Standard Deviations in X-Ray Stress and Elastic Constants Due to Counting Statistics

1989 ◽  
pp. 377-388 ◽  
Author(s):  
Masanori Kurita
1988 ◽  
Vol 32 ◽  
pp. 377-388 ◽  
Author(s):  
Masanori Kurita

AbstractX-ray diffraction can be used to nondestructively measure residual stress of polycrystalline materials. In x-ray stress measurement, it is important to determine a stress constant experimentally in order to measure the stress accurately. However, every value measured by x-ray diffraction has statistical errors arising from counting statistics. The equations for calculating the standard deviations of the stress constant and elastic constants measured by x-rays are derived analytically in order to ascertain the reproducibility of the measured values. These standard deviations represent the size of the variability caused by counting statistics, and can be calculated from a single set of measurements by using these equations. These equations can apply Lu any meuhud for x-ray stress ifiesuremenL. The variances of the x-ray stress and elastic constants are expressed in terms of the linear combinations of the variances of the peak position. The confidence limits of these constants of a quenched and tempered steel specimen were determined by the Gaussian curve method. The 95% confidence limits of the stress constant were -314 ± 25 MFa/deg.


1987 ◽  
Vol 31 ◽  
pp. 245-253 ◽  
Author(s):  
P. J. Rudnik ◽  
A. D. Krawitz ◽  
D. G. Reichel ◽  
J. B. Cohen

AbstractThe diffraction elastic constants have been measured for the 211 and 310 peaks of a high-strength, low-alloy ferritic steel using X-rays and neutrons. The X-ray measurements were performed using both a uniaxial tension and a bending device. The neutron measurements were performed using a uniaxial tensile device. Ten X-ray and four neutron measurements were made for each case. Statistical errors were calculated and compared with the standard deviations of the average values. In addition, neutron measurements were made for the 310 peak utilizing an interior probe volume.The results indicate that the calculated statistical errors and the observed standard deviations were almost the same for each radiation. The X-ray and neutron tensile device measurements yielded similar results within experimental error. Furthermore, the X-ray tensile and bending results were similar as were the neutron internal volume measurements. These results suggest that near-surface X-ray measurements adequately sample the bulk material in the case of steel, and that different measurement techniques can be used to obtain reliable diffraction elastic constants.


2005 ◽  
Vol 96 (9) ◽  
pp. 1069-1073 ◽  
Author(s):  
Ernst Eiper ◽  
Klaus J. Martinschitz ◽  
Jürgen W. Gerlach ◽  
Jürgen M. Lackner ◽  
Ivo Zizak ◽  
...  

2011 ◽  
Vol 67 (5) ◽  
pp. 409-415 ◽  
Author(s):  
Kevin H. Stone ◽  
Dayna L. Turner ◽  
Mayank Pratap Singh ◽  
Thomas P. Vaid ◽  
Peter W. Stephens

The crystal structures of the isostructural title compounds poly[(μ-benzene-1,4-dithiolato)dithallium], Tl2(SC6H4S), and poly[(μ-benzene-1,4-diselenolato)dithallium], Tl2(SeC6H4Se), were solved by simulated annealing from high-resolution synchrotron X-ray powder diffraction. Rietveld refinements of an initial structure with one formula unit per triclinic cell gave satisfactory agreement with the data, but led to a structure with impossibly close non-bonded contacts. A disordered model was proposed to alleviate this problem, but an alternative supercell structure leads to slightly improved agreement with the data. The isostructural superlattice structures were confirmed for both compounds through additional data collection, with substantially better counting statistics, which revealed the presence of very weak superlattice peaks not previously seen. Overall, each structure contains Tl—S or Tl—Se two-dimensional networks, connected by phenylene bridges. The sulfur (or selenium) coordination sphere around each thallium is a highly distorted square pyramid or a `see-saw' shape, depending upon how many Tl—S or Tl—Se interactions are considered to be bonds. In addition, the two compounds contain pairs of TlI ions that interact through a closed-shell `thallophilic' interaction: in the sulfur compound there are two inequivalent pairs of Tl atoms with Tl—Tl distances of 3.49 and 3.58 Å, while in the selenium compound those Tl—Tl interactions are at 3.54 and 3.63 Å.


1994 ◽  
Vol 27 (5) ◽  
pp. 716-722 ◽  
Author(s):  
H. Wang

The influences of step size and scanning speed on the shape of a single X-ray diffraction (XRD) peak are analyzed quantitatively. For this purpose, it is assumed that XRD peak shapes are a mixture of Cauchy and Gauss curves. Six equations are established for the calculation of position, maximum intensity and full width at half-maximum (FWHM) errors caused by step size and two for the FWHM errors caused by counting statistics. The ratio of step size to FWHM is proposed as the shape-perfect coefficient of the XRD peak. From these equations and the relationship between the FWHM and the integral width of a peak based on the pseudo-Voigt function or Voigt function, three basic elements of a single symmetric XRD peak (peak position, maximum intensity and FWHM) can be refined. The optimum step size and scanning time can also be set from them.


1986 ◽  
Vol 25 (Part 1, No. 9) ◽  
pp. 1317-1322 ◽  
Author(s):  
Nobuo Kashiwagura ◽  
Yasuharu Kashihara ◽  
Jimpei Harada

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