in situ study of the surface oxidation of fecr alloys using grazing incidence x-ray absorption...

In Situ Study of the Surface Oxidation of FeCr Alloys Using Grazing IncidenceX-ray Absorption Spectroscopy (GIXAS)

Joachim Janssena, Holger Rumpfb, Hartwig Modrowa, Ralf Rablbauerc, Georg Frommeyerc, andJosef Hormes*,a,d

a Bonn, Physikalisches Institut der Universität and b Center of Advanced European Studies and Research (CAESAR)c Düsseldorf, Max-Planck-Institut für Eisenforschung GmbHd Baton Rouge, LA/USA, Center for Advanced Microstructures and Devices

Received December 18th, 2002.

Abstract. The surface oxidation of FeCr alloys with 18, 28, and43 mass-% Cr was investigated in situ using grazing-incidence X-ray absorption spectroscopy (GIXAS) at the chromium and ironK-edges. Oxidation in air was monitored in situ in the temperaturerange from 290 K to 680 K. The standard GIXAS data analysis isextended for the treatment of a single layer model in order to esti-mate the chromium concentrations of the oxide layer and of thenear-interface substrate as well as the oxide layer thickness.XANES analysis shows transitions from b.c.c. Fe to corundum

Untersuchung der Oberflächenoxidation von FeCr Legierungen mittels GIXAS

Inhaltsübersicht. Die Oberflächenoxidation von FeCr Legierungenmit 18, 28 und 43 mass-% Chrom wurde in situ mittels Röntgenab-sorptionsspektroskopie unter streifendem Einfall (GIXAS) an denK-Kanten von Chrom und Eisen untersucht. Der Oxidationsver-lauf an Luft wurde im Temperaturbereich von 290-680 K in situbeobachtet. Die GIXAS Auswertung wurde für die Behandlungeines einfachen Schichtmodells erweitert, um so die Chromgehaltein Oxid und Grenzschicht sowie die Oxidschichtdicke quantitativ

Introduction

Solid state reactions are important in basic-scientific in-vestigations and in industrial applications. In many casesthese reactions will proceed via intermediate stages, whichoften involve unstable reaction intermediates [1]. To optim-ize and to control these reactions a detailed knowledge ofall intermediate steps is desirable. X-ray absorption spec-troscopy (XAS) is a very powerful technique for investiga-ting solid-state reactions as has been demonstrated in nu-merous publications [1�4]. In addition to solid-state reac-tions of the bulk, surface reactions are also of tremendousinterest as many reactions of industrial importance occur insurface layers (e.g., catalysis) and in cases where a solid ma-terial reacts with a gas or liquid the reactions start at the

* Prof. Dr. J. HormesPhysikalisches Institut der Universität BonnNussallee 12D-53115 BonnFax: (�49)-228-739756Email: [email protected]

Z. Anorg. Allg. Chem. 2003, 629, 1701�1708 DOI: 10.1002/zaac.200300134 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 1701

type Fe2O3 and from b.c.c. Cr to corundum type Cr2O3. The initialoxide layers are 1.1-1.4 nm thick and contain 60-90 mass-% chro-mium, while the near-interface substrate is depleted in Cr. Duringheating, iron oxide growth dominates up to 560-600 K. Then thechromium oxide layer loses its passivation effect and Cr oxidationsets in.

Keywords: Grazing incidence; X-ray absorption spectroscopy; Ironchromium alloys

abzuschätzen. Die XANES Auswertung zeigt Übergänge von b.c.c.Eisen zu korundischem Fe2O3 und von b.c.c. Chrom zu korundi-schem Cr2O3. Die Oxidschichten sind zu Beginn 1.1-1.4 nm dickund enthalten 60-90 mass-% Chrom, wogegen die Übergangszoneim Substrat chromarm ist. Während des Heizvorgangs dominiertdas Wachstum des Eisenoxids bis hin zu 560-600 K. Dann verliertdie Chromoxidschicht ihre passivierende Wirkung und starkeChromoxidation setzt ein.

surface before penetration into the bulk occurs. Here cor-rosion of steels, i.e. the reaction with either air or water, isprobably the most important example because of the eco-nomic damage caused [5]. The aim of the present paperis to demonstrate how surface sensitive X-ray absorptionspectroscopy, i.e. grazing-incidence-X-ray absorption spec-troscopy (GIXAS) [6], can be applied to study surface reac-tions. The objective of the theoretical part is to develop amethod for reflection mode GIXAS data analysis for a non-homogeneous, single-layer system. Based on this, the ele-ment concentrations of top layer and near-interface sub-strate as well as the thickness of the top layer were esti-mated. As an application of technical and theoretical inter-est we have chosen the oxidation of a set of iron chromiumalloys. The oxidation of stainless steels and, as a model sys-tem, of FeCr alloys has been extensively studied with a vari-ety of methods, which provide us with sufficient back-ground information to verify our GIXAS analysis results.Applied temperatures in investigations of the oxide layer onsteel include room temperature [7], 773-973 K for segre-gation studies [8, 9], and 1273 K [10, 11]. The formation ofoxide layers on FeCr alloys of several compositions at room

J. Janssen, H. Rumpf, H. Modrow, R. Rablbauer, G. Frommeyer, J. Hormes

temperature in air were studied and compared using angleresolved XPS (AR-XPS) for depth profiling [12]. The firststeps of the oxide formation on an FeCr surface were moni-tored in situ at low oxygen pressures with AR-XPS [13].Both studies utilize layer-model interpretation schemes. Theoxidation of Fe-17 %Cr at 473 K and 573 K in UHV at lowoxygen pressures was investigated using the energy-loss fea-tures of XPS peaks [14].

According to these and previous studies, the initial oxi-dation of a FeCr alloy takes place in three steps. These areoxygen dissociation accompanied by nucleation and lateralgrowth of Cr2O3, followed by the formation of an iron ox-ide layer containing Fe2� and Fe3�, and in the final stage,the growth of an outside Fe2O3 layer. The chromium-con-centration gradient varies from the outermost iron-rich ox-ide layer to an inner chromium-rich oxide layer. The near-surface part of the unoxidized substrate is again iron-rich.AR-XPS measurements yield estimates of the total thick-ness of the initial oxide layer on FeCr alloys ranging from1.3 nm [13] to about 3 nm [12], while the initial oxide thick-ness on stainless steel is generally given as approx. 2 nm.

Oxide layers on iron were studied in situ with XAS intransmission mode [4, 15], but a substrate thickness of onlya few nm, which is required to reduce the ratio of bulk tosurface signal, leads to difficulties in experiment and in-terpretation. Thick oxide layers on steel were recently stud-ied by conversion electron yield XAS [16], with a probingdepth of 10-100 nm. For measurements of the reflectedbeam at angles of incidence below the critical angle for totalexternal reflection (GIXAS) the vertical X-ray penetrationdepth is reduced to ca. 3-10 nm, which allows investigationof thin oxide layers. Therefore, GIXAS provides a powerfulnon-destructive, element-specific, surface-sensitive tool forin-situ studies. A grazing-incidence EXAFS study of theoxidation of stainless steel at high temperature was reportedpreviously [11].

We applied grazing-incidence X-ray-absorption spec-troscopy to FeCr alloys with 18, 28, and 43 Mass-% Cr,recording both Fe and Cr K-edge X-ray absorption near-edge structure (XANES) spectra. For the XANES analysiswe performed the required conversion of transmission-mode references to reflection mode [6]. The dynamical scat-tering theory of X-ray reflection is applied to the singlelayer model of an oxidized FeCr alloy. As a result, an ex-tended method of GIXAS data analysis is presented; it pro-vides depth information, i.e. oxide-layer thickness and ele-ment-concentration changes, simultaneously with thechemical-state information of the elements from XANESanalysis. Another advantage of GIXAS is that contri-butions of contaminating carbon layers, which complicatethe AR-XPS data interpretations, are negligible at the Crand Fe K-edge energies.

In addition to measurements of the initial oxide layer atroom temperature, the continuing oxidation process in airwas monitored in situ, while raising the temperature insmall steps from 290 K to 680 K. The influence of the dif-

2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim zaac.wiley-vch.de Z. Anorg. Allg. Chem. 2003, 629, 1701�17081702

ferent chromium contents upon the oxidation behaviourwas compared.

Experimental

Sample preparation

Electrolytic Fe (99.8 mass-%) with an impurity content of 140 ppmO and aluminothermic Cr (99.4 mass-%) with 400 ppm O wereused for the alloy preparation by induction melting in argon gasat the MPI für Eisenforschung, Düsseldorf, Germany. Three iron-chromium alloys with the nominal Cr contents of 18, 28, and43 mass-% were melted and deoxidized with C equivalent to the Oimpurity contents and then cast into a copper mould with a rec-tangular cross section of 30 mm � 60 mm. In the following, thesamples are referred to as Fe-18Cr, Fe-28Cr, and Fe-43Cr, respec-tively. Specimens of 80 x 16 x 6 mm3 were spark eroded and flycutto provide two parallel plane surfaces. The surfaces for investi-gation were wet grinded and diamond polished until a mirror finishwas obtained. High-resolution optical microscopy exhibited a lowdensity of oxide inclusions with a mean diameter of about 1 µmwithin the microstructures of the alloys.

Surface profiles of 1 mm length, recorded with a Tencor PL-10 atCAESAR, Bonn, Germany, show an rms-roughness of 25-45 A.For shorter segments of some 10-100 µm, corresponding to the firstFresnel zones for X-ray reflection, typical values are 20-30 A.

Recording of the spectra

Grazing incidence X-ray absorption spectra were recorded at beam-line BN2 in the synchrotron lab of the Electron Stretcher and Ac-celerator (ELSA) at the Institute of Physics in Bonn, Germany.The accelerator was operated in storage ring mode at 2.3 GeV withcurrents between 65 and 25 mA. A Lemmonier-type double crystalmonochromator (DCM) with Ge(220) crystals, 2d�4.0 A, was usedto scan the energy ranges 5960-6090 eV for Cr K-edge and 7070-7200 eV for Fe K-edge spectra in steps of about 0.5 eV. Scan dur-ation was 15-35 minutes, with integration times of 1.0 seconds perstep for Fe-K spectra and generally 1.5-2.0 seconds per step for Cr-K spectra, but up to 5.0 seconds per step at higher temperatures,depending on the spectrum quality. An austenitic stainless steel foilwas used as reference to calibrate the DCM, setting the first inflec-tion points in the Fe-K and Cr-K spectra to 7112 eV and to5989 eV, respectively. The grazing incidence setup has been de-scribed previously in [17�19]. Two slits with 250 micron width werelocated between the DCM and first ionization chamber to definethe beam plane and reduce divergence. The samples were mountedinside a sealed heating cell on top of a Huber goniometer. The cellatmosphere was air at 200 mbar. The reflection angle, chosen as0.28 degrees, well below the critical angles, was defined by the goni-ometer tilt and the vertical position of the third slit, located in frontof the second ionization chamber.

The sample temperature was increased from 290 K to 680 K, insteps of 20 or 40 K. Heating time was 1-5 minutes per temperaturestep. A Newport PID controller kept the temperature constant dur-ing the recording of each spectrum. Monochromator scan was in-itiated immediately after each temperature level was reached; theXANES region of interest was reached in 4-6 minutes. Repeatedmeasurements at constant temperature revealed that the oxidationrate during a scan was low compared to the oxidation rate duringthe heating periods. This kind of accelerated oxidation kinetics is

In Situ Study of the Surface Oxidation of FeCr Alloys

typical for thin oxide layers [5, 13]. The heating process for achiev-ing the next (higher) temperature was started immediately after theend of the spectral scan at the previous temperature.

Theoretical Considerations

Theory of grazing incidence X-ray absorptionspectroscopy

In the standard XAS experiment incident and transmittedintensity, I0 and IT, are measured with detection devices, e.g.ionization chambers, which provide a signal of the type I��a I�b. The offset b will be removed with dark current meas-urements. Lambert-Beer’s law yields

lnI�T

I�0�

aT

a0

� µmass ρd (1)

with sample thickness d, density ρ, mass absorption coef-ficient µmass, and the linear absorption coefficient µlin � ρµmass. The atomic absorption coefficient for a given absorp-tion edge, e.g. mK, is extracted by removing the absorptionbelow the edge as linear background and normalizing theedge jump to unity. Therefore, the transmission experimentprovides direct access to µlin(E) [20]. Fluorescence data atlarge angles of incidence can be analyzed in a similar way[20].

For small angles of incidence, the influence of scatteringcan no longer be neglected. The X-ray absorption finestructure (XAFS) features in GIXAS mode are altered andcannot be directly compared to transmission references [6].A theoretical description of dynamical scattering for vari-ous cases is given by Henke et al. [21]. Conversions ofGIXAS spectra to XAFS spectra have been performed onlyfor homogeneous systems [6, 22, 23], and not for thin-layerstructures. For an interpretation of GIXAS data, which isalso suitable for layered systems, transmission referencespectra are converted into GIXAS spectra [23�25]. In brief,the reflection at a surface is governed by Snell’s law [26]

cos θ2 �1

ncos θ1 , (2)

where θ1 is the angle of incidence, θ2 the complex angle ofrefraction, and n the complex index of refraction, whichcan be determined with transmission XAS [21]. Note thatθ2 is not the angle between surface and refracted beam. Forsmall angles of incidence, the reflected amplitude AR at thesurface of a homogeneous half space can be calculated withFresnel’s equation via the expression [26]

r �AR

A0

�θ2 � θ1

θ1 � θ2

. (3)

The reflected intensity R � �r�2 is reduced by scattering dueto surface roughness and thus the XANES features are sub-ject to an energy-dependent attenuation. Thus, the spectracalculated with (3) are modified using a roughness model

Z. Anorg. Allg. Chem. 2003, 629, 1701�1708 zaac.wiley-vch.de 2003 WILEY-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim 1703

Fig. 1 Total up and downwards propagating amplitudes ak andbk inside an infinite stack of unit layers for a beam originating fromthe top (a1) and the bottom (b4). Original beams are marked byopen arrows. The superposition ck describes a single layer on asubstrate of a second substance (shaded).

[27], which describes the surface as a function of the root-mean-square roughness. This model is applicable in the li-mit of small roughness features when compared to the Fres-nel zones [21].

With these simulated reference spectra we perform astandard XANES analysis of the GIXAS spectra, whichprovides information about the chemical state of an element[20]. The difference between transmitted and reflected spec-tra is illustrated in Figure 4 (b) and (c).

X-ray reflection of a simple layered system

In addition to the XANES analysis, retrieval of some keyinformation, from the spectra, regarding composition anddepth distribution was desired. In agreement with previousstudies of FeCr oxidation [12, 13], we applied the simplifiedmodel of a single oxide layer on top of the FeCr alloy sub-strate (Fig. 2).

The calculation of grazing-incidence X-ray fluorescencefor a general multilayer case has been performed by de Boer[28]. The entire fluorescence intensity originates from thetransmitted beam in the near surface region. In the homo-geneous half space the amplitude of the transmitted beamdecreases with depth by exp(-z/z0 ). Typical values are z0 �3-10 nm for grazing incidence, i.e. angle of incidence belowthe critical angle.

To describe the reflected beam for the case of a thin (withrespect to z0) surface layer on top of a thick substrate forangles below the critical angle and energies around the ab-sorption edge, a dynamical scattering approach is required[21, 29]. The single scattering approach, which is frequentlyused for reflection studies, is not sufficient here. Thus, weuse the dynamical scattering model, following the treatmentof Henke et al. [21], which includes the case of a finite layer,and extend it to the layer-substrate case.

First, we consider an infinite stack of individual unit celllayers of substance 1 (Fig. 1). The total downwards andupwards propagating amplitudes, Tj and Sj, in any layer j


are related by Tj�1 � x Tj and Sj � x Sj�1, respectively,where x is a complex transition factor [21, 26]. We use theforward-scattering approximation for small angles to calcu-late the transition factor. For the attenuation of the incidentamplitude with depth, also termed primary extinction [26],we write �xN� � exp(-t/t0), where t is the total thickness ofN unit layers and t0 is a material parameter. The reflectionr1 of substance 1, as defined in equation (3), is written asr1 � Sj / Tj, at each layer with an infinite half space beneath.For a deeper layer we get Tj�N � xN Tj and Sj�N � xN

r1Tj. If the initial beam comes from the top (Fig. 1 (a)), acomplete description of the amplitudes at the top and bot-tom of N layers, denoted j to j�N, can be written as: at j,downwards: a1 � 1, upwards: a2 � r1 a1, and at j�N, down-wards: a3 � xN a1, upwards: a4 � r1 xN a1. The amplitudea1 is an arbitrary parameter, which is set to unity. In theinverse situation, i.e. if the initial beam comes from the bot-tom (Fig. 1 (b)), we write (indices keep their meaning) at j,downwards: b1 � xN r1 b4, upwards: b2 � xN b4, and atj�N, downwards: b3 � r1 b4, upwards: b4 is a free param-eter.

Now, we define a superposition ck � ak � bk . The par-ameter b4 is used to include the boundary condition c4 �c3 r2 , where r2 is the reflection from a half space of a secondsubstance, which shall be below layer j�N (Fig. 1 (c)). Solv-ing this equation system yields

c1 � 1 � r1 x2N r2 � r1

1 � r1 r2

(4)

and

c2 � r1 � x2N r2 � r1

1 � r1 r2

. (5)

Then, the resulting reflected intensity is �c2 /c1�2 for N unit-cell layers of one substance with a total thickness t restingon top of a substrate. Four boundary cases are of specialinterest: (a) without a top layer we get x�1 and the reflectedamplitude is r2 , (b) for a very thick layer, setting x�0, thereflected amplitude is r1, (c) for a thin layer without a sub-strate, r2 � 0, we get (c2 /c1) � r1 (1-x2N)/(1-r1

2 x2N), thesame result as Henke et al. [21], and (d) without reflectionfrom the top layer, r1 � 0, the amplitude is (c2 /c1) � x2N r2.

Cases (c) and (d) prompt us to separate the measuredtotal reflected intensity Rmeas into two parts, as

Rmeas � g1 R1 � g2 R2 (6)

with coefficients g1 and g2. One term contains only the re-flection R1 � �r1�2 from the top layer, while the other con-tains the reflection R2 � �r2�2 from the substrate. We calcu-lated spectra �c2/c1�2 for a range of layer thickness values andwe found that the contribution of the substrate decreasesexponentially in the form g2 � exp(-α t / t0 ), where α takesthe value two and t0 is the material parameter introducedabove. Thus, the coefficient g2 provides direct access to thetop layer thickness t.


Fig. 2 Single layer model for an oxide layer of thickness t on topof an FeCr alloy. The chromium content v1

Cr in the top layer andv2

Cr in the transition zone may differ from the bulk value.

Application to the FeCr alloy system

We will now incorporate the real FeCr alloy system into thesingle-layer model, bearing in mind that the compositionmay change as a function of temperature and time (see Fig.2). The chromium content in the top layer shall be v1

Cr withv1

Fe � 1-v1Cr. If chromium enrichment takes place in the

top layer, then the unoxidized substrate must be depleted inCr near the oxide-bulk interface, because the mobility ofthe atoms is very low. The region of the substrate, whichcontributes to the reflected spectrum, is termed the tran-sition zone and is assigned an effective value, v2

Cr, for theCr content.

As in equation (6), the measured reflection spectra ofeach XANES region of interest (here at Cr-K edge) areseparated into two reference types, I and II, as

kCrmeas Rmeas � aCr

I (kCrI RCr

I ) � aCrII (kCr

II RCrII ) , (7)

where II is the contribution from the unoxidized transitionzone and I is the contribution from the oxide layer. If neces-sary, (7) may be extended to include more than one refer-ence spectrum for each reference type. Reference spectra areassigned to either I or II by their chemical state. Beforerunning a numerical fit, the measured GIXAS spectrumand the transformed references were normalized to an edgejump of unity. Normalized spectra are denoted by bracketsin equation (7). The normalization factors, e.g. kII

Cr, werecalculated from the transformed reference spectra and canbe written as a function of the Cr content, e.g. 1/kII

Cr �kII

Cr(σ) v2Cr, where the constant factors κ depend on sur-

face roughness and reference compound. Reference rough-ness σ was chosen to match the sample roughness (see be-low).

To describe the relative contribution of each referencetype to the GIXAS spectrum we write for Cr-K:

gCr1 � aCr

I kCrI / (aCr

I kCrI � aCr

II kCrII ) (8)

and

gCr2 � aCr

II kCrII / (aCr

I kCrI � aCr

II kCrII ) (9)


where g1Cr and g2

Cr correspond to the contribution of oxidelayer and substrate, respectively, see (6). Similarly, g1

Fe andg2

Fe values are calculated for Fe-K. In the calculation, theoxide layer thickness t depends upon the ratio of the appro-priate k-values of oxide layer and transition zone, i.e.

t �1

2tI,Cr0 ln �1 �

aCrI kCr

I

aCrII kCr

II� (10)

and

t �1

2tI,Fe0 ln �1 �

aFeI kFe

I

aFeII kFe

II� . (11)

The k-value ratios, kIFe / kII

Fe and kICr / kII

Cr, can be ex-pressed by the linear relations stated above; the result is aratio of transition-zone and oxide-layer chromium contentsand a constant factor of about 1.20 for Fe and 1.07 for Cr.By numerically solving

�1 �aCr

I kCrI

aCrII kCr

II�tI,Cr

0� �1 �

aFeI kFe

I

aFeII kFe

II�tI,Fe

0(12)

we can compute a corresponding set of first v1Cr and then

t for any given value of v2Cr. We expect v2

Cr to be smallerthan the corresponding bulk Cr content. By applying thisprocedure, we can determine v1

Cr, v2Cr, and t from only two

in situ GIXAS measurements, which also yield informationabout the chemical states of the present elements, and arelatively basic numerical fit.

If changes in Cr content as a function of temperature andtime are ignored, the two equations for t, (10) and (11),depend only on Cr-K and Fe-K fit results, respectively, andusually yield different values. Great differences in t for Cr-K and Fe-K indicate significant changes in Cr content.

Experimental Results and Discussion

Estimating the surface roughness parameter

Because of the experimental setup, e.g. reflecting area,sample alignment, beam divergence, slits, absorption by fillgas and kapton windows, and ionization chamber gain fac-tors, the measured spectra R� will differ from R � I / I0 bya factor, called GF. GF may change when the sample isheated and not re-aligned, but it is nearly independent ofphoton energy in the XANES region of interest. The otherparameters, sample roughness, Cr content, and XANESfeatures, influence the pre-edge (VK) and post-edge (NK)regions of the reflected spectra in a different manner. Wecalculated average values for these regions, which we chooseas 5982-5986 eV (VK) and 6020-6025 eV (NK) for Cr-Kspectra and 7105-7110 eV (VK) and 7145-7155 eV (NK) forFe-K spectra (see Fig. 3). In the ratio NK/VK, the attenu-ation factor GF divides out; therefore, the ratio NK/VKof measured spectra can be directly compared to that of


Fig. 3 Series of Fe-K GIXAS spectra of alloy Fe-28Cr at varioustemperatures. Pre-edge region (VK) and post-edge region (NK)are shown.

simulated spectra, which are a function of reference type,roughness and Cr content.

For the three alloys the roughness estimates based on Cr-K and Fe-K are in good agreement and yield, in the tem-perature range up to 500 K, for Fe-18Cr σ�2.5 nm, for Fe-28Cr σ�2.0 nm, and for Fe-43Cr σ�2.5 nm, all with anerror of ±0.5 nm. These roughness values are typical forthe polishing procedure we used and were confirmed by thesurface profile measurements.

GIXAS analysis

Figure 4 (a) shows Fe-K spectra after pre-edge subtractionand normalisation. Comparing the XANES features of themeasured spectra to those of simulated-reflection referencespectra (see Fig. 4 (b) and (c)) using a least-squares fitshows that a transition from b.c.c. FeCr to corundum type(Fe, Cr)2 O3 takes place in all temperature series. Analysisof the Cr-K spectra yields the same transition. Additionalreferences, including f.c.c. Cr, f.c.c. Fe, FeO, Fe3O4, chro-mite, and a large set of Cr-K spectra from oxidation states 0to VI [30], were used for comparison, but their contributionremained near error level or below.

Using the fit equation (12) with simulated reference spec-tra including the estimated roughness, we get aI

Cr and aIICr

for each Cr-K spectrum, i.e. at each sample temperaturevalue. The same applies to aI

Fe and aIIFe. In Figure 5, sum-

marizing the fit results, the different oxidation behaviour ofCr and Fe is clearly visible. While the fraction of oxidizediron is initially below 20 %, the fraction of oxidized chro-mium is already well above 60 %. During heating, the frac-tion of oxidized iron starts to increase continuously atabout 400 K and passes 50 % at ca. 450 K, 490 K, and530 K for sample Fe-18Cr, Fe-28Cr, and Fe-43Cr, respec-tively. Analysis of the data indicates that the fraction ofoxidized chromium remains almost constant up to 360 K,540 K, and 600 K, respectively, and then increases to 100 %within a small temperature interval of about 40 K. This ap-parent increase is connected to a decrease in Cr-K data


Fig. 4 (a) Normalized Fe-K GIXAS spectra of alloy Fe-28Cr, forthe same temperature values as in Fig. 3. Normalized transmissionspectra (dashed) for b.c.c. Iron (b) and Fe2O3 (c) compared to thecorresponding simulated reflection spectra (solid) at 0.28°, includ-ing roughness and 28 Mass-% Cr.

Fig. 5 Fit results: Fractions of oxidized references, aIFe and aI

Cr,and bulk references, aII

Fe and aIICr, at Fe-K (solid) and Cr-K (dot-

ted) edges, respectively, for the temperature series of the three alloyscontaining (a) 18, (b) 28, and (c) 43 Mass-% chromium.

quality, as the absorption (edge jump) becomes small com-pared to the total reflected intensity and approaches noiselevel. The error of the fractions is about 0.03 for Fe and0.05 for Cr. At temperatures above some 500-600 K the er-ror increases due to lower data quality. If a fraction value,usually the un-oxidized part, falls near to or below this er-


Fig. 6 Corresponding sets of Cr contents in oxide layer and tran-sition zone, v1

Cr and v2Cr, respectively, for the temperature series of

alloy Fe-28Cr. Chromium enrichment in the oxide must be ac-companied by depletion in the transition zone.

ror level, the relative error of one of the two thickness esti-mates, (10) or (11), used in equation (12) becomes verylarge. It is then only possible to calculate the oxide layerthickness based upon the absorption edge of the other ele-ment, usually Fe, until that also reaches almost completeoxidation.

We calculate the numerical solution of (12) for transitionzone chromium contents v2

Cr ranging from 5 % to 65 %.Figure 6 shows the corresponding oxide layer chromiumcontents v1

Cr for Fe-28Cr at various temperatures. At roomtemperature, v1

Cr is strongly increased to 60-85 %, while thecorresponding Fe enrichment decreases v2

Cr to 10-25 %.Samples Fe-18Cr and Fe-43Cr show similar behaviour withinitial values of v1

Cr � 65-90 % for v2Cr � 5-20 %, and

v1Cr � 75-95 % for v2

Cr �20-50 %, respectively. The oxide-layer-Cr content and the transition-zone-Fe enrichment in-crease with bulk Cr content. The relative changes arestrongest for Fe-18Cr. The Cr depletion in the transitionzone leads to a smaller contribution of unoxidized Cr,which results in large relative errors in equations (10) and(12) as aI

Cr reaches noise level.With rising temperature, up to about 540 K for Fe-28Cr,

the ratio v1Cr / v2

Cr decreases. As v2Cr is unlikely to rise far

beyond the bulk Cr content, the reason is a relative increaseof the Fe content in the oxide, i.e. a decrease of v1

Cr. Thisindicates that, after the initial passivation at room tempera-ture, Fe is oxidized much more rapidly than Cr, in agree-ment with [14, 31]. Starting at 560 K and more rapidlyabove 600 K, v1

Cr is rising again, which indicates a changein the oxidation process. It is known that the initial oxidelayer on pure Cr surfaces loses its passivation effect at about620 K and nucleation of Cr2O3 on the surface continues[32]. As the Fe oxide layer, which grows on top of the al-most pure Cr2O3 layer, has little or no passivation effect, itis reasonable to assume, that the Cr oxide barrier on FeCralloys prevents further Cr oxidation at similar temperaturesand in a similar way as on pure Cr. This explains the rapidtransition of the Cr oxide fraction aI

Cr towards 100 % and


Fig. 7 Estimate of the oxide layer thickness for Fe-18Cr, Fe-28Cr,and Fe-43Cr, (a) based on Cr-K and Fe-K spectra, and (b) usingFe-K spectra only and ignoring Cr enrichment.

the increase of the Cr content in the oxide layer (see Fig. 5).From the sets of v2

Cr and v1Cr values (Fig. 6), we deter-

mined the thickness t with equation (10) or (11). We choseintermediate transition zone Cr contents v2

Cr of 10 %, 20 %,and 30 % for Fe-18Cr, Fe-28Cr, and Fe-43Cr, respectively,to plot the oxide layer thickness vs. temperature (Fig. 7 (a)).An absolute variation of less than ±10 % in v2

Cr, which isconsidered most likely, results in a variation of about0.2 nm in thickness. The initial oxide layer thickness rangesfrom 0.9 nm to 1.1 nm for the three alloys. It appears tobe slightly higher for Fe-43Cr, but there is no significantdependency upon the bulk-Cr content. Apparently,18 mass-% Cr is sufficient to initiate the nucleation and lat-eral growth of a compact Cr2O3 passive layer, which stopsvertical growth after reaching about 1 nm thickness, inde-pendent of bulk Cr content. The steep increase of thickness(Fig. 7 (a)), at 380 K for Fe-18Cr and at about 600 K forFe-28Cr and Fe-43Cr, is a numerical artefact due to a Croxide fraction aI

Cr near 100 %, which leads to large errorsin the result of equation (10). For Fe-28Cr and Fe-43Cr, theoxide-layer thickness remains almost constant until about400 K, where it begins to increase. The growth rate is higherfor Fe-28Cr than for Fe-43Cr.

The thickness determination method used has a tendencyof slightly underestimating rough layers. A second method,based on case (c) of equations (4) and (5), was also used toestimate the oxide layer thickness. This approach yields val-ues too high for rough layers. The difference of the twois about 0.4-0.5 nm, almost independent of the total layerthickness. Therefore, the oxide layer thickness is probablysome 0.2-0.3 nm greater than shown in Figure 7 (a).

If we consider the thickness values based on Cr-K andFe-K separately (see equations (10) and (11)) and ignore thechanges in Cr content, the curves directly reflect the frac-tions in Figure 5, i.e. the Cr oxide remains almost constantin thickness up to about 560-600 K and the Fe oxide (seeFig. 7 (b)) grows continuously above some 380-400 K. The


oxidation of Fe is not prevented by the oxide layer, butslowed down compared to pure Fe [30]. Under the presentexperimental conditions, the oxide layer thickness that isdetermined directly from Fe-K, increases approximately lin-early with temperature. The slope is proportional to the en-riched transition zone Fe content. This indicates that theoxidation process is dominated by Fe3� cation migration tothe surface, rather than oxygen diffusion through the pas-sivation layer. Diffusion of Fe through compact Cr2O3 re-gions is unlikely, because the mobility and the solubility ofFe in Cr2O3 are low [14]. The main sites of Fe migrationare, therefore, faults and grain boundaries. Iron oxide isknown to form islands around the nucleation sites ratherthan to grow laterally [31]. This is in good agreement withthe facts that (a) the surface roughness increases slowly dur-ing Fe oxidation, (b) the Fe oxide does not prevent Cr oxi-dation at 620 K, and (c) the Fe oxide layer growth is notslowed by increasing thickness. The thickness values areoften the same order of magnitude as the vertical surfacevariation due to roughness and they also describe the is-land-forming oxide. Therefore, the term thickness is to beunderstood as a measure of the average absorber atomnumber per unit area.

Conclusions

The formation of thin oxide films on FeCr alloys of differ-ent compositions (Fe-18Cr, Fe-28Cr, and Fe-43Cr), con-taining 18, 28, and 43 mass-% Cr, respectively, during heat-ing from room temperature to 680 K has been characterizedusing in situ grazing-incidence X-ray absorption spec-troscopy.

The XANES analysis based on reference spectra con-verted to grazing-incidence geometry showed that tran-sitions from b.c.c. Fe to corundum type Fe2O3 and fromb.c.c. Cr to corundum type Cr2O3 take place.

A single layer model was introduced to interpret theGIXAS data and calculate the key parameters. The initialoxide layers were found to be about 1.1-1.4 nm thick. Thechromium enrichment in the oxide is very high, which re-sults in an almost compact Cr2O3 layer of about 1 nm thick-ness for all three alloys. The transition zone in the near-interface substrate is depleted in Cr, balancing the Cr en-richment of the oxide.

Further oxidation of Cr is prevented by the Cr-rich pass-ive layer up to about 620 K, similar to the behaviour ofpure Cr surfaces. Further oxidation of Fe is not preventedby the oxide layer, but slowed compared to the oxidation ofpure Fe. The linear increase of the thickness of the Fe oxidewith temperature, starting at ca. 400 K, is proportional tothe enhanced Fe content in the upper substrate. As a result,the respective enrichments of Cr and Fe in both oxide andsubstrate are reduced.

Comparing the three alloys, the growth of the oxide-layerthickness is slowed down with increasing Cr content. How-ever, a bulk-Cr content of 18 mass-% is sufficient for theformation of a passivation layer. Greater Cr contents do


not improve this passivation layer significantly. The mainsites of Fe oxidation, i.e. surface defects and grain bound-aries, remain unchanged. The reduced Fe-oxidation rate, aresult of the Cr passive layer, can be explained by the lowerconcentration of Fe in the transition zone.

Acknowledgments. The authors would like to express their thanksto the staff at the MPI für Eisenforschung, Düsseldorf, and atCAESAR, Bonn, for their support and to M. Löcker at SiLab,Bonn University, for assistance with the optical microscopy. Finan-cial support by the Deutsche Forschungsgemeinschaft (DFG) inSchwerpunktprogramm 1010: Reaktivität von Festkörpern is grate-fully acknowledged.

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in situ study of the surface oxidation of fecr alloys using grazing incidence x-ray absorption...

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