Diagnostic Nano-Analysis of Materials Properties by Multivariate Curve Resolution Applied to Spectrum Images by S/TEM-EELS

Materials Transactions, Vol. 50, No. 5 (2009) pp. 964 to 969 Special Issue on Nano-Materials Science for Atomic Scale Modification #2009 The Japan Institute of Metals

Diagnostic Nano-Analysis of Materials Properties by Multivariate Curve Resolution Applied to Spectrum Images by S/TEM-EELS Shunsuke Muto, Tomoko Yoshida and Kazuyoshi Tatsumi Department of Materials, Physics and Energy Engineering, Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan The data cube of spectrum imaging (SI) by scanning TEM (STEM) and electron energy-loss spectroscopy (EELS) or energy-filtering TEM (EF-TEM) can be treated as the two-dimensional data array, each row corresponding to the EELS spectrum at a specific position. A multivariate curve resolution (MCR) technique can then apply to the dataset, which decomposes the set of spectra into the product of the constituent pure spectral components and their corresponding relative composition matrices without any reference spectra. This method allows us to provide a two dimensional spatial distribution map of different chemical states incorporated even when the multiply spectra overlap with one another. Several application examples are presented. [doi:10.2320/matertrans.MC200805] (Received November 4, 2008; Accepted December 9, 2008; Published January 28, 2009) Keywords: spectrum image, multivariate curve resolution, transmission electron microscopy, electron energy-loss spectroscopy

1.

Introduction

Chemical analysis based on state-of-the-art (scanning) transmission electron microscopy ((S)TEM) has enabled us to obtain a two dimensional elemental map with a spatial resolution of less than 1 nm.1) In current analytical TEM/ STEM instruments an energy dispersive X-ray (EDX) spectrometer and an electron energy-loss spectrometer (EELS) are standard analytical tools; the energy resolution of EDX is approximately 100 eV, while that of EELS is typically 1 eV or less, depending on the type of spectrometer and/or electron source. (S)TEM-EELS techniques have been thus developed particularly for chemical state analysis at localized areas and subsequently for visualizing the spatial distributions of the specific chemical states with high spatial resolution, called spectrum imaging (SI).2,3) SI in (S)TEM-EELS can be done in two ways:2,3) Spectrum imaging based on energy-filtering TEM (EFTEM-SI) is realized by first taking a number of EFTEM images by scanning the narrow energy slit over the energy loss spectrum of interest, while STEM-EELS-SI is done by scanning the focused electron beam on the sample with an EELS recorded at each position. A typical example is mapping of graphitic carbon in carbon-related materials4) because the characteristic sharp peak at 284 eV associated with the transition from the 1s to sp2 -

state appears at lower energy side of the 
transitions. However the characteristic features associated with specific types of chemical bonding are often overlaid on the other features or another absorption edge of a different element, and hence it is not always possible to select only the characteristic feature by the energy slit. The obtained data set in either type of SI has the same structure, called a ‘data cube’, as shown in Fig. 1:2,3) in case of EFTEM-SI, the energy interval between the EELS data sampling points is determined by the energy slit width, typically 1–5 eV (Fig. 1(a)). In STEM-EELS-SI, on the other hand, one can set any value for the energy dispersion and the spatial resolution is limited by the electron probe size and the scan step (Fig. 1(b)). EFTEM-SI is preferred when you focus on a single element and the ELNES profile shows a distinct

difference for each chemical state of interest, detectable by poor energy resolution. STEM-EELS-SI is more preferred for the cases where subtle spectral changes are to be detected with better energy resolution and/or plural types of absorption edges are to be analyzed. In both methods, the edge overlapping problem has limited their capabilities. In the fields of analytical chemistry data processing techniques based on linear algebra theories, called ‘chemometrics’, have been developed;5) chemometrics is a useful family of techniques to analyze large datasets, generally known as multivariate statistical analysis (MSA),6) and it basically seeks the number of components and the concentration of each component incorporated in a set of spectral data recorded from the samples in which the composition of the constituent phases, ingredients or reactants varies with time or spatial positions. Principal component analysis (PCA) is one of the most popular MSA approaches. PCA has been applied to EDX7) and EELS8,9) line scans, and also recently to EELS-SIs to extract and map the bonding components.10) The general advantage of PCA is to reduce the dimensionality of an original large dataset by finding a minimum number of variables that describe the original dataset without losing any significant information. PCA extracts the principal components in the descending order of their information contents. The extracted spectral profile of the second or higher order component, however, does not always allow straightforward interpretation, because the procedure involves eigenanalysis to the data matrix, which ‘rotates’ the spectra, sometimes showing unrealistic negative intensities. In the present study, we attempted to apply an alternative MSA technique to EELS-SI data sets, in which the decomposed spectra are not rotated and can be directly interpretable in conventional manners, but it requires a priori knowledge of the number of components incorporated. Once the number of components is known, a pure spectral profile of each component can be extracted without any reference spectra recorded from the pure materials, such powerful techniques being called self modeling curve resolution (SMCR) or multivariate curve resolution (MCR).11) When the spatial

Diagnostic Nano-Analysis of Materials Properties by Multivariate Curve Resolution Applied to Spectrum Images by S/TEM-EELS

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distribution maps of different chemical bonding states incorporated are obtained, you can make a ‘diagnosis’ upon the materials properties, just as a medical doctor does on the disease by reading x-ray photos and computer tomography (CT) images, for instance. In the next section the principle of the method are briefly reviewed. An application example for STEM-SI is presented. And then several standing problems in this method are discussed and finally the present work is summarized.

3.

2.

It is possible to reduce the number of possible solutions by means of constraints derived from the physical/chemical nature and a priori knowledge of the problem under study. More intensive discussion on this issue is given in Ref. 15). In the application examples to be presented in the following section the obtained results are nearly unique solutions within the accuracies allowed by the given signal-to-noise ratios, because of a large number of experimental spectra in the datasets fit by a few components under the non-negativity constraint in addition to the normalization constraint.

Brief Overview of MCR Method

The structure of a data cube in EELS-based SI is ideal for MCR. The EEL spectrum is supposed to be a linear combination of multiple ELNES features with different weights, each corresponding to a different chemical state depending on the position. One can extract a single EEL spectrum from the SI data cube at a position corresponding to a single pixel. The objective of MCR is to extract concentration profiles and pure component spectra with as few assumptions about the data as possible. Give an m  n matrix X that is product of an m  k matrix of concentration profiles C, and n  k matrix of pure component spectra S, where k is the number of components, X ¼ CST þ E;

ð1Þ

where the superscript T demotes the transpose of the matrix. E is the residual matrix with the data variance or statistical noise unexplained by CST . The goal is to obtain physically meaningful C and S. The SI data set consists of a set of intensities Iðx; y; EÞ, the energy-loss value at the spatial position (x; y) and energyloss E, as already shown in Fig. 1. The data can thus be expressed by the three dimensional array Xðmx ; my ; nÞ, whose variables respectively correspond to the pixel (channel) coordination numbers of the x and y directions and energy-loss E. However, the spatial coordinates can be equivalently treated and thus the data is essentially bilinear, expressed by the array Xðm; nÞ, where m ¼ mx  my , as shown in Fig. 2. Now each row in the matrix ST on the right hand side of eq. (1) stands for a pure component EEL spectrum and if each row vector of ST is normalized in its intensity (and the total core-loss cross sections are not very different for the component spectra), the m-th value of the kth column of the matrix C denotes the relative composition of the k-th component spectrum (k-th row of ST ) at the m-th spatial coordination. This is a two-way, bilinear model and the alternating least-square (ALS) method12) is usually utilized as a solution of a straightforward regression problem where initial estimates for C and ST are generated initially using either random numbers, eigenvalue decomposition, or dissimilarity criterion.13) In all examples used in this report random numbers were used to generate initial estimates for C because it is fast and provides a good numerical starting point for ALS. We adopted a faster, accurate and more robust algorithm, called the modified alternating least-squares (MALS) method.14) The program is coded on MatLab, which facilitates numerical array manipulations in matrices and mathematical operations between matrices.

Uniqueness of the MCR Solution

MCR, however, has an intrinsic difficulty in that the solution of eq. (1) for C and ST is ambiguous; or in other words, there is rotational and scale freedom. It is clear that if no constraints are considered, there are an infinite number of possible solutions of the following equation for any nonsingular matrix T: D ¼ Cold Sold T ¼ ðCold TÞðT1 Sold T Þ ¼ Cnew Snew T

4.

Application Examples

In the application examples shown below, a JEM2100F TEM (Schottoky type field emission electron gun) equipped with a Gatan TRIDIEM imaging filter was used for acquiring SI data. 4.1

Chemical states map of nitrogen in TiO2 by EFTEM-SI/MCR Photocatalytic reactions at the surface of TiO2 under UV light irradiation are well known but it was reported that the substitutional doping of N into TiO2 contributed to narrowing of band gap, thus providing a visible-light response.16) It is thus important to find the local chemical states effective for the visible-light responsiveness. The EFTEM-SI method thus applied to the N-K ELNES: 20 EFTEM images were collected by scanning an energy slit of 2 eV a width from 380 eV to 420 eV on the energy-loss axis at the interval of 2 eV. The area consisting of 100  150 pixels, as framed by a solid line in Fig. 3, was used, and thus 15000 spectra could be utilized for the spectral decomposition. In the present case, the number of components was assumed to be two, and 200 iterative least square fitting yielded a sufficiently converged result. The resolved spectra are shown in Fig. 4(a). We attempted the MALS regression assuming three components, which yielded no physically significant result. The depth distributions (SI) of the components #1 and #2 are shown in Fig. 4(b). The grayscale of each image in (b) was calibrated such that it reflects the approximate relative concentration of each component. It should also be noted that the chemical state of component #1 (not visible-light responsive) is localized around the depth regions at 30 and 100 nm from the surface, while that of component #2 is distributed over the entire implanted regions. It is not yet clear why the single peak component shows the bimodal distribution, but presumably because the NOx and/or N2 gas molecules are formed and escaped away when the N concentration exceeds a certain value. More detailed discussion on the present material is published elsewhere.17–19)

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S. Muto, T. Yoshida and K. Tatsumi

(a) x EF-TEM y

EF-images

(b)

E

e– x

x

y

y

E

Specimen ADF

EELS

EELS

Fig. 1 Two types of spectrum imaging data cube with the same data structure. (a) Energy-filtering TEM (EF-TEM). (b) STEM-EELS. x and y are the spatial coordinates in the image, and E is the energy-loss axis.

mx

mx

my nE

× my nE

X

= ST(nE,2) ×

C(2, mx×my) Re-align

Component spectra

2D spatial distribution maps

Fig. 2 Schematic representation of the MCR procedure for the case where the number of components incorporated is 2. The data cube is transformed to the two-dimensional matrix, X, which is resolved into the spectral matrix, S and the concentration matrix, C. Each row in C can be rearranged in the original order to represent the concentration map of the corresponding spectral component in the column of S.

4.2

Degradation analysis of Li-ion secondary battery positive electrode by STEM-EELS-SI/MCR The next application example of the SI-MCR technique is a diagnostic analysis of degradation of a Li-ion secondary battery positive electrode. Among candidate materials for

positive electrodes, LiNi0:8 Co0:15 Al0:05 O2 is most promising for high-power use relatively at higher temperatures.20,21) The presence of a NiO-type phase was confirmed in degraded samples after repeated charge/discharge cycling tests, which is localized around the grain surface and

Diagnostic Nano-Analysis of Materials Properties by Multivariate Curve Resolution Applied to Spectrum Images by S/TEM-EELS

(a)

TiO2 surface

967

(b)

glue

N+-implanted zone 50 nm

Fig. 3 (a) XTEM image of Nþ -implanted TiO2 sample. (b) A set of EF-TEM image taken from the same area of (a) using the N K edge. The framed area was used for MCR analysis. The detailed recording conditions are described in text.

(a)

(b) Comp. #1

Comp. #2

Intensity (a.u.)

Component #1

Component #2

380

385

390 395 400 Energy loss (eV)

405

410

Fig. 4 Resolved N K edge spectra (a) and depth distribution of each component (b,c).

boundaries.22,23) However, one should clarify the overall distributions of the degraded areas over the entire secondary particles in relation with the electrolyte contact and also how those areas are evolved by cycling tests. We thus prepared TEM thin films of the electrodes covering the whole secondary particles by FIB, and carried out a spectrum imaging (SI) technique using a scanning transmission electron microscope (STEM). A HAADF image of a active material particle is shown in Fig. 5. An SI was taken from this area, with the probe size of 5 nm, scan step of 40 nm and 201  180 pixels in total were scanned. The spectrum acquisition time was 0.5 s at each position. The number of detector channels was 2k in the dispersion direction and the spectra were recorded at the energy range of 400–1000 eV with 0.3 eV/channel, covering from O K- to Ni L2;3 -edge. The sample drift was corrected during the measurements at every 5 acquisitions. The pre-edge background was subtracted from each absorption edge in each spectrum by power-law modeling. It is expected that the three ELNES spectra were highly

2 µm Fig. 5 Dark-field STEM images of samples after 500 cycling test at 80 C, simultaneously recorded during SI.

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S. Muto, T. Yoshida and K. Tatsumi

(a) Comp. #1

(c) #3

(b) #2

2 µm

(d)

Component #1 Component #2 Component #3

530

Fig. 6

540

780 790 Energy loss (eV)

860

870

(a)–(c) Spatial distributions of resolved components shown in (d) for the sample after 500 cycling test at 80 C.

correlated with one another because a set of characteristic chemical bonding states correspond to one single phase included in the sample ROI. We thus processed the SI data set including all three absorption edges: after subtracting the pre-edge background from each edge, specific energy ranges were picked up the ranges of 500–570 eV for O Kedge and white-line peaks for Co and Ni L2;3 -edges, 270 channels in total. The pre-edge background and post-edge continuum transition intensities were included as small as possible so as to minimize the plural loss due to the nonuniform sample thickness. The data array then consisted of 201  180  270 points, which was reshaped into the twodimensional array of X(201  180, 270). Furthermore, the carbon binder regions surrounding the oxide particle was carefully removed by applying the mask, since the binder was found to contain oxygen, exhibiting the ELNES profile very similar to the degraded phase in the oxide particle, which turned out to seriously affect the curve resolution results. In order to minimize the rotational ambiguities of the MCR solution, the non-negativity constraint for the both spectral and concentration matrices and the normalization constraint for each row of the spectral matrix (pure spectral profile) are imposed. For the latter constraint the 1-norm instead of the Euclidian norm (2-norm)14) is adopted because the spectral intensity of an element corresponds to the cross section for the core-loss and the normalization constraint

by the 1-norm of each spectral profile under the nonnegativity constraint allows us direct interpretation of the concentration profile as the relative concentration of each component. MCR applied to the present datasets by assuming two, three and four components, and resolution into four components was found to be irrelevant, because the fourth component looks like residual noise rather than a physically significant spectrum. The spatial distribution of each resolved component are shown in Figs. 6(a)–(c) for the sample after 500 cycling tests at 80 C, assuming that there contained three components. The pure spectral profiles are shown in Fig. 6(d). The total concentrations of the three components are calculated from the concentration matrix, as shown inset. It is apparent from the O-K ELNES spectral features that Component #1 and 2 respectively corresponds to the original layered phase, degraded NiO-type phase. This assignment is further reinforced by the fact that the associated Co- and NiL2;3 ELNES accordingly show trivalent and divalent whiteline intensity ratios. The O-K ELNES of Component #3 is characterized by a large prepeak and can be assigned to a Lideficient phase, by comparing the reported spectra from Li1x Ni0:8 Co0:2 O2 (x ¼ 0:07{0:74).24) The L3 /L2 ratio of Component #3 shows the value larger than that of the trivalent phase, which also confirms the assignment. Accord-

Diagnostic Nano-Analysis of Materials Properties by Multivariate Curve Resolution Applied to Spectrum Images by S/TEM-EELS

ing to the relative prepeak intensities reported in 24), x (Li composition) 0 for Component #1 and x > 0:7 for Component #3. The NiO-type phase is considerably increased at the grain surfaces and boundaries, and Li is also deficient from place to place. The detailed analyses will be published elsewhere.25) 5.

Concluding Remarks

We presented usefulness of a multivariate curve resolution (MCR) technique applying to spectrum images obtained by S/TEM-EELS, and it successfully gave the spatial distributions of different chemical states overlapping one another at the same energy region. Another effective application of the method is to extract site-specific ELNES from the dataset recorded under electron channeling conditions.26) The present MCR is effective when the number of components incorporated in the dataset is given or a priori known, which is not always the case. A practical solution for this issue is to first apply PCA to the data and the derived number of principal component is a good starting value for the first trial. The present two-way analysis is extended to multiway analysis by recording additional spectral data such as characteristic X-ray (EDX, WDX spectra) and cathodoluminescence simultaneously together with the EELS acquisition. This can impose very strong additional constraints on the data and mathematically guarantees the uniqueness of the resolved solutions, which is now underway as our next extension of the method. Acknowledgements We are very grateful to Dr. T. Oikawa, Mrs. E. Okunishi and N. Endo at Akishima works of JEOL Ltd. for cooperation in recording EFTEM-SI and STEM-SI images. The present work was supported in part by Grants-in-Aid for Scientific Research (KAKENHI) in Priority Area (#474) ‘‘Atomic Scale Modification’’ and ‘‘Kiban-Kenkyu A’’ from MEXT, Japan.

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