Characterization of supported metal oxide particles by variable angle xrayphotoelectron spectroscopyPeter ten Berge, Vaneica Young, and Stanley R. Bates Citation: Journal of Vacuum Science & Technology A 7, 1729 (1989); doi: 10.1116/1.576035 View online: http://dx.doi.org/10.1116/1.576035 View Table of Contents: http://scitation.aip.org/content/avs/journal/jvsta/7/3?ver=pdfcov Published by the AVS: Science & Technology of Materials, Interfaces, and Processing Articles you may be interested in Characterization of an ultrashallow junction structure using angle resolved x-ray photoelectron spectroscopy andmedium energy ion scattering J. Vac. Sci. Technol. B 26, 298 (2008); 10.1116/1.2834689 Thin oxide-free phosphate films of composition formed on the surface of vanadium metal and characterized by x-ray photoelectron spectroscopy J. Vac. Sci. Technol. A 24, 1179 (2006); 10.1116/1.2204924 Angleresolved xray photoelectron spectroscopy method for the thickness measurement of metal oxide/metalultrathin films J. Vac. Sci. Technol. A 11, 2303 (1993); 10.1116/1.578366 Preferential sputtering in oxides as metals and revealed by xray photoelectron spectroscopy J. Vac. Sci. Technol. 16, 798 (1979); 10.1116/1.570090 XRay Photoelectron Spectroscopy on Magnetic Metals J. Appl. Phys. 40, 1395 (1969); 10.1063/1.1657684

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Characterization of supported metal oxide particles by variable angle x-ray photoelectron spectroscopy

Peterten BergeandVaneica Young Departmento/Chemistry. University o/Florida. Gainesville. Florida 32611

Stanley R. Bates Department 0/ Materials Science and Engineering. University 0/ Florida. Gainesville. Florida 32611

(Received 15 August 1988; accepted lOOctober 1988)

The preliminary results of a newly developed method to determine the particle size distribution of a solid supported dispersed phase are presented. It is based on a modification of a theoretical model proposed by Kuipers et al. and employed intensity data obtained using variable angle x-ray photoelectron spectroscopy (V AXPS). The heart of the computer program generated is a nonlinear least-squares algorithm based on the Marquardt-Levenberg procedure. The test calculations show that the average particle size diameter of particles in heterogeneous catalysts can be determined with an accuracy of 16%. Comparison of particle size distributions obtained from transmission electron microscopy and V AXPS shows significant differences, which can partly be explained by fundamental differences of the techniques. The method appears to be a promising approach, which we hope to improve in the near future.

I. INTRODUCTION

Heterogeneous catalysts generally consist of dispersed active phases on inert supports. Therefore, it is important to obtain more information about the physical and electronic nature of the dispersed phases. X-ray photoelectron spectroscopy (XPS), a surface-sensitive technique, has been shown to be an excellent tool for catalyst characterization. Since XPS is sensitive to all elements except hydrogen, it has a large field of application. However, for catalyst characterization, it has mostly been applied as a qualitative technique. Relatively few efforts have been made to quantify the properties of cata­lysts by XPS. I

-7

Several models are available in the literature on the use of quantitative XPS analysis for dispersed phase heterogeneous catalysts. For a catalyst with element i in support compound k and element p in support s, the intensity ratio of the XPS signals Ii,k IIp,s can be expressed as2

,4

Ii,k = Ii,k (00) X tPk [1 - exp( - dkIAi,k)]

Ip,s Ip,s (00 ) 1 - tPk [ 1 - exp( - dkl Ap,k) ] (1)

where tPk is the geometric coverage, dk is the layer thickness of k, and A i,p,k are the inelastic mean free paths (IMFP's) of i and p, respectively. As shown by Kuipers et al.4 the latter term is a geometric term, which can be symbolized by T( tP k ,d k ). The geometric term shown in Eq. ( 1) is oversim­plified' because it introduces two systematic errors. The first is due to the neglect of averaging over the angular distribu­tion of the surface element with respect to the analyzer. The second is due to the erroneous assumption that a dispersed phase can be treated as a thin layer of constant thickness.

To correct for the latter error, a new attenuation function (the exponential part of the geometric term) was derived.4

The supported material was assumed to consist of spherical, monodisperse particles. Then, the attenuation function fl depends on the diameter of the supported spherical particles 2Rk and on the IMFP's of the supported material k and the support material s:

fli,p,k = 2(Ai,p,k12Rk)2[1- {(2R kIA i,p,k) + 1}

xexp( -2R k IA i,p,d], (2)

where fli,p,k is a shorthand notation for the two different attenuation functions, fl i.k and flp,k of the supported materi­al and the support. For hemispherical, monodisperse parti­cles the attenuation function has form:

fli,p.k = 2 (Ai,p.k IRk )2[ 1 - {RklAi,p,k + 1}

X [exp( - Rkl Ai,p.k) ]. (3)

Thus, the attenuation function takes different forms depend­ing on the shape of the particles. The model cannot deter­mine the shape of the particles, but only the best parameters for a given particle shape. We have assumed hemispherical particles based on transmission electron microscopy data. For monodisperse particles, the geometric coverage tPk and the particle radius Rk are not independent. When particles are not monodisperse, which is always the case for real parti­cles, Rk must be replaced by (R k ), the average particle radi­us. In this case, tPk and (R k ) can be regarded as independent. For example, the area covered by a hemisphere with a radius of lO nm could also be covered by five hemispheres each with a radius of 4.5 nm.

Correction for the first systematic error involved two further adjustments, which dealt with the angular averaging of layer thickness and with the angular distribution of the underlying support, If the XPS signals are reported under varying angles of detection {}, these adjustments can be ruled out. This means that the replacement of Ai,p,k by A i,p,d (}) = Ai,p,k sin {} in Eq. (3) results in an expression which is usable for variable angle XPS (V AXPS). In princi­ple, it is possible to obtain an infinite number of equations by varying the angle of detection. Since the number of param­eters is finite, an "overdetermined" system8 can always be obtained.

In this paper we describe the preliminary results of our efforts to develop a nonlinear least-squares algorithm to de-

1729 J. Vac, Sci. Technol. A 7 (3), May/Jun 1989 0734-2101/89/031729-04$01.00 © 1989 American Vacuum Society 1729

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1730 Berge, Young, and Bates: Characterization of supported metal oxide particles 1730

tennine the maximum likelihood estimates of ¢k' (dk),A.i.k,A.p.k' and Ii.k(oo)/Ip.s(oo). The program is first tested with calculated values. Then a MnO, on a C-foil sample is used to test the program with experimental data from V AXPS. The choice ofMnOx is motivated by our need to characterize the particle size distribution of supported metal oxide particles on carbon substrates. The results are referenced to electron microscopic data.

II. EXPERIMENTAL

Both V AXPS and TEM are used to analyze the MnOx on a C-foil sample. Therefore, MnOx must be deposited onto specially prepared copper grids so that both techniques may be applied to the same sample. The copper grids are prepared by covering them first with a polymer substrate using a 1 % Fonnvar in chlorofonn solution9 and then lightly coating them with carbon. Using a Veeco VE 400 evaporator, the manganese oxide is vapor deposited onto the grid by resisti­vely heating a tantalum basket filled with manganese chips (Alpha Products, m3N7). The manganese chips have a very thick layer of oxide on them. The pressure during evapora­tion is 1 X 10- 5 Torr or lower. The deposition rate was ~O.I nm/s, as measured by a quartz-crystal thickness monitor. Total deposition is ~4.0 nm.

X-ray photoemission spectra have been obtained using a Kratos XSAM 800 spectrometer utilizing AI Ka x-rays (1486.6 eV). Photoemission angles of 0°, 15°,30°,45°,60., 75·, and 90· are used. The pressure in the analysis chamber is 4 X 10-'1 Torr. Peak deconvolution of the spectra is done by a Digital Equipment Corp. Micro PDP-II computer. The transmission electron micrographs have been obtained on a Jeol 2000 CX electron microscope. The resolution of the microscope is ~ 1 nm. Electron diffraction micrographs show that the manganese deposited consists of a mixture of manganese oxides. This is unavoidable because the samples are exposed to air during the transfer process. No efforts have been made to elucidate the exact fractional composition of the MnO, material, since this is beyond the scope of the present project. It is noted, however, that the ring patterns indicate the presence of MnO, Mn02, and r-MnlO,. The calculations are perfonned on a Commodore 64 computer.

III. RESULTS A. Theoretical

A computer program named "V AXPS-PSD" has been written in CBM Basic. The heart of the program is a nonlin­ear least-squares algorithm based on the Marquardt-Leven­berg procedure, \0 a flow chart of which is shown in Fig. 1. As can be seen from the flow chart, the input consists of the photoemission angle and the corresponding ratio of the pho­toemission intensities. The program accepts input from ei­ther the keyboard or from floppy disk. Then initial values for the coverage, the average particle diameter, the IMFP's of the overlayer and support material, and the ratio of the pho­toemission intensities ( = infinity ratio) from a thick layer of overlayer material (thick is ~ 10A.overlayer material) and from the pristine support are introduced. From these initial val­ues, an intensity ratio is calculated by using Eq. (I). After

J. Vac. Sci. Technol. A, Vol. 7, No.3, May/Jun 1989

iNPUT: 9 and ii,k (9) / Ip,s (9)

INPUT: INITIAL VAL-LJES FOR ~k ' <Rk> , /ci,k '

/cp,s and li,k (9)00/ Ip,s (9)00

CALCULATION : [Ii,k (9) / Ip,s (9) I calc.

CALCULATION OF RESIDUALS

RS; = li,k (9) / Ip,s (9) . [Ij,k (S) lip,s (9) lcalc.

CALCULATION MARQUARDT VECTOR:

;l = .( J T J + /c . I r' . J T (RS)

CALCULATION OF NEW VALUES FOR ~k ' <Rk> \k '/cp,s and Ij,k (9)00Ilp,s (9)00

FIG. I. Flow chart of the VAXPS-PSD nonlinear least-squares algorithm.

calculating the squared residuals with respect to the experi­mental ratios, an iterative cycle is entered, in which the Mar­quardt vector is applied. The iteration stops as soon as the value of the square of the residual in the previous cycle equals the next one or the ceiling for the number of iterations is reached. In theory, the maximum likelihood estimators of the five parameters are thus obtained. The only constraints on the parameters are that they must be positive real numbers. The program is evaluated by assessing its ability to regenerate parameter values for test series, produced by as­signing values to the parameters and calculating intensity ratios using Eq. (3) (as modified for V AXPS). The effect of assuming different initial values for the parameters has been observed. In theory the program should converge to the same set of maximum likelihood estimators, independent of the initial values. A representative set of such calculations is shown in Table I.

The leftmost column of Table I shows the selected param­eter values for the infinity ratio, the average particle diame­ter, the coverage, and the IMFP's of the overlayer and sup­port material. The efficiency of the program is tested by varying one or more parameters. The blank spots in the table indicate that the actual value is used for the calculation of the best fit parameters. The results of the convergencies turn out to have significant deviations from the selected values in most cases. The average deviations for the particle diameter from the actual values for the test series 1, 2, 3, and 4 are

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1731 Berge, Young, and Bates: Characterization of supported metal oxide particles 1731

TABLE I. V AXPS·PSD convergencies for four test series.

Input value Output value Input value Output value Input value Output value Input value Output value

Test series I Inf. ratio (0.5) 0.5 Dmtr. (10 nm) 13 11.75 7 Cvrg. (0.5) 0.5 Ovrlyr. (I nm) 1.17 Spprt. (1.5 nm) 1.77

Test series 2 Inf. ratio (0.5) 0.56 Dmtr. (2 nm) 3 2.43 1.5 Cvrg. (0.1) 0.09 OVrlyr. (I nm) 1.22 Spprt. (1.5 nm) 1.95

Test series 3 Inf. ratio (0.5) 0.51 Dmtr. (10 nm) 13 11.24 9 Cvrg. (0.95) 0.95 Ovrlyr. (I nm) 0.51 Spprt. (1.5 nm) 1.73

Test series 4 Inf. ratio (0.5) 0.51 Dmtr. (7 nm) 9 8.3 5 Cvrg. (0.75) 0.75 Ovrlyr. (I nm) 1.75 Spprt. (1.5 nm) 1.57

18%, 18%, 10%, and 15%, respectively. This results in an overall average deviation of 16%. This value will be used as the relative standard deviation for the average particle diam­eter due to program limitations.

B. Experimental

Transmission electron microscopy is used as a reference technique. A particle size distribution of a MnO x on a C-foil sample is obtained by measuring - 200 arbitrary particles on a micrograph, that is magnified 2000 000 X (Fig. 2). The fractions are calculated using volume weighing. This is done to make the resulting distribution better comparable to XPS results: surface atoms as well as atoms below the surface contribute to the intensity of an XPS signal, giving a value for an average particle size somewhere between volume and surface average size. The volume weighed average particle diameter, as calculated from Fig. 2, is 7.2 nm. Note that the distribution is almost Gaussian shaped.

The results of the calculations for the experimental data are represented in Table II. The initial values for the infinity ratio and for the particle diameter are obtained by fitting an arbitrary value and the average diameter from the electron micrograph, respectively. The value for the coverage isesti­mated from several electron micrographs. Approximations for the values of the electron IMFP's are calculated using a universal IMFP relationship proposed by Szajman et al. II Evaluation of Table II results in an average particle size of 3.47 ± 1.24 nm. Since the uncertainty in the diameter by the program was 16%, the uncertainty in the position of the average particle diameter in a particle size distribution would be 0.56 nm. The particle size distribution thus ob­tained is represented in Fig. 3.

J. Vac. Sci. Technol. A, Vol. 7, No.3, May/Jun 1989

0.5 7.94 0.5 0.8 1.19

0.51 1.7 0.1 0.85 1.35

0.52 9.32 0.95 0.45 1.44

0.51 5.96 0.75 1.26 1.13

0.7 0.59 0.3 0.37 12 10.96 8 8.55

0.46 0.57 1.19 0.71 1.72 1.19

0.6 0.55 0.6 0.56 1.5 1.7 3 2.44

0.09 0.09 0.86 1.23 1.36 1.96

0.6 0.57 0.6 0.57 13 11.01 9 9.12

0.94 0.94 0.73 0.63 1.8 1.48

0.6 0.56 0.4 0.44 9 8.2 5 6

0.73 0.77 1.85 1.15 1.57 1.11

IV. DISCUSSION

During the course of developing this method, we have encountered several problems which have not been com­pletely resolved. They involve both limitations imposed by the data collection process and limitations imposed by the nonlinear least-squares algorithm. These are briefly dis­cussed as follows. It is preferable to obtain the infinity ratio experimentally. In principle, this can be done by making measurements on the bulk materials. However, bulk samples of manganese oxides suffer from severe charging, while car· bon substrates and MnOx particles on carbon substrates do not. This forces us to introduce the infinity ratio as a fifth variable parameter into the program. Another difficulty in­volves the dependency of the intensity ratio on the photoe­mission angle. According to the model, the intensity ratio should be larger at smaller photoemission angles [see Eqs.

30

25

20

~ 15 g

10

5

o 4.0 5.3 5.9 6.6 7.3 7.9 8.6 9.2 9.9 10.6

diameter (nm)

FIG. 2. Particle size distribution of MnOx on a C·foil sample, as obtained from the electron micrograph.

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1732 Berge, Young, and Bates: Characterization of supported metal oxide particles 1732

TABLE II. Results of fitting the best parameters to the experimental data.

Input value Output value Input value Output value Input value Output value Input value Output value Input value Output value

Infinity ratio 0.2 0.11 ± 0.09 0.1 0.08 ± 0.16 Diameter 4 3.57 ± 0.72 4 3.65 ± 2.32 Coverage 0.3 0.19±0.11 0.3 0.24 ± 0.25 IMFP(MnO,) I 1.39 ± 0.48 1 1.27 ± 1.19 IMFP(C) 1.5 1.54 ± 0.15 \.5 1.03 ± 1.39

( 1 ) and (2) ). However, for some of the samples this was not the case. Limitations imposed by the nonlinear least-squares algorithm are evident from the tables. From the convergen­cies in Table I, it can be seen that the parameters converge in groups (diameter and IMFP's, infinity ratio, and coverage). This is a result of the mathematical manipulations in the equations used in this model. A possible remedy might be to apply different weighing factors for the parameters in order to achieve simultaneous uniform convergence.

There are two fundamental limitations inherent in the model itself. In Eqs. (1), (2), and (3) the IMFP of a sup­port-originating photoelectron is considered as if all sup­port-originating photoelectrons travel through the overlayer material. This is true only when the coverage is unity for the heterogeneous catalyst. In our calculations we use the calcu­lated II value for the IMFP of carbon itself as initial param­eter. The second limitation results from the fact that the model assumes that the supported particles are uncontamin­ated. Thus, if the particles contain a carbon contamination layer, a three-layer model would be more appropriate. We could not discern any experimental evidence for carbon con­tamination of the MnO x particles. In all likelihood, any such contamination is masked by the strong C 1, peak of the sub­strate. In order to treat the three-layer case, the equations of Kuipers et al. would have to be completely modified.

The particle size distribution, as obtained with V AXPS, differs significantly from the one obtained with TEM. Be­sides the imperfection of the method of determining a parti­cle size distribution with V AXPS data, the TEM measure­ment itself may contribute to some of this discrepancy. First, the resolution limit of the electron microscope will prevent

1.0

g 0.5

U g

o 2 3 4 5

diameter (nm)

FIG. 3. Particle size distribution, as obtained from XPS data by using a nonlinear least·squares algorithm.

J. Vac. Sci. Technol. A, Vol. 7, No.3, May/Jun 1989

0.1 0.08 ± 0.08 0.2 0.11 ± 0.10 0.2 0.11 ± 0.14 3.5 3.33 ± 1.36 3.5 3.37 ± 0.89 3. 75 3.45 ± 0.93 0.3 0.24 ± 0.13 0.3 0.19 ± 0.12 0.3 0.19 ± 0.17 I 1.17 ± 0.78 1.22 ± 0.55 1.31 ± 0.52 1.5 1.16 ± 0.62 1.5 1.96 ± 0.36 1.5 1.05 ± 0.65

the detection of the smaller particles; this will cause a parti­cle size distribution shift to higher values. Second, the differ­ence in the nature of the average value, as pointed out above, makes the particle size distribution from TEM shift to high­er values relative to distribution from V AXPS. Finally, it has been suggested to us that the presence of different chemical species of manganese dioxides (MnO, Mn20 3, and Mn02 )

could complicate the comparison, because these species have different inelastic mean free paths. The suggestion is that the particles with the smallest inelastic mean free path could be responsible for most of the substrate intensity attenuation, but contribute least to the overlayer intensity.

These preliminary results certainly demonstrate the possi­bilities for this method to provide a means of determining particle size distributions on supported heterogeneous cata­lysts. As a continuation of the development of this method, we are addressing the effect of constrained parametrization and the effect of chemical speciation, since these are the ea­siest to investigate. The results of these studies will be report­ed in the near future.

ACKNOWLEDGMENTS

We are grateful for the support of the National Science Foundation (Grant No. RI1-850S120). P. ten Berge is grateful for the support of the Dutch Government. We thank D. Hoelzner and L. M. Yeh for their assistance in the charac­terization (TEM) and in the preparation of the samples. Finally, we thank P. Holloway for the use of his evaporator.

IS. C. Fung, J. Cata!. 58,454 (1979). 2J. P. Angevine, 1. C. Vartuli, and W. N. Delgass, in Proceedings of the Sixth International Congress on Catalysis, 1976, edited by G. C. Bond, P. B. Wells, and F. C. Tompkins (Chemical Society, London, 1977), Vol. 2, p.611.

'F. P. J. M. Kerkhof and A. Moulijn, J. Phys. Chern. 83, 454 (1979). 4H. P. C. E. Kuipers, H. C. E. van Leuven, and W. M. Visser, Surf. Sci. Int. Ana!' 8, 235 (1986). 'c. Defosse, J. Electron Spectrosc. Relat. Phenom. 23,157 (1981). 6R. Bouwman and P. Biloen, Surf. Sci. 41, 348 (1974). 7c. D. Wagner, Anal. Chern. 44,1050 (1972). "Fundamental Formulas o/Physics, edited by D. H. Menzel (Dover, New York, 1960), Vol. I, p. 80.

9D. G. Drummond, J. R. Microsc. Soc. 70, I (1950). 'OW. Murray, Numerical Methods/or Unconstrained Optimization (Aca­

demic, London, 1972). "J. Szajman, L. Liesegang, J. G. Jenkin, and R. C. G. Leckey, J. Electron.

Spectrosc. Relat. Phenom. 23, 97 (1981).

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