Quantitative phase analysis and thickness measurement of surface-oxide layers in metal and alloy powders by the chemical-granular method

Applied Surface Science 133 Ž1998. 129–147

Quantitative phase analysis and thickness measurement of surface-oxide layers in metal and alloy powders by the chemical-granular method Pierre Bracconi a

a,)

, Lars Nyborg

b

UniÕersite´ de Bourgogne, Faculte´ des Sciences et Techniques, Laboratoire de Recherches sur la ReactiÕite ´ ´ des Solides (CNRS UMR 5613), BP 400, F-21011 Dijon Cedex, France b Chalmers UniÕersity of Technology, Department of Engineering Metals, S-41296 Goteborg, Sweden ¨ Received 28 February 1997; accepted 7 February 1998

Abstract The principles of the chemical-granular analysis of metal and alloy powders are reviewed and the results are compared with those provided by the spectroscopic analytical techniques XPS, AES and SIMS, including ion etching in their depth-profiling mode, when they are applied to the same materials. Several examples are analysed and it is shown that the chemical-granular method alone can provide the very same information as depth profiling. However, it is averaged over a macroscopic powder sample in contrast to one or a few single particles. Nevertheless, it is the combination of the chemical-granular and depth-profiling analyses that really provides an unparalleled description in quantitative terms of the phase composition and microstructure of either multiphase andror irregular surface layers resulting from oxidation, precipitation or contamination. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Chemical-granular analysis; Metal powder; Alloy powder

1. Introduction The contamination of particles of metal and alloy powders by elements of low atomic number, especially by oxygen, is generally strongly localised at their surface, where these elements may either react to form protective layers of compounds with more or less definite composition and structure or be simply adsorbed. This chemical aspect proves particularly important in the context of Powder Metallurgy ŽPrM., where the surface thus turns out to be the specific pathway into the final material for such impurities. The first step in controlling the purity and )

Corresponding author. E-mail: [email protected].

purity-related properties of PrM products is clearly to understand the surface chemical state of powders as they actually enter the densification processes. The major difficulty in assessing the chemical and microstructural features of a surface Že.g., oxide. phase resides in its usually very low concentration Žin the material as a whole. and very small dimensions. The solution to a problem linked with the surface chemistry of a particulate solid is generally searched for in resorting to surface analytical techniques ŽSAT. mostly based on electron or ion spectroscopies. Despite their vast record of successful applications, those techniques have certain inherent limitations. It is the aim of the present paper to show how fruitfully

0169-4332r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 1 9 4 - 9

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P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

they can be complemented by the more traditional approach of conventional analytical chemistry. This approach consists in investigating the relation between composition and granularity, namely, particle size or surface area. Here, it is referred to as the chemical-granular method ŽCGM.. 1.1. Limitations of surface analytical techniques It is not the authors’ purpose to discuss and compare the nature and advantages of extensively documented SATs, but just to emphasise where their application to the analysis of powders is confronted with difficulties. Most arguments developed in this section are based on well established experimental facts and theories relating to the interaction of electrons and ions with solid matter. The elemental composition and the thickness of the surface-oxide layer on the flat surface of bulk metallic samples are currently and reliably determined using Auger electron spectroscopy ŽAES., X-ray photoelectron spectroscopy ŽXPS. or secondary ion mass spectroscopy ŽSIMS.. The depth profile of a particular element, which is a plot of its concentration vs. depth under the surface, is currently accessible by resorting to controlled ion etching combined to one of the above SATs. In principle, angle-resolved AES or XPS w1–4x might be thought of as nondestructive alternatives, though limited in depth to only a few nanometers, i.e., to the escape depth of the emitted electrons. In fact, they require definite orientation of the analysed surface with respect to the electron analyser and, as shown for instance by Gunter and Niemantsverdriet w5x, a very large error results from applying angle-resolved XPS to rough surfaces. As for powders the situation is such that no significant dependence of the photoelectron current intensity is to be expected as could be verified by Cross and Dewing w6x. The so-called Tougaard method w7x, which is based on the numerical analysis of a single photoelectron spectrum, including a large section of its background on the low kinetic energy side, constitutes another approach to the nondestructive depth profiling of plane surfaces. Indeed, in a first step, the sophisticated numerical deconvolution procedure of the inelastic background and true photoelectron spectra is carried out by assuming and testing different types Žreferred to as classes. of concentration profiles of

the analysed elementŽs. in the surface region and in the substrate. From the best physically consistent results Žshowing only non-negative corrected intensities., it is possible in practice w8x to differentiate between an overlayer, an embedded Žburied. layer and a diffuse homogeneous distribution Žalloying.. However, in the case of an oxidised metallic surface, the interest of this would just be to confirm that oxygen is segregated in a surface-oxide layer – a trivial piece of information, in fact. Accordingly, the whole method would just come down to a refined background subtraction procedure and a traditional elemental analysis from the integrated photoelectron intensities. To the authors’ knowledge, the effect of surface roughness Žsuch as that of the outer surface of a powder bed. on the performance of the Tougaard method has not been investigated for itself, and it would be a mathematically difficult task to make sensible predictions based on considerations of the fundamental integral equation w9x, by trying, for instance, to incorporate a statistical distribution of photoelectron-emergence angles from the surface. Additional specific difficulties likely to limit the applicability of the Tougaard method in the present context should be expected from the fact that the photoelectron spectra of the metalŽs. in the substrate and of its Žtheir. oxidised states in the oxide layer have also to be desummed beforehand and also because the stoichiometry in the surface-oxide layer is generally an unknown element of the problem. Thus, in practice, the major limitations of SATs in their application to depth profiling result from the process of erosion by ion bombardment. They are both chemical and geometrical in nature, as the local chemistry of the analysed surface area Žincluding the subsurface., as well as its local orientation Žwith respect to primary beam and detector., simultaneously are key parameters of the etching process and are modified by it. When a layer of powder either stuck on or encrusted in a support is analysed, these limitations are likely to be accentuated, which may then reflect in a deterioration of the depth resolution. 1.1.1. Measurement of etched depth The etched depth is usually calculated from the experienced etching time and the experimentally determined etch rate. The etch rate calibration is currently carried out on model systems in essentially

P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

two ways. One way is to measure the time required to etch through an evaporated or elecrodeposited flat and continuous surface film of independently known thickness. Oxide films of Ta 2 O5 over Ta substrate constitute the most popular such calibration system. The use of deposited films made of the very material to be analysed is of course desirable but not always realisable. The alternative way is to measure the crater depth in the same bulk material as the surface film as a function of sputtering time using appropriate optical or mechanical measurement devices. The important points in these calibration procedures are Ž1. that flat surfaces have to be used so that erosion proceeds homogeneously at least initially and Ž2. that the average erosion rate remains constant with time, i.e., with sputter depth. This is no longer the case when dealing with powder particles of irregular shape just as with rough Že.g., fractured. surfaces of bulk materials. However, as will be shown later on, the CGM approach provides here an independent possibility for nonlocal depth-scale calibration. 1.1.2. Influence of etching on depth resolution The physical–chemical processes involved in surface etching by ion bombardment, which eventually affect the depth resolution, are well identified and documented throughout the literature w10,11x. In short, they consist of Ži. ion-beam mixing, Žii. matrix effects which include preferential sputtering and the so-called chemical effects Žwhich relate specifically to the action of adsorbed species, such as the enhancement of the ionisation yield of metallic elements by adsorbed oxygen., and Žiii. microgeometrical or topography effects. Their respective influences all add up in the achievable depth resolution but contribute differently to its variation with etched depth w10,11x. In practice, depth resolution also directly depends on etching parameters, principally ion mass, ionbeam energy and incidence angle. Based on literature reviews by Wittmaack w12x, Lea and Seah w13x and research papers by Barna et al. w14x and Likonen et al. w15,16x, it appears that in standard etching conditions of flat surfaces with layered structure, the practical relative interface width D zrz increases with decreasing film thickness and that the ultimate interface width cannot be reduced below around 1 nm even under the most favourable sample and

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analytical conditions. With surface films a few nanometers thick, ultimate D zrz values of about 0.2–0.3 should be reasonably expected. In order to successfully apply ion-beam etching and SAT to powder samples, an appropriate selection of analysis conditions, as well as an understanding of the effect of the Žessentially spherical. shape of particles on the analytical results used, are required. Provided this is accomplished, SAT associated with ion-beam etching will, indeed, give consistent and quite reliable information, as shown by several authors w6,17–24x. At this point, one may question whether a difference in achievable depth resolution may exist between analyses of flat surfaces and powder surfaces. For metal and alloy powders, and based on the literature data analysed in Appendix A, one is entitled to state that for the range of layer thickness of interest in the present context, typically 1–10 nm, the answer to that question is no. 1.1.2.1. Practice in application of SATs to powders. Depending on the analytical technique used, two different situations exist: either the lateral resolution is high enough to permit selection of appropriate analysis areas locally on individual particles, as in AES depth profiling and dynamic SIMS, or the analysis covers an area including several particles as in XPS or static SIMS. The former situation is normally more easily handled since the essential matter is to know the orientation of the local surface element analysed, something that is quite readily accomplished in the case of spherically shaped powders w20x. The latter situation Že.g., XPS depth profiling. requires greater attention and more complex and elaborate models. Such models or procedures based on either 2-D or 3-D representations are available w18x. Most of them deal, at least in their original concept, with the situation of a homogeneous surface layer on a powder substrate. However, the surface products may be heterogeneous in composition and thickness w22x, and particulate surface products may indeed exist w25x. One way of handling this in XPS depth profiling has been presented by Gonzalez-Elipe ´ et al. w26x. Although their work concerns studies of catalyst materials, their approach in dealing with the presence of inclusions in or within the etched thickness has general applicability. They assume a dispersed phase consisting of monosized cubic inclu-

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P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

sions on the surface and within the subsurface region, and apply a layer-by-layer sputtering model to this idealised globular structure. By considering the total contribution from exposed inclusions and from inclusions buried within the information depth below the surface, profiles are constructed which compare well with experimental results. Another way of handling the presence of particulate products on powder surfaces is to compare the experimental composition-depth profile with theoretical ones predicted for homogeneous surface-layer coverage on powder. Nylund and Olefjord w23x applied this approach in XPS depth profiling on Alpowder. They found that, although the AloxiderAl-metal intensity ratio before ion etching indicated an oxide thickness of 2 nm, the AloxiderAl-metal intensity ratio corresponding to the oxidermetal interface position was reached after 6-nm ion etching. This latter value was shown to be consistent with that Ž5.5 nm. determined by means of AES depth profiling on individual particles. Thus, it is essential that surface studies be based on the combination of several, or at least two, different surface analytical techniques. As will be shown in this paper, the information will be even further enhanced by the combination of SAT and CGM. In fact, it is inferred that cross-linkage of results between the two approaches is essential in either direction. CGM alone does not give any direct information on the nature and relative amounts of different surface-oxide phases but provides an independent way of controlling the thickness determined by SAT. Also, nondestructive analysis by means of XPS, including the determination of surface composition and layer thicknesses smaller than the effective electron escape depth, is connected with certain limitations. One obvious drawback already mentioned is the inability to use angle-resolved measurements or the unconfirmed applicability of the Tougaard method due to the powder shape. Even so, the orientation of the sample is important, since only those parts of the powder-particle surfaces that are both irradiated by the X-rays and seen by the analyser are analysed, and the effect of powder shape must be considered if one wants to determine the actual aÕerage angle of electron escape Žas it certainly deviates from that of the experimental configuration.. Thus, different experimental configurations and particle shape will im-

pose more or less severe difficulties. Applying a simple model based on the projection of a sphere covered with a thin layer, Cross and Dewing w6x came to the conclusion that the oxide thickness is overestimated by a factor of 2 if the flat surface approximation is used. This consideration is strictly valid only for very thin layers. Carney et al. w27x developed arguments to further suggest that an effective escape depth factor sin a s 0.5 Žwhere a would normally represent the angle between the surface and the analyser axis. should prevail for powder analyses regardless of the experimental set up and the actual value of a . Nyborg et al. w21x calculated for a specific experimental set up Žin which a s 38.5 and sin a s 0.62. that the escape depth factor for analysis of powder should range from 0.48 to 0.76 for oxide thickness over attenuation-length-ratio values rang¨ w28x modelled the structure of ing from 0 to 4. Unal an irregular oxide film on a flat substrate by islands of equal thickness superimposed on a continuous regular film. He showed that the average thickness extracted from the ratio of the XPS intensities of the oxide and substrate always underestimates the true mean thickness Žratio of film volume over substrate area.. The difference becomes substantial when the true mean thickness becomes equal or larger than the inelastic mean free path ŽIMFP. of the photoelectrons, and depending also on the surface coverage and relative height of the islands. All above examples demonstrate the need for detailed approaches in order to successfully interpret the results of surface analyses of powders. 1.2. The chemical-granular approach Evidence will be given in Section 2 that the combination of the CGM with SATs, coupled or not with ion etching, significantly enhances the quantitative description of reaction products on particle surfaces, and thus improves the general understanding of the chemical processes that take place on powder materials. Besides, utilisation of the CGM alone can also provide essential information on powder surface-related chemistry as shown in Section 2.1 below and in the literature as well w25x. The most generally appropriate concentration Ž C . and surface Ž S . variables to use in the present context are dimensionless weight fractions f Že.g., in m g

P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

gy1 or ppm. and specific surface area S Že.g., in m2 gy1 ., respectively. The slope of a C–S plot, dCrdS, will then directly measure surface concentrations in units of mass per surface area Že.g., in m g my2 .. At first sight, the requisite for this would be that the surface concentration just considered be really constant, i.e., independent of particle size or surface area. This proves to be the fact in many cases, making the evaluation of surface composition quite simple. Nevertheless, as will be shown later, steps in or bending of C–S curves may also be treated and can, in fact, provide indication of powder particle size dependent distribution of either surface compounds or bulk inclusions as well as. The following development makes explicit reference to metal and metal-oxide phases, but the formulae are general and applicable to other systems. 1.2.1. Expressions for the concentration of surfaceoxide phase(s) The basic microstructural model and the analytical and granular parameters are defined in Fig. 1. One considers a spherical particle of outer diameter D, consisting of a metal core covered with a continuous surface-oxide layer of uniform or mean thickness t. Transposing the following development to other definite geometrical shapes is trivial. The symbol r represents densities, f weight fractions and the metallic and oxide phases are indexed ‘met’ and ‘ox,’ respectively. In the simplest case, where a single surface-oxide phase covers a core of pure

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metal or alloy, the exact analytic expression of the weight fraction of oxide phase and its limit as trD ™ 0 are given by: f ox s

1 y Ž 1 y 2 trD .

3

rox

3

3 Ž 1 y 2 trD . rmet q 1 y Ž 1 y 2 trD . rox

rox 6 trD

f

rmet y Ž rmet y rox . 6 trD rox 6 t f . rmet D

Ž 1.

In most instances, the density of the overall composite material does not significantly depart from the density of the metal, so that the geometrical specific surface area of the composite sphere may be written as SGEOM f 6rrmet D and: f ox f rox = t = SGEOM . Ž 2. In the particular case of ultrafine powders, such as nanometric iron powders w29,30x, the exact expression for the composite density r Žcalculated from 1rr s f metrrmet q f oxrrox . may have to be used and Eq. Ž2. then takes the form: rmet f ox2 y 1 q f ox s rox = t = SGEOM . Ž 3. rox Eqs. Ž1. – Ž3. may be readily adapted to different simple microstructures of the surface film. In case the oxide layer consists of several dispersed phases, for instance of contiguous islands of equal thickness, the mean density of the surface layer will be used as rox . If the layer is made of concentric sublayers of density r i and thickness t i , Eq. Ž1. will be written as:

ž

/

Ý 6 ri ti f ox f

Fig. 1. Basic model of a spherical metal particle covered with a continuous and chemically homogeneous surface-oxide layer.

i

rmet D

s SGEOM

Ý ri ti .

Ž 4.

i

For powders made of particles of irregular shape andror with a rough surface, a single-particle linear dimension or the corresponding geometric surface are no longer pertinent granular parameters. In such cases, and within the limit of thin layers, Eqs. Ž3. and Ž4. can still be used by substituting the true surface area of the material to SGEOM . In most, if not all practical cases, encountered in PrM, the surface area Ž S BET . as calculated by the BET procedure from vapour adsorption experiments will prove to be a good estimate of the true surface area.

P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

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1.2.2. Types of C–S plots to be expected with metallic granular materials Let the surface-oxide phase i be a binary oxide of generic formula Mi, nOm and oxygen content Žwhere M represents molar masses.: Oi s

m MO

.

m MO q n M M i

Ž 5.

The total oxygen concentration in the powder is expressed by:

Ý 6 r i t i Oi COtot

Ž ppm. s10

6

Ý f i Oif10 i

or 10 6 SBET

6

i

rmet D

Ý r i t i Oi .

Ž 6.

Fig. 2. Prototype C – S plots: Ž1. COcore s 0, t s cst; Ž2. COcore s cst, t s cst; Ž3. COcore sstep variation, t s cst; Ž4. COcore s cst, t s varying; Ž5. COcore s cst, no surface-oxide layer.

i

The total oxygen content may also include a contribution from the core of the particle COcore originating either from dispersed oxide inclusions or from dissolved oxygen, when chemically allowed. With f met s 1 y Ý i f i : COtot s f me COcore q 10 6

Ý f i Oi i

s COcore q 10 6 Ý f i Oi y COcore

ž

f COcore q S BET

i

Ý fi i

/

Ý Ž 10 6 Oi y COcore . ri t i .

Ž 7.

i

Thus, by analysing various powder-size fractions for oxygen and plotting COtot vs. either SBET or 1rD, various curves will be obtained as illustrated in Fig. 2. First, and provided that COcore and the surface-layer thickness and composition are independent of granularity, linear C–S plots are expected. Their intercept will either be zero Žcurve 1 in Fig. 2. in case the material contains no internal oxide inclusions or be a measure of the concentration of oxygen COcore associated with these inclusions Žcurve 2 in Fig. 2.. In either case, the slope value dCrdS contains information about the chemical, microstructural Žthickness. and structural Ždensity. characteristics of the surface-oxide phases. Since, usually to a very good approximation, C core < 10 6 Oi , evaluating dCrdS directly provides the numerical value of the compound term Ý i Oi r i t i .

By nature, the number of internal inclusions may differ from one particle to another and COcore may prove to be a constant only for reasons of statistical nature. But also, the probability of finding an inclusion may gradually or abruptly vanish as the particle size decreases below a certain threshold. Such characteristics will obviously result either in a gradual bending of or in a step in the C–S plots, as illustrated in Fig. 2 by curves 3 and 4. Finally, the trivial C–S plot illustrated by curve 5 in Fig. 2 emphasises the fact that C–S plots may formally indicate the absence of surface segregation. 1.2.3. Surface concentration and equiÕalent layer mean thickness As already mentioned, if dimensionless weight fraction is selected as the concentration variable and specific surface area as the granular parameter, the slope of a C–S plot will have the dimension of surface concentration in unit mass per unit surface area, typically expressed in practical unit m g my2 . Dividing the surface concentration so obtained by the specific gravity of the surface phaseŽs. provides one with the thickness of the equiÕalent surface layer which, in turns, is defined as the continuous layer of uniform thickness, the volume of which is equal to that of the actual layer. This may or may not correspond to the actual physical dispersion state, and additional information based on direct imaging

P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

using local analytical technique with sufficient lateral resolution are needed to answer the question. 1.2.4. Comparison with analysis by XPS and other SATs In contrast with CGM and the utilization of C–S plots, XPS is a direct and easy way of quantitative surface analysis in terms of oxidation state and, thus, of local phase composition. In addition, and provided that photoelectrons from the metal core can be detected, it is possible to extract from the corrected integral photoelectron intensities the value of the mean thickness of the surface-oxide layer based on the approximation of the equivalent plane layer and on numerical values for the IMFP of the photoelectrons into the oxide phaseŽs.. Nevertheless, in the case of a rough surface, as already mentioned, but also with surface-oxide layers made of islands or containing inclusions, and keeping in mind the difficulty to assess precise value for the IMPF in compounds w31x, the interest of CGM is obvious in affording a possibility of controlling the consistency of the various, just mentioned, approximations or numerical estimates of parameters that are used in interpreting XPS data. SATs using focused beams of either electrons ŽAES. or ions ŽSIMS. provide significantly higher lateral resolution than XPS, since, typically, submicron features can be probed. This becomes a crucial advantage when dealing with chemically heterogeneous surface layers or particulate surface compounds. A further major advantage of SATs lies in their high sensitivity, in the sense that they measure local concentrations compared to global concentration by CGM. For example, let us consider a 100-m m spherical steel particle covered by a monolayer of adsorbed water molecules. The global concentration of oxygen would amount to about 2 ppm, whereas the fractional photoelectron intensity IO rIFe , measured by means of XPS, would be about 10%. Typically, SATs are capable of measuring surface concentrations of less than 1% of a monolayer ŽAES. or even 1 = 10y6 ŽSIMS.. Such figures would correspond to global concentrations expressed in fractions of ppm or ppb, respectively. Finally the different and complementary character of CGM lies in the fact that it produces data that are

135

averaged over a lot of particles in a powder sample whereas electron- and ion beam-based techniques can probe comparatively fewer particles. 2. Comparison of experimental thickness determinations by CGM- and SAT-based depth profiling (SAT-DP) As outlined in Section 1, CGM can be used for the determination of the thickness of the equivalent oxide layer on the surface of metallic powder. This thickness can also be estimated by means of SAT-DP. Various experimental results previously published by the authors and other relevant data of similar nature taken from literature dedicated to PrM and surface science allow us to compare the merits of these two approaches. The considered materials, namely highpurity beryllium powder and various steel powders, suffice to illustrate all the basic prototypes of C–S plots defined in the previous section and assess the performance and relative interest of CGM. 2.1. CGM applied to beryllium powder The surface chemistry of beryllium is relatively simple and makes the case exemplary with respect to CGM, because light nonmetallic elements are practically insoluble in it and can form only a few definite binary compounds ŽBeO, Be 2 C, Be 3 N2 , etc... Some metal elements, such as cobalt or nickel, are soluble in Be and may provide examples for the trivial C–S plot as in curve 5 in Fig. 2; others, especially Fe and Al, may also form an intermetallic phase of varying thermal stability. In contrast, the granular characteristics of the investigated Brush-Wellman SP-65 powder are not simple, because the brittle metal is comminuted Žby impact attrition. and particles of indefinite shape and irregular surface are produced and specific surface area proves to be the pertinent granular parameter w32x. It was measured by the BET modelling of krypton physisorption at liquid nitrogen temperature. The C–S plots of elements O and H in Fig. 3, as well as those of the molecular species H 2 and H 2 O, measured by thermal desorption w33x, were all observed to fit the C–S plot of type 1 in Fig. 3. Indeed, the intercepts were, in all cases, either strictly zero or of the same order of magnitude as the detection limit of the analytical technique. Based on this, it can be

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P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

Fig. 3. C – S plots for beryllium powder of Ža. total oxygen; Žb. total hydrogen.

easily demonstrated that all the hydrogen in the material is initially bound to oxygen in one or several surface species, and the local stoichiometry in the surface layer can be readily calculated from the ratio of the slopes of the C–S plots for O and H in Fig. 3. It was found to be: BeO, 0.6 H 2 O. Deeper insight was afforded by additional phase analysis and quantitative thermal desorption. First, X-ray diffractometry showed that only a fraction the BeO is actually crystallised as such, the complement being necessarily engaged Žfree or combined. in some amorphous phase w32x. Second, temperatureprogrammed thermal desorption allowed the identification and measurement w33x of two binding states for water which were finally identified as dissocia-

Fig. 5. Comparison of the fractional intensities of Be 0 1s, Beq 1s, O 2y 1s, OHy and C1s photoelectrons measured on an unetched powder pellet to the values recalculated from the composition and thickness data appearing in Fig. 4.

tively adsorbed water and hydroxyl ions within an amorphous hydrated oxide. The detailed surface layer microstructure shown in Fig. 4 could thus be quantitatively assessed in the frame of the equivalent surface layer assumption by calculating the mean thickness of the intermediate sublayers by means of Eq. Ž6.. Although this could be done without resorting to any SAT-based depth profiling, XPS analysis on unetched as-received powder was performed and the results of both procedures are compared in Fig. 5. In fact, it is the XPS intensities that have been recalculated from the results of CGM and the graphical comparison emphasises the high degree of consistency of both approaches. 2.2. Combined CGM and SAT-DP applied to steel powders

Fig. 4. Average phase composition and microstructure of surfaceoxide and adsorption layer on Be powder particles.

2.2.1. High-speed steel: CGM and AES-DP Figs. 6 and 7 compare the CGM and AES-DP procedures of thickness determination for high-speed steel powder. The first figure shows the C–S plot in terms of ppm of oxygen vs. mean particle size Žarithmetic mean of sieves openings. of the size fractions analysed. The second illustrates a typical AES depth profile obtained on the powder. The slope of the straight line fitted to the data in Fig. 6 is 3.5 = 10 3 ppm m m Ž3.5 = 10y9 m.. As in all other cases considered in this paper, this fit is a standard linear regression of the concentration data on the

P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

granular data. From XPS analysis of the same powder, the surface oxide is known to consist mainly of iron oxide w34x. Assuming, as a first approximation, this to be Fe 2 O 3 Ž r s 5.26 g cmy3 , O Fe 2 O 3 s 0.30., and using the alloy density value r s 8.2 g cmy3 , the equivalent oxide layer thickness is calculated to be t ox s 3.1 nm. The corresponding thickness value estimated from AES depth profiles, such as the one in Fig. 7, is found to be 4.0 Ž"0.5. nm expressed in Ta 2 O5 units Žetching was done using a 2-kV Arq beam rastered over 2 = 2 mm2 and the etch rate was calibrated on flat oxidised Ta samples.. The estimation is done from the etch-depth value at which the O signal intensity equals the mean of its maximum and minimum. It appears that both methods give t ox values in the range 3–5 nm. However, that correlation can be improved by taking into account the fact that oxides on steel surfaces are sputtered at typically lower rates than Ta 2 O5 over Ta. Indeed, for standard conditions of sputtering of surface oxides on 304L steel Ž4-kV Arq beam., Tapping et al. w35x measured sputter rate values relative to Ta 2 O5 in the range of 0.75 to 0.80. This implies, in the present application, that the estimation of the oxide thickness from AESDP may be reduced to 3.0–3.2 nm. Thus, comparing the two methods of extracting the mean oxide thickness and considering the various factors involved in the procedures, a satisfactorily close correlation is found. An ultimate refinement of the CGM procedure would be to account for the fact that actual surface phase is not strictly pure Fe 2 O 3 . However, this would not significantly change the t ox value extracted from the C–S plot. An error is also ex-

Fig. 6. Tool steel powder. C – S plot for total oxygen.

137

Fig. 7. Tool steel powder. Auger electron depth profiles of oxygen and metallic components Fe, Ni and Ti.

pected in AES-DP due to measuring oxide thickness at half-oxygen intensity. For the range of thickness values of interest here this introduces an underestimation of t ox of about 10% Žsee Eq. ŽA3... 2.2.2. Gas-atomised 304L stainless steel: CGM combined with dynamic SIMS profiling and XPS analysis A nitrogen-atomised stainless steel powder has been investigated using the combination of techniques just mentioned. The aim was to arrive at a thorough and accurate quantitative description of the oxidation state of the surface of the particles in the very state as they are introduced in the industrial hot-extrusion process w36x. Here again, CGM proves to be an irreplaceable complement to SAT. First, an XPS investigation of different sieved-size fractions, including in particular one fine Ž40 to 50 m m. and one coarse fraction Ž355 to 500 m m., was carried out without resort to ion etching. Only oxidised states of iron, chromium and manganese were detected and the respective relative 2p photoelectron intensities measured. In contrast, no signals corresponding to the metallic state of the same elements could be observed, thereby allowing one to set a lower limit to the total thickness of the surface-oxide and contamination layers of about 6–8 nm Žthat value corresponding to three times the estimated IMFP of the photoelectrons.. SIMS profiling of the two extreme size fractions yielded reproducible results of the type shown in Fig. 8. The etching rate was calibrated by measuring crater depths in the bulk

138

P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

Žextruded. alloy sample. The profiles in Fig. 8 were acquired in favourable instrumental conditions from a small rastered area on the top of a single large particle. Nevertheless, the only reliable piece of information that can be extracted is that chromium oxide is buried below an outer layer of iron and manganese oxides at an approximate mean depth of 6.3 nm, tentatively estimated from the maximum of the Cr signal. Such a situation is in general qualitative accordance with the mechanism of high-temperature oxidation Žand resulting oxide scales microstructure. of bulk samples of 304L stainless steel w37x. In fact, Fig. 8 is illustrative of the problems associated with ion etching of heterogeneous surfaces of multicomponent materials as already outlined in Section 1. The collective strong decrease of all signals at great depth Žsuch that the alloy core is reached. is meaningless in terms of chemical composition but reflects, instead, the deterioration of the secondary yield of the alloy elements when they are no longer enhanced by locally available oxygen. CGM has been applied here in a dual way. Total oxygen Ži.e., in the entire surface-oxide layer and alloy core. and the fraction of oxygen bound to iron in the outermost oxide layer have been measured in separate experiments in the different size fractions of the powder. As justified w36x, heat treating the powder in hydrogen atmosphere allows the selective reduction of iron oxide. The associated weight loss

Fig. 8. Gas-atomized 304L stainless steel powder. Ion microprobe depth profiles ŽIMP-DP. recorded on one particle from a 355 to 500 m m size fraction. Dotted lines and values for E1 and E compare the position of the Cr2 O 3 sublayer below the surface MnO and Fe 2 O 3 layer as they can be inferred the combination of CGM, XPS and IMP-DP.

Fig. 9. Gas-atomised 304L stainless steel powder. C – S plots for total oxygen, and oxygen bound to iron in the surface iron oxide as measured by selective hydrogen reduction using TGA.

can be measured by thermogravimetry and the weight fraction of iron oxide thus measured independently of XPS. The resulting C–S plots appear in Fig. 9. The C–S plot for iron oxide shows zero intercept and strict linearity. These features, again, are evidence Ža. of the localisation on the surface of the reducible iron oxide phase and Žb. of the invariance with particle size of its volume fraction in the outermost layer made of iron and manganese oxides. Assuming this outer layer has a uniform thickness, E1 , the fraction of manganese oxide in the powder can be computed from the fraction of iron oxide extracted of Fig. 9 and the ratio of the Mn over Fe XPS intensities. The C–S plot for total oxygen exhibits a linear section for particles with diameters larger than 100 m m, and some departure from linearity at smaller particle sizes Žthat last feature is addressed separately in Section 2.2.4 below.. The intercept of the linear section is a measure of the oxygen fraction in the core of the particles arising from internal oxide inclusions. From the difference between the fraction of surface oxygen measured by the slope and the fractions of oxygen in the iron and manganese oxide phases, the fraction of chromium oxide is readily obtained. Then, by means of Eq. Ž7. the total oxide layer thickness, E, can be computed rather accurately since all necessary parameters have been evaluated. The value E s 8.2 nm is obtained. Finally, assuming Cr2 O 3 to form a continuous and regular inner layer its thickness E2 is estimated at 2.4 nm

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Fig. 10. Gas-atomised 304L stainless steel powder: situation Žc. represents the most likely phase composition and microstructure in the oxide layer. Situations Ža. and Žb. can be ruled out. It would not be possible to discriminate the hypothetical situation Žd. from situation Žc..

and E1 at 5.8 nm. Accordingly, the most likely average surface microstructure of the oxide film on particles in the range 100–500 m m is sketched in Fig. 10c. Instead, and based on the same arguments, the situations represented by Fig. 10a and b can be ruled out whereas Fig. 10d exemplifies potential limitations of the procedure. For instance, the occurrence of either globular inclusions of additional, e.g., ternary oxide phases, or of a discontinuous Cr2 O 3 sublayer could not be discriminated in that way and would require careful SAT-DP or Auger microprobe imaging to be tentatively confirmed. In evaluating the sublayer thicknesses, no use was made of numerical values of either IMFP of photoelectrons or etch rate. The consequence is that the final figures so obtained are certainly more accurate and statistically more representative than those that could have been obtained using any single SAT-DP. 2.2.3. Iron-base superalloy: CGM and AES-DP applied to heterogeneous surface structures In the two cases considered previously, the surface oxide appeared to be more or less strictly homogeneous in thickness. This is not a general rule.

Instead, particulate compounds are often formed or oxide islands generated. Such more complicated surface-layer microstructures may arise as the powder, along its thermal history Že.g., during atomisation. experiences selective oxidation, surface segregation of elements and variable overall oxidation rates. The situation of a heterogeneous surface structure is illustrated in Fig. 11, which is a SEM micrograph of a gas-atomised Fe-base superalloy particle. Particulate reaction products in the submicron range are visible on the surface. AES line scans showing the distribution of Ti, C and O over the surface are superimposed on the micrograph. They were recorded after slight ion etching which removed the thin surfaceoxide layer beside the particulate compounds and adventitious surface carbon as well. As can be seen, the levels of Ti, C and O are simultaneously high as the line scans pass over the reaction products. Thus, it is inferred that particulate Ti x ŽO,C. y in the submicron size range is present on the surface together with a continuous oxide layer consisting of mainly Fe oxide as well as Cr and Ni oxides w34x. In this type of situation, assessment of a mean oxide thickness from a C–S plot becomes question-

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Fig. 11. Fe-base super alloy powder. Micrograph of a representative selected area on the surface of one particle showing submicron surface particulate compound particles. Traces of Ti, C and O Auger signals intensity recorded along the horizontal white line are shown.

able. However, as demonstrated now, the combination of CGM and SAT can again be utilised to extend the quantitative description of the powder surface composition. First and although the powder is covered in part by particulate products which contain oxygen, the C–S plot in Fig. 12 still shows a linear relationship between oxygen content and specific surface area. This may be taken to mean that the coverage of particulate Ti-compounds is independent of alloy particle size. Furthermore, using the same assumptions as for the tool steel above one can estimate the aÕerage oxide thickness at 3.5 nm, a

Fig. 12. Fe-base super alloy powder. C – S plot for total oxygen.

composite value, however, characteristic of the particulate Ti-compounds and thin surface-oxide layer on the other parts of the surface. The actual oxide film thickness t ox may be determined independently from the AES depth profile in Fig. 13. This profile was recorded on a single steel particle Žanalysis area: 10 = 10 m m2 ; 2-kV Arq beam rastered over 2 = 2 mm2 at 558 incidence angle.. Considering only the initial rapid decay of the oxygen signal profile, and based on a number of different such profiles, t ox is estimated at about 2 nm, which, once recalculated into stainless steel surface-oxide units instead of Ta 2 O5 , reduces to 1.5–1.6 nm. That value differs significantly from the one Ž3.5 nm. extracted from the C–S plot and that discrepancy can be used as an indicator for estimating the size and coverage of the Ti x ŽO,Y. y particles on the alloy surface. More precisely, if we let f S,ox and f S,comp be the fractional surface coverage of the oxide film and compounds respectively Ž f S,ox q f S,comp s 1., and use Eq. Ž7. with the approximations COcore < 10 6 Oox and < 10 6 Ocomp , we may write: Slope C–S plot rcompOcomp f t ox f S ,ox q t f rox Oox rox Oox comp S ,comp s 3.5 nm,

Ž 8.

where t comp represents the average thickness of the c o m p o u n d p a rtic le s. If th e v a lu e o f rcompOcomprrox Oox is not much different from unity, and using t ox s 1.5 nm and t comp s 100 nm, one gets f S,comp s 0.02.

Fig. 13. Fe-base super alloy powder. Auger electron depth profiles of oxygen and metallic components Fe, Ni and Ti.

P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

In contrast, judging from the initial and final O signal intensities in the AES depth profile only, one estimates from Eq. Ž8. the coverage at 0.15, which would correspond to an average Ti-compound particle size of ; 16 nm. There is therefore reason to believe that there exists a distribution of compoundparticle size extending to sizes significantly smaller than 100 nm. The conclusion here is that we arrive at an improved quantitative description compared to a situation where, for instance, only AES-DP was applied. AES-DP alone would only tell that the surface is covered by a 2-nm surface oxide and, at best, also indicate the presence of compound particles, whereas the high lateral-resolution analysis in the form of AES line scans pinpoints the presence of the Ti x ŽO,C. y particles. In order to derive the precise surface coverage of those particles, one would need to perform extended high-resolution analysis of the material. 2.2.4. Nonlinear C–S plots The application of CGM is, as evidenced by the examples presented, quite straightforward when dealing with homogeneous surface layers yielding linear C–S plots. As also demonstrated for the Fe-base superalloy powder, such linear relations may be found for composite surface structures. The situation, however, becomes somewhat more complicated when this relationship does not hold over the entire particle-size range investigated. There are observations that the linear relation fails to hold at the extremes of the C–S plot, either at the largest or smallest particle sizes. An example of the former is referred to by Water et al. w24x in their study on Ni-base superalloy powders. They found, using AES depth profiling, that the average oxide thickness was size-independent and compared its value to CGM data on total oxygen. Consistency in terms of mean oxide thickness around 5 nm was found for alloy particles - 150 m m in diameter. In contrast, for larger alloy particles, the weight fraction of total oxygen rose because of increasing surface over volume ratio associated with increasingly convoluted dendritic surface structure. At small particle sizes, the C–S plot may deviate from linearity as illustrated in Fig. 9 for the weight fraction of total oxygen in a gas-atomised 304L powder. The observed oxygen weight fraction, 252

141

ppm, for 45 m m particles is significantly lower than the 315 ppm figure extrapolated from the linear fit to the low 1rD section of the C–S plot. That difference may reflect a different surface-oxide thickness as surface-bound oxygen makes up the major part of total oxygen in smaller particles. Accordingly, it is actually observed that the smallest particles of atomised powder may deviate significantly in surface composition and oxide thickness compared to larger particles w38x. As demonstrated in Fig. 4-d of Ref. w38x for gas-atomised 12%Cr-steel powder, the average oxide thickness measured by means of AES depth profiling is the same, about 5.5 nm, for particles larger in diameter than about 40 m m. Below that limit, it decreases with particle size down to about 3 nm, a value characteristic of room temperature oxidation. Although it has not been justified, this type

Fig. 14. Water-atomised 304L stainless steel powder. Ža. C – S plot of total oxygen; Žb. average surface-oxide layer thickness measured by AES-DP.

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of situation may exist for other powders, and would then reflect in the C–S plots. To account for the observed difference in total oxygen of the 304L powder mentioned above, at constant bulk oxygen level the total oxide thickness has to be reduced by 30% from 8.2 down to 5.6 nm. An alternative explanation may also be found in a lower bulk oxygen content in the fine fraction. This would require that the probability of finding oxide inclusions is decreased significantly below a certain particle size because of, for instance, steric exclusion of large exogenous oxide inclusions from small alloy particles. The possible existence of either effects just discussed is directly and uniquely pointed to by the C–S plot, which informs about the need for additional metallographic examination. In all previous examples, the weight fraction of oxygen was observed to scale with the specific surface area of the powder, or at least within a certain particle size interval w24x. However, for materials such as water-atomised 304L powder, which possesses both irregular particle shape and strong particle-size-dependent oxidation w39x, no single mean oxide layer thickness can be assessed in any size range. From the C–S plot in Fig. 14a we can see that there is a continuous increase in oxygen weight fraction with increasing particle size. In the course

of water atomisation, the powder experiences essentially an oxidising environment in the form of water vapour, i.e., with unlimited availability of oxidant. Consequently, the main factor controlling the oxidation rate is the cooling rate Ži.e., particle size.. This is clearly demonstrated by the correlation between the average oxide thickness and the average particle size shown in Fig. 14b found by means of AES-DP. Indeed, oxide thickness increases from about 4 nm at 25-m m particle size to about 30 nm at 200-m m particle size. Standard linear regression of thickness data on particle size data gives the relationship: t ox Ž m m. s 0.15 = 10y3 D 0.99. Fig. 14b is based on AES-DP data collected on at least ten particles taken from each of the five different particle-size fractions Žsieve ranges.. The average oxide thickness is then assessed to the mean size of each sieve range. To account for the effect of the convoluted shape of the particles, the analytical procedure w40x Ži. considers only analyses of areas oriented as the flat etch rate calibration samples, and Žii. includes only profiles where the C signal arising from contaminants exhibit a rapid initial decay. Reconsidering the CGM plot in Fig. 14a in the light of AES-DP results in Fig. 14b would be as follows. Introducing a surface shape factor K Žtrue surface area over surface area of equivalent sphere.,

Fig. 15. Water-atomised 304L stainless steel powder. Representative SEM micrographs of particles from sizes fractions: Ža. - 43 m m, Žb. ) 175 m m.

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Table 1 Granular and chemical parameters of the water-atomised stainless steel powder Size fraction

D Ž m m. a

SGe om Žm2 rg. b

S BET Žm2 rg.

tox Žnm. a

wOtot x Žppm.

wOsurf x Žppm.

SiO 2 Žwt%. c

- 43 m m 43–61 m m 61–104 m m 104–175 m m

30.0 52.0 82.5 139.5

0.0250 0.0144 0.00909 0.00537

0.0554 0.0386 0.0360 0.0356

4.0 8.2 13.8 19.0

1800 2000 2200 2400

320 450 740 1000

46 38 30 23

a

Ref. w41x, paper VIII, Fig. 5. SGe om s 6rŽ r D .. c In oxide layer. Complements are Fe and Cr oxides.

b

the expression for the total oxygen concentration COtot in ppm, developed from Eq. Ž7., would be: COtot s COcore q COsurf

ž

s COcore q 1 = 10 6 Oox K

6

rmet D

/

t ox .

Ž 9.

Thus, the dependence of oxygen fraction on surfaceoxide thickness has to be interpreted in terms of varying bulk oxygen content or surface shape factor, or both. As evident from the SEM micrographs in Fig. 15a–b, K is dependent on particle size. This is confirmed by the comparison of the BET and geometric Ži.e., of equivalent sphere. surface areas in Table 1. The table also includes the fraction of oxygen bound to the surface calculated from its expression in Eq. Ž9.. Subtracting these values from the total oxygen in the various size fractions, one arrives at a bulk oxygen content of about 0.15 wt%, approximately independent of particle size. The total oxygen content of the powder before sieving is 0.21 wt% and obviously its major part, about 70%, is actually bound inside the particles, not to their surface.

3. Discussion and conclusion When SATs and depth profiling are applied to the analysis of irregular layers or rough surfaces, particularly on powders, their high degree of sophistication is not commensurate with their performances, expressed in terms of accuracy of the true concentration profile and also in terms of depth resolution at the nanometer scale. The present publication has

been aimed at demonstrating the interest of complementing the utilisation of SAT-DP by a chemicalgranular approach exploiting conventional chemical analysis and granulometry or surface area measurement. The example of a beryllium powder has been presented first in order to show how to obtain from an elaborate CGM procedure alone the detailed quantitative surface phase analysis and the measure of an equivalent mean thickness of the various surface phases by assuming them to form continuous regular layers. The final picture so obtained compared well with the result of a routine XPS analysis of the same material. In the following considered examples, consisting of various steel powders, it was shown that the corresponding more complicated surface situations could be more reliably or exhaustively comprehended when SAT-DP was complemented by CGM Že.g., in the case of iron base superalloy. or vice versa Že.g., in case of gas-atomised 304L stainless steel powder.. Indeed, the major improvement brought about by CGM is certainly that one is no longer bound to rely, for instance, on ion etching to define the depth scale and measure the layer thickness. Instead, in the various investigated cases, CGM appears to be accurate enough to serve rather as a reference for ion etching on those materials in their powdered state. And the same conclusion is likely to apply to other metals and alloys and also to nonmetallic systems, such as ceramic powders. This is all the more likely as charging effects further complicate the practical application of SAT to such materials by shifting the energy scale. Moreover, it is clear that SAT or CGM used alone would not give the complete picture of heterogeneous orrand irregular surfaces, such as consecutive surface layers of different chemical

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composition or composite surface structures of thinner and thicker reaction products. A main concern addressed in the application examples presented was the determination of oxidelayer thicknesses. For as-received gas-atomised powder of any nature, such thicknesses are typically in the range of 2–10 nm. The error in extracting the thickness value of a 1-phase oxide layer from a C–S plot would typically amount to less than 10% if the uncertainty on the mean particle size of a powder sample taken from a sieved size fraction is considered dominant, or even significantly less if only the quality of the linear least squares fit to the data is taken into account ŽAppendix B.. The uncertainty in the overall phase composition of a multiphase oxide layer is more difficult to appreciate and is somewhat case dependent. We assume that, in current situations, it should not contribute, again, by more than 10%. Evidently, this figure should be reduced if a reasonably accurate assessment of the nature and proportion of surfaceoxides phases is provided independently by SAT. In comparison, the error associated with the exact density values of the surface phases, due, for instance, to an unknown departure from stoichiometry or poor crystallisation, is certainly negligible. Thus, the total error in a standard application of the CGM method may safely be estimated at less than 20%. For the determination by means of, e.g., AES depth profiling, the errors in thickness estimation result from Ži. the uncertainty in oxidermetal-interface positioning related to depth resolution as discussed in Section 1.1.2 and Žii. the fact that the inflexion-point method usually applied theoretically underestimates the actual oxide thickness value. The oxide thickness reported for the application examples on powders are obtained from non-deconvoluted AES-DP using the condition I ŽO. s w I ŽO. max y I ŽO. min xr2 for equivalent etch-depth positioning. This condition is associated with the error function profile, which results from the sputtering of a stepfunction profile w3,11x as, e.g., a regular and homogeneous oxide layer on a flat substrate. However, the measure does not account for the effect of the electron attenuation length l. Accounting for this socalled l-effect is quite straightforward and commonly applied in SAT applications to flat surfaces. Now, this can also be done in the case of powder

surface as is demonstrated in Appendix C, based on a comparison of the measured O profile for tool steel powder with that predicted for the exponential decay of the OŽKLL. intensity. For this particular example, one may conclude that the measure at half O intensity underestimates the oxide thickness by 13%. But more generally, considering reasonable variation ranges of the instrumental and sample factors involved, the relative theoretical error associated with reading the layer thickness at half-maximum intensity of the profile would, in most cases, be about 10%, extending to 20% for very shallow layers, and provided that other factors do not affect significantly the depth resolution. An even equal, if not more important factor is the assessment of etch rate for the material studied. Here, the calibrated rate on a standard material may constitute a reproducibility of "10%, which would raise the final relative error D trt to 20–30%. A further complication may also arise from the fact that the etch rate on the studied material may significantly differ from that on the calibration standard. Indeed, it may just be impossible to elaborate a reference etch rate standard with the specifications required for that purpose and the very same chemical composition as the surface film under investigation. Here, the error involved cannot be appreciated a priori. However, as pointed out above, the combined GCMrSAT approach provides here an excellent way of controlling the etch rate, and should be recommended in all situation where proper calibration of etch rate is not practicable.

Appendix A. Comparison of SAT-based depthprofile resolution with model thin films and with powders From AES and XPS, depth-profiling analyses on metal and alloy powders reported on in the literature w17,19,20,40x, we find that depth resolution, D z, typically ranges between 1 and 6 nm for layer thicknesses of 1 to 10 nm as estimated from the same profiles. D z is measured by the depth-scale interval corresponding to the 0.84–0.16 interval on the reduced-intensity scale defined by Imax s 1 and Imin s 0. Accordingly, D zrz is obtained by dividing D z

P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

Fig. 16. Compiled data of depth resolution of AES-DP on thin films and powders.

by the depth measured at half-reduced intensity. It is implicitly assumed that the reduced profiles fit the error function. A limited number of depth-resolution data relating to thin films deposited on flat substrates and with thickness below ca. 10 nm have been compiled by Hofmann w42x and by Lea and Seah w13x. They are plotted together with the data relating to powders in Fig. 16. The similar magnitude and thickness dependence of both sets of data tend to show that, for such shallow oxide layers and standard analytical conditions, the depth resolution of Auger depth profiling is determined by the same physical phenomena, independent of surface topography. As justified in Appendix C, the calculated curve in Fig. 16 represents the error Žunderestimation. associated with measuring z at half-reduced intensity for average analytical and sample conditions Ž lsin a s 0.8.. Strictly, the experimental abscissa values of the data points in Fig. 16 should be increased by the corresponding correction calculated from Eq. ŽA.3..

Appendix B. Assessment of errors in measurements by the CGM The numerical estimate of the mean layer thickness or oxygen surface concentration is extracted from the slope, b, of the straight line fitted to the experimental points in the C–S plot, according to Eq. Ž6. or Eq. Ž7.. Generally, just as in Figs. 6, 9 and

145

12, the intercept, a s COcore is negligible compared to the term 10 6 Oi and its contribution to the slope in Eq. Ž7. may be neglected. Thus, the relative error on t ox will be essentially dominated by the uncertainty in b, s b , generated by the least-squares analysis. In all examples considered in the results section or in the literature w18,22,25x, the least-squares fit consists in a standard linear regression of the ordinates Y Žconcentrations. on the abscissa X Žgranular parameter., although, from a mathematical standpoint, applying a Y on X regression to a C–S plot is not strictly correct, since this assumes that all the experimental error is concentrated in the concentration data. Instead, should the error in the granular parameter be dominant, a linear regression of X on Y would be appropriate, and, if errors in both coordinates are significant, more elaborate least squares procedures have to be preferred w43–45x. However as may be anticipated the differences between the various estimates of b Žor a. by the different fitting methods are smaller than any particular estimate of s b . Using three fitting methods Žnamely standard linear regressions, the major axis and the reduced major-axis methods. we have calculated relative errors s brb ranging from 3.8 to 4.5% and from 6 to 7% for the two C–S plots in Fig. 9 for total oxygen and for oxygen bound to iron, respectively. However the s brb values so obtained only measure the ‘degree of linearity’ of the C–S plot. They do not integrate the a priori estimated uncertainty or probable error in the experimental data which, in the case of CGM, is usually more important in the granular parameter. Since generally sieved size fractions are analysed, one may choose to set the uncertainty D X on any X Ž1rD or S BET . at the arithmetic mean of the values of 1rD or 6rr D corresponding to the upper and lower sieve opening for every size fraction considered. For the sieve ranges used in the result section, one arrives at typical relative errors D XrX of 11–17%. If the errors in the Y data are comparatively negligible, these D X may be used to weight the X values in a X on Y weighted linear regression. For the two experimental C–S plots in Fig. 9, the s brb values so obtained are now 4% and 10%, respectively. If the uncertainty in the phase composition of the oxide layer is neglected, they may be regarded as typical estimates of the final relative error on t ox . Otherwise the theoretical rela-

P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

146

tive errors of the estimated average oxygen content and density of the oxide layer have to be appreciated and added to s brb. Appendix C. Assessment of electron attenuation effect on thickness determination by AES depth profiling The Auger electron intensity emitted from the surface of a homogeneous oxide layer on a flat substrate can be expressed as: t ox I Ž 0 . s I` 1 y exp y , Ž A.1 . lsin a

ž

/

where I` is the intensity recorded from an infinitely thick layer, t ox the true layer thickness, l the electron attenuation length, and a the take-off angle. Assuming layer-by-layer sputtering down to depth t Žmeasured from the initial surface., the measured intensity will be: t ox y t I Ž t . s I` 1 y exp y . Ž A.2 . lsin a

ž

/

Considering experimental conditions for which the angle between the normal to the analysed surface and the CMA-axis is 308, which makes an average a equalling about 408 Žsin a s 0.64., and using lOŽK LL. s 1.25 nm in Fe 2 O 3 as derived from the data of Seah and Dench w31x, we may construct a theoretical intensity decay using Eq. ŽA.2.. By setting an initial value of the layer thickness and applying an iterative procedure, we may then arrive at a reasonable fit between the initial parts of the resulting theoretical curve and of an experimental profile. Indeed, fitting the tail part of an experimental profile below ; 10% of the maximum intensity would require inclusion of a second exponential decay function with lower characteristic decay length than the electron attenuation length as observed in SIMS-DP for instance in Ref. w15x. Fig. 17 shows the experimentally recorded oxygen KVV intensity vs. etch depth for AES depth profiling on a tool steel particle together with the theoretical curve derived as outlined above. The depth profiling is carried out using a 2-kV Arq beam rastered over a 2 = 2-mm2 area. The AES analyses are performed with a 10 kV electron beam rastered over an area, about 5 = 5 m m2 , oriented on average

Fig. 17. Illustration of the error involved in measuring t ox from half-maximum intensity of the Auger depth profile of oxygen.

at 558 of ion incidence on a single 150-m m particle. It appears that there is a reasonably good fit between the two curves in Fig. 17, thus supporting the conclusion that the extrapolation of the theoretical curve to I Ž t . s 0 provides a measure of the true oxide thickness, here found to be 4.8 nm. The usual measure of oxide thickness at half oxygen intensity Žcf. Fig. 17. gives 4.25 nm. The difference between these two measures is 0.55 nm. The very same value can be computed from Eq. ŽA.3. which is derived from the ratio of Eq. ŽA.2. over Eq. ŽA.1. under the constrain Ž I Ž t ..rŽ I Ž0.. s 1r2, using the above mentioned values for lOŽK LL. and sin a : D t s t ox y t Ž I Ž t . rI Ž 0 . s1r2 . s t ox y lsin a Ln

ž

1

1 q

2

2 exp Ž ytox rlsin a .

/

.

Ž A.3 . The fit between the experimental and theoretical curves in Fig. 17 could, in fact, be even further improved by decreasing the oxide thickness value towards, say 4.6 nm. However, this cannot be justified from a phenomenological point of view, and there is also reason to suppose that sputtering-induced effects Žbeam mixing and local angular variation. will give a slight difference between the initial parts of the two curves.

P. Bracconi, L. Nyborgr Applied Surface Science 133 (1998) 129–147

Nevertheless, the comparison here shows that the underestimation of t ox by neglecting the l-effect is all the more important as the oxide layer is thinner. For lOŽK LL. ranging from 1 to 1.5 nm and sin a from 0.5 to 0.7, lsin a will vary between 0.5 and 1.05. Based on Eq. ŽA.3. we may evaluate the relative error D t ox rtox at 11–23% for t ox s 3 nm and at 3–7% for t ox s 10 nm.

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