Using X-ray Photoelectron Spectroscopy To Evaluate Size of Metal

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Using X-Ray Photoelectron Spectroscopy to Evaluate Size of Metal Nanoparticles in the Model Au/C Samples Mikhail Smirnov, Alexander V. Kalinkin, Andrey V. Bukhtiyarov, Igor P. Prosvirin, and Valerii I. Bukhtiyarov J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b02090 • Publication Date (Web): 04 May 2016 Downloaded from http://pubs.acs.org on May 6, 2016

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The Journal of Physical Chemistry

Using X-Ray Photoelectron Spectroscopy to Evaluate Size of Metal Nanoparticles in the Model Au/C Samples Mikhail Yu. Smirnov,*,† Alexander V. Kalinkin,† Andrey V. Bukhtiyarov,†,‡ Igor P. Prosvirin,†,‡ and Valerii I. Bukhtiyarov†,‡ †

Boreskov Institute of Catalysis SB RAS, Lavrentieva ave, 5, Novosibirsk 630090, Russia ‡

Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090

* e-mail: [email protected]; tel.: +7 3833 269 527; fax: +7 3833 308 056

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ABSTRACT: The work demonstrates the possibilities to determine the size of gold nanoparticles in the planar model Au/C systems based on the data of XPS using Davis’ method. The size of gold particles was evaluated using the normalized intensity ratio of the Au 4f7/2 and Au 3d3/2 lines excited by high-energy radiation Ag Lα (hν = 2983.4 eV). STM was used for direct control of the particle sizes. It is shown that the Davis’s method gives a satisfactory estimation of the size of gold particles deposited on the planar support, and the comparison of the XPS and STM data can provide an assumption of the geometric shape of the particles.


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1.

INTRODUCTION.

The XPS method provides detailed information on the chemical composition of the surface of solids and electron state of the elements forming the surface.1 Understanding of the mechanism of interaction of the reaction medium with the catalyst surface advanced greatly when XPS was used to study the model systems prepared as the nanoparticles of the active component (metal) supported with vacuum deposition over the thin film of support on the substrate of high-melting metal.2-4 When working with the model supported catalysts it is important in some cases to obtain the data on the size of particles of the supported metal immediately from analysis of XPS spectra without involving any additional structure methods. This information is necessary when investigating the socalled “size effect” in catalysis, when the particles of the active component of different sizes demonstrate different catalytic activity. There are two approaches to solving this problem today. The first approach is based on the fact that for the fine metal particles within the supported catalyst the binding energy (BE) of XPS lines characterizing the metal often depends on the particle size, growing higher as the particle size decreases. This phenomenon helps sometimes to quantitatively evaluate the particle size (d).5,6 The main drawback of this approach is that the dependence of the binding energy on the particle size is not universal and as such requires a preliminary work for calibration inevitably involving a structural method. In the other approach suggested by Davis the mean particle size of the supported metal is estimated with the help of the ratio of the intensities of two photoemission lines (or Auger-lines) of metal with significantly differing kinetic energies of photoelectrons (KE).7 The method of calculation is based on the dependence of the length of the inelastic mean free path of electron in substance (λ) on its kinetic energy. This approach features a number of advantages. The calculations engage solely the XPS data. The results of evaluation depends weakly on the support nature, specific 3 ACS Paragon Plus Environment


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area and roughness of its surface,7 and the λ values for any line in the XPS spectrum can be calculated with the use of Tougaard Quases-IMFP-TPP2M software with the formula suggested in.8 Earlier Davis’ method was used in refs 9-11 to determine the mean particle size for palladium, rhodium and nickel in the samples of powder catalysts, showing good agreement of the estimates obtained with XPS data with the results of transmission electron microscopy (TEM). However, there is a drawback in Davis’ method. As the standard radiations Al Kα and Mg Kα are used, the number of elements that have the pairs of the intensive lines with significantly differing KE in the XPS spectra is limited.7 The modern spectrometers equipped with the high-energy sources of radiation, for instance, based on monochromatized line Ag Lα (hν = 2984.3 eV), greatly widens the list of such elements. With the help of this type of radiation it becomes possible to study quite important systems with the supported gold and platinum particles with the use of 3d and 4f lines of these elements.12,13 Earlier we have shown an advantage of the use of radiation Ag Lα and Pt 3d5/2 line when studying Pt/Al2O3 catalysts with a low content of the active component.12,14,15 In this paper we show how to use Davis’ method to determine the size of the gold particles supported on the surface of the highly oriented pyrolytic graphite (HOPG) as radiation Ag Lα is used to register the XPS spectra. To calculate the mean particle size ( ) we used the normalized intensity ratios of Au 4f7/2 (KE ~ 2900 eV) and Au 3d3/2 (KE ~ 680 eV) lines obtained from the spectra of the samples of particles of the supported gold and gold foil. In addition, the mean size of the gold particles ( ) in all samples was determined from the histograms of the size distribution

of the particles obtained with STM. In order to reach the best agreement between the values of

and obtained with XPS and STM, respectively, the geometric shape of the gold particles was

varied (sphere, hemisphere, and truncated hemisphere) when calculating the particle size with Davis’ method.


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2.

EXPERIMENTAL SECTION

A single crystal of highly oriented pyrolytic graphite HOPG SPI-3 (“Structure Probe Inc.”, USA) was used as a support for preparing the Au/C samples. The samples were prepared and the XPS spectra were recorded in SPECS spectrometer (Germany). XPS spectra were registered with the help of monochromatized radiation Ag Lα (hν = 2984.3 eV). The high sensitivity and resolution of the spectral lines were provided by PHOIBOS-150-MCD-9 hemispheric analyzer with nine-channel detector. The photoelectrons were collected by the detector in the direction normal to the sample surface. When determining the precise value of the binding energy of the photoemission lines the C 1s line of graphite was used as an internal standard, its binding energy taken equal to 284.6 eV. With this method of calibrating the binding energies of the Au 4f7/2 and Au 3d3/2 lines for the gold foil and thick gold film deposited on HOPG were equal to 84.0 and 2291.6 eV, respectively. Before XPS study the graphite sample was mounted on the substrate of stainless steel and annealed for 1 hour in ultrahigh vacuum at 600 °C. The survey XPS spectra of such samples contained only the photoemission and Auger lines of carbon. Gold was deposited on graphite surface using EFM3 electron beam evaporator (“Omicron”, Germany) in UHV; the substrate temperature under deposition was close to RT. Two series of the samples were prepared for the study. In the first series the initial HOPG was used as the support; these samples were marked as Au/HOPG after the gold deposition. In the second series the support surface was shortly treated by argon ions with ion gun before gold depositing in order to create defects (argon pressure PAr = 3×10-6 mbar, accelerating voltage 0.5 kV, time of treatment 4 s). The samples obtained on such support were marked as Au/HOPG-A. STM images were obtained in UHV 7000 VT ultrahigh vacuum scanning tunneling microscope (RHK Technology, USA) operating on constant current mode. To process and analyze the obtained images the XPMPro 2.0 executive software of the microscope was used. For each 5 ACS Paragon Plus Environment


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sample the histograms of the size distribution of Au particles were plotted taking into account more than 300 particles. 3.

METHOD OF CALCULATION OF Au PARTICLES SIZE BY XPS DATA When calculating it is supposed that Au particles have the same shape and size and are

characterized with homogeneous distribution over the support surface. As the photoelectron spectra are recorded, the electrons registered by the detector leave Au particles in the direction normal to the sample surface. The intensity of photoemission from an atom located inside the gold particle, taking into account shielding by all above-laying atoms, is = e⁄λ , where

(1)

- is the intensity of photoemission from non-shielded atom;

z

- is the distance from the considered atom to the outer border of the particle with vacuum in the direction normal to the graphite surface;

λi

- is the length of the inelastic mean free path of electron in gold.

In expression 1 index i is used to mark the electron level of gold atom, from which the photoemission of electron takes place, i.e. i = 4f7/2, 3d3/2 (below i = 4f, 3d for brevity). The total intensity of the signal of line i from all atoms in the particle is calculated by integrating expression 1 over the whole volume of the particle considering its size and shape. Supposing that the

concentration of Au particles over the support surface is N cm-2, the total intensity of the signal

from all particles located on 1 cm2 of the support equals (see Appendix) = Here

ρ

∙ ∙ ∙ λ ∙ . 10

(2)

- density of gold, 19.3 g/cm3; 6 ACS Paragon Plus Environment

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NA

- Avogadro’s number, 6.022×1023 mole-1;

µ

- molecular mass of gold, 196.97 g/mole;

- function of the geometric parameters of the particle, the formula of which depends on the particle shape;

R

- radius of particle of spherical or hemispherical shape, nm.

The dimension factor 1/1021 appearing in expression 2 accounts for the fact that the values of R, z, λi are given in nm, whereas the density is measured in g/cm3. In Appendix the expressions of the

function are derived for the particles of spherical, hemispherical and truncated hemispherical shape (Figure 1). The corresponding expressions for are given in Table 1.

a

c

b

R

h = αR d = 2R

d = 2R

Figure 1. Particles of gold of hemispherical (a), truncated hemispherical (b) and spherical (c) shape over HOPG surface. For the intensity of the signal from the gold foil with conditionally endless thickness the following expression was obtained:



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-

1 1 = * ∙ ∙ + e⁄λ d, = * ∙ ∙ ∙ λ . 10 10

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(3)

Using the expressions 2 and 3 for two lines of gold, Au 4f7/2 and Au 3d3/2, one can determine the value of the normalized intensity ratio (NIR): NIR ≡

4f ∙ 3d 45

= . 3d ∙ 4f 67

(4)

With the given shape of gold particles in the model sample, the substitution of the values of intensities of photoemission lines measured for Au/C sample and for foil as well as of expressions

for functions 45 and 67 from Table 1 into expression 4 gives the equation the solution of which allows us to determine the mean particle size. The easiest way to solve equation 4 is by graphic method. Figure 2 shows the dependence of the ratio of the functions 45 ⁄67 on the diameter = 2R of the particles of spherical (1), hemispherical (2), and truncated hemispherical (3) shape.

If we draw a line parallel to the abscissa axis, the ordinate of which is equal to NIR value calculated from the intensities of photoemission lines of the given sample, then in the crossing point of this line with the 45 ⁄67 curve we shall obtain the value of diameter on the abscissa axis. 4.

RESULTS AND DISCUSSION 4.1. Au/HOPG. Figure 3 shows the STM image and histogram of size distribution of the

gold particles for one of the samples Au/HOPG obtained by depositing gold over the flat surface of graphite. The gold particles have rounded shape. The distribution of particles over the graphite surface is strongly inhomogeneous with the particles mostly concentrated at the support steps. Quite the same picture has been observed with the similarly prepared samples of the platinum particles

deposited on the flat graphite surface.16 Table 2 gives the mean sizes of the particles for 8 ACS Paragon Plus Environment

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Table 1. Function 89 : for the particles of different geometrical shape (see Figure 1).

Particle shape Hemisphere Truncated hemisphere Sphere

− 2λ ∙ ⁄λ ?

∙ ⁄λ ∙ 1 − A ? − 2λ ∙ ⁄λ λ + A ?, A = ℎ⁄

− 2λ ∙ ⁄λ ? + ∙ λ − 2λ ∙ + λ ∙ e>⁄λ + ∙ λ ∙ 2 + λ ∙ e>⁄λ 6



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F4f / F3d 1.0 1

0.8 2 3

0.6

0.4 0

2

4

6

8

10 d , nm XPS

Figure 2. Dependences of the ratio 45 ⁄67 on size of Au particles built for the particles of spherical (1), hemispherical (2), and truncated hemispherical (3) shape. The height to radius ratio of the particles of truncated hemispherical shape is equal to α = h/R = 0.6.

Table 2. XPS parameters of gold lines and mean diameter of the gold particles determined by XPS and STM data for the series of samples Au/HOPG. CDE4f*/ G, CDE3d6/ G,

cps

27.2

442

2291.8

46.6

2291.6

94.8

eV

1

84.1

2291.7

2

84.2

3

84.2

cps

3d ,

NIR

eV

Sample

4f ,

, nm

,

hemisphere

sphere

nm

0.539

4.5

2.2

1.5

588

0.693

9.0

4.5

2.5

1137

0.730

10.4

5.2

3.0


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100×100 nm

Portion of particles, % 30 20 10 0 0

2

4

6

8

10 d, nm

Figure 3. STM image (left) and histogram of size distribution of Au particles (right) in Au/HOPG sample 3.

the whole series of the samples Au/HOPG calculated by the histograms. According to the assigned numbers, the samples in the Table 2 are arranged in increasing amount of the deposited gold. Table 2 shows the values of intensities and binding energies of photoemission lines Au 4f7/2 and Au 3d3/2 obtained for the series of samples Au/HOPG. The intensities of the lines expectedly grow with the amount of deposited gold. The binding energies BE(Au 4f7/2) and BE(Au 3d3/2) for all samples in the series are close to 84.0 and 2291.6 eV measured for the gold foil and thick gold film deposited on the flat surface of HOPG. The intensities of photoemission lines obtained for the samples were used to calculate NIR taking into account that the intensities of the same lines recorded in the same conditions for the gold foil 4f = 5316 cps and 3d = 43981 cps. Solution of equation 4 by graphic method determined the diameters of the particles supposing that the particles have spherical or

hemispherical shape; the values are given in the corresponding columns in Table 2. It is seen that the 11 ACS Paragon Plus Environment


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values calculated by XPS data are closer to the corresponding values of supposing the particles are of spherical shape. The presumption on the spherical form of the particles should be considered rational. It follows from the fact that the interaction between the gold particle and carbon atoms on the flat surface of graphite is weak, and the particle shape is determined by interaction between the gold atoms. We should note that the agreement between the values of diameter calculated by XPS data and determined from STM histograms could be considered no more than satisfactory. We suppose that the reason for the observed differences is related to the peculiarities of calculation in consideration that all particles are of the same size. As STM data show, the

samples feature the particles of various sizes, with the width of size distribution growing with the mean size of the particles. It is evident that the largest particles contribute the most into the XPS intensities of Au 4f7/2 and Au 3d3/2 lines, which implies that the estimate calculated by XPS data should give a higher value than the mean size determined by STM. Indeed, as follows from Fig. 3,

for sample 3 (mean size = 3.0 nm) STM image shows the particles of 5-6 nm, which are likely

to determine the calculated value of , which is equal to 5.2 nm considering the spherical shape

of the particles. This problem could be solved by multiplying the right part of expression 2 by the function of size distribution of the particles. However, the purpose of this work is to study the possibility to estimate the particle size using solely XPS data, and under these conditions the function of distribution is unknown. It is not improbable that non-homogeneous distribution of the gold particles over the surface with their concentrating primarily near the steps, where the particles form 3D-agglomerates, also

produces a certain effect increasing .

4.2. Au/HOPG-A. Figure 4 gives the STM images of two samples Au/HOPG-A prepared by depositing gold over the graphite surface previously activated by Ar+ bombardment. The samples differ in the amount of deposited gold. The images presented in Figure 4 show that Au particles have 12 ACS Paragon Plus Environment

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Portion of particles, % 40

100×100 nm

a

30 20 10 0 0 100×100 nm

2

4

6

8

10 d, nm

6

8

10 d, nm

Portion of particles, % 50

b

40 30 20 10 R

0 0

2

4

Figure 4. STM images (left) and histograms of size distribution of Au particles (right) in Au/HOPG-A samples 5 (a) and 8 (b).

a rounded shape. The particles are distributed uniformly over the surface. It is supposed that in the process of gold deposition over HOPG the metal particles are fixed mainly over the structural defects formed during the surface bombardment.17-20 Figure 4 also gives the histograms of particles distribution by size, which were used to determine the mean diameter of particles. The values



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of obtained for all studied samples are given in Table 3. According to the assigned numbers, the samples in Table 3 are arranged in increasing amount of the deposited gold.

Table 3. XPS parameters of gold lines and mean diameter of the gold particles determined by XPS and STM data for the series of samples Au/HOPG-A. BE, eV

4f ,

4f7/2

3d3/2

cps

4

84.6

2292.8

5

84.5

6

3d , cps

NIR

10.6

218

2291.7

20.1

84.3

2291.9

7

84.3

8 9

Sample

, nm

,

h,

hemisphere

sphere

nm

nm

0.4022

1.32

0.66

1.5

0.6

357

0.4920

3.36

1.68

3.35

1.6

43.3

754

0.5031

3.63

1.81

4.5

1.4

2291.9

62.2

1110

0.4909

3.34

1.67

4.5

1.3

84.2

2291.8

70.9

1313

0.4729

2.92

0.73

4.9

1.1

84.2

2291.7

90.0

1456

0.5414

4.56

1.14

6.6

1.7

Table 3 presents the values of the intensities of Au 4f7/2 and Au 3d3/2 lines measured for the samples series Au/HOPG-A, as well as the corresponding values of the binding energies BE(Au 4f7/2) and BE(Au 3d3/2). The intensities of the lines grow with the amount of the deposited gold. The binding energies of the photoemission lines of gold in the studied samples also change, BE(Au 4f7/2) and BE(Au 3d3/2) in all samples being higher than the values obtained for gold foil (84.0 and 2291.6 eV), which could be explained by the final state effect of photoemission from the small particles.5 However, the fact that for Au particles deposited in similar conditions over the flat HOPG surface the binding energies BE(Au 4f7/2) and BE(Au 3d3/2) do not seem to depend on the size of the deposited particles and are very close to the values for bulk gold (see Table 2) makes it 14 ACS Paragon Plus Environment

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feasible that there is a chemical interaction between the gold particles and defects on the graphite surface in the samples Au/HOPG-A.13,19 According to the STM data as the amount of gold in the sample Au/HOPG-A increases, the mean size of particles grows, whereas the binding energies

BE(Au 4f7/2) and BE(Au 3d3/2) decrease from 84.6 to 84.2 eV and from 2292.8 to 2291.7 eV, respectively, approaching the values for bulk gold. The measured intensities of the photoemission lines Au 4f7/2 and Au 3d3/2 were used for calculating NIR. By solving equation 4 by graphic method on the assumption of spherical and hemispherical particle shape we determined the mean diameters of particles the values of

which are given in Table 3. It is clear that a better agreement with the STM data is reached on the assumption of hemispherical particle shape. Thus, the gold particles differ in shape over the flat and defective surfaces of HOPG. The gold particles are likely to form stronger chemical bonds with the surface defects, as a result of which adhesion of gold to the graphite surface grows, and the particle shape changes from spherical over the flat surface of HOPG to hemispherical over the defective surface of HOPG-A.

The graphical comparison of and is presented in Figure 5. We should note a good

agreement between these values for the finest particles, d < 4 nm. For larger particles the agreement between the results of STM and XPS methods can be taken as no more than satisfactory, with > . In our opinion, a significant factor resulting in the difference can be that the shape of

the particles is not perfectly hemispherical one. Thus, a number of STM studies of Au/HOPG systems with a support previously activated by ion bombardment showed that the particles of the supported gold have a flattened shape, and the particle height h is lower than its lateral radius R.17,18,20-23 The reason for the particle shape becoming flattened as the number of the atoms in them increases can be related to that the surface of graphite with defects has a higher surface energy as compared with the flat surface, and the adhesion of gold to the defective surface is stronger. 15 ACS Paragon Plus Environment


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dXPS, nm 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0

2

4

6

8 dSTM, nm

Figure 5. Comparison of the values of mean diameter of the gold particles in samples Au/HOPG-A measured by STM ( ) and calculated from XPS data on assumption of the hemispherical shape

of the particles ( ). The line corresponds to the coincidence of and .

Therefore in Appendix we derive an expression for 45 ⁄67 on the assumption that the particle shape is a truncated hemisphere with radius R and height h = αR (α < 1) as shown in Figure 1b. The

expression obtained for is given in Table 1. If we write over equation 4 in the form 4f ∙ 3d 45 A,

= 3d ∙ 4f 67 A,

(5)

and suppose that the particle radius R is determined from the size obtained by STM then the solution of equation 5 in α results in determining the particle height. Figure 6 presents an example of the graphic solution of equation 5 for one of the samples, and Table 3 gives the values of h determined by this method for all studied samples Au/HOPG-A. We should note that the calculated values of the height as well as ratios h/R agree well with those measured in refs 19,20. 16 ACS Paragon Plus Environment

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F4f / F3d 0.6 NIR 0.4

0.2 α = 0.525 h = 1.7

0.0 0

0.2

0.4

0.6

0.8

1.0

α

Figure 6. Dependence of 45 ⁄67 ratio on parameter α, which determines the height h of the particles with the shape of truncated hemisphere and with the specified particle size. The graph is crossed with the straight line corresponding to NIR in sample 9. We should also mention that another reason of the observed difference between and

can be that the STM method overestimates the lateral size of a particle supported over the surface, and the real diameter can be down to ~60% of the value measured by STM, as it has been reported in refs 17,21. 5.

CONCLUDING REMARKS

In this work we tried to use Davis’ method7 for evaluation of the size of particles of supported metal in the model planar systems Au/C with the use of XPS data. For exciting photoemission we used monochromatized radiation Ag Lα. The particle size was calculated with the use of normalized intensity ratio of Au 4f7/2 and Au 3d3/2 lines on the assumption of various geometric shapes of the gold particles on the graphite surface. It appeared that for the samples Au/HOPG prepared by 17 ACS Paragon Plus Environment


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depositing gold over the flat graphite surface calculated value of even in consideration of the spherical shape of the particles significantly exceeds the value obtained from STM data, which is a result of the wide histogram of size distribution of gold particles and a determinative contribution of the relatively large particles into the intensities of XPS lines. For the samples Au/HOPG-A prepared on the defective surface of graphite the best result is obtained on the assumption of hemispherical and truncated hemispherical shape of the gold particles. It seems that the difference in the shape of the metal particles for the samples Au/HOPG and Au/HOPG-A is a result of the different adhesion of gold to the flat and defective surface of graphite. In spite of the dependence of the result of calculation on the particle shape, it is supposed that this method can be used for evaluation of the size of supported particles also in other model systems, for which studying with microscopy methods is problematic. These systems include, for example, the particles of metals or their oxides on the oxide supports prepared as thin polycrystalline films on the bulk metal substrate, similar to those we have studied in refs 6,24-26. In addition to this the study has shown that an increase in the energy of exciting radiation in XPS expands significantly the list of chemical elements which can be studied with Davis’ method. The use of Ag Lα radiation makes it possible to evaluate the size of the particles of active component over the support surface considering only the data of XPS for the samples of the model planar systems containing Au or other important catalytic elements, such as W, Re, Os, Ir, and Pt. Thus the investigators get an additional tool for studying the effects related to the changing in the size of the particle of active component under the influence of the reaction medium, for instance, in the deactivation of the catalysts. ACKNOWLEDGMENTS The authors thank Russian Science Foundation (project 14-23-00146) for the financial support. 18 ACS Paragon Plus Environment

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APPENDIX A1.

The expressions for evaluation of the mean size of the gold particles over HOPG

surface To conduct the evaluation we used the spectra of Au 4f7/2 and Au 3d3/2 lines of the samples of the deposited gold particles and gold foil recorded with the use of Ag Lα radiation. Below the expressions for the particles of hemispherical, truncated hemispherical, and spherical shapes are derived. A1.1. Particles of hemispherical shape. In the left part of Figure A1 a hemispherical particle of gold with diameter d = 2R located over the surface of the support (HOPG) is depicted. It is shown that the photoelectrons are collected in the direction normal to the support surface.

e

-

hν

r

0 dz

R

d = 2R

z

Figure A1.

When calculating the intensity I(i) of photoemission line i (i = Au 4f7/2, Au 3d3/2) it is necessary to consider that the atoms located deep into the particle are shielded by the above-laying atoms, and the signal is attenuated exponentially on the length of the photoelectrons path z:



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= e⁄λ .

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(A1)

In top view the hemispherical particle looks as a circle with radius R, and the number of nonshielded atoms in the particle is equal to the number of atoms fitting into the area bounded by the circumference with radius R. As we move into the depth of the particle in the direction normal to the support surface for the distance z, the number of atoms subject to shielding expressed by formula A1 decreases monotonously. To calculate the number of atoms the emission of the electrons out of which is shielded by a layer with thickness z it is the most convenient way to use a reversed image of the particle given in the right part of Figure A1. In this case the number of atoms dn contained in the layer with thickness dz at the distance z from the base of the particle (corresponding to the coordinate z = 0) is equal to: dP = Q d, ∙

1 1 ∙ = ∙ ∙ 10 10

− , d,.

(A2)

Using expressions A1 and A2 we can determine the intensity of photoemission from one particle: >

>

1 + ∙ dP = ∙ ∙ ∙ + 10

− , ∙ e⁄λ d,.

(A3)

Taking the integral in the right part of expression A3 and multiplying by the number of gold particles N per 1 cm2 of HOPG surface produces the intensity of the photoemission signal from 1 cm2 of the sample: >

= + ∙ dP =

∙ ∙ ∙ λ ∙ , 10

where is the function depending on the particle radius: 20

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(A4)

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=

− 2λ ∙ ⁄λ ?.

(A5)

The intensity of the photoemission line i of the sample of bulk gold with the surface area 1 cm2: -

1 1 = * ∙ ∙ + e⁄λ d, = * ∙ ∙ ∙ λ . 10 10

(A6)

Let us write expressions A4 and A5 obtained for the photoemission lines Au 4f7/2 and Au 3d3/2 from the sample Au/HOPG and from bulk gold in the explicit form: 4f =

∙ ∙ 4f ∙ λ45 ∙ 45 , 10

3d =

∙ ∙ 3d ∙ λ67 ∙ 67 , 10

4f = 3d =

1 ∙ ∙ 4f ∙ λ45 ; 10*

(A7a)

(A7b)

(A7c)

1 ∙ ∙ 3d ∙ λ67 , 10*

(A7d)

which give the normalized intensity ratio of the Au 4f7/2 and Au 3d3/2 lines as expression A5 is used

for the functions : NIR ≡

4f ∙ 3d 45

= = 3d ∙ 4f 67

− 2λ45 ∙ ⁄λST ? . − 2λ > ⁄λVW X 67 ∙ Uλ67 − + λ67 e

(A8)

Expression A8 is included in Table 1 and then used for evaluation of the size of Au particles of hemispherical shape.



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Page 22 of 30

A1.2. Au particles of truncated hemispherical shape. The particles of truncated hemispherical shape can be presented as a hemisphere with a top cut off by a plane parallel to the base of the hemisphere and located at the height from the base h = αR (α < 1) (Figure A2).

z

dz

z

dx

0

d = 2R

x

h

r

x

Figure A2.

The intensity of the photoemission signal from the particles of such shape can be calculated using expression A3 with R being replaced with h in the upper limit of integration: Y

@>

= + ∙ dP = ∙ ∙ ∙ + 10

− , e⁄λ d,.

(A9)

After taking the integral in expression A9 for the intensity of photoemission line we get the expression similar to (A4): @>

= ∙ + dP =

∙ ∙ ∙ λ ∙ A, , 10

(A10)

in which A, =

∙ ⁄λ ∙ 1 − A ? − 2λ ∙ ⁄λ λ + A ?.


(A11)

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Expression for functions A, is included in Table 1, and their ratio is used for writing the equation similar to equation A8 which helps to find the particle height on the condition that the value for the particle radius is determined independently with STM data (see equation 5 and Figure 6 in the text). A1.3. Au particle of spherical shape. Calculation of the intensity of photoemission line of the spherical particle can be conducted if the particle is divided into two hemispheres, upper and lower (Figure A3). The expression for the intensity of the signal from the upper hemisphere has been given above in formulas A4 and A5. It is necessary to add to it the intensity of the signal from the lower hemisphere in order to obtain the intensity from the whole particle.

dz

R z

0

z

δ

x

dx

r

x

Figure A3.

In the lower hemisphere we select a layer of atoms with radius r and thickness dz, located at distance z down from the particle center (Figure A3). In the selected layer we choose the ring with the mean radius x ≤ r and width dx. In the volume of the selected ring 2[d[d, the number of gold

atoms dn is equal to: dP =

1 ∙ ∙ 2[d[d, = \ ∙ 2[d[d,. 10 23 ACS Paragon Plus Environment


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Page 24 of 30

Contribution from the atoms within the ring into the total photoemission signal taking into account the shielding by all above-laying atoms is equal to: 2π[\ ∙ ∙ exp ^− Here a = √

,+δ ` d[d,.

(A12)

λ

− [ is the distance from plane z = 0 to the outer surface of the upper hemisphere, on

which the atoms are located that participate in the shielding of the signal from the atoms in the selected volume ([d[d,) in the lower hemisphere. The photoemission signal created by the atoms of the lower hemisphere of one particle: >

√> f f

2\ + e⁄λ c +

[ ∙ exp d−

√

− [

λ

e d[ g d,.

(A13)

With taking sequentially the integrals in expression A13 and multiplying the result by the surface concentration of the particles, the contribution into the signal from the lower hemispheres is equal to: 3λ λ ∙ 2 ∙ λ ∙ k − λ ∙ + λ ∙ e>⁄λ + ∙ 2 + λ ∙ e>⁄λ l. 7hij = ∙ 10 4 4

Addition of the expression for 7hij to the one earlier obtained for the intensity of the

hemispherical particles (expressions A4 and A5), which can be marked as mn , results in the total

intensity of the line from all spherical particles located on 1 cm2 of the support surface: = mn + 7hij =

mn ∙ ∙ ∙ λ ∙ E + 27hij G, 10

where


(A14)

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mn

=

7hij

− 2λ ∙ ⁄λ ?,

(A15a)

3λ λ = − λ ∙ + λ ∙ e>⁄λ + ∙ 2 + λ ∙ e>⁄λ . 4 4

The normalized intensity ratio for the particles of the spherical shape is equal to: mn 4f ∙ 3d 45 45 + 2457hij

NIR ≡ = = mn . 7hij

3d ∙ 4f 67 67 + 267


(A15b)


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Page 26 of 30

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Table of Contents (TOC) Image

e-

I (3d) ∝ λ3d ⋅ F (R, λ3d ) hν

I (4f ) ∝ λ4f ⋅ F (R, λ4f )

Au particle λ3d R

λ4f

HOPG


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Using X-ray Photoelectron Spectroscopy To Evaluate Size of Metal

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