scholarly journals A simple extrapolation method for clustered eigenvalues

Author(s):  
Nilima Nigam ◽  
Sara Pollock
1995 ◽  
Vol 236 (4-5) ◽  
pp. 451-456 ◽  
Author(s):  
B.L. Burrows ◽  
M. Cohen

1992 ◽  
Vol 7 (8) ◽  
pp. 2049-2058 ◽  
Author(s):  
Y. Ma ◽  
J. Gj⊘nnes

The site occupancy of ternary atoms in three L12-structured intermetallic phases, Al62.5+XTi25−Y(Fe, Ni, or Cu)12.5–Z found in three laser processed intermetallic systems was studied by the axial ALCHEMI (Atom Location by Channeling Enhanced Microanalysis). The ternary atoms in all three intermetallic phases were found preferentially to occupy the Al sublattices, although slight differences in occupancy among them were detected. A simple extrapolation method of calculating delocalization correction factors for various characteristic x-ray emissions was described, which was proved to be practically useful in ALCHEMI analyses. In order to compare the axial ALCHEMI analysis with the planar ALCHEMI in an experimental perspective, the planar ALCHEMI analysis was also carried out on the phase alloyed with Cu, which showed results in broad agreement with those of the axial ALCHEMI analysis on the same phase. Nevertheless, owing to much weaker channeling effects the planar ALCHEMI analysis gave apparently worse statistics in its results. In the end, various sources of errors in the ALCHEMI analyses at the present stage are discussed.


Author(s):  
Zenji Horita ◽  
Ryuzo Nishimachi ◽  
Takeshi Sano ◽  
Minoru Nemoto

Absorption correction is often required in quantitative x-ray microanalysis of thin specimens using the analytical electron microscope. For such correction, it is convenient to use the extrapolation method[l] because the thickness, density and mass absorption coefficient are not necessary in the method. The characteristic x-ray intensities measured for the analysis are only requirement for the absorption correction. However, to achieve extrapolation, it is imperative to obtain data points more than two at different thicknesses in the identical composition. Thus, the method encounters difficulty in analyzing a region equivalent to beam size or the specimen with uniform thickness. The purpose of this study is to modify the method so that extrapolation becomes feasible in such limited conditions. Applicability of the new form is examined by using a standard sample and then it is applied to quantification of phases in a Ni-Al-W ternary alloy.The earlier equation for the extrapolation method was formulated based on the facts that the magnitude of x-ray absorption increases with increasing thickness and that the intensity of a characteristic x-ray exhibiting negligible absorption in the specimen is used as a measure of thickness.


Author(s):  
M. Watanabe ◽  
Z. Horita ◽  
M. Nemoto

X-ray absorption in quantitative x-ray microanalysis of thin specimens may be corrected without knowledge of thickness when the extrapolation method or the differential x-ray absorption (DXA) method is used. However, there is an experimental limitation involved in each method. In this study, a method is proposed to overcome such a limitation. The method is developed by introducing the ζ factor and by combining the extrapolation method and DXA method. The method using the ζ factor, which is called the ζ-DXA method in this study, is applied to diffusion-couple experiments in the Ni-Al system.For a thin specimen where incident electrons are fully transparent, the characteristic x-ray intensity generated from a beam position, I, may be represented as I = (NρW/A)Qωaist.


2021 ◽  
Vol 210 ◽  
pp. 143-155
Author(s):  
Zihan Yang ◽  
Zhenghe Song ◽  
Xueyan Zhao ◽  
Xingxiang Zhou

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