scholarly journals Defocused travelling fringes in a scanning triple-Laue X-ray interferometry setup

2021 ◽  
Vol 54 (5) ◽  
pp. 1403-1408
Author(s):  
C. P. Sasso ◽  
G. Mana ◽  
E. Massa
Keyword(s):  
Measurement Accuracy ◽  
Systematic Errors ◽  
Lattice Parameter ◽  
Silicon Lattice ◽  
X Ray ◽  
Interference Fringes ◽  
Reliable Model ◽  
The Difference ◽  
Separate Crystal

The measurement of the silicon lattice parameter by a separate-crystal triple-Laue X-ray interferometer is a key step for the realization of the kilogram by counting atoms. Since the measurement accuracy is approaching nine significant digits, a reliable model of the interferometer operation is required to quantify or exclude systematic errors. This paper investigates both analytically and experimentally the effect of the defocus (the difference between the splitter-to-mirror and analyser-to-mirror distances) on the phase of the interference fringes and the measurement of the lattice parameter.

Precision Lattice Parameter Measurements with Guinier Camera and Counter Diffractometer: Comparison and Reconciliation of Results

1982 ◽  
Vol 26 ◽  
pp. 11-24 ◽  
Author(s):  
Allan Brown
Keyword(s):  
Measurement Errors ◽  
Systematic Errors ◽  
Lattice Parameter ◽  
Precision Measurements ◽  
Compound A ◽  
X Ray ◽  
Random Measurement ◽  
Precise Characterization ◽  
The Difference

Different procedures used in precision measurements of lattice parameters are, strictly, only valid if they can be shown to give results that are mutually reproducible. For this purpose reproducibility is defined in terms of the parameters a. and standard deviations a. obtained for X-ray specimens of one or more reference materials. The requirement is that all systematic errors should be minimized to a level below that of the random measurement errors. Where these have a Gaussian distribution the significance of the difference, Δa°, between two , measurements can then be Let;Led by evaluating . Thus, if K < 2 the difference, Δa°, cannot be distinguished from the effects of random measurement errors. This condition should be met for specimens of the same sample if reproducibility is good. For K ≥ 3 the value of Δa° is then taken to reflect real differences in the crystalline Jattice of two X-ray specimens of a given compound. A basis is thus created for the study of solid solubility and for the precise characterization of crystalline compounds.

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.

Measurement of the Silicon Lattice Parameter by Scanning Single Photon X-Ray Interferometry

2018 ◽  
Author(s):  
Ulrich Kuetgens ◽  
Birk Andreas ◽  
Kathrin Friedrich ◽  
Christoph Weichert ◽  
Paul Kochert ◽  
...  
Keyword(s):  
Single Photon ◽  
Lattice Parameter ◽  
Silicon Lattice ◽  
X Ray

An Experimental Examination of Error Functions for Bragg-Brentano Powder Diffractometry

1992 ◽  
Vol 36 ◽  
pp. 663-670 ◽  
Author(s):  
H.W. King ◽  
E.A. Payzant
Keyword(s):  
High Temperature ◽  
Systematic Errors ◽  
Lattice Parameter ◽  
Parameter Determination ◽  
Experimental Examination ◽  
X Ray ◽  
Error Functions ◽  
Computer Methods ◽  
Single Function ◽  
High Temperature Furnaces

AbstractA single function for the elimination of errors in precision lattice parameter determination has not been developed for the Bragg-Brentano x-ray diffractometer method, because of the different angular dependencies of the systematic errors. A review of the error functions shows that all but one can be calculated from the instrumental settings and known properties of a sample under investigation. The residual sample displacement error can be then be eliminated by using extrapolation plots or computer methods to correct the data to cosθcotθ plots. The slopes of cosθcotθ plots can also be used to align high temperature furnaces and low temperature cryostats mounted on x-ray diffractometers.

High-precision absolute lattice parameter determination of SrTiO3, DyScO3 and NdGaO3 single crystals

2012 ◽  
Vol 68 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Martin Schmidbauer ◽  
Albert Kwasniewski ◽  
Jutta Schwarzkopf
Keyword(s):  
High Resolution ◽  
High Precision ◽  
Room Temperature ◽  
Systematic Errors ◽  
Lattice Parameter ◽  
Parameter Determination ◽  
X Ray Diffraction ◽  
X Ray ◽  
Bond Method

The lattice parameters of three perovskite-related oxides have been measured with high precision at room temperature. An accuracy of the order of 10−5 has been achieved by applying a sophisticated high-resolution X-ray diffraction technique which is based on the modified Bond method. The results on cubic SrTiO3 [a = 3.905268 (98) Å], orthorhombic DyScO3 [a = 5.442417 (54), b = 5.719357 (52) and c = 7.904326 (98) Å], and orthorhombic NdGaO3 [a = 5.428410 (54), b = 5.498407 (55) and c = 7.708878 (95) Å] are discussed in view of possible systematic errors as well as non-stoichiometry in the crystals.

A study of the local atomic structure in Hg0.80Cd0.20Te using x-ray diffuse scattering

1993 ◽  
Vol 8 (4) ◽  
pp. 855-863 ◽  
Author(s):  
J.P. Quintana ◽  
J.B. Cohen
Keyword(s):  
Diffuse Scattering ◽  
Volume Measurement ◽  
Lattice Parameter ◽  
Near Neighbor ◽  
Cation Sublattice ◽  
Thermal Diffuse Scattering ◽  
X Ray ◽  
X Ray Scattering ◽  
The Difference ◽  
Thermal Diffuse

The local atomic arrangements in a commercial n-type wafer of Hg0.8Cd0.8Te were investigated by measuring the diffuse x-ray scattering in two volumes in reciprocal space. A change in contrast between the two measurements was achieved by making one volume measurement at 12037 eV and a second volume measurement at 12270 eV, i.e., near the HgLIII edge. The difference between these two measurements yielded intensity only due to Hg–Hg, Hg–Te, and Hg–Cd pair interactions. In all three patterns, peak-like features were apparent at the forbidden Bragg peak positions on thermal diffuse scattering ridges that joined major Bragg reflections; these are primarily attributed to second order displacement effects on the mixed cation sublattice. The first two Warren–Cowley short-range order parameters were determined to be α½½0 = −0.050(26) and α110 = 0.118(35). Simulations of the structure revealed small ordered regions with a preference for 3:1 Hg–Cd near-neighbor configurations. The near-neighbor Hg–Te bonds contract from that calculated from the average crystal's lattice parameter, and this Hg–Te distance is less than the distance in HgTe.

Improved Techniques of Lattice Parameter Measurements Using two X-Ray Beams

1972 ◽  
Vol 16 ◽  
pp. 367-378 ◽  
Author(s):  
Seigo Kishino
Keyword(s):  
Gallium Arsenide ◽  
Gallium Phosphide ◽  
Lattice Parameter ◽  
Perfect Crystal ◽  
Double Crystal ◽  
X Ray ◽  
Gallium Arsenide Phosphide ◽  
The Difference ◽  
The One ◽  
Crystal Arrangement

AbstractTwo kinds of improved techniques are described for precise measurement of lattice parameters with an accuracy of 1 ∼7x10-5, in both of which a differenoe of Bragg angles between two X-ray beams such as K α1 and K β1 is measured.In the first technique, which was applied to relatively imperfect crystals such as gallium arsenide, gallium arsenide phosphide, and gallium phosphide, two different diffraction planes were utilized for two radiations such as CuK α1 and CuK β1 in order to reduce the difference of the Bragg angles to the order of several minutes of arc.In the second technique, which was applied to a nearly perfect crystal such as silicon, a double crystal arrangement of parallel setting was used, where lattice parameter of the specimen was relatively measured in comparison with the one of the first crystal which was known beforehand.

Scanning X-ray interferometry and the silicon lattice parameter: towards relative uncertainty?

1999 ◽  
Vol 9 (2) ◽  
pp. 225-232 ◽  
Author(s):  
A. Bergamin ◽  
G. Cavagnero ◽  
G. Mana ◽  
G. Zosi
Keyword(s):  
Lattice Parameter ◽  
Relative Uncertainty ◽  
Silicon Lattice ◽  
X Ray

Application of convergent-beam illumination methods to the study of lattice distortion across the interface

1992 ◽  
Vol 50 (1) ◽  
pp. 232-233
Author(s):  
Zuzanna Liliental-Weber ◽  
T. Kaneyama ◽  
M. Terauchi ◽  
M. Tanaka
Keyword(s):  
Spatial Resolution ◽  
Lattice Distortion ◽  
Large Angle ◽  
Lattice Parameter ◽  
Gaas Layer ◽  
X Ray Diffraction ◽  
X Ray ◽  
Accuracy Measurement ◽  
The Difference ◽  
Convergent Beam

A high accuracy measurement of the lattice parameter can be obtained by x-ray diffraction. However, these methods have low spatial resolution and are limited by sample thickness. Therefore, for heterolayers much better information about local distortions near the interface can be obtained by electron microscopy using convergent-beam illumination. Large-angle convergent-beam electron diffraction (LACBED) patterns and convergent-beam imaging (CBIM) were applied to study of the lattice distortion across the interface of the GaAs epilayer grown on [001] GaAs substrate and the GaAs layer grown at 200°C (called the low-temperature (LT) layer). These LT GaAs layers are grown by molecular beam epitaxy from As oversaturation and are known to be As rich. Particle-induced x-ray studies reveal up to 1.5 % extra As. This excess As leads to the expansion of the lattice parameter up to 0.15% when measured by x-ray diffraction along the (004) reflection. From this study, it was expected that a cubic expansion of the lattice parameter would be equal in all three directions. However, TEM studies do not reveal the formation of dislocations at the interface, which would be expected taking into account the difference in the lattice parameter across the interface . Convergence beam illumination methods were applied to study in detail the strain, lattice parameter variation, and crystallographic distortion across the interface, since these methods have spatial resolution several orders of magnitude higher than x-ray diffraction. A CBED pattern taken in the substrate and in the layer with an incidence close to the [530] direction (exact orientation [0.869 0.495 0]) reveals the lattice parameter change, since the position of the cross of the 1113 and 1113 lines changes when an electron beam is placed in the substrate and the layer, respectively (Fig. la,b).

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