of three or more reflections from the crystal. Based on these, 3D strain and stress fields in the crystal are successfully determined. This approach is demonstrated on a focused ion beam milled micro-crystal from which six reflections could be measured. Since information from more than three independent reflections is available, the reliability of the phases retrieved from the coherent diffraction data can be assessed. Our results show that rapid, reliable 3D coherent diffraction measurements of the full lattice strain tensor in specific micro-crystals are now feasible and can be successfully carried out even in heavily distorted samples.

Microstructure and strain in electrodeposited Cu/Ni multilayers

1996 ◽  
Vol 11 (11) ◽  
pp. 2825-2833 ◽  
Author(s):  
David van Heerden ◽  
Emil Zolotoyabko ◽  
Dan Shechtman
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Computer Simulations ◽  
Lattice Strain ◽  
Strain Relaxation ◽  
Diffraction Peak ◽  
X Ray Diffraction ◽  
Interfacial Dislocation ◽  
X Ray ◽  
Transmission Electron

Electrodeposited Cu/Ni multilayers with different modulation lengths Λ = 4–18 nm were examined by means of x-ray diffraction and transmission electron microscopy. Preferred orientations of [111], [110], and [001]-types, as determined from relative x-ray diffraction peak intensities, were seen in the multilayers. By means of computer simulations of the measured x-ray diffraction spectra, several parameters of the multilayers, such as Λ-values and fluctuations ΔΛ, as well as lattice strain, were determined. Multilayers having large Λ were found to be fully relaxed due to interfacial dislocation formation. In short Λ [001]-texture multilayers partial strain relaxation occurs, probably due to the incorporation of Cu into the Ni layers. Both of the processes lead to the diffuse Cu/Ni interfaces. Short wavelength multilayers with a [111]-preferred orientation were almost fully strained. The importance of the [111]-texture in the improvement of mechanical strength of Cu/Ni multilayers resulting from its enhanced ability for stain accommodation is discussed.

X-ray diffraction peak broadening and lattice strain in LaNi5-based alloys

2000 ◽  
Vol 298 (1-2) ◽  
pp. 138-145 ◽  
Author(s):  
Yumiko Nakamura ◽  
Keisuke Oguro ◽  
Itsuki Uehara ◽  
Etsuo Akiba
Keyword(s):  
Lattice Strain ◽  
Diffraction Peak ◽  
X Ray Diffraction ◽  
X Ray ◽  
Peak Broadening

scholarly journals Simultaneous Multi-Bragg Peak Coherent X-ray Diffraction Imaging

Crystals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 312
Author(s):  
Florian Lauraux ◽  
Stéphane Labat ◽  
Sarah Yehya ◽  
Marie-Ingrid Richard ◽  
Steven J. Leake ◽  
...  
Keyword(s):  
Bragg Reflection ◽  
Volume Ratio ◽  
X Ray Diffraction ◽  
X Ray ◽  
Crystal Substrate ◽  
In Series ◽  
Diffraction Imaging ◽  
Diffraction Patterns ◽  
Lattice Planes ◽  
Oriented Parallel

The simultaneous measurement of two Bragg reflections by Bragg coherent X-ray diffraction is demonstrated on a twinned Au crystal, which was prepared by the solid-state dewetting of a 30 nm thin gold film on a sapphire substrate. The crystal was oriented on a goniometer so that two lattice planes fulfill the Bragg condition at the same time. The Au 111 and Au 200 Bragg peaks were measured simultaneously by scanning the energy of the incident X-ray beam and recording the diffraction patterns with two two-dimensional detectors. While the former Bragg reflection is not sensitive to the twin boundary, which is oriented parallel to the crystal–substrate interface, the latter reflection is only sensitive to one part of the crystal. The volume ratio between the two parts of the twinned crystal is about 1:9, which is also confirmed by Laue microdiffraction of the same crystal. The parallel measurement of multiple Bragg reflections is essential for future in situ and operando studies, which are so far limited to either a single Bragg reflection or several in series, to facilitate the precise monitoring of both the strain field and defects during the application of external stimuli.

scholarly journals X-ray imaging of silicon die within fully packaged semiconductor devices

2021 ◽  
pp. 1-7
Author(s):  
Brian K. Tanner ◽  
Patrick J. McNally ◽  
Andreas N. Danilewsky
Keyword(s):  
Synchrotron Radiation ◽  
Feasibility Studies ◽  
Monochromatic Radiation ◽  
X Ray Diffraction ◽  
Divergent Beam ◽  
X Ray ◽  
X Ray Imaging ◽  
Setting Process ◽  
Diffraction Imaging ◽  
Lattice Planes

X-ray diffraction imaging (XRDI) (topography) measurements of silicon die warpage within fully packaged commercial quad-flat no-lead devices are described. Using synchrotron radiation, it has been shown that the tilt of the lattice planes in the Analog Devices AD9253 die initially falls, but after 100 °C, it rises again. The twist across the die wafer falls linearly with an increase in temperature. At 200 °C, the tilt varies approximately linearly with position, that is, displacement varies quadratically along the die. The warpage is approximately reversible on cooling, suggesting that it has a simple paraboloidal form prior to encapsulation; the complex tilt and twisting result from the polymer setting process. Feasibility studies are reported, which demonstrate that a divergent beam and quasi-monochromatic radiation from a sealed X-ray tube can be used to perform warpage measurements by XRDI in the laboratory. Existing tools have limitations because of the geometry of the X-ray optics, resulting in applicability only to simple warpage structures. The necessary modifications required for use in situations of complex warpage, for example, in multiple die interconnected packages are specified.

Problems Associated with Kα Doublet in Residual Stress Measurements

1979 ◽  
Vol 23 ◽  
pp. 333-339
Author(s):  
S. K. Gupta ◽  
B. D. Cullity
Keyword(s):  
Residual Stress ◽  
Silicon Powder ◽  
Lattice Parameter ◽  
Diffraction Peak ◽  
Parameter Determination ◽  
X Ray Diffraction ◽  
X Ray ◽  
Analysis Techniques ◽  
The Difference ◽  
Similar Accuracy

Since the measurement of residual stress by X-ray diffraction techniques is dependent on the difference in angle of a diffraction peak maximum when the sample is examined consecutively with its surface at two different angles to the diffracting planes, it is important that these diffraction angles be obtained precisely, preferably with an accuracy of ± 0.01 deg. 2θ. Similar accuracy is desired in precise lattice parameter determination. In such measurements, it is imperative that the diffractometer be well-aligned. It is in the context of diffractometer alignment with the aid of a silicon powder standard free of residual stress that the diffraction peak analysis techniques described here have been developed, preparatory to residual stress determinations.

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