A Polynomial Extrapolation Method for Finding Limits and Antilimits of Vector Sequences

1976 ◽  
Vol 13 (5) ◽  
pp. 734-752 ◽  
Author(s):  
S. Cabay ◽  
L. W. Jackson
Keyword(s):  
Extrapolation Method ◽  
Polynomial Extrapolation ◽  
Vector Sequences

Polynomial Extrapolation Method

2011 ◽  
pp. 137-142
Author(s):  
Zhizhong Sun ◽  
Xiaoping Niu ◽  
Henry Hu
Keyword(s):  
Extrapolation Method ◽  
Polynomial Extrapolation

point-Analysis Using the Extrapolation Method in the Analytical Electron microscope

1990 ◽  
Vol 48 (2) ◽  
pp. 430-431
Author(s):  
Zenji Horita ◽  
Ryuzo Nishimachi ◽  
Takeshi Sano ◽  
Minoru Nemoto
Keyword(s):  
Electron Microscope ◽  
Extrapolation Method ◽  
X Ray ◽  
Absorption Correction ◽  
Point Analysis ◽  
Analytical Electron ◽  
Analytical Electron Microscope ◽  
Data Points ◽  
Identical Composition ◽  
X Ray Absorption

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.

Quantitative x-ray microanalysis and thickness determination using ζ factor

1996 ◽  
Vol 54 ◽  
pp. 580-581
Author(s):  
M. Watanabe ◽  
Z. Horita ◽  
M. Nemoto
Keyword(s):  
Diffusion Couple ◽  
Extrapolation Method ◽  
Thin Specimen ◽  
Beam Position ◽  
X Ray ◽  
Thickness Determination ◽  
Experimental Limitation ◽  
X Ray Absorption

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.

Sign in / Sign up

Export Citation Format

Share Document