Determination of Cliff-Lorimer k factors by analysis of crystallized microdroplets

The Cliff-Lorimer ratio technique for thin foils was used to determine a set of k factors at 120 kV for calibration of the energy dispersive X-ray analyser on a Philips EM400 analytical electron microscope. The standards used were the crystallized forms of microdroplets of solutions of inorganic salts. These experimental data were compared with other experimental work and found to agree within the experimental error with theoretical k factors.     

Determination of the Cnl parameter in the Bethe formula for the ionization cross-section by the use of Cliff-Lorimer KAB factors obtained at different accelerating voltages in a TEM

There is a clear advantage in using theoretical K_AB factors to perform quantitative microanalysis, because they do not have to be experimentally determined. To compute K_AB factors, we need a very good parameterization of ionization cross-sections. If the b_nl parameter in the Bethe formula for the ionization cross-section is not a function of the element (A or B), then only the C_nl parameter is required to compute K_AB factors. In this paper we present a new method to measure C_nl based on the ratio of K_AB factors obtained at different accelerating voltages.     

Experimental determination of light-element k-factors using the extrapolation technique: Oxygen segregation in aluminium nitride

It is shown that quantitative light-element (Z < 10) analysis and κ-factor determination of light elements can be routinely conducted, analogous to quantification of elements with Z >, using X-ray energy-dispersive spectroscopy. The extrapolation technique was used to determine the κ-factors, κ_OAI = 0.88 ± 0.10 and κ_NAI = 1.61 ±0.22 at zero thickness. These values are found to be in good agreement with theoretically calculated κ-factors. The limitations and applicability of the extrapolation technique for light-element analyses are discussed. An example of light-element quantification is provided in the analysis of oxygen segregation to inversion domain boundaries in aluminium nitride.     

A study of factors influencing the accuracy of quantitative X-ray analysis of thin foil specimens

Needle-shaped specimens were used to determine experimental values of X-ray intensity ratios for L/K and M/L lines. These ratios can be used to determine k_AB factors for L and M lines. They also provide necessary data for absorption correction with the X-ray intensity ratio method. Recent theoretical calculations of k_AB factors are evaluated and new constants in the parametrization of ionization cross-sections for L and M lines are presented. The average X-ray production per unit thickness has been measured as a function of mass thickness for a stainless steel specimen using acceleration voltages of 100 and 200 kV. An increase in X-ray production by more than 20% was found at 100 kV for mass thicknesses up to 1 mg/cm² while at 200 kV the increase was about 5%. The contamination spot method for thickness measurements has also been investigated using needle-shaped specimens. The reported overestimate of thickness using this method can be explained by the formation of broad contamination layers around the deposited spots.     

The quantitative analysis of thin specimens: a review of progress from the Cliff-Lorimer to the new ζ-factor methods

A new quantitative thin‐film X‐ray analysis procedure termed the ζ‐factor method is proposed. This new ζ‐factor method overcomes the two major limitations of the conventional Cliff‐Lorimer method for quantification: (1) use of pure‐element rather than multielement, thin‐specimen standards and (2) built‐in X‐ray absorption correction with simultaneous thickness determination. Combined with a universal, standard, thin specimen, a series of ζ‐factors covering a significant fraction of the periodic table can be estimated. This ζ‐factor estimation can also provide information about both the detector efficiency and the microscope–detector interface system. Light‐element analysis can also be performed more easily because of the built‐in absorption correction. Additionally, the new ζ‐factor method has several advantages over the Cliff‐Lorimer ratio method because information on the specimen thickness at the individual analysis points is produced simultaneously with compositions, thus permitting concurrent determination of the spatial resolution and the analytical sensitivity. In this work, details of the ζ‐factor method and how it improves on the Cliff‐Lorimer approach are demonstrated, along with several applications.     

An innovative optical-based method and automation system for rapid and non-destructive measurement of the web thickness of microdrills

In this paper, an innovative optical-based method and automation system for measuring the cross-sectional web thickness of microdrills is introduced. The presented measuring method is a rapid and non-destructive means based on the use of an optical micrometer (OM) as essential equipment to determine the cross-sectional outer diameter and the dual cross-sectional flute depths of the microdrill. To this end, the OM must be set to a particular orientation so that the included angle between the optical measuring plane of the OM and the central axis of the microdrill is consistent with the helix angle of the helical flutes of the microdrill, and the microdrill must be rotated around its central axis for implementing the measurement. The cross-sectional web thickness of the microdrill can thus be calculated through the difference between the determined cross-sectional outer diameter and dual cross-sectional flute depths. An optical-based measuring automation system was constructed for implementing the proposed method through an established automated measuring process. Experiments to measure the web thickness of microdrill samples were conducted. It showed that the presented method and automation system could achieve good repeatability and accuracy with sufficient efficiency. The proposed measuring method, combined with the constructed measuring automation system, had been validated feasible and effective for the web thickness measurement of certain microdrills.     

An experimental method for calibration of the plasmon mean free path

Transmission electron microscopy specimens in the form of elongated, conical needles were made using a dual‐beam focused ion beam system, allowing the specimen thickness to be geometrically determined for a range of thickness values. From the same samples electron energy loss maps were acquired and the plasmon mean free path (λ) for inelastic scattering was determined experimentally from the measured values of specimen thickness. To test the method λ was determined for Ni (174 ± 17 nm), α‐Al₂O₃ (143 ± 14 nm), Si (199 ± 20 nm) and amorphous SiO₂ (238 ± 12 nm), and compared both to experimental values of λ taken from the literature and to calculated values. The calculated values of λ significantly underestimate the true sample thickness for high accelerating voltages (300 kV) and large collection angles. A linear dependence of λ on thickness was confirmed for t/λ < 0.5–0.6, but this method also provides an approach for calibrating λ at sample thicknesses for which multiple scattering occurs, thus expanding the thickness range over which electron energy loss spectroscopy can be used to determine the absolute sample thickness (t/λ > 0.6). The experimental method proposed in this contribution offers a means to calibrate λ for any type of material or phase that can be milled using a focused ion beam system.     

Experimental and theoretical determination of kAFe factors for quantitative X-ray microanalysis in the analytical electron microscope

Quantitative X-ray microanalysis in the analytical electron microscope involves the use of Cliff-Lorimer k_AB factors to relate measured X-ray intensities from elements A and B to their composition. This study has generated a wide range of these factors for both K and L X-ray lines. The values of the k factor for each element is ratioed to Fe, rather than to Si as has been common practice to date. The use of k_AFe rather than k_ASi factors reduces the uncertainty in the values due to variations in the efficiency of individual energy dispersive spectrometers, thus making the values more universally applicable. New calculations of the value of k_AFe have been made from first principles, encompassing all of the most recent values of the cross-section for X-ray ionization. Comparison of the experimental results with both the calculations and existing k factor data has been made. Close attention has been paid to minimizing the errors in both the experimental and theoretical calculations to reduce the overall error in quantification of X-ray energy dispersive spectra in the analytical electron microscope.     

An improved pendulum method for the determination of the center of gravity and inertia tensor for irregular-shaped bodies

An improved Trifilar Torsional Pendulum (TTP) for the experimental determination of the Center of Gravity (C.G.) and inertia tensor (the three moments of inertia and the three products of inertia) for an irregular-shaped body is proposed and developed. In the improved apparatus, a universal joint is adopted to facilitate the adjustments of the C.G. of the body in line with the pendulum axis. To enhance the precision of the measurement, a tri-coordinate measuring machine is employed to measure the coordinates of the predefined points and vectors of axes, which are then used for calculating the C.G. and inertia tensor for an irregular-shaped body. The theoretical fundaments of an improved TTP, the experimental setup, data processing procedures, and error estimation for measuring C.G. and inertia tensor are presented. With the proposed TTP and data processing procedure, the relative error in the determination of the moments of inertia can be estimated within 1%, and the deviation of the measured C.G. to the theoretical C.G. is within 1.5 mm. An example is given to demonstrate the effectiveness of the new approaches.