Surface segregation of Si on Fe single crystal surfaces and interaction with carbon

418

Surface

Science 173 (1986) 418-438 North-Holland. Amsterdam

SURFACE SEGREGATION OF Si ON Fe SINGLE CRYSTAL AND INFUSION WITH CARBON H. DE RUGY

SURFACES

* and H. VIEFHAUS

Max-Planck-Institut ftir Eisenforschung GmhH., D 4000 DiisseidorJ: Fed. Rep. of German,) Received

2 December

1985; accepted

for publication

26 March

1986

AES and LEED are apptied to the study of silicon surface segregation on Fe-3wt%Si single crystals between 400 and 900°C. The variations of the Si coverage with time at a given temperature or with the temperature at equilibrium show a strong orientation dependence. For the (100) orientation. the diffusivity and segregation enthalpy of silicon on iron could be derived from the measurements. Lateral interactions between segregated atoms are better observed in the presence of a third element. The study of the Fe-Si-C ternary system thus confirmed the weakness of the Si-Si lateral interactions. It also showed that the repelling of Si by C on the surface is mainly due to a site competition reaction, whereby the strong B-C repulsive interaction plays a minor role.

1. Introduction In previous publications the equilibrium surface segregation of metalloids (C, N, S, 0, P) on iron single crystals was studied by Auger electron spectroscopy (AES) and low energy electron diffraction (LEED) within the solid solution range H-51. The experimental observations showed marked differences between several surface orientations which are not fully explained by the existing segregation theories. The best results were always obtained for (100) oriented surfaces for which in some cases segregation enthalpies could be derived from the experimental data. This work was recently extended to the Fe-Sn [6] and Fe-Si binary systems. Many material properties of solids (like corrosion, adhesion, intergranular by the segregation of cohesion, surface reactivity,. . . ) are strongly influenced impurities or alloying elements to the interfaces (surface or grain boundaries). Since the development of surface analytical tools, growing interest has been shown for interface segregation phenomena. However, the basic thermodynamical concept was derived more than a century ago by Gibbs [7]. The major * Present

address:

ISA Riber,

BP 231, 92503 Rueil-Malmaison,

0039-602%/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

France.

B.V.

H. de Rugy, H. Viefiaus

/ Surface segregation of Si on Fe and interaction with C

419

inconvenience of Gibbs’ theory is that it cannot be correlated to experimental data, since it involves the surface energy of solids, which is largely unknown especially in the case of multi-component systems. For this reason later theoretical or semi-empirical approaches were generally focused on other aspects of this problem using the elasticity theory [8,9], the bond breaking theory [lO,ll] or a combination of both theories [12-161 and more recently also electronic structure calculation [17-191. In spite of considerable theoretical improvements during the last five years the problem of quantitative description of segregation phenomena at a free surface has not been solved so far. A reason for this is certainly the lack of detailed experimental data. Only very few of 45 experimental investigations on surface segregation reported recently [14] give reliable quantitative information. In many cases no temperature variation is performed or the calibration of the surface concentration is inadequate. Only very few examples of detailed and accurate measurements for binary solid solutions could be found in the literature. A brief look on the necessary requirements to perform an ideal equilibrium surface segregation experiment indicates that this is indeed a difficult task: (1) The diffusivity and/or concentration of the segregant have to be high enough to ensure that equilibrium is reached in reasonable times and to avoid depletion near the surface region upon segregation. (2) No significant desorption or evaporation of surface atoms is allowed to occur. (3) Temperature and concentration have to be varied over some interval within the solid solution range. (4) It should be possible to prepare different oriented surfaces of a single crystal sample. (5) No disturbing impurity should be present at the surface. (6) The experimental parameters, temperature, bulk concentration and surface coverage should be measurable with accuracy. Points (1) and (2) are directly linked to the physicochemical properties of the binary system. Together with point (3) they determine the useful temperature and concentration ranges for the investigations, which should be as wide as possible. Points (4) and (5) are associated with the preparation (including cleaning) of the sample and this is often the most time consuming and most critical step. Difficulties may also arise from temperature and coverage calibrations. The binary Fe-Si system is not really an ideal system for these studies since normally the useful bulk concentration interval is very limited. Its upper limit is the appearance of an ordered cY’-phase at about 10 at% Si, while the lower concentration limit is given, for experimental reasons, by the cu-y phase transition occurring for bulk Si concentrations below about 5 at%; within the range of 5 to 10% Si single crystal samples may be grown by the well-known Bridgeman method. For lower concentration the very time consuming and

420

H. de Rugy. H. Viefhnus / Surface segregation of SI on Fe and interaction

with C

delicate strain and anneal method has to be applied which was not possible for the investigations to be presented in this paper. In spite of these restrictions the study of Fe-Si alloys is of general interest because Si is a common alloying element for steels and influences several material properties. Fe-Si alloys with 3-4 wt% Si are widely used as industrial transformer steels, where grain orientation improves the magnetic properties. Addition of Si sometimes gives a good combination of strength and ductility for steels. This also may improve the resistance to stress corrosion cracking [21]. On the other hand Si is assumed to have as well a beneficial as a detrimental effect on secondary hardening of steels [22]. In all these cases, interfacial segregation phenomena are suspected to play a significant role. Although no direct correlation can be made between grain boundary and surface segregation, the study of the latter may give some information on the grain boundary segregation tendency of silicon in iron. For this purpose the equilibrium and kinetics of silicon segregation to the three low index planes of Fe-3wt%Si were studied by LEED and AES. Investigations on the ternary Fe-Si-C system were also performed.

2. Experimental procedure The major difficulty in the study of equilibrium segregation in a binary system arises from the presence of surface active impurities on the surface. In commercial Fe-Si steels C, S and P segregate to the free surface depending on temperature and annealing time. Preliminary studies have shown that these impurities present as trace elements in the bulk could cause displacement of Si from the surface upon heating. As these elements prove very difficult to eliminate from a thick solid specimen, it is most important to start with very high purity material. Several authors have already tried to study Si surface segregation on Fe-Si alloys, but none of them was able to observe equilibrium segregation because of surface contamination by impurities [23-261. The basic iron material used for the present work had an impurity content of less than 10 wt ppm for N and 0 and less than 15 wt ppm for C. All other elements were below 1 wt ppm. After alloying with high purity Si, single crystals of Fe-3%Si were grown from the melt by the Bridgeman method and cut along (100) (110) and (111) planes with a precision of better than +l”. By those treatments the carbon bulk concentration was increased to about 40 wt ppm and that of S to 3 wt ppm. the concentrations of P and N remained unchanged. The sliced samples of 10 mm diameter and 0.5 mm thickness were metallographically polished before introducing into the standard LEED/Auger system. Heating of the samples was achieved by applying a DC current to a tantalum wire disposed into the ceramic sample holder. On top of the sample

H. de Rugy, H. Vie&m

/ Surface segregution of% on Fe and inreraction with C

421

Fe LMV (652eV)

~

a t

:

0

10

20

Fig. 1. Angular

dependence

ttlt Fngle 3Ga of the Si (L,;Vv)

1 b

Ib

~~

hi;;ng,

0

and Fe (L,M,,V)

Auger signals and their ratio.

holder the specimen was fixed by a small cylinder made of pure iron foil. The sample was isolated from the heating wire and could be grounded by the iron cylinder. The sample temperature was measured with an accuracy of f 5” by a Pt/Pt-Rh thermocouple fixed to the sample surface and which had been calibrated against an optical pyrometer at higher temperatures. All Auger spectra were recorded using a CMA with a coaxial electron gun at normal incidence. In order to minimize the influence of the primary electron beam current, densities of less than 5 mA/cm2 were used at 2 keV primary energy and a modulating voltage of 5 VP_,. For a proper quantification of the Auger spectra not only the specimen to analyser distance but also the angle between samples surface and analyser axis had to be adjusted with precision. This angle was kept equal to 90” (or fy = O”) since any slight deviation from this value could give rise to drastic changes in the Si(92 eV)/Fe(651 eV) peak height ratio due to the influence of electron channelling effect 1271 as shown in fig. 1. Ultimate depletion of the residual sulfur was reached by usual ion sputtering cycles at high sample temperatures until no sulfur could be determined on the surface by AES, even for prolonged annealing at 900°C. Si surface segregation was studied in the temperature range 400 to 900°C. An interesting side effect was observed during the

422

H. de Rugv, H. Viejiiaus / Surface segregation of Si on Fe and interaction with C

cleaning procedure: although no carbon was present on the sample surface the bulk concentration of carbon was lowered and became at last negligible. This could not be attributed to either ion sputtering of carbon nor desorption of carbon from the surface since at such high sample temperatures all carbon is dissolved in the bulk. The depletion of carbon from the sample upon high temperature heat treatment is more likely due to diffusion from the crystal into the iron foil. A similar behaviour is described by the well-known Darken experiment [28] and is explained in terms of different carbon activities within the foil and the single crystal. Silicon is known to increase significantly the carbon activity coefficient in iron [29], because of a strong repulsive interaction between Si and C in iron, which also results in a much lower solubility of carbon in Fe-Si alloys. At the end of the cleaning procedure no other elements than Fe and Si could be detected by AES within the temperature range 500 to 900°C (fig. 2). However, keeping the specimen at low temperatures for a long time could lead to slight oxidation of the adsorbed Si even for base pressures in the range 10P” mbar. Before the final cleaning process to remove sulfur from the bulk several studies were performed on the ternary system Fe-Si-C. Sulfur did not disturb the observations since it segregates at high temperature, whereas carbon segregation occurs at low temperatures. This is due to the much slower diffusivity and lower bulk content of sulfur compared to carbon. In addition, carbon doped specimens were investigated. Doping with carbon was achieved by equilibration at high sample temperatures in flowing gas mixtures of

0

200

LOO

Fig. 2. Auger spectrum

600

kVl

of the clean (100) surface

of a Fe-3wt%

single crystal.

H. de Rugy, H. Viefhaw / Surjaee segregation

of Si

on Fe and interaction with C

423

CH,/H, [30]. Bulk concentration of 20 and 40 wt ppm were obtained, as determined by chemical analysis. But since each heat treatment changed the bulk carbon concentration (see above) and no bulk analysis could be performed in situ, the carbon concentration was never known with high precision for the individual experiments. The sulfur free specimens were subjected to a short anneal at 900°C prior to each experimental run in order to establish a well defined surface state. From that point the temperature was lowered stepwise down to 5OO*C, and increased again to high temperatures in order to verify the good reproducibility of the results. At each step of temperature change the Si(92 eV), Fe(651 eV) and if present the C(272 ev) Auger peaks were recorded after stabilizing the sample temperature. In a previous study [l] it was shown that for sample temperatures above 500°C segregation equilibrium for carbon is reached instantaneously. In order to avoid cont~nation of the spectrometer by evaporation of Si and Fe, temperatures above 900°C were applied only for short periods. No significant evaporation occurred within the studied temperature range. The carbon surface coverage has been assumed to be proportional to the C(272 eV)/Fe(651 eV) peak height ratio. For silicon the contribution of the atoms in the first atomic layer, i.e. within the information depth for Si Auger electrons had to be taken into account. This is generally quite a delicate problem, but in the present case this contribution of the “ volume signal” was small (less than 5% of the saturation signal). This is because of the small bulk concentration of Si and Si Auger electrons (92 eV) have a low inelastic mean free path. Any inaccuracy of the volume signal would have little effect on the final results except for very low coverages. In the latter case another source of error is the overlapping of the Si(92 eV) and the Fe(86 eV) Auger peaks. For these reasons quantification of the low Si surface coverage has to be considered with caution. LEED experiments were performed in order to gain information on the two-dimensional structure of the segregated species and to derive from a surface model a calibration for an estimation of
3. LEED results and adsorption structures As for all other binary iron systems studied up to now the LEED pattern for Si saturation coverage in a (100) oriented surface corresponds to the completion of a c(2 x 2) surface structure. However, in the case of Si surface

424

H. de Rum, H. VieJzaur / Surface segregatmn

Fig. 3. LEED ~(2x2) additional spots).

structure

on (100) orientation

of Si on Fe and lnteractmn wrth C

(note

the splitting

of one pair

of the

segregation this c(2 x 2)Si structure shows some particular features, i.e. at saturation coverage a splitting of the c(2 x 2) reflexes and/or the substrate reflexes is observed in dependence on electron primary energy, as may be seen from fig. 3. This splitting is completely reproducible for different samples at Si saturation level. No definite explanation for this reflex splitting will be given here as this feature needs further systematic LED investigations. Further indications for a nearly well ordered Si overstructure come from the fact that the segregated Si atoms may be replaced continuously by other impurity atoms having a higher segregation enthalpy. During this replacement always a well ordered c(2 x 2) structure is detectable after replacing some of the Si atoms at the surface. In spite of this discrepancy in comparison to earlier surface segregation studies on Fe(lOO) oriented samples the c(2 X 2)Si structure was used to evaluate the surface coverage of Si from the Auger peak height ratio R, = Si(92 eV)/Fe(651 eV) at saturation coverage (8 = 1, which corresponds to half a monolayer of Si atoms). This leads to a surface concentration of 6.1 X lOi segregated Si atoms per cm2 for the c(2 X 2)Si LEED structure. A further estimation of the Si surface coverage was performed by oxygen adsorption at saturation [5]. On the (111) oriented face a p(1 x 1) LEED structure was observed at Si surface saturation but again additional features could be detected which need

H. de RUD, H. Viefhaus / Surface segregation of Si on Fe and interaction with C

425

further detailed LEED investigation to explain these deviations from a real p(1 x 1) structure. The recorded peak height ratio R, for the Si surface saturation level on the (111) orientation is larger by a factor 1.07 than the R, value for the (100) orientation. If we take calibration for the Auger peak height ratio from the (100) results we calculate a surface concentration of 6.5 x 1014 Si atoms per cm2, which is in good agreement with the theoretical value of 7.0 X 1014 S atoms per cm2 for a perfect p(1 X 1) Si layer on Fe(ll1). The same calculation of the surface concentration as above gives for a Si saturated (110) orientation, characterized by a c(7 X 1) LEED pattern. a surface concentration of about 6.0 X 1014 Si atoms per cm’. This should be compared to the theoretical value of 6.2 X lOI Si atoms per cm’, assuming 5 Si atoms per unit mesh of the c(7 X 1) superstructure on the Fe(ll0) surface. Thus, at saturation, the surface concentration of Si is within the range of (6-7) x lOi atoms per cm2 for all three orientations. A difference appears between the (110) and (111) planes on one hand and the (100) orientation on the other hand: while the Si coverage remains constant on (110) and (111) within the experimental error up to 9OO”C, it drops significantly on (100). As a consequence of these observations no thermodynamical data can be derived for the (110) and (111) orientations (no temperature dependence); therefore we shall focus our attention mainly on the (100) plane (section 5).

4. Surface segregation kinetics To study segregation kinetics (100) samples were sputter cleaned at room temperature and then isothermically heated at temperatures between 440 and 560°C. The build-up of Si segregation was followed by AES and translated in terms of the ratio C,/C,(eq) of the surface concentration at a time t to that at equilibrium (fig. 4). Assuming that the rate limiting step is the diffusion of segregant to the surface and further a constant enrichment factor (i.e. ratio of the segregant concentration within the segregation layer of thickness d to that in the first layer underneath), McLean [8] has given a description of segregation kinetics. But it has been shown by several authors [31l36] that this concept of a constant enrichment factor is wrong, except for very short times. Crank [37] has given a solution for diffusion out of a semi-infinite solid with ideal sink: C, = 2C”( m/7ry2,

(1)

with C, = area1 surface concentration of the segregant, C, = bulk concentration of the segregant, and D = diffusivity of the segregant. The diffusion coefficients derived by fitting the points of fig. 4 with eq. (1) are used for the Arrhenius plot of fig. 5. From the straight line in this fig. 5 an

H. de Rugp, H. Viefhaw / Surface segregatron of SI on Fe and rnreraction with C

426

0’

I

60 t (mid

30

Fig. 4. Segregation

kinetics

on (100). The solid curves represent

a least squares

fitting with eq. (1).

activation energy for Si diffusion of Q = 289 kJ/mol and a pre-exponential factor of D, = 400 cm2 s-’ are derived. These values are in good agreement with those of Brommer and ‘t Hooft determined by magnetic Zener relaxation which are Q = 287 kJ/mol and D, = 500 cm2 s-’ [38].

0 lcm2r11 lo-‘3

t

Fig. 5. Arrhenius

plot of the silicon bulk diffusivities

in Fe-3”oSi

H. de Rugs, If. Viefhaus / Surface segregation of Si on Fe and ~ntera~tiQnwith C

427

Up to now there are only very few studies on the influence of the samples orientation on segregation kinetics. In the present case this influence is considerable, since the results on (loo), (110) and (111) orientation differ strongly. The shape of the kinetic curves remains the same, but for the same segregation rate the temperature for the (111) oriented sample had to be increased by about 100°C. This corresponds to a difference of two orders of magnitude for the diffusivities derived from the surface segregation kinetics. If we assume bulk diffusion to be isotopic the reason for this difference in surface segregation kinetics may be that the jump probability for the Si atoms to get from the second atomic layer to the surface layer is quite different; i.e. rather low in the case of the (111) oriented sample, so that diffusion within the bulk layers is not the rate determining step for Si enrichment on the surface. A further problem for the derivation of diffusion data from surface segregation kinetics may arise from the presence of impurities on the surface. What happens for example if Si diffuses towards a carbon contaminated surface instead of a clean surface? In order to achieve this, two equilibrium states are considered (see section 5.2): at low temperature the surface is saturated with carbon, and the repulsive interaction between C and Si in the bulk is such, that Si is repelled from the first atom layers and is not detected within the information depth of the Si-LW Auger electrons (a few A); at higher temperature C is entirely dissolved in the bulk and Si segregates to the surface not far from the saturation level. Hence, by heating the sample from 450 to 480°C the concomitant dissolution of C towards the bulk and segregation of Si towards the surface is produced (fig. 6). The kinetics of each event are different, for carbon (interstitial) diffuses much faster than silicon (substitutional). This leads to a decomposition in two steps: first, during the C dissolution the

RT

L50°C

I

I

2

L

LBOQC

-

TIME [mm] Fig. 6. Segregation

of carbon

and silicon on a (100) surface

(after ref. IS]).

H. de Rugy, H. Vtefhaus / Surface segregation of Si OR Fe and inteructiun with C

428

diffusion of Si is slowed down due to the interaction with C atoms coming in the opposite direction; in the second step, as soon as the flow of C atoms reduces, the Si segregation rate increases rapidly. This illustrates very well the difference in segregation rates in the presence or absence of impurities. 5. ~uilib~~

surface segregation

5.1. The binary Fe-S

system

Results of Si equilibrium segregation to the (100) oriented surface of Fe-3wt%Si are shown in fig. 7. This plot is a composition of data from three separate experiments. The scatter is representative of the reproducibility of the measurements. Saturation is almost reached at 500°C while the coverage remains relatively high at 900°C which is in qualitative agreement with the segregation theories. The simplest of these is the well known adaptation of Langmuir’s adsorption isotherm applied to segregation phenomena by McLean [8]. According to McLean’s model, the relation between fractional coverage and temperature is:

8(X, T)=

XK(T)

(21

I-X+XK(T)

with dH, RT

AS,

, i where X = concentration of the segregant in the regular solid solution, segregation enthalpy of the segregant, and dS, = segregation entropy segregant. or K(T)=exp

t9 -=mexp l-8

0

-

+R

X

I

600

300

Fig. 7. Si fractional

ewerage

at equilibrium

900

!c

on a (100) surface.

(3) AH, = of the

H. de Rugv, H. Viej.%aus / Surface segregation of Si on Fe and interaction with C

I

In&

9OO’C

85O’C

8OO’C

Fig. 8. In f?/(l - B) versus l/T

700°C

750-c

429

I 650-I

plot for Si equilib~um surface segregation on a (100) surface.

A plot of log S/(1 - t?) versus l/T is represented in fig. 8 for four sets of experiments (eventually different from those shown in fig. 7). The values of AH, and AS, deduced from a linear regression are: AH,=

-4Si4kJ/mol,

AS,=

-15&l

J/mol.K.

There can be some controversy regarding the significance of these values and the constancy of the segregation enthalpy. The simplifying hypotheses made by McLean are that all the adsorption sites are equivalent and that any lateral interaction among adsorbed atoms can be ignored. Because of the high symmetry of the (100) plane and of the existence of an ordered, again high symmetry overstructure, the first assumption is very likely to be verified. But for the same reason there must be some lateral interaction in the surface plane responsible for this ordered structure. The thermodyna~c formalism accounting for these interactions has been developed by Fowler and Guggenheim [39] within the quasichemical approximation, where a constant bond energy between pairs of nearest neighbour atoms was assumed. McLean’s equation (eq. (4)) is only modified by introducing a coverage dependent term which is proportional to the interaction energy w between segregated atoms and the number of nearest neighbours (as they are defined in the bulk) in the surface plane zp: I? -=exp l-8

(

-

AH, + 2~~4.~0 RT

+ds R

i .

(5)

The value of w can be directly measured [40] or, at least in theory, approximated from bulk thermodynamical data, which would be useless in the present case since the number of first neighbours in the (100) atomic plane of a bee

430

H. de Rugy. H. Vie&w

/ Surface segregation

of Si on Fe and interaction with C

lattice is zero (there are no atoms at bulk nearest neighbour distance a/o). Fowler’s equation reduces thus to McLean’s Nevertheless, there can be some second or third order interactions, but it becomes then more difficult to determine the role played by them in the segregation behaviour. The only way is really to vary the Si bulk concentration and draw the segregation isotherms, for their shape is specific of each model. Unfortunately, this was not possible in the present case, as mentioned in the introduction. The original idea of this work was to try to gain further information on the lateral interactions in the (100) surface plane by favouring the concomitant segregation of a new kind of atoms (section 5.2). Carbon was chosen because it segregates in a convenient temperature range, has been studied extensively on pure iron [l], and is known to interact strongly with silicon in the bulk of iron. Nevertheless, one is tempted to compare the measured value of AH, with the one predicted by the theories. The entropy term AS, is generally ignored in the predicting theories, and will not be considered within the following discussion. Our purpose is less to review the various models on a theoretical basis than to mention the problems eventually encountered by applying them. In McLean’s model the driving force for segregation is due to the elastic energy caused by the atomic size difference in the lattice [8]. This has been criticized and most of the authors agree nowadays that AH, is the sum of an elastic term and a “bonding term” accounting for the chemical interaction between neighbouring atoms. Several forms of the elastic strain energy have been proposed [12,14,16]. Assuming that the choice of the appropriate form for the elastic term has been made, the atomic radii in the solid solution must be determined. The definition of the radius of each atom as one half of the distance of closest approach within the pure material may lead to different values if an element presents various crystal structures. In order to avoid this difficulty a few authors [12-141 suggest the use of the Seitz radius, defined as the radius of a sphere whose volume is that of the unit cell divided by the number of atoms in the cell, and which is supposed to be independent of crystal structure or coordination. The Seitz radii for iron and silicon are 1.41 and 1.67 A, respectively [41]. Most recently [13.14], the elastic term is ignored for solute atoms being smaller than the solvent atoms. In the other case the elastic force is proportional to the square of the radius difference. Using the above-mentioned values for iron and silicon, this leads to a significant contribution of the elastic strain energy in the range of 100 kJ/mol depending on the chosen model. However, one must be cautious in assimilating the radius of a solute atom in the solid solution with its Seitz radius, for considerable differences between them may be observed. Lattice parameter measurements in the Fe-Si solid solution show that the lattice parameter decreases with increasing silicon content [42], indicating that the dissolved silicon atoms are smaller than the iron atoms. The size reduction of the silicon atoms upon mixing with iron can

be explained by an electron transfer from the 3p and 3d levels of siticon to the 3d levels of iron [43]. The consequence is naturally a drastic change in the quantitative prediction of the elastic term since no elastic force is involved for solute atoms which are smaller than the solvent atoms. Considering the Seitz radius would thus induce for iron-silicon an error of a factor of two compared with the ex~~me~tally determined value of A&. The prediction of the bonding term is even more problematic. Since the calculations account for interactions between pairs of nearest or next nearest neighbours a surface model has to be assumed. Often the segregation is considered to be limited to the topmost layer. However, calculations [11,19,44] and experiments [45,46] have shown that the solute concentration in the few next layers is not strictly equal to that within the bulk. This will not affect the measurements significantly since both the Si bulk concentration and the informatjon depth for Si LW Auger electrons are rather small, but it should be taken into account in the calculations. A more important question is the position of the segregated Si atoms. For the bond breaking model the segregated atoms are assumed to be located in substitutional sites of the first atom layer. The observations for the Fe-Si system to be discussed later suggest that silicon behaves similar to C, 0 and S which lie in the fourfold hollow sites on the Fe(100) surface (see ref. 1471, for example). This would eliminate (at least partly) the lateral bonds with iron atoms in the adsorbed layer, and therefore a m~ification of the bonding term should be considered. The evaluation of the pairwise interactions from bulk properties may also be a source of error. By using the enthalpy of mixing for the derivation of the interaction energy between unlike atoms it should be noted that this contains already a contribution of the elastic strain energy [lS,lS]. The approximation of the interaction energy between like atoms using the sublimation enthalpy is also very cautious, as pointed out by W~nblatt and Ku !lZ] and may lead to errors of a factor of two or more. Within the bond breaking model only first neighbour interactions are generally taken into account, although it is well established that second or third order interactions may play a significant role. For instance, measurements of the interaction energies in iron silicon samples show that there is only a factor of two between first order and second order interaction energies for the bulk f40]_ Tsong also showed that the lateral interactions between silicon atoms segregated on W(~~~ are at their highest level in third neighbour positions 1481, For these reasons the calculations should not be limited to first order interactions. The last point concerns the variation of the segregation enthalpy with surface orientation. The results of section 3 show clearly that the segregation enthalpy differs strongly from one orientation to the other. Although the orientation dependence is sometimes taken into account [11,12,49] the peculiar

H. de Ruw, H. Viefhaus / Surface segregation of SI on Fe and interaction wth C

432

behaviour of the (100) orientation for the FeeSi system with respect to (110) and (111) surfaces could not be predicted. An attempt of applying several predicting theories to the Fe-Si solid solution system shows that many assumptions and approximations of these models must be revised. In the present state no quantitative prediction of the segregation enthalpy seems to be reliable. 5.2. The ternary Fe-Si-C

system

The thermodynamical analysis of solute segregation in ternary regular solutions has been worked out by Guttmann [50] who studied the interaction between alloying element and impurity at the surface and grain boundaries of steels. According to Guttmann’s model the fractional coverages of Si and C would be linked with the temperature at equilibrium by the relations: eSi

1 - 89,- ftki

0,. 1-

e, - e,,

= l_~_Xsiexp(-~+A$~.

=

1_

2_

xsi exp( - $

+ A$

The segregation enthalpies can be decomposed simplified in dilute solutions as follows: A Hsi = AH;

+ 2asiFe4, - cx’&,

AH,

+ 2c+Fet3C - “‘8si.

= AH:

) in three

terms which can be

These expressions reduce to the Fowler equation (eq. (5)) for a binary alloy coefficients since +,re = zptisiFe. For a ternary alloy, ignoring the interaction would lead to constant segregation enthalpies (AH:, AH:) as in McLean’s model. Thus the ternary interaction is taken in account in the third term of the expression of A Hsi and AH,- (eqs. (8) and (9)). The common coefficient CX’ manifests the synergetic effect between silicon and carbon with respect to iron. If a’ were positive (attractive interaction), this effect would enhance the segregation of each solute by lowering the segregation enthalpies and result in the interaction between silicon and the cosegregation of both. However, carbon in iron is known to be highly repulsive [51], which implies (Y’< 0. In that case. the strong segregant, here C, repels the other from the surface, as was observed in the past [52]. Unfortunately, no reliable interpretation of the data has ever been made because of the presence of numerous impurities. It should be pointed out that (Y’accounts for a lateral interaction between silicon and carbon atoms and thus is proportional to the number of first neighbours in the surface plane t( which is equal to zero for a (100)

H. de Rugy, H. Viefiats

/ Surface segregution of St’ on Fe and interaction wifh C

433

orientation. We should, therefore, expect again a weak surface interaction, but care must be taken regarding the significance of zp in the case of interstitial impurities: a coordination number of interstitial sites should be introduced. But its lateral component in the adsorbed layer is hard to define since the adsorbed carbon atoms are likely to be located in the same kind of sites as the silicon atoms, but at a level intermediate between the adsorbed layer and the first surface layer because of the size difference. Variations of Bsi and f?, with the temperature for different carbon concentrations are shown in figs. 9a-9c. Ten experiments have been carried out by varying the C bulk concentration upon annealing or carburizing in four specimens. For the sake of clarity, only the two extremes and another have been presented since the evolution between the extremes is continuous and well reproducible. Fig. 9c represents the highest C content, close to the solubility limit (40 wt ppm). As its bulk concentration decreases, the carbon segregates at lower temperatures (figs. 9b and 9a) until no segregation occurs (fig. 7) because of too slow kinetics. At high carbon bulk concentration the characteristic LEED ring pattern of graphite could be observed after attainment of saturation by further lowering the temperature. The shape of the carbon Auger peak is then modified and its intensity increases. This phenomenon will be ignored in the remainder of this paper since it does not account for segregation but for precipitation. Thus qualitatively carbon behaves as in the binary Fe-C system. This is not true for the silicon which exhibits an identical behaviour only when the whole carbon is dissolved in the bulk, i.e. at high temperatures and low C concentrations. But as soon as carbon segregates, the silicon level falls until Si is completely repelled from the surface at carbon saturation. A quantitative interpretation of the curves in the same manner as previously is not possible because of the high imprecision on the term 1 - I!&- 19,~ at lower temperatures. Nearly all the sites being occupied by silicon or carbon atoms, the value of 1 - 8, - es, is very low and of the same order of magnitude as the sum of the errors on #c and 19,~. The scatter in the In 6,,/(1 - es, - 8,) versus l/T plot is then very large. In order to limit the error on 8c, we tried a least squares fitting of the experimental points by a @=

A/T+B I+A/T+B

type of function as suggested by the McLean compatible shape of the distribution. By determining the coefficients A and B, analytical curves 8,(T) could be associated to each C concentration with satisfying agreement. The same was not possible for Si since no simple analytical function seemed appropriate for a least squares fitting over the whole interval. Our last resort consisted in trying to compare the experimental data with theoretical curves by making adequate hypotheses. This was made possible by setting &-(T) in

434

H. de Rugy. H. Viefhaus / Surfuce segregatroPr of.5 on Fe und inteructton wwh C

Fig. 9. Si and C fractional coverages at equilibrium on (100) surface for increasing bulk carbon content cc up to 40 ppm: cc (a) i cc (b). cc (c) = 40 ppm; cc. (a) and cc- (b) are unknown but less than 40 ppm (see text). Solid lines are analytical Bs,( T) and e,(T) curves.

eq. (6). It WLIS assumed that (Y’= CYsire= 0, the values of AH: then deduced from the binary system results: AH;

= - 48 kJ/mol,

AS:

= - 15 J/mol-

and ASi

being

K.

The analytical 8s,( T) curves derived by this way are drawn in full lines in figs. ‘)a-% together with the 8,(T) curves. The reasonable agreement obtained supports the assumptions made previously, thus: czsiFe = 0 - this is an answer to the question raised by the study of the binary system; lateral interactions among Si atoms can be ignored and the segregation enthalpy may be considered as independent of the coverage, which is in accord with McLean’s description. cy’ = 0 - the displacement of silicon by carbon is not caused by a strong repulsive lateral interaction in the surface plane, but can be attributed to a simple site competition effect; carbon exerts its influence on the silicon segregation only through the number of sites it leaves free, but its chemical nature plays no role. This was confirmed by the next experiment which involves sulfur as a third adsorbate. Sulfur, is known to be more surface active than C or Si, and has the same saturation coverage which corresponds again to the completion of a c(2 x 2) structure on (100) orientation, but unlike B,i and &., 0, does not show a temperature dependence at equilibrium in the range 500-900°C and remains equal to unity, as well on iron [2] as on iron-silicon(100). However, equilibrium is not always reached at these temperatures, depending on the S bulk concentration. In the present case the S content was certainly less than 1 ppm, and a sixty hours anneal at 800aC was necessary for the sulfur to reach a coverage of approximately 8, = 0.5. No noticeable variation of the S Auger peak height was then observed during the measurements. Attention is focused on the fact that this is a noes-equilibria state where sulfur acts as a lock for about half of the avaifable surface sites. Fig. IO shows the variations of es, and i9, with the temperature on a (100) oriented surface partly covered by sulfur (8, e 0.5) and on the same surface after ion bombardment (8, = 0). A comparison of these data can be made in the light of our interpretation, Sulfur is the most active species and. therefore, will tend to occupy all the available surface sites. This process is only limited by the segregation rate which is negligible at the considered temperatures. Its coverage remains thus constant (0 = 0.5). Carbon, as the next most surface active species, cannot displace S. Consequently, its coverage at saturation is Bc = 1 - Ss = 0.5 (up to 550°C). As soon as the temperature is reached, at which the carbon coverage in the absence of S would be 0.5, Q decreases and keeps following the same curve as in the S free sample (over 700°C). Silicon can only emerge when the others leave a few sites free. i.e. over

Fig. 10. Influence of sulfur on the C and Si surface segregation. Solid cirdes and squares: es = 0: open circles and squares: 8, = 0.5.

700°C. The difference between the silicon coverages with 6s = 0.5 and 8, = 0 seems to be rather constant and equal to 0.5, as if there was a one to one exchange between sulfur and a part of the silicon atoms, This exchange has no influence on the carbon behaviour, which is only a proof, rigorously, that the C-S and C-Si interactions are identical. Such a coincidence is not predicted by the bulk properties of the compounds, and we would rather con&de that no fateraf interaction is involved in the segregation process. This conclusion differs from the supposition of McMahon f52] or Guttmann [53] who saw in the displacement of silicon by carbon the effect of the repulsive Si-C interaction (my’ strongly negative). It was verified that setting negative values for 1~’ in eqs. (8) and (9) gives a poorer agreement with the experimental data. On the other hand a theoretical study on the effect of a surface active impurity on surface segregation in a binary alloy [S4] describes very well the behaviour observed with C on Fe-3%Si(lOO). This is not a surprise for the calculations are also based on eqs. (6) and (7) with constant ANand AS. There the problem of constancy for AH is posed again. It has been shown that AH,, does not vary with the carbon bulk concentration and is independent of the fractional coverages. This is not true for the values of AHc derived from eq. (7) and the t!&,(T) and &(T) curves: they yield - 140 kJ/mol (fig, 9a), - 180 kJ/moi (fig. 9b) and - 210 kf/mol at 40 ppm C (fig. SC). These values must be compared to the results of Grabke on pure iron [2] which differ by a factor of two: - 73 kJ/mol at 10 ppm C to -90 kJ/mof at 90 ppm C. Thus adding the impurity carbon to iron-silicon introduces a site competition effect without affecting the silicon free energy of segregation while alloying 3% silicon to iron alters significantly not only the activity but also the segregation enthalpy of carbon. No quantitative thermodynamical interpretation can yet be given.

H. de Ru@, H. Viefhaus / Surface segregation of Si on Fe and interaction wirh C

437

6. Conclusion Surface segregation kinetics and equilibrium segregation studies of Si enrichment on (100) (110) and (111) oriented surfaces of a Fe-3%Si single crystal exhibit a strong orientation dependence of the observed features. Equilibrium surface segregation of Si on a (100) oriented surface shows Langmuir behaviour and a segregation enthalpy of AH = - 48 i: 4 kJ,/mol is derived from the experimental results. This is a low value in comparison to previous results on different binary systems Fe-X with X = C, N. S, P and it indicates a low tendency of Si for surface segregation in binary iron alloys. Existing theories on surface and grain boundary segregation do not allow a satisfactory prediction of the surface segregation enthalpy because of too crude approximations and partly wrong assumptions. For (100) oriented samples the bulk diffusion coefficient for Si in a-Fe was evaluated from surface segregation kinetics. Surface segregation of Si and C in a ternary Fe-Si-C system may be explained by a simple site competition reaction. In spite of a very strong interaction between Si and C within the bulk there seems to be no or only weak lateral interaction on the surface.

One of the authors (HR) is grateful for financial support by a fellowship awarded by the Max-Planck-Gesellschaft zur Forderung der Wissenschaften e.V. and for hospitality and facilities extended to him during his stay at the Max-Planck-Institut fur Eisenforschung GmbH. at Dusseldorf. HR also acknowledges partial financial support from the Institut de Recherches de la Siderurgie Francaise (IRSID). We appreciate many helpful discussions with Professor H.J. Grabke.

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