3-D Graphing of Xrf Matrix Correction Equations

X-ray spectrometry is an old technique dating back some sixty-odd years and although most of the early interest revolved around the qualitative aspects of the method it wasn't long before attempts were made to obtain quantitative data. One of the first recorded attempts was that by Coster and von Hevesey who in 1923 accurately determined the amount of hafnium in zirconium using tantalum as an internal standard. Glocker and Schreiber were the first to attempt calculation of X-ray characteristic line intensity from first principles although no attempt was made at that time to correct for secondary fluorescence. In von Hevesey's book, “Chemical Analysis by X-Rays,” published in 1932 , a whole chapter is devoted to what is called “Disturbing effects and their avoidance.” Among the effects discussed were primary and secondary absorbtion and third element effects. Matrix correction equations were developed although most of the quantitative work at that time was done using internal standards.

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3-D Graphing of XRF Matrix Correction Equations

Advances in X-ray Analysis ◽

10.1154/s0376030800018358 ◽

1994 ◽

Vol 38 ◽

pp. 649-656

Author(s):

Anthony J. Klimasara

Keyword(s):

Dimensional Space ◽

Correction Term ◽

Three Dimensional ◽

Calibration Plot ◽

Two Dimensional ◽

Matrix Correction ◽

Image Position ◽

Correction Equations ◽

Calibration Plane ◽

Three Dimensional Space

Abstract The Lachance-Traill, and Lucas-Tooth-Price matrix correction equations/functions for XRF determined concentrations can be graphically interpreted with the help of three dimensional graphics. Statistically derived Lachance-Traill and Lucas-Tooth-Price matrix correction equations can be represented as follows: 1 where: Ci -elemental concentration of element “i” Ij -X-Ray intensity representing element “i” Ai0 -regression intercept for element “i” Ai -regression coefficient Zj -correction term defined below 2 Ai0, Aj , and Zi together represent the results of a multi-dimensional contribution. li, Ci, and Zi can be represented in three dimensional Cartesian space by X, Y and Z. These three variables are connected by a matrix correction equation that can be graphed as the function Y = F(X, Z), which represents a plane in three dimensional space. It can be seen that each chemical element will deliver a different set of coefficients in the equation of a plane that is called here a calibration plane. The commonly known and used two dimensional calibration plot is a “shadow” of the three dimensional real calibration points. These real (not shadow) points reside on a regression calibration plane in this three dimensional space. Lachance-Traill and Lucas-Tooth-Price matrix correction equations introduce the additional dimension(s) to the two dimensional flat image of uncorrected data. Illustrative examples generated by three dimensional graphics will be presented.

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Computer programs for the calculation of x-ray intensities emitted by elements in multi-layer structures

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100134685 ◽

1990 ◽

Vol 48 (2) ◽

pp. 216-217

Author(s):

G.F. Bastin ◽

H.J.M. Heijligers ◽

J.M. Dijkstra

Keyword(s):

Software Package ◽

Light Element ◽

Matrix Correction ◽

Excellent Performance ◽

Element Analysis ◽

X Ray ◽

Know How ◽

Accurate Knowledge ◽

Layer Structures ◽

Bulk Matrix

For the calculation of X-ray intensities emitted by elements present in multi-layer systems it is vital to have an accurate knowledge of the x-ray ionization vs. mass-depth (ϕ(ρz)) curves as a function of accelerating voltage and atomic number of films and substrate. Once this knowledge is available the way is open to the analysis of thin films in which both the thicknesses as well as the compositions can usually be determined simultaneously.Our bulk matrix correction “PROZA” with its proven excellent performance for a wide variety of applications (e.g., ultra-light element analysis, extremes in accelerating voltage) has been used as the basis for the development of the software package discussed here. The PROZA program is based on our own modifications of the surface-centred Gaussian ϕ(ρz) model, originally introduced by Packwood and Brown. For its extension towards thin film applications it is required to know how the 4 Gaussian parameters α, β, γ and ϕ(o) for each element in each of the films are affected by the film thickness and the presence of other layers and the substrate.

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Embracing Uncertainty: Modeling Uncertainty in EPMA—Part II

Microscopy and Microanalysis ◽

10.1017/s1431927620024691 ◽

2021 ◽

Vol 27 (1) ◽

pp. 74-89

Author(s):

Nicholas W.M. Ritchie

Keyword(s):

Beam Energy ◽

Uncertainty Modeling ◽

Matrix Correction ◽

Correction Model ◽

X Ray ◽

Starting Point ◽

Uncertainty Calculation ◽

The Matrix ◽

Measurement Design ◽

New Framework

AbstractThis, the second in a series of articles present a new framework for considering the computation of uncertainty in electron excited X-ray microanalysis measurements, will discuss matrix correction. The framework presented in the first article will be applied to the matrix correction model called “Pouchou and Pichoir's Simplified Model” or simply “XPP.” This uncertainty calculation will consider the influence of beam energy, take-off angle, mass absorption coefficient, surface roughness, and other parameters. Since uncertainty calculations and measurement optimization are so intimately related, it also provides a starting point for optimizing accuracy through choice of measurement design.

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