Practical Aspects and Advanced Applications of XEDS

Appendix

17.1.1 People

Chuck Fiori (1938–September 15, 1992). The DeskTop Spectrum Analyzer (DTSA) software package was originally developed by the late Chuck Fiori with Bob Myklebust and Carol Swyt. They worked at the National Institutes of Standards and Technology (NIST) and the National Institutes of Health (NIH) in late 1980s.

Joseph (Joe) I. Goldstein was born in Syracuse, NY, on January 6, 1939 and died on June 27, 2015; he founded the Lehigh short course, inspired a generation using AEM, and recruited a young DBW to join him.

17.1.2 Questions

Q17.1:

Compare and contrast the k-factor and the ζ-factor approaches to quantification.

Q17.2:

What is the single most important variable that affects your decision to use either of these two approaches? Explain why you chose that variable.

Q17.3:

Why should you simulate the spectra that you hope will be generated from your specimen before proceeding to gather them experimentally?

Q17.4:

What can you do to minimize ice and carbon contamination on your XEDS detector

Q17.5:

Why has it proven so difficult to detect single atoms in thin foils using XEDS while EELS has been able to do this for many years?

Q17.6:

Distinguish the several different definitions we use for analytical sensitivity.

Q17.7:

Why does a single column of atoms in a thin foil not give rise to an XEDS spectrum containing the signal from these atoms alone?

Q17.8:

What does your answer to question 17.5 lead you to conclude about the real spatial resolution of analysis by XEDS?

Q17.9:

Why are there so many characteristics of your XEDS detector that you have to determine prior to XEDS analysis when, by comparison, an EEL spectrometer is relatively free of such requirements?

Q17.10:

If you have a single atom of element B in an analyzed volume containing 100 atoms of element A, can you estimate, to a first approximation, how long you need to gather a spectrum in order to say with 99 % confidence that that atom of A is present. Choose a reasonable set of experimental variables (including kV, beam current probe size, detector collection angle etc.). State any further assumptions.

Q17.11:

Simulate X-ray spectra to confirm the conditions (the beam current, specimen thickness, acquisition time and accelerating voltage) for 1.0 wt% and 0.3 wt% detection levels of a high Z element in a relatively low Z material, e.g., Cu in Al.

Q17.12:

Similar to the above question; simulate X-ray spectra to confirm the conditions for 1.0 wt% and 0.3 wt% detection levels of a low Z element in a relatively high Z material, e.g., P in Ga.

Q17.13:

Questions 17.11 and 17.12 are for estimation of minimum mass fraction (MMF). Based on your estimated conditions in the above question, how many solute atoms are included. The number of solute atoms is equivalent to the minimum detectable mass (MDM).

Q17.14:

Plot the absorption loss curves of major X-ray lines in your materials systems using Eq. 17.27 and estimate the critical specimen thickness below 10 % absorption.

Q17.15:

Using Eq. 17.28, estimate spatial resolution values for your specimen in conventional and aberration-corrected AEMs, and plotted as a function of the specimen thickness. This plot is essentially same as Fig. 36.5c in W&C. Using this plot, determine the required specimen thickness especially for the aberration-corrected AEM.

17.1.3 Appendix 1. Error Analysis in the ζ-factor Method

As described in Sect. 17.3.3, we need an iterative calculation for determination of compositions and specimen thickness including the absorption correction in the ζ-factor method. It is not very straightforward to estimate errors in such an iterative process but there is an alternative approach for the error calculation. In an n component system, we determine compositions and thickness from n characteristic X-ray intensities via n ζ factors in the ζ-factor method. Obviously, both the n X-ray intensities and n ζ factors are independent variables, and their errors need to be taken into account if you want to determine the error estimation independently. Let’s denote the errors in X-ray intensity and the ζ factor for the jth component as ∆I _j and ∆ζ _j , respectively.

First, we determine the error-free composition(s) C _i and thickness t from n intensities and n ζ factors without their errors. Then, we calculate the compositions and thickness with an error contribution of jth X-ray intensity by substituting I _j  + ∆I _j for I _j . The composition and thickness with the error of jth intensity are expressed as C _i (∆I _j ) and t(∆I _j ), respectively. You have to repeat this process for all X-ray intensities independently. Similarly, the errors in each individual ζ-factor are incorporated by substituting ζ _j  + ∆ζ _j for ζ _j , and composition and thickness with errors of the z-factor are expressed as C _i(∆ζ _j ) and t(∆ζ _j ), respectively. Finally, the errors in the compositions and thickness are given as:

$$\begin{aligned} &\Updelta C_i =\sqrt{\sum_{j=1}^n\left[C_i(\Updelta \zeta_j) - C_i\right]^2+\sum_{j=1}^n\left[C_i(\Updelta I_j)-C_i\right]^2}\\ &\Updelta t=\sqrt{\sum_{j=1}^n\left[t (\Updelta \zeta_j)-t\right]^2+\sum_{j=1}^n\left[t(\Updelta I_j)-t\right]^2} \end{aligned}$$

(17.35)

(17.35)

This approach requires 2n times extra calculations of compositions and thickness after determination of the error-free values (yes, it is a bit complicated and tedious!). However, we can easily adapt this approach to computational codes and it is applicable to any iterative calculation (e.g., the matrix correction procedures for bulk-sample analysis in an EPMA such as ZAF and ϕ(ρz)). The full error analysis procedures for the ζ-factor determination and estimation can be found in the paper by Watanabe and Williams (2006).

17.1.4 Appendix 2. Calculation of the Specimen Density

In the ζ-factor method, we first determine the specimen thickness as the mass thickness ρt as we described above. To convert the mass thickness to the absolute specimen thickness, we need values of the specimen density at individual analysis points. The specimen density can be estimated from Eq. 35.27 in W&C, i.e., the mass divided by the unit-cell volume. So we need some crystallographic information to determine the unit-cell volume. Otherwise, the density can be calculated as a first approximation by taking a weighted mean (ρ = ΣC _j ρ _j ) or a harmonic mean (1/ρ = ΣC _i /ρ _j ) from the density values of the individual component elements.

For example, Fig. 17.38 shows the composition dependence of the specimen density in the Au-Cu system. All the symbols in this figure represent the densities calculated from reported lattice parameters using Eq. 35.27 in W&C. The dashed and solid lines indicate the estimated values from the simple weighted mean and the harmonic mean, respectively. The ρ values estimated by the harmonic mean describe the density very well. In fact, the harmonic-mean approach may work especially well for close-packed condensed systems, such as metallic alloys and intermetallic compounds . For other materials systems such as ceramics and glasses (even not crystalline), the density value needs to be estimated differently.

Fig. 17.1

a Example of energy resolution determination using the Ni Kα peak from the NiOx test specimen . For the determination, the NiOx plug-in in Gatan DigitalMicrograph was used. b The determined energy resolution of XEDS systems of three different instruments (100, 200, and 300 kV), plotted against the process time setting

Fig. 17.2

Determined P/B (Fiori definition) plotted against the IHC, measured from three different instruments operated at 100, 200, and 300 kV

Fig. 17.3

Comparison of X-ray spectra obtained from the same NiOx test specimen in the same instrument at different periods of time

Fig. 17.4

Calculated absorption ratios of the O Kα, Ni Lα and Ni Kα lines, plotted against the ice thickness (a) and the carbon thickness (b) in front of the detector active area

Fig. 17.5

a Main dialog of the NiOx plug-in package. b Sub-dialog for determination of the collection angle and the relative detector efficiency , and c An example of the output for the determination of the collection angle and the relative detector efficiency in a 200 kV instrument

Fig. 17.6

a Main dialog of the NiOxIceC plug-in package. b An example of the output for determination of the accumulated layer thicknesses of ice and carbon, measured in a 300 kV UHV instrument with a windowless XEDS detector

Fig. 17.7

Screen shot of DTSA running via SheepShaver under a Windows platform

Fig. 17.8

Screen shot of the main dialog for thin-specimen spectrum generation in DTSA

Fig. 17.9

Screen shots of the dialogs for detector parameters (a), for detector geometry configuration (b), and for channel settings (c)

Fig. 17.10

Screen shot of the dialog for physics choice

Fig. 17.11

Example of simulated X-ray spectra from the NIST SRM2063a thin specimen. a Noise-free ideal spectrum. b Spectrum with random noise

Fig. 17.12

Simulated result for a generated X-ray spectrum from the SRM2063a thin specimen

Fig. 17.13

Comparison between generated (black) and emitted (red) X-ray spectra from the SRM2063a thin specimen (a) and the X-ray signal loss in % due to X-ray absorption within the specimen, plotted against the X-ray energy (b)

Fig. 17.14

Comparison between emitted (red) and detected (blue) X-ray spectra from the SRM2063a thin specimen (a) and the X-ray signal loss in percent due to absorption in the detector, plotted against the X-ray energy (b)

Fig. 17.15

Comparison of X-ray spectra from the SRM2063a thin specimen before (blue) and after (orange) broadening due to the detector electronics (a) and the detector energy-resolution plotted against the X-ray energy (b)

Fig. 17.16

Screen shot of the dialog for output choice

Fig. 17.17

Simulated X-ray spectrum with a selected energy range of 1–4 keV from MoS_2, showing pathological overlaps between the Si Kα (red) and Mo Lα (blue) peaks

Fig. 17.18

Simulated X-ray spectrum from HfO₂ with KLM markers for Cu and Mo. Since the Hf L-line family is superimposed on the Cu L-line family, a Cu grid is not advisable for X-ray analysis of materials containing Hf

Fig. 17.19

a Comparison of three X-ray spectra simulated at different thicknesses of 50, 100, and 300 nm of Ni₃Al intermetallic compound in a 200 kV instrument with an X-ray take-off angle of 25º. These spectra were normalized by the maximum peak intensity of the Ni Kα line. b The signal losses (%) of the Ni Kα, Ni Lα and Al Kα lines due to the absorption into the specimen, plotted against the specimen thickness

Fig. 17.20

Comparison of three X-ray spectra of NiAl simulated at different tilt angles of −15º, 0º, and +15º

Fig. 17.21

a A comparison of two spectra from a NiOx test specimen , simulated at 200 kV for take-off angles of ± 70º. b The take-off angle dependence of P/B of the Ni Kα peak (using the Fiori definition)

Fig. 17.22

a Comparison of two X-ray spectra from a 100-nm-thick Fe-0.15 wt%P simulated with and without noise in a 200 kV instrument for 100 s. Two highlighted regions indicate the net peak (I) and background (b) intensities. The peak visibility (b) and detectability (c) ratios of the P Kα line in Fe, plotted against the P composition C_P for 100-nm-thick films. The error bars represent the 3σ (99 % confidence limit) range determined from 50 simulated spectra with different random noise conditions

Fig. 17.23

MMF of P in Fe, determined from simulated X-ray spectra of a thin foil of Fe-5 wt% P using the GRM equation, plotted against the specimen thickness

Fig. 17.24

a Analyzed volume of Fe determined based on the Gaussian broadening model for LaB₆-AEM (d = 10 nm), FEG-AEM (d = 2 nm) and AC FEG-AEM (d = 0.2 nm), plotted against the specimen thickness. b The MDA of P in Fe calculated from the MMF in Fig. 17.23 with the analyzed volume size

Fig. 17.25

a  Set of X-ray intensity maps of Pb L and O K lines taken from a triple point in a Pb-based oxide Pb(Mg_1/3Nb_2/3)O₃-35 mol%PbTiO₃ and an ADF-STEM image. b A set of composition maps of Pb and O with a specimen thickness map quantified by the ζ-factor method (Gorzkowski et al. 2004)

Fig. 17.26

Flow chart of the quantification procedure for the ζ-factor method with the X-ray absorption correction (Watanabe and Williams 2006)

Fig. 17.27

ζ-factors of K lines determined in a 200-kV JEOL JEM-ARM200CF, plotted against the X-ray energy. The open circles are the measured values from the SRM2063a glass thin-film; the closed circles indicate the estimated values by parameter optimization based on the measured values (Watanabe and Wade 2013)

Fig. 17.28

Comparison of the absorption loss of the oxygen Kα intensity in various oxides, plotted against the specimen thickness. Dashed and dot-dashed lines represent 5 % and 10 % losses, respectively

Fig. 17.29

Summary of an application of the ζ-factor method to quantification of boundary segregation in a low-alloy steel. a ADF-STEM image in the vicinity of a grain boundary, b Ni composition, c Mo composition, d thickness, e Ni boundary excess, f Mo boundary excess, and g R maps

Fig. 17.30

Detector efficiency curve for a JEOL JEM2-ARM200CF with a JEOL Centurio X-ray detector (Watanabe and Wade 2013)

Fig. 17.31

Comparison of input/output count rate of a large solid-angle SDD at three different time constants on an aberration-corrected STEM JEM-ARM200CF

Fig. 17.32

a HAADF-STEM image of TiO₂-supported Au nanoparticles and X-ray maps of Au (left) and RGB color overlay with O, Au and Ti (right), acquired using an JEOL JEM-ARM200F with the large collection angle SDD system: total acquisition times are (b) 1 min and (c) 6 min

Fig. 17.33

Tilt series of Ti Kα maps around a W contact-plug in a pillar-shaped specimen at different tilt angles between 0° and 170° with 10° steps. Signals in these elemental maps were enhanced by applying the MSA reconstruction to the original X-ray SIs

Fig. 17.34

a 3D-reconstructed Ti distribution around the W contact-plug created using 37 Ti K maps at tilt angles between 0°–180° with a 5° step, partially shown in Fig. 17.33: a at 45° from all primary x, y and z axes and 2D projected Ti distributions along the z axis (b), x axis (c), and y axis (d)

Fig. 17.35

a HAADF-STEM image and a set of elemental maps of Ga, N, and In obtained from an In doped GaN nano pyramid structure using an instrument with an improved X-ray collection system. b Selected slices of the In distribution around one of the pyramid structures reconstructed from the dual-axes XEDS tomography datasets (two orthogonal-axis tilt-series of X-ray spectrum images with ± 60^o in 3^o steps)

Fig. 17.36

a An HAADF-STEM image from a LaMnO₃/SrTiO₃ interface, elemental maps of (b) La, (c) Sr, (d) O, (e) Mn, (f) Ti, (g) RGB color-overlay image of LaMnO₃ and RGB color-overlay image of SrTiO₃

Fig. 17.37

Set of quantitative X-ray maps from a [100]-projected GaAs specimen: a HAADF-STEM image, b Ga K intensity, c As K intensity, d color overlay of Ga K (red) and As K (green), e Ga composition, f As composition, and g thickness

Fig. 17.38

Comparison of calculated density values by weighted (dashed line) and harmonic (solid line) means with those determined from reported lattice parameters summarized by Okamoto et al (1987)