Embracing Uncertainty: Modeling Uncertainty in EPMA—Part II

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.

Embracing Uncertainty: Modeling the Standard Uncertainty in Electron Probe Microanalysis—Part I

2020 ◽  
Vol 26 (3) ◽  
pp. 469-483
Author(s):  
Nicholas W. M. Ritchie
Keyword(s):  
Surface Roughness ◽  
Expert System ◽  
Coating Thickness ◽  
Electron Probe ◽  
Uncertainty Modeling ◽  
Measurement Model ◽  
Standard Uncertainty ◽  
X Ray ◽  
Error Bars ◽  
New Framework

AbstractThis is the first in a series of articles which present a new framework for computing the standard uncertainty in electron excited X-ray microanalysis measurements. This article will discuss the framework and apply it to a handful of simple, but useful, subcomponents of the larger problem. Subsequent articles will handle more complex aspects of the measurement model. The result will be a framework in which sophisticated and practical models of the uncertainty for real-world measurements. It will include many long overlooked contributions like surface roughness and coating thickness. The result provides more than just error bars for our measurements. It also provides a framework for measurement optimization and, ultimately, the development of an expert system to guide both the novice and expert to design more effective measurement protocols.

Lama I - A General Fortrah Program for Quantitative X-ray Fluorescence Analysis

1976 ◽  
Vol 20 ◽  
pp. 515-528 ◽  
Author(s):  
Daniel Laguitton ◽  
Michael Mantler
Keyword(s):  
Input Data ◽  
Fluorescence Analysis ◽  
Matrix Correction ◽  
X Ray ◽  
Fundamental Parameters ◽  
The Matrix ◽  
Film Form

A comprehensive Fortran IV program designed to perform the matrix correction in x-ray fluorescence analysis is described. Specimens and standards can be in bulk or film form. All necessary fundamental parameters are provided by internal routines thereby requiring a minimum of input data.

The Analysis of Oil Additives Using Fundamental Influence Coefficients

1981 ◽  
Vol 25 ◽  
pp. 177-180
Author(s):  
H. M. West
Keyword(s):  
Atomic Number ◽  
Oil Industry ◽  
Mathematical Methods ◽  
Correction Model ◽  
X Ray ◽  
Average Atomic Number ◽  
Oil Additives ◽  
Influence Coefficients ◽  
The Matrix

One of the most important applications o£ XRF in the oil industry has been in the analysis of oil additives which range from Mg to Ba. In such a low atomic number, hydrocarbon matrix, small variations in the additives cause pronounced changes in the average atomic number of the matrix and hence give rise to strong interelement effects. In recent years a number of mathematical methods have been developed to correct the measured X-ray intensity of the analyte litie for these considerable effects. This paper describes a method for the determination of Zn,Ba,Ca,CI,S,P and Mg in oil additives using a concentration based correction model in which influence coefficients (alphas) are applied.

A robust method for determining the Duane-Hunt energy limit from EDS

1990 ◽  
Vol 48 (2) ◽  
pp. 210-211
Author(s):  
Robert L. Myklebust ◽  
Charles E. Fiori ◽  
Dale E. Newbury
Keyword(s):  
Electron Probe ◽  
Beam Energy ◽  
Potential Drop ◽  
Matrix Correction ◽  
Energy Limit ◽  
Energy Excitation ◽  
X Ray ◽  
Beam Voltage ◽  
Lower Beam ◽  
Quantitative Electron Probe Microanalysis

The electron beam energy is a parameter required for quantitative electron probe microanalysis. In fact, it occurs in all parts of the ZAF type matrix correction procedure as well as in all of the other matrix correction procedures. Recently, there has been much interest in analyzing materials using lower beam voltages. Since the correction procedures use the so called “overvoltage” term (beam energy/excitation energy), uncertainties in the beam voltage will generate larger errors than when high beam voltages are used. The user may well be faced with an instrument that does not have a very precise voltmeter to measure the beam voltage, or the reported voltage may not actually represent the potential drop from the filament to ground (specimen). The true beam energy may differ from the “measured” potential drop by several hundred volts.It is difficult and potentially exciting to measure the beam voltage with a calibrated voltmeter; however, we have a built-in method available in the energy-dispersive x-ray detector.

Lateral resolution of the electron microbeam analysis

1978 ◽  
Vol 36 (1) ◽  
pp. 542-543
Author(s):  
H.J. Dudek
Keyword(s):  
Quantitative Analysis ◽  
Depth Resolution ◽  
Lateral Resolution ◽  
Cylindrical Particle ◽  
Correction Procedure ◽  
X Ray ◽  
Element Concentrations ◽  
Microbeam Analysis ◽  
The Matrix

The chemical inhomogenities in modern materials such as fibers, phases and inclusions, often have diameters in the region of one micrometer. Using electron microbeam analysis for the determination of the element concentrations one has to know the smallest possible diameter of such regions for a given accuracy of the quantitative analysis.In th is paper the correction procedure for the quantitative electron microbeam analysis is extended to a spacial problem to determine the smallest possible measurements of a cylindrical particle P of high D (depth resolution) and diameter L (lateral resolution) embeded in a matrix M and which has to be analysed quantitative with the accuracy q. The mathematical accounts lead to the following form of the characteristic x-ray intens ity of the element i of a particle P embeded in the matrix M in relation to the intensity of a standard S

Analysis and lattice imaging of a transitional event on garnets

1978 ◽  
Vol 36 (1) ◽  
pp. 270-271
Author(s):  
J.Y. Laval
Keyword(s):  
Yttrium Iron Garnet ◽  
Reciprocal Lattice ◽  
Transitional Zone ◽  
Lattice Imaging ◽  
Yttrium Iron ◽  
X Ray ◽  
Ionic Process ◽  
The Matrix ◽  
High Resolution Technique ◽  
Iron Garnet

The exsolution of magnetite from a substituted Yttrium Iron Garnet, containing an iron excess may lead to a transitional event. This event is characterized hy the formation of a transitional zone at the center of which the magnetite nucleates (Fig.1). Since there is a contrast between the matrix and these zones and since selected area diffraction does not show any difference between those zones and the matrix in the reciprocal lattice, it is of interest to analyze the structure of the transitional zones.By using simultaneously different techniques in electron microscopy, (oscillating crystal method microdiffraction and X-ray microanalysis)one may resolve the ionic process corresponding to the transitional event and image this event subsequently by high resolution technique.

Phase identification in SiC whisker reinforced Al2O3-R2O3-based composites

1992 ◽  
Vol 50 (1) ◽  
pp. 152-153
Author(s):  
C.M. Sung ◽  
K.J. Ostreicher ◽  
M.L. Huckabee ◽  
S.T. Buljan
Keyword(s):  
Analytical Electron Microscopy ◽  
Phase Identification ◽  
Reinforced Composites ◽  
Ion Milling ◽  
X Ray ◽  
Binary Oxides ◽  
Analytical Electron ◽  
The Matrix ◽  
Second Phases ◽  
Convergent Beam

A series of binary oxides and SiC whisker reinforced composites both having a matrix composed of an α-(Al, R)2O3 solid solution (R: rare earth) have been studied by analytical electron microscopy (AEM). The mechanical properties of the composites as well as crystal structure, composition, and defects of both second phases and the matrix were investigated. The formation of various second phases, e.g. garnet, β-Alumina, or perovskite structures in the binary Al2O3-R2O3 and the ternary Al2O3-R2O3-SiC(w) systems are discussed.Sections of the materials having thicknesses of 100 μm - 300 μm were first diamond core drilled. The discs were then polished and dimpled. The final step was ion milling with Ar+ until breakthrough occurred. Samples prepared in this manner were then analyzed using the Philips EM400T AEM. The low-Z energy dispersive X-ray spectroscopy (EDXS) data were obtained and correlated with convergent beam electron diffraction (CBED) patterns to identify phase compositions and structures. The following EDXS parameters were maintained in the analyzed areas: accelerating voltage of 120 keV, sample tilt of 12° and 20% dead time.

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

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.

Improving x-ray map resolution with image restoration techniques

1996 ◽  
Vol 54 ◽  
pp. 598-599
Author(s):  
Richard B. Mott ◽  
John J. Friel ◽  
Charles G. Waldman
Keyword(s):  
Image Restoration ◽  
Hubble Space Telescope ◽  
Extensive Literature ◽  
Small Object ◽  
X Rays ◽  
X Ray ◽  
Mapping Parameters ◽  
The Matrix ◽  
The 1960S ◽  
Map Resolution

X-rays are emitted from a relatively large volume in bulk samples, limiting the smallest features which are visible in X-ray maps. Beam spreading also hampers attempts to make geometric measurements of features based on their boundaries in X-ray maps. This has prompted recent interest in using low voltages, and consequently mapping L or M lines, in order to minimize the blurring of the maps.An alternative strategy draws on the extensive work in image restoration (deblurring) developed in space science and astronomy since the 1960s. A recent example is the restoration of images from the Hubble Space Telescope prior to its new optics. Extensive literature exists on the theory of image restoration. The simplest case and its correspondence with X-ray mapping parameters is shown in Figures 1 and 2.Using pixels much smaller than the X-ray volume, a small object of differing composition from the matrix generates a broad, low response. This shape corresponds to the point spread function (PSF). The observed X-ray map can be modeled as an “ideal” map, with an X-ray volume of zero, convolved with the PSF. Figure 2a shows the 1-dimensional case of a line profile across a thin layer. Figure 2b shows an idealized noise-free profile which is then convolved with the PSF to give the blurred profile of Figure 2c.

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