J Mater Sci (2015) 50:493–518
`DOI 10.1007/s10853-014-8685-2
`
`R E V I E W
`
`Performing elemental microanalysis with high accuracy and high
`precision by scanning electron microscopy/silicon drift detector
`energy-dispersive X-ray spectrometry (SEM/SDD-EDS)
`
`Dale E. Newbury • Nicholas W. M. Ritchie
`
`Received: 14 July 2014 / Accepted: 25 October 2014 / Published online: 12 November 2014
`Ó Springer Science+Business Media New York (outside the USA) 2014
`
`Abstract Electron-excited X-ray microanalysis per-
`formed in the scanning electron microscope with energy-
`dispersive X-ray spectrometry (EDS) is a core technique
`for characterization of the microstructure of materials. The
`recent advances in EDS performance with the silicon drift
`detector (SDD) enable accuracy and precision equivalent to
`that of the high spectral resolution wavelength-dispersive
`spectrometer employed on the electron probe microana-
`lyzer platform. SDD-EDS throughput, resolution, and sta-
`bility
`provide
`practical
`operating
`conditions
`for
`measurement of high-count spectra that form the basis for
`peak fitting procedures that recover the characteristic peak
`intensities even for elemental combination where severe
`peak overlaps occur, such PbS, MoS2, BaTiO3, SrWO4,
`and WSi2. Accurate analyses are also demonstrated for
`interferences involving large concentration ratios: a major
`constituent on a minor constituent (Ba at 0.4299 mass
`fraction on Ti at 0.0180) and a major constituent on a trace
`constituent (Ba at 0.2194 on Ce at 0.00407; Si at 0.1145 on
`Ta at 0.0041). Accurate analyses of low atomic number
`elements, C, N, O, and F, are demonstrated. Measurement
`of trace constituents with limits of detection below 0.001
`mass fraction (1000 ppm) is possible within a practical
`measurement time of 500 s.
`
`Contribution of the United States Government; not subject to U.S.
`copyright.
`D. E. Newbury (&) N. W. M. Ritchie
`Materials Measurement Science Division, National Institute of
`Standards and Technology, Gaithersburg, MD 20899, USA
`e-mail: dale.newbury@nist.gov
`
`Introduction
`
`Origins: electron probe microanalysis with wavelength-
`dispersive spectrometry
`
`Electron-excited X-ray spectrometry for the measurement
`Query of elemental composition on the microstructural
`scale has been an important part of the materials charac-
`terization arsenal since the invention of the electron probe
`microanalyzer (EPMA) in 1951 by Castaing [1, 2]. Cas-
`taing not only produced the first working EPMA instrument
`but he also established the framework for the fundamental
`measurement science of
`the technique,
`including the
`physical basis for a practical quantitative analysis method.
`For the first two decades of the EPMA technique, the dif-
`fraction-based wavelength-dispersive X-ray spectrometer
`(WDS) was the only practical way to measure the X-ray
`intensities. Castaing recognized that the complex depen-
`dence of the WDS efficiency on photon energy made it
`impractical
`to develop a quantification procedure that
`compared different elements measured at different photon
`energies. Besides the variable solid angle of the WDS that
`is dependent on photon energy, four or more diffractors
`with different d-spacings and scattering efficiencies are
`needed to satisfy Bragg’s equation over the photon energy
`range of interest from 100 eV to 10 keV. To overcome this
`measurement dilemma, Castaing developed the ‘‘k-ratio’’
`protocol based on measuring the characteristic X-ray
`intensity, I, for the same element in the unknown and in a
`standard of known composition:
`k ¼ Iunknown=Istandard:
`The characteristic X-ray peak intensity is corrected for
`background and measured under identical conditions of
`beam energy, known dose, and detector efficiency for both
`
`ð1Þ
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`494
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`J Mater Sci (2015) 50:493–518
`
`Fig. 1 Distribution of
`[(measured - true)/true 9
`relative errors
`100 %] using the k-ratio protocol with WDS measurements and
`matrix corrections with the NBS ZAF procedure FRAME (1975) [5].
`Note that the histogram bins have a width of 1 % relative
`
`is
`region that
`the principal
`near-surface composition,
`sampled by electron-excited X-rays, rendering the analyt-
`ical
`results unrepresentative of
`the material being
`measured.
`Throughout the development of quantitative electron-
`excited X-ray microanalysis, researchers rigorously tested
`the method by measuring as unknowns carefully selected
`multi-element materials whose microscopic homogeneity
`could be first confirmed by EPMA and whose overall
`composition was measured by independent chemical ana-
`lysis. The distribution of measured relative errors, defined
`as
`
`Relative error ¼ Measured concentrationReferenceð
`eferenceŠ  100 %;
`
`Þ=
`ð3Þ
`
`½ R
`
`as determined by a mature version of the k-ratio/matrix
`correction procedure in 1975 is shown in Fig. 1 for WDS
`measurements of major1 constituents [5]. This distribution
`can be characterized by a standard deviation of 2.5 %
`relative, so that approximately 95 % of the analyses fall
`within the span of ±5 % relative error.
`
`1 Note: in this paper, the following arbitrary convention for broadly
`classifying the concentration range will be followed:
`
`‘‘major,’’ mass concentration C [ 0.1 (more than 10 wt%)
`‘‘minor’’ 0.01 B C B 0.1 (1–10 wt%)
`‘‘trace’’ C \ 0.01 (\1 wt%).
`
`ð2Þ
`
`unknown and standard. By measuring the same peak under
`identical conditions, the same efficiency value effectively
`appears in both the numerator and denominator of Eq. (1)
`as a multiplier of the intensity, and thus the efficiency
`quantitatively cancels in the k-ratio.
`Castaing further described the basis for the physical
`calculations that are necessary to convert the suite of k-
`ratios into mass concentrations, which after substantial
`further contributions by numerous authors (see Ref. [3] for
`Heinrich’s detailed account of these developments) take
`the following form:
`Ci=Cstd ¼ ki ZAFc;
`where Cstd is the mass concentration of the element of
`interest in the standard; and Z, A, F, and c are the ‘‘matrix
`correction factors’’
`that calculate the compositionally
`dependent interelement effects of electron scattering and
`energy loss (Z), X-ray self-absorption within the specimen
`(A), and secondary X-ray emission following self-absorp-
`tion of the electron-excited characteristic (F) and contin-
`uum (c) X-rays. Importantly for the Castaing standards-
`based k-ratio method, the standards required do not have to
`closely match the composition of the unknown, which is an
`enormous advantage when dealing with complicated multi-
`the k-ratio
`element unknowns. Suitable standards for
`measurements include pure elements (e.g., Al, Si, Cr, Fe,
`Ni, etc.), while stoichiometric compounds can be used for
`those elements that are not in solid form in a vacuum (e.g.,
`MgO for O), that are highly reactive (e.g., KCl for K and
`Cl),
`that deteriorate under electron bombardment (e.g.,
`FeS2 for S), or that have a low melting temperature (e.g.,
`GaP for Ga and P).
`The extremely sharp focal properties of the WDS forced
`EPMA analysts to develop procedures to establish and
`maintain the critical condition of identical detection effi-
`ciency when measuring the separate intensities for the
`unknown and standards required for Eq. (1) [3]. To place
`the specimen reproducibly within the narrow spatial range,
`spanning a few micrometers, over which the WDS had
`constant X-ray transmission, a fixed-position optical
`microscope with a shallow depth of focus was incorporated
`into the EPMA at the coincident focal position for all
`spectrometers. The condition of the specimen surface was
`recognized to be another critical requirement [4]. It came to
`be understood early in the development of EPMA that the
`specimen had to metallographically polished to a very high
`degree of surface finish, but not chemically etched. To
`create contrast in optical metallography, chemical etching
`typically produces topography through orientation-depen-
`dent etch rates in different grains and phases, but even fine-
`scale topography can influence measured X-ray intensities,
`especially for low-energy photons. Moreover,
`in some
`cases, chemical etching induces changes in the surface/
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`495
`
`Further development: energy-dispersive X-ray
`spectrometry
`
`The development of semiconductor-based X-ray detection
`in the 1960s led to the first successful energy-dispersive
`X-ray spectrometer (EDS) using lithium-compensated sil-
`icon [Si(Li)-EDS] operated on an electron-column instru-
`ment, an EPMA [6]. As compared to the narrow
`instantaneous energy range of the WDS, the Si(Li)-EDS
`provided a view of the entire excited X-ray spectrum from
`a threshold of approximately 100 eV (modern perfor-
`mance) to the Duane-Hunt limit set by the incident beam
`energy, up to 20 keV or higher. This wide energy range
`enabled detection of all elements, with the exception of H
`and He (modern performance), at every location sampled
`by the beam, which provided an enormous advantage when
`dealing with complex microstructures where local segre-
`gation can create unexpected compositional variation and
`where unexpected elements can be localized as inclusions.
`Comprehensive elemental analysis capability, combined
`with the relative simplicity of non-focusing line-of-sight
`detection, the large solid angle of collection which exceeds
`that of WDS by at least a factor of 10, and the long-term
`operating stability, resulted in the enthusiastic acceptance
`of EDS, especially by the rapidly developing scanning
`electron microscope (SEM) community. The combination
`of SEM imaging with EDS X-ray microanalysis has given
`the materials community one of its most powerful micro-
`structural characterization tools [2].
`The capability of Si(Li)-EDS to perform quantitative
`X-ray microanalysis was established soon after its intro-
`duction by several members of the microanalysis commu-
`nity, most of whom had extensive WDS quantitative
`microanalysis experience [7–11]. Thus, the initial EDS
`implementation of quantitative analysis was based upon
`their experience with the WDS k-ratio protocol. The EDS
`could be used in an equivalent manner by measuring the
`intensities for the unknown and appropriate standards
`under the same carefully controlled conditions of surface
`condition (highly polished), beam energy, known dose
`(beam current 9 detector live time), beam incidence angle,
`detector elevation angle (‘‘take-off angle’’), and detector
`efficiency (e.g., constant detector-to-target distance to yield
`constant detector solid angle). The enormous advantages of
`the EDS over WDS for analysis were quickly recognized:
`(1) all elements in the unknown were measured simulta-
`neously minimizing the dose to the specimen; (2) the large
`solid angle of the EDS relative to WDS further improved
`efficiency of detection which lowered the necessary dose
`relative to WDS; and (3) the stability of the EDS meant
`that the spectra of standards could be archived and recalled
`as needed. Since the measured EDS spectrum consists of
`the characteristic X-ray peaks superimposed on the X-ray
`
`continuum, various strategies were developed to determine
`characteristic intensities,
`including digital filtering for
`background removal followed by multiple linear least
`squares (MLLS) fitting and background modeling under the
`peak window constrained by the continuum intensity
`measured in energy windows where no peaks occurred [8,
`10]. The background-corrected characteristic intensities
`for the unknown and the standards were used to calculate
`k-ratios followed by the matrix correction procedure. The
`k-ratio matrix correction procedure with the Si(Li)-EDS
`was demonstrated to be capable of achieving relative errors
`within the WDS distribution for major constituents when
`the characteristic X-ray peaks did not suffer significant
`overlap from the peaks of other elements. An example is
`shown in Table 1 for the Si(Li)-EDS analysis of gold-
`copper alloys (NIST Standard Reference Material 482)
`where the observed relative errors range from -1.6 to
`1.0 %, falling well within the WDS analysis error distri-
`bution of Fig. 1.2 Further development of the EDS quan-
`titative microanalysis method enabled accurate analyses
`when significant peak overlaps occurred providing the
`intensities of the mutually interfering species were similar.
`
`Typical SEM/EDS microanalysis practice
`
`Despite the level of analytical accuracy demonstrated for
`the EDS k-ratio/matrix corrections protocol and the avail-
`ability of this procedure within most commercial imple-
`mentations of EDS analytical software, modern SEM/EDS
`microanalysis practice has developed along a different
`trajectory that minimizes the need for the user’s expertise.
`As an unintended consequence, EDS microanalysis as
`performed in the SEM has acquired an unfortunate repu-
`tation as a ‘‘semi-quantitative’’ technique. This situation
`has developed because of three contributing factors: (1) the
`rise of standardless analysis which now dominates EDS
`quantitative analysis [14]; (2) the severe effects of speci-
`men geometry on the accuracy of X-ray microanalysis
`which occur no matter which analytical protocol is fol-
`lowed, standards-based or standardless [15]; and (3) the
`occasional but significant failures in qualitative analysis,
`i.e., incorrect elemental identification, which immediately
`undermines confidence in the method [16–18].
`
`The rise of ‘‘standardless’’ quantitative analysis
`
`By necessity, WDS measures each element in the sample
`relative to the same element in an appropriate standard to
`
`2 Materials analyzed in this paper include NIST Standard Reference
`Materials, NIST microanalysis research materials (glasses), natural
`minerals, and stoichiometric compounds confirmed to be homoge-
`neous on a micrometer lateral scale.
`
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`J Mater Sci (2015) 50:493–518
`
`Table 1 Si(Li)-EDS analysis of NIST Standard Reference Material 482 Copper–Gold Alloysa (all concentration values in mass fraction)
`
`Cu (certified)
`
`Analyzed
`
`Rel. error (%)
`
`Au (certified)
`
`Analyzed
`
`Rel. error (%)
`
`0.198
`
`0.396
`
`0.599
`
`0.798
`
`0.198 ± 0.002
`
`0.399 ± 0.001
`
`0.605 ± 0.001
`
`0.0
`
`0.8
`
`1.0
`
`0.797 ± 0.001
`
`-0.1
`
`0.801
`
`0.603
`
`0.401
`
`0.200
`
`0.790 ± 0.002
`
`0.594 ± 0.002
`
`0.402 ± 0.002
`
`0.199 ± 0.003
`
`-1.4
`
`-1.6
`
`0.1
`
`-1.2
`
`Total
`
`0.988
`
`0.993
`
`1.007
`
`0.996
`
`Analysis performed with Cu Ka and AuLa; beam energy = 20 keV; quantitative calculations with NIST Desktop Spectrum Analyzer [12];
`uncertainty expressed as 1r from the measured counts (from Ref [13])
`a See footnote 2
`
`eliminate the need to accurately know the spectrometer
`efficiency. Because the EDS spectrum provides, in every
`measurement, the complete photon energy range revealing
`all characteristic X-ray peaks and the X-ray continuum
`background, it became attractive to develop an alternative
`approach
`for
`quantitative EDS microanalysis
`that
`employed the whole spectrum. The so-called ‘‘standardless
`analysis’’ method requires only the EDS spectrum of the
`unknown and eliminates the need to measure standards
`locally or to specify the electron dose [2, 14]. ‘‘Standard-
`less analysis’’ seeks to provide the necessary standard
`intensity for the denominator of Eq. (1) for each element in
`the unknown either by theoretical calculation of X-ray
`generation and propagation in a pure element target (‘‘first
`principles’’ standardless) or by the use of a library of actual
`standards measured on a well-characterized EDS detector
`at several beam energies under defined conditions that can
`be related to the efficiency as a function of photon energy
`of the local EDS (‘‘remote standards’’ standardless). The
`resulting suite of k-ratios is then subjected to the same
`matrix correction calculations of Eq. (2). Because a true
`first principles implementation of standardless analysis
`requires an extensive database of X-ray parameters such as
`the ionization cross section, X-ray fluorescence yield,
`X-ray mass absorption coefficient, and others, many of
`which are poorly known, especially for the L-shell and
`M-shell X-ray families, the ‘‘remote standards’’ method,
`which actually anchors the quantitative calculations to a
`suite of archived experimental measurements, is the basis
`for the typical modern software implementation.
`The performance of a recent commercial version of
`‘‘standardless analysis’’ is shown in the error histogram of
`Fig. 2. While this error distribution appears similar to that
`of the classic k-ratio protocol with WDS or EDS as shown
`in Fig. 1, it is in fact much broader, with the errors binned
`in increments of 5 % relative error, compared to the 1 %
`relative error increments of Fig. 1. For this particular
`implementation of standardless analysis, the width of the
`error range that
`is necessary to capture 95 % of the
`analytical results is approximately ±30 % relative. While
`this level of performance may be adequate for some
`
`123
`
`Fig. 2 Distribution of relative errors observed for a commercial
`implementation of standardless analysis (2013). Note that
`the
`histogram bins have a width of 5 % relative
`
`applications, the prospective user of the analytical results
`of such a procedure needs to be aware of the inherent
`limitations imposed by such a wide error distribution.
`Table 2 provides specific examples of the application of
`this standardless analysis procedure to the analysis of metal
`sulfides. While the analytical accuracy achieved for FeS
`(troilite, a meteoritic mineral) is excellent with relative
`errors less than ±2 % for S and Fe, the relative errors for
`the analysis of FeS2 (pyrite), CuS (covellite), ZnS (sphal-
`erite), and PbS (galena) exceed 20 % relative, a level of
`performance so poor that
`it would not be possible to
`properly assign the formula for these compounds from the
`analyzed mass concentrations.
`Another often overlooked consequence of using the
`standardless analysis procedure is the requirement that the
`calculated concentrations must be internally normalized to a
`sum of unity. This requirement occurs because the relation of
`the electron dose and the absolute EDS efficiency of the
`measured spectrum to the remote standards database is lost
`so that internal normalization is needed to place the calcu-
`lated concentration values on a meaningful scale. That the
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`
`Table 2 Standardless analysis
`of sulfides (2013 Commercial
`Software)
`
`497
`
`Compound
`
`Metal
`
`Analysis
`
`Relative error (%)
`
`Sulfur
`
`Analysis
`
`Relative error (%)
`
`FeS
`
`FeS
`
`CuS
`
`ZnS
`
`SrS
`
`CdS
`
`Sb2S3
`PbS
`
`0.635
`
`0.466
`
`0.665
`
`0.671
`
`0.732
`
`0.778
`
`0.717
`
`0.866
`
`0.629
`
`0.642
`
`0.764
`
`0.762
`
`0.758
`
`0.808
`
`0.739
`
`0.914
`
`-1.0
`
`38
`
`15
`
`14
`
`3.6
`
`3.8
`
`3.1
`
`5.5
`
`0.365
`
`0.534
`
`0.335
`
`0.329
`
`0.268
`
`0.222
`
`0.283
`
`0.134
`
`0.371
`
`0.358
`
`0.236
`
`0.239
`
`0.242
`
`0.192
`
`0.261
`
`0.086
`
`1.8
`
`-33
`
`-30
`
`-28
`
`-10
`
`-13
`
`-7.8
`
`-36
`
`analyzed mass concentration total of all constituents in a
`standardless analysis equals exactly 1.000 (100 wt%) may
`seem comforting, but the internal normalization that must
`occur does in fact represent a loss of critical information. In
`the standards-based k-ratio/matrix corrections protocol per-
`formed with WDS or EDS, the sum of the individual con-
`stituents rarely coincides exactly with unity, but tends to vary
`from 0.98 to 1.02, as shown in the example presented in
`Table 1, a consequence of the inevitable errors that arise in
`measuring the characteristic intensities and in calculating the
`matrix correction factors. Analytical totals outside of this
`range can occur because of uncontrolled deviations in the
`experimental conditions between measuring the unknown
`and standards (e.g., differences in coating thickness or in the
`thickness of native surface oxides), but a low analytical total
`may also reveal the presence in the analyzed volume of a
`previously unrecognized constituent. For example, a region
`of the specimen that is oxidized rather than metallic will
`contain oxygen at a concentration from 0.2 to 0.3 mass
`fraction. The analytical total if oxygen is not considered
`(either by directly measuring its X-ray intensity and making
`the appropriate matrix correction calculation or by indirectly
`calculating oxygen by the method of assumed stoichiometry
`of the cations) will be 0.7–0.8, significantly below unity,
`which should trigger the curiosity of a careful analyst to
`further examine the measured spectrum and discover the
`oxygen peak. While this may seem a trivial example that
`even a novice analyst should not miss, in fact as we enter an
`era in which much of our data are collected under automa-
`tion, the lack of manual inspection combined with the loss of
`a meaningful analytical total by the standardless method will
`result in questionable data appearing in the final results that
`may be difficult to review after collection and processing. As
`discussed below, a more frequently encountered source of
`deviation in the analytical total is the impact of uncontrolled
`‘‘specimen geometry,’’ i.e., the effects of size, shape, and
`local surface inclination on beam electron—specimen
`interaction and the generation and propagation of X-rays, on
`the measured X-ray intensities. A ‘‘zeroth’’ level assumption
`in standards-based and standardless analysis procedures is
`
`that the specimen composition is the only factor affecting the
`X-ray intensities. When the specimen geometry deviates
`from the ideal flat surface placed at known angles to the
`incident electron beam and the X-ray spectrometer, very
`large effects on the X-ray intensities can occur, especially
`when low-energy and high-energy photons are measured in
`the same analysis.
`Despite these limitations, the simplicity of operation
`required for standardless analysis, which only requires the
`analyst to measure the EDS spectrum of the unknown and
`to specify the beam energy and the X-ray emergence angle,
`has resulted in its widespread acceptance by the SEM/EDS
`community. Based on our informal surveys of the field,
`probably more than 98 % of reported quantitative EDS
`microanalysis results are obtained with some implementa-
`tion of standardless analysis. However, the modest ana-
`lytical performance revealed in Fig. 2 and Table 2 is surely
`a major contributor to the reputation of SEM/EDS as only
`achieving ‘‘semiquantitative’’ results, while the internal
`normalization of all results to unity conveys a false sense of
`accuracy and confidence.
`
`Specimen geometry effects: we can be our own worst
`enemies when it comes to performing accurate
`quantification
`
`When analytical results are automatically normalized, an
`even more egregious source of large, uncontrolled, and
`likely unrecognized errors in SEM/EDS microanalysis
`arises from specimen geometry effects [2]. The line-of-sight
`acceptance of the EDS spectrometer enables the analyst to
`record an X-ray spectrum from almost any location where
`the beam strikes the specimen, which can be a useful feature
`in qualitatively surveying the complex microstructure of a
`specimen with complex topography. However, specimen
`geometry effects such as shape and local surface inclination
`to the beam can have a profound impact on electron scat-
`tering and even more importantly, on the path length along
`which X-rays must travel to the detector and along which
`they suffer absorption. These ‘‘geometric effects’’ modify
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`Analysis with a compromised sample shape: all forms
`Analysis of K411: Bulk polished, 600 Grit, In-hole, Chips, Shards
`80
`
`BULK
`
`8.8
`8.6
`Mg (normalized weight percent)
`
`11.5
`
`11.4
`
`11.3
`
`Fe (normalized weight percent)
`
`Bulk K411
`
`Shards_overscan
`
`Shards_fixed-beam
`
`Macroscopic chips
`
`Surface voids
`
`Bulk-600grit
`
`0
`
`1
`
`2
`
`9
`8
`7
`6
`5
`4
`3
`Mg (normalized weight percent)
`
`10
`
`11
`
`12
`
`70
`
`60
`
`50
`
`40
`
`30
`
`20
`
`10
`
`0
`
`Fe (normalized weight percent)
`
`Fig. 4 Analysis of NIST SRM 470 (K411 glass) in various geometric
`forms (flat, polished bulk; scratched surface after 600-grit grinding;
`shallow surface holes, chips, and shards) using the k-ratio protocol
`with SDD-EDS measurements and NIST DTSA-II. Plot of Fe
`(normalized weight percent) vs. Mg (normalized weight percent) [19]
`
`the standardless analysis method, the inevitable internal
`normalization to unity eliminates the important information
`provided by the analytical total that would reveal the impact
`of specimen geometry effects.
`An example of how serious the impact of specimen
`geometry can be upon analytical accuracy is illustrated in
`Figs. 3 and 4 for the analysis of a microscopically homo-
`geneous glass, NIST SRM 470 (K411),
`the complete
`composition of which is listed in Table 3. Table 3 also
`contains the results of a standards-based k-ratio protocol
`analysis of NIST SRM 470 (K411 glass) prepared in the
`ideal specimen geometry of a flat, highly polished surface
`(0.1 lm alumina final polish) with a thin (\10 nm) carbon
`conductive coating for charge dissipation. The relative
`errors as compared to the SRM certificate values for the
`average of 20 analyses range from -1.1 to 1.8 %. Fig-
`ure 3a shows a plot of the distribution from 20 analyzed
`locations for the concentrations of magnesium and iron,
`elements which were chosen because the large difference
`in their photon energies, 1.254 keV for MgKa, b and
`6.400 keV for FeKa, make them differentially sensitive to
`geometric effects since the low-energy photons of Mg
`suffer much higher absorption compared to the high-energy
`photons of FeKa [19]. The cluster of the analyses is seen to
`be very narrow, with one exception. A reasonable question
`the analyst might ask is whether this outlier represents an
`actual deviation in the local composition or arises from
`some other factor. Upon review of the analyzed locations,
`the outlier in Fig. 3 was in fact determined to be the
`consequence of an analysis that was performed in a scratch
`that remained after final polishing,
`thus representing a
`
`Fig. 3 a Analysis of NIST SRM 470 (K411 glass) as a flat, highly
`polished bulk sample (final polish with 100 nm alumina) using the
`k-ratio protocol with SDD-EDS measurements and NIST DTSA-II.
`Plot of Fe (normalized weight percent) vs. Mg (normalized weight
`percent) for 20 randomly selected analyses. Note the outlier (circled).
`b Analysis of NIST SRM 470 (K411 glass) as a flat, but slightly
`scratched bulk sample (scratches remaining after 1 lm diamond
`polish) using the k-ratio protocol with SDD-EDS measurements and
`NIST DTSA-II. Plot of Fe (normalized weight percent) vs. Mg
`(normalized weight percent) for 20 randomly selected analyses
`
`the measured relative elemental intensities in ways that
`have nothing to do with the composition of the specimen.
`The physical basis assumed for the matrix correction factors
`of Eq. (2), which are needed for quantification with both the
`k-ratio standards protocol and the standardless method, is
`that the compositional difference between the unknown and
`the standard(s) is the only factor that affects the measured
`X-ray intensities. When a quantitative analysis of a topo-
`graphically irregular specimen is performed following the
`k-ratio/standards protocol, the analytical total will deviate
`significantly from unity in response to deviations from the
`ideal flat, highly polished specimen geometry. However, in
`
`123
`
`Merck Exhibit 2233, Page 6
`Mylan Pharmaceuticals Inc. v. Merck Sharp & Dohme Corp.
`IPR2020-00040
`
`

`

`J Mater Sci (2015) 50:493–518
`
`499
`
`(a)
`
`12
`
`Analysis of K411: Bulk polished and All Geometries
`
`SRMvalue
`
`024681
`
`0
`
`Bulk K411
`
`All Geometries
`
`1
`
`0
`
`20
`
`40
`60
`80
`100
`Raw Analytical Total (weight percent)
`
`120
`
`140
`
`Analysis of K411: Bulk polished and All Geometries
`
`80
`
`70
`
`60
`
`50
`
`40
`
`30
`
`20
`
`Bulk K411 All Geometries
`
`1
`
`SRMvalue
`
`01
`
`0
`
`0
`
`20
`
`40
`
`60
`
`80
`
`100
`
`120
`
`140
`
`Raw Analytical Total (weight percent)
`
`Mg (normalized weight percent)
`
`(b)
`
`Fe (normalized weight percent)
`
`Fig. 5 Analysis of NIST SRM 470 (K411 glass) in various geometric
`forms (flat, polished bulk; scratched surface after 600-grit grinding;
`shallow surface holes, chips, and shards) using the k-ratio protocol
`with SDD-EDS measurements and NIST DTSA-II: a Mg (normalized
`weight percent) vs. the raw analytical total (weight percent), including
`oxygen calculated by assumed stoichiometry [19], b Fe (normalized
`weight percent) vs. the raw analytical total (weight percent), including
`oxygen calculated by assumed stoichiometry [19]
`
`standardless analysis
`information,
`losing this critical
`enables risky analytical behavior with SEM/EDS which
`contributes enormously to the dismissal of SEM/EDS as
`being only ‘‘semi-quantitative.’’ Unless the specimen
`geometry is carefully controlled, SEM/EDS analysis is
`subject to errors so broad as to render the compositional
`results of questionable value for many applications.
`
`Qualitative analysis failures
`
`A separate but extremely significant issue is the reliability
`of elemental identification in the EDS spectrum. The crit-
`ical first step of qualitative analysis obviously must be
`correct if the subsequent quantitative analysis is to have
`any value at all. Automatic identification of the charac-
`teristic peaks in the EDS spectrum is a valuable software
`
`123
`
`Table 3 SEM/SDD-EDS analysis of NIST SRM K411 glass
`
`Element
`
`SRM
`certificate
`
`EDS analysis
`
`SDa
`
`Relative
`error (%)
`
`O
`
`Mg
`
`Si
`
`Ca
`
`Fe
`
`0.424
`
`0.0885
`
`0.254
`
`0.111
`
`0.112
`
`0.428 (stoich)
`
`0.0876
`
`0.258
`
`0.111
`
`0.114
`
`0.022
`
`0.045
`
`0.053
`
`0.026
`
`0.031
`
`0.9
`
`-1.1
`
`1.6
`
`0
`
`1.8
`
`Conditions: polished specimen; E0 = 20 keV; analysis following the
`k-ratio protocol with standards using the NIST DTSA-II software;
`standards included the pure elements Mg, Si, and Fe; Ca from SRM
`470 (glass K412), with oxygen calculated on the basis of assumed
`stoichiometry of the cations
`a 20 analyses
`
`geometric effect rather than a true compositional variation.
`This surface roughness effect
`is illustrated for a more
`severe situation in Fig. 3b, which shows the results from 20
`analyses at randomly selected locations on the scratched,
`irregular surface that remained after polishing with 1 lm
`diamond particles. The results show both a systematic shift
`in the apparent concentrations and a broadening in the
`distribution.
`the analyses reported in
`The surface analyzed for
`Fig. 3b did not appear to be especially rough when viewed
`in an SEM image. When the SRM 470 (K411 glass) is
`prepared in more extreme geometric forms, including the
`scratched surface that remains after grinding with 600 grit
`silicon carbide, fracture surfaces, and fragmented particles,
`and then analyzed following the same k-ratio/standards
`protocol used for the results in Table 3, the normalized
`concentrations for magnesium and iron are found to span a
`much broader range, as shown in Fig. 4 [19]. The range of
`apparent concentrations obtained from the irregularly
`shaped specimens is so extreme, spanning nearly an order
`of magnitude for each constituent, that the results would be
`of dubious value for most applications that depend on an
`accurate composition for proper interpretation.
`Analysis with the standards-based k-ratio/matrix cor-
`rections protocol reveals the impact of geometric effects on
`X-ray microanalysis through the behavior of the raw ana-
`lytical total [19]. Figure 5a and b individually plot the
`normalized magnesium and iron concentrations against the
`total from the k-ratio/standards analysis
`raw analytical
`procedure, showing how well the raw analytical total is
`correlated with the magnitude of the relative error. This
`example illustrates well the pitfalls of blindly attempting to
`quantitatively analyze the EDS spectrum obtained from
`randomly shaped objects. Because of the inevitable nor-
`malization that must occur in the standardless analysis
`procedure, the important clue that the raw analytical total
`provides that will identify such dubious analyses is lost. By
`
`Merck Exhibit 2233, Page 7
`Mylan Pharmaceuticals Inc. v. Merck Sharp & Dohme Corp.
`IPR2020-00040
`
`

`

`J Mater Sci (2015) 50:493–518
`
`Fig. 7 a Gold, beam energy 20 keV, showing correct identification
`of the Au L-family and M-family [16–18]. b Gold, beam energy
`10 keV, showing misidentification of the Au M-family as the Zr
`L-family and Nb L-family [16–18]
`
`robust and reliable results, the prudent analyst will inspect
`each tentative elemental assignment that is suggested by
`the automatic peak identification software and confirm or
`correct the identification by carefully considering possible
`alternatives using software tools to explore the database of
`characteristic X-ray energies.
`In some circumstances,
`achieving identification with a high deg