Comparative study of morphology and surface composition of Al–Cr–Fe alloy powders produced by water and gas atomisation technologies

Applied Surface Science 210 (2003) 318–328

Comparative study of morphology and surface composition of Al–Cr–Fe alloy powders produced by water and gas atomisation technologies A.V. Krajnikova,*, V.V. Likutina, G.E. Thompsonb a

Institute for Problems of Materials Science, 3 Krzhyzhanivsky Street, Kiev 03142, Ukraine Corrosion and Protection Centre, University of Manchester Institute of Science and Technology, P.O. Box 88, Manchester M60 1QD, UK

b

Received 26 November 2002; accepted 15 January 2003

Abstract The morphology and surface composition of Al–Cr–Fe alloy powders of 0–63 and 63–100 mm size fractions, produced by gas and water atomisation, have been studied by scanning electron microscopy and Auger electron spectroscopy. While gas atomised particles are of spherical shape, water atomised powders are usually irregular in shape with a complex branched relief. The morphology and composition of surface oxides have been estimated. The surface oxide film is composed of aluminium oxides/hydroxides and contains no Fe and Cr atoms. Two to five water molecules are associated with one Al2O3 molecule on the surface of powders. The surface oxide film has a non-uniform thickness, with thick oxide islands separated by thinner oxide film. The parameters of the surface film morphology, such as the island coverage, the oxygen content and the thin film thickness, depend on the atomisation technology used and powder size fraction. Heavily and weakly oxidised powder groups present in all powder fractions are distinguished by Auger spectra analysis. Relationships between heavily and weakly oxidised powder groups are discussed as a function of atomisation technology and size fraction. # 2003 Elsevier Science B.V. All rights reserved. Keywords: Aluminium powder; Water atomisation; Surface segregation; Oxide film; AES

1. Introduction Alloying of aluminium with transition and rareearth metals is one of the promising ways for development of new alloys [1–4]. For example, Al–Cr–Fe base materials are often alloyed with Zr, Ti, Ni, V, etc. for high temperature applications [5–9]. Since transi-

*

Corresponding author. Tel.: þ380-44-4440294; fax: þ380-44-2446483. E-mail address: [email protected] (A.V. Krajnikov).

tion metals (TMs) usually have very low solubilities in the Al matrix, technologies of rapid solidification (RS), followed by appropriate compacting are necessary to secure the necessary compositions. Various technologies of gas atomisation (GA) have gained the largest ground [1] despite their high production expenses and increased explosiveness. Highpressure water atomisation (WA) has been found recently to show promise for production of high quality powders for various applications [10,11]. The main advantages of this approach are high manufacturability, low production price and operational

0169-4332/03/$ – see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0169-4332(03)00150-8

A.V. Krajnikov et al. / Applied Surface Science 210 (2003) 318–328

safety. However, surface oxidation and contamination of the powders remain the subject of discussions. Surface oxidation of GA powders has been studied previously in [12–15]. In particular, Nylund and Olefjord [14], and Osbilen et al. [15] showed experimentally that the surface film is essentially non-uniform in thickness. A part of the surface is covered with coarse islands of Al2O3 or Al(OH)3, depending on the atomisation conditions, while the thickness of the oxide film covering the rest of the surface does not usually exceed a few nanometers. However, no quantitative estimations of the parameters of surface oxide film morphology were made on the base of the above cited conception. The previous work [14,15] has been developed further by Krajnikov et al. [16] for analysis of the structure of surface oxides in WA powders. In particular, a semi-empirical model has been developed to estimate the main parameters of the surface oxide film, such as coverage, thickness and composition. Based on this model [16], it was concluded that the oxidation level of WA powders is generally similar to that of GA powders. A set of high performance Al–Zn–Mg and Al–Zn–Mg–Cu base alloys have been developed with the use of WA powders [17]. Here, a comparative study of the chemistry and morphology of Al–Cr–Fe alloy powders, produced by argon and water atomisation, is presented. The model of Krajnikov et al. [16] is further improved and used to determine the main characteristics of surface oxides in the selected alloys.

2. Experimental The alloy powders are shown in Table 1. Alloy 1 powders were atomised by both argon (G1) and water

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(W1). Alloy 2 powder, of increased Fe and Cr contents, was water atomised under similar to alloy W1 conditions (W2) and used to examine possible contributions of the bulk composition. After atomisation, all powders were sieved in several size fractions. In general, particle diameters varied in the range 0–200 mm, while approximately 60% of the total mass corresponded to 0–100 mm size fractions. Two size fractions, namely fine <63 mm (G1f, W1f and W2f) and coarse 63–100 mmm (G1c, W1c and W2c), were employed. The morphology of powder particles was examined by scanning electron microscopy (SEM). Characterisation of the chemistry and thickness of surface oxides was carried out by AES. The Auger analyses were performed in the ultra-high vacuum chamber (about 107 Pa) of the scanning Auger microprobe JAMP10S, JEOL. The accelerating voltage of the primary electron beam and the beam current were 10 kV and 10 nA, respectively. The diameter of the beam was approximately 1 mm. The spectra were recorded in the derivative mode, dN(E)/dE against the kinetic energy, E, with a cylindrical mirror analyser. The energy resolution, DE/E, of the analyser was approximately 0.6%. Auger peaks of aluminium, iron, chromium, carbon and oxygen were detected either on the surface or in subsurface layers. As a measure of the surface concentration of element i, the relative Auger peak height ratios, ri ¼ Ii /IAl, are reported, where Ii and IAl are the intensities of element i and Al (Al KLL) Auger peaks. A minimum of 20–30 spectra was usually accumulated from individual particles and the results were averaged for each powder sample. The root-mean-square deviations of mean values were calculated to characterise the scatter in data. Depth profiles were obtained using argon at 8 MPa pressure and an accelerating voltage

Table 1 Alloy composition (mass%) Alloy number

Atomisation technology

Size fraction (mm)

Fe

Cr

Zr

Mo

Al

G1f G1c W1f W1c W2f W2c

Gas atomisation Gas atomisation Water atomisation Water atomisation Water atomisation Water atomisation

63 63–100 63 63–100 63 63–100

1.5 1.5 1.5 1.5 10 10

8 8 8 8 11.3 11.3

– – – – 1.3 1.3

– – – – 1.3 1.3

Balance Balance Balance Balance Balance Balance

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of 3 kV for 0–70 min for sputtering. The sputtering rate was approximately 0.4 nm/min from sputtering a SiO2 film of known thickness. Aluminium signals appear at high energy (Al KLL 1394 eV) and at low energy (Al LMM). In contrast to the KLL series, the Al LMM peak is sensitive to chemical effects [18]. Oxidation of Al results in a clear energy shift of the Al LMM peak, which amounts to 14 eV. The Al LMM peak recorded from the metallic surface is positioned at a higher kinetic energy (approximately at 68 eV) than the peak obtained from an oxidised surface (approximately at 54 eV). Thus, the low-energy Al peaks can be used to determine the chemical state of Al by measuring the following peak ratios: rO ¼ IO /IAl KLL, rme ¼ IAl LMM (68 eV)/IAl KLL and rox ¼ IAl LMM (54 eV)/IAl KLL.

3. Results 3.1. Powder morphology Typical micrographs of WA and GA powders demonstrate a pronounced difference in particle morphology. GA powders are usually of spherical shape (Fig. 1a and b), as expected from the literature [19]. Fine particles tend to form agglomerates and fine satellites are frequently seen on the surface of coarser powders. The main features of WA powders are a complex relief and irregular shape of individual particles (Fig. 1c and d). This observation correlates well with studies of WA Al–Mg and Al–Zn–Mg alloy powders [16,20]. However, WA powders are remarkable in

Fig. 1. Typical micrographs of gas (a, b) and water (c, d) atomised powders at lower and higher magnifications.

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Fig. 2. Typical Auger spectra recorded from the powder surface for the cases of weak (a) and heavy (b) surface oxidation.

their diversity: some particles have relatively smooth surfaces, similar to GA powder, while others have increased roughness. Evidently, the very irregular shape of WA powder is due to specific solidification conditions. Then, if the particles are cooled and solidified before the surface tension can change, the liquid teardrops are fragmented by the shock of the atomising water into spheres. However, the WA technology provides relatively high uniformity of the bulk compositions of individual particles, which are weakly dependent on the particle shape and size fraction [20]. 3.2. Surface chemistry Fig. 2 shows two different types of the Auger spectra, which are typically recorded from the surface of both GA and WA powders. In the first case (Fig. 2a), both components of the Al LMM peak, namely, Al LMM 68 eV and Al LMM 54 eV, are simultaneously observed on the powder surface. In the second case (Fig. 2b), only oxidised component of the Al LMM peak at 54 eV is recorded on the surface, while the metallic signal at 68 eV does not exceed the noise level. Therefore, the spectra correspond to comparatively less and more oxidised particles.

The attenuation length of Auger electrons, l, is known to depend on their kinetic energy. In particular, the value of l for the Al LMM peaks is approximately 0.6 nm [16]. The flux of Auger electrons emitted from a surface decays exponentially, so that 95% of the electrons contributing to an Auger peak come from within a depth 3l from the surface. If the metallic Al LMM peak is detected (Fig. 2a), the oxide thickness should therefore not exceed a threshold value of 1.8 nm at least on a certain part of the surface. If the metallic Al LMM peak is completely attenuated (Fig. 2b), then the surface is completely covered with a rather thick, i.e. >1.8 nm, oxide film. Therefore, two powder fractions, which differ in oxidation level, can be distinguished in GA and WA powders using AES spectra and denoted as weakly and heavily oxidised fractions. As an oxidation criterion, the presence or absence of the reliably detected, e.g. rme > 0:05, metallic component of the Al LMM peak is taken. The Auger peaks of Fe and Cr are detected on the surface of some particles. No essential difference in Cr and Fe behaviour is observed between alloys 1 and 2. The intensities of the detected peaks are usually weaker as those expected from the Fe and Cr bulk compositions. Therefore, Fe and Cr do not form the surface oxides and are attenuated by the surface film.

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Table 2 Mean values of the relative intensities of Auger peaks and calculated effective thicknesses of the surface oxides in various powder fractions Alloy number

Oxidation state

Part of fraction (%)

rox

rme

rO

dox (nm)

G1f

Weakly oxidised Heavily oxidised

5–15 85–95

Limited number of particles 0.78  0.10

0.10  0.04

4.2  0.4

0.84

G1c

Weakly oxidised Heavily oxidised

85–95 5–15

0.86  0.07 Limited number of particles

0.24  0.03

3.03  0.10

0.61

W1f

Weakly oxidised Heavily oxidised

80–90 10–20

1.7  0.3 Limited number of particles

1.5  0.2

3.7  0.4

0.32

W1c

Weakly oxidised Heavily oxidised

85–95 5–15

1.3  0.2 Limited number of particles

1.9  0.2

3.44  0.11

0.24

W2f

Weakly oxidised Heavily oxidised

50–70 30–50

0.91  0.05 1.2  0.2

1.17  0.19 0.16  0.04

3.04  0.16 3.21  0.15

0.25 0.82

W2c

Weakly oxidised Heavily oxidised

85–95 5–15

1.03  0.9 Limited number of particles

0.75  0.9

3.0  0.2

0.36

This is in agreement with the results of other works [21]. Typical impurities, such as C, S, P and Ca, are detected on the surface of some powders. Powders with a detected C peak account for 90–95% of the total number of studied particles. A pronounced C peak is a common feature when samples are not prepared in situ. This signal originates from a thin contamination layer due to atmospheric contamination and disappears after a light cleaning by argon sputtering for a few minutes. Detailed analysis showed that the presence of carbon on a powder surface is caused by hydrocarbon and/or carbon/oxygen compounds [14,22]. Segregated P, S and Ca atoms are also accumulated in a very thin subsurface layer of about 30–40% of the powders. Contaminated raw materials, circulating water and drying conditions are considered to be possible sources of contamination. The mean values of rO, rme and rox, with the rootmean-square errors, are given in Table 2 for various powder fractions. Weakly oxidised particles dominate in all coarse fractions studied. The oxidation state of fine particles is more dependent on the alloy composition and atomisation technology. The weakly oxidised powder group covers approximately 15% of the total mass in W1f fraction, 40% in W2f and more than 90% in G1f powder. In contrast to rme, the parameters rO and rox are relatively weak functions of the oxidation state and fluctuate between 3.0 and 4.0 and 0.8–1.3

(except for W1f powder, where rox amounts to 1.7), respectively (Table 2).

4. Discussion 4.1. Estimation of effective surface oxide thickness For a very rough estimation, the morphology of surface oxides can be approximated by a uniform film of effective thickness dox. The value of dox is written as follows [23]:  ox
me me   I D l dox ¼ lox sin y  ln me  þ 1 (1) I Dox lox where Iox and Ime are the intensities of the oxidised and metallic components of the Al LMM peak recorded from the powder surface, D and l are the atomic density and the attenuation length, the indexes ‘ox’ and ‘me’ correspond to the surface oxide film and the underlying substrate metal, and y is the angle between the sample surface and the electron analyser (y ¼ 42 and sin y ¼ 0:67 for the JAMP-10S Auger microanalyser). The parameters used for dox calculation are as follows. Dox and Dme were taken as 46.05 and 60.24 at/nm3 for the oxide and the metal substrate, respectively [18]. The values of l were estimated on the basis of the wellknown formula of Tanuma–Powell–Penn [24] and

A.V. Krajnikov et al. / Applied Surface Science 210 (2003) 318–328 Table 3 Electron attenuation lengths calculated by Tanuma–Penn–Powell prediction formula Auger peak

Electron energy (eV)

Electron attenuation length (nm)

Al LMM (oxidised) Al LMM (metallic) O KLL Al KLL

53.4 66.4 510 1394

0.56 0.57 1.45 3.07

   

0.08 0.09 0.27 0.58

shown in Table 3. Detailed justification of the selected approach for the calculation of l has been given previously [16]. The results of the calculation, averaged over each powder fraction, are shown in Table 2. For weakly oxidised particles, dox varies from 0.25 to 0.6, while it

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exceeds 0.8 for heavily oxidised powder. Eq. (1) was also applied to calculate the values of dox for all individual particles; the results are summarised in the form of histograms in Fig. 3. In general, two maxima are seen, illustrating the presence of weakly and heavily oxidised groups in all powder fractions. The histograms are approximated by a combination of two Gaussian distributions describing bell-shaped curves similar to the normal (Gaussian) probability distribution function obtained from the following equation: ! A ðd  dox Þ2 yðdÞ ¼ y0 þ pffiffiffiffiffiffiffiffi exp  (2) w2 w p=2 where y0 is the baseline offset, A the total area under the curve from the baseline, dox the centre of the peak

Fig. 3. Histograms illustrating the number of particles as a function of the effective thickness of surface oxide film calculated by Eq. (2) for various powder groups.

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Table 4 Parameters of the Gaussian curves of Fig. 3 Alloy number

d1ox

w1

A1

d2ox

w2

A2

W1f W1c G1f G1c W2f W2c

0.30 0.40 0.14 0.35 0.31 0.31

0.05 0.31 0.05 0.24 0.36 0.22

0.13 0.09 0.005 0.09 0.08 0.10

0.75 0.95 0.58 1.05 1.06 1.05

0.154 0.16 0.21 0.10 0.14 0.15

0.02 0.01 0.10 0.01 0.03 0.01

that corresponds to the mean effective oxide thickness, and w is the standard deviation. All parameters of Eq. (2) derived from the approximated curves are summarised in Table 4. In terms of effective thicknesses, the values of dox for weakly oxidised powder groups (d1ox in Table 4) are 0.30– 0.40 nm (with the only exception for G1f, where d1ox ¼ 0:13). The variation of the effective thicknesses for heavily oxidised particles (d2ox in Table 4) is 0.75– 1.05 (0.58 for G1f). The parameter A, shown in Table 4, which illustrates relationships between two oxidation groups in each size fraction, correlates qualitatively with the estimations shown in Table 2. As shown in [16], the values of Auger peak intensities are insufficient for the description of the film morphology. A method based on Eq. (1) gives a very rough estimation of the film thickness and is mainly used to illustrate the presence of two oxidation groups. As mentioned before, the oxide film is of non-uniform thickness and its composition and parameters depend upon atomisation and handling conditions. Following [14,15], the morphology of the non-uniform oxide film is approximated by a combination of coarse islands and thin inter-island films. A model developed by Krajnikov et al. [16], allows determination of the main parameters of the non-uniform film, including the island coverage, the oxygen concentration and the thin film thickness. The model was applied to WA Al–Mg–Si alloy powders [16]. The surface covered with coarse islands was estimated about 60% of the total, while a thickness of the interparticle film was typically 3–8 monolayers. 4.2. Improved model for surface oxide morphology It is of interest to apply the model of Krajnikov et al. [16] for analysis of powders of similar composition

produced by GA and WA technologies. The following two assumptions of the original model can be redefined for improvement of modelling. First, the composition of the surface oxides was formerly supposed to correspond to Al2O3. Since powders produced by different technologies are under comparison now, it is reasonable to consider the oxide composition as a model parameter. Second, the original model simulates in-depth distributions of the intensities of all principal peaks of Al and O (rO, rme and rox) as a function of model parameters and compares the simulated curves with the experimental profiles obtained by means of ion etching in AES. The oxide film characteristics (z, x and the height of islands) are then determined by fitting the calculated and experimental curves. A sharp inflection is predicted to exist on both experimental and calculated profiles, which corresponds to the point of removal of the thin surface film (z ¼ 0) during ion etching. The accuracy of the curve fitting is dependent on the accuracy of the determination of the inflection point. Unfortunately, the above inflection on the experimental curves is usually rather smooth, as discussed previously in [16], and this reduces the accuracy of model predictions. It is now suggested to consider the coarse islands as three-dimensional or infinite height structures, because their real heights, which were model parameters in the original model, are too large to be removed by etching under the conditions employed. This new assumption reduces the number of model parameters and simplifies the fitting procedure. Summarising, the original model [16] can be improved and its usage can be simplified by adopting the following modifications. 1. The surface concentration of oxygen, C is taken as a model parameter. 2. The height of coarse islands is considered to be infinite. 3. The relative intensities of all O and Al peaks, such as rO, rme and rox, recorded from as-sputtered powder surfaces are used for model calculation instead of fitting the full experimental and calculated profile curves. This avoids a possible inaccuracy caused by uncertainty in the determination of the inflection point at the experimental profiling curves.

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Fig. 4. Coarse oxide island coverage (x) of the powder surface as a function of the thin oxide film thickness (z) calculated for heavily and weakly oxidised groups of both size fractions of GA and WA powders of alloys 1 and 2.

All mathematical equations, including some principal initial formulas, which are similar to those presented previously [16], are shown in Appendix A. 4.3. Modelling results The parameters C, z and x are calculated with the use of Eqs. (A.14)–(A.16) in Appendix A. Since the equations set is singular, their solution is represented as functions x ¼ xðzÞ and C ¼ CðzÞ. The value of C is a very weak function of z. Since the variation of C with z does not exceed 4–6% over the range of z used, this value is considered to be constant. The modelling results are presented in Fig. 4 in the form of functions x ¼ xðzÞ for all powder groups. The calculated oxygen

concentrations, C, together with the maximum values of z and x, derived from Fig. 3, are summarised in Table 5. The physical meaning of the maximum z and x are the film thickness for an extreme case of islandfree surface film and the island coverage for a further extreme case of z ¼ 0, respectively. WA and GA powders show similar levels of the oxygen content (Table 5). There is no direct correlation between the oxide composition and the values of z and x. The values of C in all powders vary from 0.71 to 0.83, corresponding to the formulas Al2 O3  2H2 O and Al2 O3  5H2 O, respectively. Therefore, the surface films in both WA and GA powders contain hydrated molecules: Two to five water molecules are associated in average with one Al2O3 molecule.

Table 5 Modelling results Alloy number

Oxidation state

C

xmax

zmax

xpractical

zpractical

G1f G1c W1f W1c

Heavily oxidised Weakly oxidised Weakly oxidised Weakly oxidised

0.81 0.77 0.8 0.75

0.97 0.93 0.67 0.75

4 3.6 1.8 2.1

0.71 0.48 0.05 0.13

3 2.6 1.8 1.9

W2f

Weakly oxidised Heavily oxidised

0.77 0.71

0.81 0.95

2.5 4

0.25 0.54

2 3

W2c

Weakly oxidised

0.83

0.72

2.1

0.11

1.9

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The curves x ¼ xðzÞ satisfy Eqs. (A.14)–(A.16) for GA powders at larger x and z values than those for WA powders with the exception of W2f oxidised group powder (Fig. 4). In other words, the surface of the GA powders is usually more oxidised than that of the WA powders. For two extreme cases, the structure of the surface oxides in GA powders can be simulated either as a set of three-dimensional islands covering 95–97% of the surface or as an island-free, uniform oxide film with a thickness of 3–4 monolayers (Table 5). The equation solutions for WA powders are located in a relatively narrow region and are weak functions of granulometric and chemical compositions (Fig. 4). The W2c group is generally more oxidised than other WA powders, while the weakly oxidised W2f group shows the lowest z and x values. The use of Auger peak intensities recorded after a prolonged ion etching narrows the region of equation solutions and enables determination of realistic values of x and z. The values of rO, rme and rox recorded from as-etched powder surface were recalculated by Eqs. (A.12) and (A.13) to obtain the values of island coverage, x. If x is known, then the real values of z can be unambiguously determined using the x ¼ xðzÞ dependencies. The calculated values of x and z pairs are shown in Table 5 for each powder group. So-called weakly and heavily oxidised groups are seen to differ mainly in their surface coverages (Table 5). For weakly oxidised powders, the parameter x varies between 0.05 and 0.48. In case of heavy oxidation, x is about 0.54–0.71. The values of z are overlap for all the powders and vary from 2 to 3 monolayers. Therefore, this parameter is a weak function of the applied technology or chemical composition and is mainly dependent on storage and handling conditions.

5. Conclusions 1. Individual particles of WA and GA powders of similar compositions are essentially different in powder shape and morphology. While all GA particles are spherical in shape, WA particles are of very irregular shape with a complex relief. 2. The developed theoretical model is applied to describe the morphology of surface oxides in terms of oxygen concentration and oxide thickness. The surface film in GA and WA powders contains

mainly aluminium oxide with hydrated water: Two to five water molecules are associated with one Al2O3 molecule. Fe and Cr do not contribute to the formation of the surface oxides. The structure of surface film is non-uniform in thickness. A part of the surface is covered with coarse oxide islands separated by thinner oxide film. 3. Both GA and WA powders contain weakly and heavily oxidized powder fractions. The coarse oxide islands cover 55–70% of the surface in heavily oxidized fractions while the island coverage in weakly oxidized powder does is less than 50%. The heavily oxidized powders dominate in fine size fraction of GA powder and amount to 30– 50% of the total mass in fine WA powders of alloy 2. All other powder groups contain 80–95% of weakly oxidized powders. 4. The oxidation of powder surface is mainly determined by the island coverage, while the thickness of interparticle film is almost independent of atomisation technology and powder composition. Acknowledgements The authors acknowledge financial support of the NATO Science for Peace Program (Project SfP 973264) and the US Air Force Office of Scientific Research (STCU Partner Project 061).

Appendix A The proposed model does not describe either kinetics or atomistic mechanisms of the surface oxide formation and focuses on the estimation of the most important morphological parameters of the surface oxides using the formal morphological similarity of the oxides formed on the powder surface during atomisation and oxide films deposited onto a metal substrate. The model is based on the following main assumptions. (a) A binary aluminium-oxygen system is considered. (b) The aluminium substrate is initially clean and homogeneous in composition.

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(c) There is an exponential attenuation of the electron beam intensity through each layer of the film-substrate system. Ninety-five percentage of the total intensity of Auger peaks is attenuated within a layer of 3l. (d) A part of the surface is covered with rather thick oxide islands, when the rest of the surface is covered with a thinner oxide film. All islands are randomly distributed over the powder surface and have the same dimensions. The coverage x and the thickness of the thin film z are model parameters. (e) The thicknesses of all islands are considered to be by an order of magnitude greater than the values of 3l. Thus, the islands can be approximated as three-dimensional formations of an infinite thickness. (f) Both oxide film and islands are homogeneous in composition and in thickness. The model parameter C is the concentration (in atomic parts) of oxygen in the film and the islands. (g) All Al atoms in the oxidised state are concentrated in the oxide film and the islands, while all Al atoms in the metallic state are contained in the substrate. So, Al atoms from the oxides and from the substrate do not contribute to the Al LMM (54 eV) and to the Al LMM (68 eV) peaks, respectively. Under given approximations, the total intensity of the oxygen Auger peak consists of the contributions of two main structural elements and is written as IO ¼ IO ðiÞ þ IO ðf Þ

(A.1)

where IO(i), IO(f) are the intensities of the O signal emitted by the islands and the oxide film, respectively. The total intensity of any Al Auger peak is given as a sum of three components: IAl ¼ IAl ðiÞ þ IAl ðf Þ þ IAl ðs; f Þ

(A.2)

where IAl(i) and IAl(f) are similar to the abovedescribed terms; IAl(s, f) is the intensity of the Al signal recorded from a part of the substrate covered by the film. The contribution of the first layer of the film to IO(f) is given by
 d 1 IO ðf Þ ¼ Ið0ÞSO Cð1  xÞ exp  (A.3) lO

327

where SO is the relative sensitivity for oxygen atoms, d the monolayer thickness, l the attenuation length of Auger electrons calculated by [24], and the index O corresponds to the oxygen. The relative sensitivity factors used are as follows: SAl/SO ¼ 4:93 and SAl KLL/SAl LMM ¼ 2:465. The intensity of the O peak from kth layer of the film is written as
 dðk  1Þ k IO ðf Þ ¼ Ið0ÞSO Cð1  xÞ exp (A.4) lO Summing all layers, the IO(f) intensity is calculated as IO ðf Þ ¼

z X 1  expðzd=lO Þ IOk ¼ Ið0ÞSO Cð1  xÞ 1  expðd=lO Þ k¼1

(A.5) By analogy, similar calculation procedures are applied to all other terms, giving the following expressions: IO ðiÞ ¼ Ið0ÞSO Cx

1 1  expðd=lO Þ

IAl ðf Þ ¼ Ið0ÞSAl ð1  CÞð1  xÞ

IAl ðiÞ ¼ Ið0ÞSAl ð1  CÞx

(A.6)

1  expðzd=lAl Þ 1  expðd=lAl Þ (A.7)

1 1  expðd=lAl Þ

(A.8)

expðzd=lAl Þ 1  expðd=lAl Þ

(A.9)

IAl ðs; f Þ ¼ Ið0ÞSAl ð1  xÞ

The following notations are used to simplify the previous expressions: SAl ; 1  expðd=ðlAl cos yÞÞ SO A :¼ Ið0Þ ; 1  expðd=ðlO cos yÞÞ
 zd mðzÞ :¼ exp ; lAl cos y
 zd ZðzÞ :¼ exp lO cos y B :¼ Ið0Þ

(A.10)

As a result, the following equations are obtained: Ime ¼ Bð1  xÞm;

Iox ¼ Bð1  CÞð1  mð1  xÞÞ;

IO ¼ ACð1  Zð1  xÞÞ

(A.11)

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Using relative intensities, Eq. (A.11) are re-written to the following form: rox ð1  xÞm ¼ rme ð1  CÞð1  mð1  xÞÞ; A rO ð1  CÞð1  mð1  xÞÞ ¼ rox Cð1  Zð1  xÞÞ; B A (A.12) rO ð1  xÞm ¼ rme Cð1  Zð1  xÞÞ B where A SO 1  expðd=ðlO cos yÞÞ ¼  B SAl 1  expðd=ðlAl cos yÞÞ

(A.13)

The given equations set is singular because the intensities of high- and low-energy peaks of aluminium are not independent. Taking two equations and one of three main parameters (the thickness of a thin film z), a quadratic equation for C ¼ CðzÞ and x ¼ xðzÞ is obtained. ½aðZ  mÞ C2 þ ½mða þ bÞ  Za þ m C  m ¼ 0 (A.14) x¼1

1  Cð1 þ bÞ mð1  CÞ  bZ

(A.15)

where
 A rme a :¼ ; B rO


 A rox b :¼ B rO

(A.16)

Expressions (A.14)–(A.16) can be used for calculation of x ¼ xðzÞ and C ¼ CðzÞ on the basis of a set of experimental values of rO, rme and rox.

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