ToF atom-probe fim investigation of surface segregation in dilute alloys

Surface Science 78 (1978) 419-438 0 North-Holland Publishing Company

ToF ATOM-PROBE FIM INVESTIGATION OF SURFACE SEGREGATION IN

DILUTE ALLOYS *

Yee S. NG and T.T. TSONG Department of Physics, The Pennsylvania State University, University Park, Pennsylvania

16802, USA

Received 27 March 1978; manuscript received in final form 27 June 1978

A time-of-flight atom-probe field ion microscope was successfully employed for the first time to investigate surface segregation in dilute alloys. We were able to achieve a single atomic layer resolution and obtained the absolute concentrations of alloy species of each surface layer. Cr atoms are found to segregate to the surface of Stainless Steel 410 whereas no segregation of the minority species was found for Pt-8% W and Pt-5% Ru. The first layer concentration of Cr in the (110) plane of Stainless Steel 410 at 500°C was found to be 38.5 f 12.5% and 63.4 * 10.2% respectively for samples with near surface layers Cr average concentration of 6.3 + 2.1% and 11.9 f 2.5%. The heat of segregation of Cr to the (110) plane of Stainless 410 was found to be 3.43 and 3.92 kcal/mole respectively from the two sets of data. The data also gives the difference in surface tensions between iron and chromium at this plane to be 269 and 282 erg/cm* respectively. Segregation studies on the (012) plane as well as on a gram boundary of Stainless Steel 410 were also done. In some cases, though the first surface layer is enriched with Cr in Stainless Steel 410, the near surface layers show a depletion of Cr. In Pt-8% W and Pt-5% Ru, our concentration depth profiles with a single atomic layer resolution show no segregation or depletion of the minority species either for the top layers or for the near surface layers.

1. Introduction

Highly disperse, supported alloys are known to have unique catalytic properties. They often show selectivity and activity quite different from the base metals, and some of them ‘even show a greater resistance to poisoning than do monometallic supported catalysts [ 1,2]. These unique properties arise from surface segregation of minority species to the alloy surfaces, which are directly exposed to the reacting molecules.

The evidence of surface segregation has been mainly established through AES technique although other techniques have also been used [3-81. Considerable theoretical work has also been reported [9-211.

* This work was supported by the National Science Foundation, Grant No. DMR-76-11418.

419

420 Y.S. Ng, T.T. Tsong / ToF atom-probe FIM investigation

Although significant qualitative information can be derived with the general surface techniques, accurate composition of surface layers is still difficult to obtain [15,22]. Alloys prepared by different metallurgical techniques are known to exhibit different surface morphologies [23]. This makes a meaningful comparison of AES results from different laboratories even more difficult.

When macroscopic techniques are used to determine the composition below the first surface layer, ion etching technique is generally used for a gradual removal of surface layers. In some cases, by changing the glancing angle or the energy of the incident electron beam, information on the composition depth profile can be derived. These techniques, however, suffer from a modest spatial resolution and also from the problem of converting the intensity of the signals detected to the absolute composition of the sample. The problem of spatial resolution is especially difficult to surmount since a surface sputtered by ions is by no means atomically flat. Furthermore, the sputtering efficiency is often different for different elements. This makes the composition depth profiles of surface segregation derived from general surface techniques quite unreliable. Such difficulties, however, do not

exist in the time of flight (ToF) atom-probe field ion microscopy [24,2.5]. Surfaces prepared by field evaporation are atomically flat. In general, field evaporation removes all the atoms in a surface layer completely before the next layer is field evaporated. Moreover, the surface morphology usually can be reproduced and characterized in a routine basis. We have demonstrated recently that the absolute

composition of surface layers can be obtained from a ToF atom-probe experiment with a single atomic layer spatial resolution [26]. We report here a comprehensive atom-probe investigation of surface segregation in dilute alloys. We found that Stainless Steel 410 (88% Fe, 1 l%Cr, 1% Mn) to have Cr enriched top surface layer. For Pt-8% W and Pt-5% Ru, no segregation down to about 10 atomic layers depth was detected. From our result, we have derived the heat of segregation as well as the difference in surface tension between iron and chromium metals. We have alsO detected an enrichment in Cr at a grain boundary in Stainless Steel 410.

2. Basic theoretical backgrounds

There are two widely used models for surface segregation [15,18,20]. In ideal dilute solution cases [19], the surface concentration of solute, Xs, in atom fraction has been related to its bulk concentration X, by

x& - xs) = [xb/(l - xb)l exp@/RT) , (1)

where Q is the heat of segregation. If Q is large and positive, surface segregation should occur. Two methods for estimating Q have been suggested. One is based on the concept of bond breaking. This model predicts that the component in the alloy with a lower heat of sublimation should segregate to the surface [11,18]. The second model is based on the elastic strain and it predicts that segregation should

Y.S. Ng, T.T. Tsong / ToF atom-probe FM investigation 421

occur whenever the size difference between the constituents is large [20]. In the bond breaking model the heat of segregation is given by [ 181

e = (WZ)(H, - H*) ) (2)

where Z is the coordination number of a bulk atom, M is the number of broken bond for an atom in the surface, and HA and HB are the sublimation energies of the solute atoms A and the solvent atoms B. In the size difference model, Q is given by

PO1 Q = (24nKGr3e2)/(3K + 4G) , (3)

where K is the bulk modulus of the solute, G is the shear modulus of the solvent,

r = (rWtvent + rWtute)/2 and e is (rsorute - rsolvent )/rmtite with rWtvat and rsotute representing respectively the radius of solute and solvent atoms,

For the non-ideal solution, a regular solution model is assumed. It has been shown [22] that in a binary alloy solution the composition of the surface monolayer is given by

X,/(1 - X,) = [X&l - X,)] exp [(oB - o*) a/RT]

x exp W + m> l 7 Kl -x,)2-(xb)21+~~[(x~)2-(1 -x,)21 , i

where X, and Xr, are the solute atom fractions in the surface monolayer and the bulk, respectively. In this formula, $I and uB are the surface tensions of pure

metals A and B respectively. Of course, in the binary alloy solution, A and B represent solute and solvent atoms respectively, a is the molar surface area, T is the absolute temperature, R is the ideal gas constant, and fi is the regular solution

parameter which is given by [ 221

a = uH,/xb(l - xb), (5)

where AHm is the heat of mixing. Or we can express S2 in terms of bulk activity coefficient rb [lo].

fi = RTln(yb)/(l -X,)’ . (6)

The packing parameter I gives the fraction of the atom’s nearest neighbors which are in the same plane parallel to the surface as the atom in consideration. Similarly m is the fraction of nearest neighbors which are in the adjacent parallel plane. For instance, in a bee lattice, an atom has 8 nearest neighbors, so a (011) plane has 4 nearest neighbors in the plane of the atom and 2 nearest neighbors in the plane below the atom. Thus in the case Z = &I= 418 and m = 218.

Although these are other more sophisticated multilayer models [lo,1 11, here we will use the ideal and regular solution monolayer models for analyzing our experimental results.


3. Experimental procedures

The time-of-flight atom-probe field ion microscopy, invented by Erwin W. Mueller, is the most sensitive analytical instrument presently known [24]. The instrument has already been employed to investigate grain boundary segregation [28], precipitation in alloys [29,30], depth profiles of thin oxide layers [31], the composition of metal oxides [32] and nitrides ]33], depth profiles of ion irradiated samples [34], field evaporation products of semiconductors [35], and other studies with a sensitivity unobt~nable by other techniques 1361.

The details of the FIM and the energy compensated time-of-flight atom-probe can be found elsewhere [24-261. A schematic diagram of the energy compensated ToF atom-probe FIM is shown in fig. 1. An external gimbal system is being used to manipulate the field-ion tip so that any desired site of the tip surface can be positioned to the small probe hole at the center of the mirror. Only ions going through the probe hole can enter the 163” toroidal deflector and are detected by the 40 mm diameter Chevron double channel-plate-screen assembly, which has a single ion detection capability. In this instrument, the energy deficits resulting from the premature field evaporation f38] are eliminated by the energy focusing capability of the comb~na~on of straight path sections and the 163” toroidal deflector. The detlector voltage can be set for the field evaporated ions within a certain energy range to arrive isochronously and focused at the detector 1251. A mass resolution of better than l/2000 can be routinely achieved. Moreover, the double channel plate detector can eliminate afterpulses to less than one in 1000 primary events [39], thus an excellent rejection of artifacts is possible.

The samples tips @‘t-8% W, Pt-5% Ru and Stainless Steel 410) were prepared in the following ways. For the platimum based alloys, CaClz is used as a cold etching solution and the polishing voltage was set to 2-1OV ac. For the Stainless Steel 410, an etching solution of 50% H3P04, 50% HzS04 was used. The polishing voltage was set to 5 V dc. The alloy tips were then mounted in the usual way [37], cryogenically cooled inside the microscope chamber at -80 K, and annealed for 10 set in vacuum (-10e9 Torr) to stren~hen the tip before an expe~ment. The tip was then field evaporated to a complete endform in imaging gases Ne or Ar of pressure ranging from 5 X 10e6 to 2 X lo-’ Torr.

After the crystal planes were identified, a mass spectrum of the alloy was usually taken in order to find out its compositions. Then the Pt-8% W and Pt-5% RU tip were annealed to -800 and .v7500C respectively for 15 set in the absence of an applied field and were quenched to -80 K. The Stainless Steel 410 was annealed to 500 + 50°C for 3 to 5 min in the absence of an applied field and was quenched to -80 K. The quenching rate of the tips is estimated [40] to be about 3000”Clsec.

The diffusion length of Cr during the quenching period is estimated as follows. For bulk diffusion 1411 of Cr in Stainless Steel 410, D, = 2.53 cm2/sec, and Q = 56.5 kcal/mol. The root mean square displacement amount to less than 0.3 a by quenching the tip from 773 to 80 K with a quenc~ng rate of 3O~‘C/sec.

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424 Y.S. Ng, T.T. Tsomg / ToF atom-probe FIM investigation

Thus the quenching process practically freezes the tip surface in its thermal equili- brium condition at 773 K. Our estimation is consistent with a previous conclusion [42,43]. Thus, we did not have to maintain our sample tip at an elevated temperature when we were taking data as done in AES experiments [5].

The higher temperature (750-800°C) was measured with an optical pyrometer with an accuracy of k2O”C. The lower temperature (500°C) was measured by a Detect IR Scope infrared viewer by Varo, Inc. with an estimated accuracy of -+5O”C. A thermal endform of the tip was always obtained after an annealing. A thermal endform of a Pt-8% W tip imaged in lo-’ Torr Ne is shown in fig. 2a. The bright dot in the center of the (001) plane signifies the position and the size of the probe hole. With the probe hole aimed at the center of the (001) plane, only ions field evaporated from the (001) plane can be detected. Fig. 2b shows the first layer after some field evaporation. When the first layer was completely field evap-

Fig. 2. (a) An FIM image of a Pt-8% W tip after annealed at 800°C for 15 sec. The image was taken in lo-’ Torr of Ne at 80 K. The white dot at the center signifies the size and position of the probe hole. The thermal endform of the tip is clearly seen. (b) An FIM image of the same tip as in (a) after some field evaporation. (c) Ar FIM image of the same tip as in (a) after the fist layer has been field evaporated. The dark image at the center is the image of the probe hole in the mirror.

Y.S. Ng, T.T. Tsong / ToF atom-probe FIM investigation 425

orated, the tip returned to its field evaporation endform as shown in fig. 2c. The dark image at the center is the image of the probe hole in the mirror. One can easily notice that even the normal size of the (001) plane is slightly larger than the probe hole, so the data from all layers were truly from the (001) plane.

This procedure was used for Pt-8% W, Pt-5% Ru. In the case of Stainless Steel 410, a slight modification was being taken. After the Stainless Steel 410 was annealed at 5OO’C for 5 min, a thermal endform as shown in fig. 3 was obtained with Ar-Ne gas mixture. Here, the Ar image of (011) plane is clearly seen at a field of -2.2 V/A, and the probe hole (white circle) was aimed at the edge of the (011) plane as shown. As the plane receded, we moved the probe hole to match the reced- ing edge of the first layer. Therefore, we not only got the concentration of Cr in the first layer, butalso its distribution from the edge to the center of the (011) plane as will be discussed later. Extreme care was taken not to mix up signals from the top layer to the rest of the layers.

Unfortunately, after the first layer was gone, the imaging voltage was beyond

the best image voltage of Ar and no clear FIM image can be seen. It was then difficult to distinguish the surface layers. Since no significant deviation in the composition among near surface layers was detected, we used the simpler monolayer

Fig. 3. An FIM image of a Stainless Steel 410 tip after annealing at 500°C for 5 min as imaged in Ar-Ne gas mixture. The white circle signifies the position of the probe hole. Notice that free space field ionization of Ar already occurs.

426 YS. Ng, T.T. Tsong / ToF atom-probe FIM investigation

segregation model for our data analysis. For the calculation of the heat of segregation, we used the average concentration of the near surface layers as the bulk concentration. We have also done the segregation study in a (012) plane of the Stainless Steel 410. Since the size of (012) plane was slightly smaller than our probe hole, the field evaporated product might not come from the first layer alone. We therefore present here only a depth profile near this high index plane.

4. Result

4.1. Stainless Steel 410

The Stainless Steel 410 tip was annealed twice at .5OO”C, once for 3 min, case (a), and the other for 5 min, case (b). Since Stainless Steel 410 cont~s about 1% Mn, about 11% Cr, and about 88% Fe [42], it is safe to assume that we are looking at an approximately Fe-Cr system. The concentration of Cr and Fe for the annealed cases in the (011) plane is shown in fig. 4. The lower data points are from the case (a) and the upper data points are from case (b). The first layer was enriched with Cr. The next surface layer concentration of Cr in the two cases is not the same due to different history of the tip.

We must realize here that the number of Cr and the number of Fe signals detected provide us only the apparent compositions [44]. A special technique to convert this apparent concentration to a real concentration has recently been developed 1441 (see also Appendix). In table 1, we list both the apparent concentration in % (F& of Cr as well as the real concentration in % v&l of Cr in the (011) plane of Stainless Steel 410. In all these cases, a total of less than 1% of Mn was detected, and therefore was ignored in our discussion.

We have also investigated the surface segregation of Cr to the (012) plane of Stainless Steel 410. The tip was annealed at 500°C for 3 min. The sequential num-

““1 ““8llb.I Of cr STAINLESS STSEL 410

,s! 1 A-- (011) PLANE 1.y.r “--

.A-“- ..f t

~, , , , , , , , , , ._, , , ,

J ,s! -I_..._ ..--‘4--

l‘l.C -“..#A- %

:’ Nus,,C.t 01 f*

0 50 100 150

Fig. 4. The number of Cr signals detected versus the number of Fe signals detected for a (011) plane of Stainless Steel 410 after annealing at 500°C. The lower data points are obtained for annealing the tip for 3 min and then quenched, or case (a). The upper data points are for annealing for 5 min and then quenched, or case (b).

Tab

le 1

D

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(001

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St

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410

Con

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FCr

(%)

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.B.

(kca

l/mol

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ize

(oF

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2)

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(erg

/cm

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anne

alin

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r se

greg

atio

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udie

s c

(13.

58

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0.9

5)

a

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r d

Nea

r su

rfac

e

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(38.

71*

18.1

3)

(8.1

1 f

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1)

(38.

54 +

- 12.

46)

b 1.

3 0

269

124

(6.3

f

2.11

)a

3 +

43

1st l

ayer

0

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e la

yers

(63.

04

f 21

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(15.

29

t 5.

9)

(63.

35

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.19)

b

3 g2

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282

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aled

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“0-l Number of Cr _--

20 /..

._d 30 ,-““d-“-

z--- _--- .-.--..--

__-?-- .:- STAINLESS STEEL 410 _-

,.&:- (012) PLANE

JO ._._.I ”

8’ , Number of Fe

0 I I , , , , , I I I I

a I I I 1 1

50 I 0 IO 200

60 1, % of Cr STAINLESS STEEL 410

(012) PLANE

50 100 150 200 Fe+Cr

b (22-l i, (44.2lil DEPTH

Fig. 5. (a) The number of Cr signals detected versus the number of Fe signals detected in the (012) plane of a Stainless Steel 410 tip after annealing at 500°C for 3 min. Notice the sharp rise in the number of Cr at the beginning, or the near top surface layers. (b) the depth profile of (012) plane of Stainless Steel 410 after annealing at SOO’C for 3 min. Same tip as (a).

ber of Cr signals plotted against the number of Fe signals is shown in fig. Sa. The real concentration (%) of Cr versus depth is shown in fig. Sb.

The depth in this case was estimated from the. evaporation rate at the (001) plane when the probe hole was aimed at the (012) plane. By evaporating 28 layers of the (001) plane, 182 (Cr f Fe} signals were detected at the (012). Therefore we estimated that 20 particles detected would approximately be equivalent to 4.42 ,& in depth. Since the probe hole was slightly bigger than the (012) plane, it was difficult to obtain the composition depth profile with a single atomic layer resolution. Fig. 5b shows only a general depth profile.

Fig. Sb was plotted in the following way. For particles (Cr t Fe) 1 to 20, the concentration of Cr for these particles is 44% and is signified by the solid bar from (Cr + Fe) = 0 to (Cr + Fe) = 20 in fig. 5b. The concentration of Cr from particles

(Cr + Fe) 10 to 30 is 12.6% and is plotted as a solid bar from (Cr + Fe)= 10 to

Y.S. Ng, T. T. Tsong / ToF atom-probe FfM inv~s~iga~i~n 429

(Cr + Fe) = 30. The vertical dashed lines signifies the statistical uncertainty of the measurement (see Appendix). It is clear from this plot that not only Cr segregates to the top (012) plane of Stainless Steel 410, but the concentration of Cr in the first layer is also much higher than 44% since 20 particles corresponds to nearly 4 to 5 layers in depth in (012) plane. The lower concentration of Cr below the first layer may pull down the real concentration of Cr in the first layer if we interpret the particles 1 to 20 as coming from the first layer. This argument is further supported by the fact that most of the Cr signals come in before the Fe signals in the first 20 (Cr + Fe) signals detected, as can be seen in fig. 5a.

4.2. Pt-8% wand Pt-5% Ru uIIoys

We have also investigated the depth profile of the I’-8% W and Pt-5% RU alloys. These tips were annealed at 8Od”C and 750°C respectively for -10-15 set and then the probe hole was aimed at the near center of the (001) plane. A layer by layer dissection was painfully taken. Thus we achieved true single atomic layer resolution in these depth profties.

Fig. 6a shows both the real concentration depth profile and the apparent concentration depth profile of the Pt-8% W. The upper square data points are the apparent concentration and the lower circular data points are the real concentration. We notice that even in the bulk the apparent concentration of W is higher than 8% as expected from our statistical consideration [44]. The apparent concentration of W in the second layers is seen to be slightly higher than all other layers, giving a false impression that W atoms segregate to the second layers. However, we did find that the field evaporation rate of the second layers was twice that of other layers because of the difficulty involved in controlling the rate right after the large first layers were field evaporated. After properly accounting for this effect as explained in the Appendix, the concentration of W at the second layers falls to the normal value. In fact no enrichment of W was found up to 14 layers depth. Later in the work with I?-5% Ru we were more careful to maintain a constant field evaporation rate for all surface layers. Fig. 6b shows that no significant segregation of Ru to the Pt(OO1) plane occurred either.

To obtain a statisti~~y reliable amount of data, the same tips were annealed again to the same temperature. The signals were sorted according to the sequence of the surface layers field evaporated. Then in both cases, the evaporation rate was calibrated (see Appendix) with 100 layers deep inside the bulk in the (001) plane. With a known concentration inside the bulk and an assumption of constant evap oration rate, the real concentration of Ru and W at the surface of Pt-5% RU and Pt-8% W was found to be -5% and -8% respectively as shown in figs. 6a and 6b. To make sure than no depletion of one species occurred by repeated annealing, we compared the apparent concentration of the minority constituent from the first half to the second half of the measurements. No detectable difference was found.


Pt-8%W (001)

01 .., ., ., .., (

0 5 IO 15

a DEPTH IN ATOMIC LAYERS

Pt-5%Ru (001)

I O jij4367$9

t IO

b DEPTH 1N ATOMIC LAYERS

Fig. 6. (a) Concentration depth profile of the Pt-8% W (001) plane after annealing at 8OO”Cfor -15 sec. The upper square data points signify the apparent concentration of W and the lower circular data point signify the real concentration depth profile of W. The evaporation rate of the 2nd layer was found to be double that of the other layers. (b) Real concentration depth profile of the Pt-5% Ru (001) plane after annealimg at 750°C for -15 sec. Evaporation rate is assumed to be constant in all layers.

4.3. Grain boundary segregation on Stainless Steel 410

We have also studied a grain boundary segregation in the Stainless Steel 410. The result is listed in table 2. The value off& was obtained by using Fes4 as a calibrator (see Appendix).


Table 2 Grain boundary segregation data in Stainless Steel 410

Conditions a Fcr (%) fcr(%%) b

In the grain boundary Just outside the grain boundary

(17.07 f 3.22) (6.4 + 0.97) (7.76 + 3.38) (4.2 ?: 1.04)

a This tip had been annealed at SOO’C for 3 min. b All for had been calculated using Fe54 as a calibrator.

This tip was annealed at 500°C for 3 min. We have to recognize here that the probe hole covered a surface area of -10 A in diameter, while the grain boundary in this case was no more than -3 W wide, The real concentration of Cr in the grain boundary thus may actually be much higher than what we show here. We also found that the evaporation rate in the grain boundary is higher than that just outside the grain boundary. Fortunately, we can use FeS4, whose isotopic abundance is known, as our calibrator, so that the different evaporation rate in and outside the grain boundary can be calculated and the real concentration of Cr can be estimated as discussed in the Appendix.

5. Discussion

5.1. Heat of segregation

The heat of segregation of dilute alloy can be derived from the experimental conditions and result. In the case of Stainless Steel 410, the heat of sublimation [45] of Fe is 99.55 kcal/mol and that of Cr is 94.34 kcal/mol. In (011) plane of bee material, 2 = 8, AZ = 2, and therefore theoretically Quu = 1.3 kcal/mol was obtained from the ideal solution bond breaking monolayer model according to eq. (2). For the size difference model, the shear modulus G of the solvent [46] is 81.2 X 10” dyne/cm’ for Fe and the bulk modulus of the solute [47] is 1.9 X lOI2 dyne/cm2 for Cr. Values of r and E are known [48]. Substituting these values into eq. (3), QLyeo’ = 0.026 kcal/mol is obtained.

For Pt-8% W and Pt-5% Ru, the heat of segregation was found to be close to or less than zero by the same methods. Sure enough, our experimental results did not show any surface segregation in both I’-8% W and Pt-5% Ru. A phot~mis~on study of Pt-Ru alloys gives the same conclusion [49].

‘Ihe experimental value of Q was calculated using eq. (1) and is listed in table 1 for the (011) plane of Stainless Steel 410. It is interesting to note that the experimental values of Q for the (011) plane with two different Cr near surface concentrations in cases (a) and (b) are extremely close. ‘Ihey are 3.43 kcal/mol and 3.92 kcallmol respectively.

432 Y.S. Ng, T. T. Tsong / ToF atom-probe FIM investigation

These values of the heat of segregation derived from experimental data are much higher than the theoretical value of 1.3 kcal/mol. The discrepancy may be due to the fact that we have included some of the surface atoms from the edge of the (011) plane (see experimental procedure and fig. 4) which has a lower coordination number and therefore a higher heat of segregation. Our data show that the concentration of Cr near the edge of the (001) plane is higher than that near the center of the plane as can be seen from fig. 4.

5.2. Surface tensions difference

Q can be derived from eq. (6). The activity coefficient for Fe-Cr [45] has been found to be -1.81 for Stainless Steel 410. Sz is found to be 2.37 kcal/mol. With our experimental values of surface concentration of Cr on the (011) plane and by using eq. (4) (aFe - 8’)a was derived to be 2.26 kcal/mol and 2.37 kcal/mol for cases (a) and (b) as shown in table 1.

The molar surface area a can be calculated as follows. The atomic volume V, is given by [15]

V, = V,/N = M/Np , (7)

where V, is the molar volume, p is the density, M is the atomic weight and N the Avogadro number. Thus the area per atom A, is given by [50]

A, = f(Va2’3 = f(M/Np)2’3 , (8)

where f is a structure factor. The value off for melts of bee solids [SO] is 1.12. Therefore the molar surface area a is given by [ 151

a = NA, = jN1’3 (M/p)2’3 (9)

With the known value [47] of p, we have acr = 3.54 X 10s cm*/mol and ar+ = 3.5 X lo8 cm*/mol. We take an average value of a = 3.52 X 10s cm*/mol. With our experimental results for Stainless Steel 410 the difference in surface tensions between Fe and Cr, (uFe - uCr) can be calculated. For the case (a), (uFe - uCr) of 269 erg/cm2 was found and for the case (b), (uFe - uC’) was found to be 282 erg/cm*. All of these values are listed in table 1.

Theoretically, the experimental result can be compared with an extrapolated value [ 151 given by

u = 0.1 6(HSub)/a , (10)

where Hsub is the sublimation energy of the pure solid. From eq. (10): oCr=

1.78 X lo3 erg/cm* and uFe = 1.904 X 1 O3 erg/cm* are obtained. Therefore (uFe - ocr)tr,eor = 124 erg/cm*, which is only about 45% of our experimental Values, The cause of this discrepancy is not entirely clear. It may be due to uncertainty in taking the differences between two large uncertain values of heat of sublimation

]451.


6. Conclusion

(a) The Cr atoms are found to segregate to the surface of Stainless Steel 410 whereas no segregation of the minority species were found for Pt-8% Wand Pt-5% Ru.

(b) We have demonstrated that the ToF atom-probe FIM can be used for surface segregation studies with a single atomic layer spatial resolution.

(c) The first layer concentration of Cr in Stainless Steel 410 was found to be (38.5 + 12.5)% for a sample with a near surface average concentration of (6.3 f 2.1)% and to be (63.4 + 10.2)% for a sample with a near surface average concentration of (11.9 + 2.5)% in the (011) plane at 500°C. These values are much higher than the theoretical value and an earlier AES result [6].

(d) Surface segregation of Cr to the (012) plane was also observed although a single atomic layer resolution was not achieved due to the size of the probe hole. Segregation of Cr to a grain boundary in the Stainless Steel 410 was also observed, though the absolute concentration of Cr in the grain boundary could not be derived with any certainty due to the smaller size of the grain boundary compared with the area covered by the probe hole.

(e) In general, though the first surface layer is enriched with Cr in Stainless Steel 410, the near surface layers show depletion of Cr in many cases, sometimes as deep as 20 A. The depletion is in agreement with a previous investigation [42].

(f) The heat of segregation of Cr to the (011) plane of Stainless Steel 410 was found to be 3.43 and 3.92 kcal/mol in the two cases (a) and (b) that we have studied. The difference in surface tensions between Fe and Cr in this plane was found to be 269 and 282 erg/cm2 in these two cases.

(g) Extreme care must be taken to avoid losing the top layer by accidental field evaporation before collecting data. A segregated Cr rich layer is found to field evaporated at a field of -2.5 V/A. This is much lower than the -3.5 V/A needed for field evaporating the non-Cr enriched layers. In our case, we used Ar-Ne mixed gas. An Ar FI image appears below 2.2 V/A which was used for the aiming purpose.

(h) For all the alloys we have investigated so far, no preferential field evapora-

tion of a species is found. However, this may occur for some alloys. In such cases, a careful correction of the composition of each layer has to be made.

(i) Future work will focus not only on the composition of each surface layer but also on a possible structure of the segregated atoms.

Acknowledgement

The author wish to thank Mr. S.B. McLane for technical assistance and Dr. S.V. Krishnaswamy for discussion and the Stainless Steel 410 wire.


Appendix A

Derivation of the absolute composition of the dilute alloys with a calibrator

It has been shown [44] that in a binary dilute alloy (B,A), there is a higher probability of field evaporating more than one majority species B atom and be detected as a single B signal in the oscilloscope trace than that of the minority species A. The average number of A signals detected by the atom-probe for each high voltage pulse is given by [44]

?iA = 1 - exp(+?$dfA@) , (A.11

where et is the transmission coefficient of the atom-probe, ed is the detector efficiency of the ion detector, fi is the average real number of atoms field evaporated per pulse, and fA is the real atomic fraction of species A. e&g is the average total number of signals detected per pulse. Similarly for B atoms,

En = 1 - exp(-etedf@) . (A.2)

The apparent concentration of A species, F A, as directly derived from atom- probe data can be related to the real concentration, fA, by [44]

F‘4= 1 - exp(-e,edf,QT)

2 - exp(-e,edf#) - exp(-e,edfuR) * tA.3)

One must be aware that this analysis is valid for two species systems, therefore the isotopes should not be distinguished from each other when eq. (A.3) is used. For example, if an Fes4 and an Fes6 come in the same trace in the scope for Fe-Cr alloy, the apparent number of Fe detected in this trace is counted as one. However, there are two unknows, etedn and fA, in eq. (A.3). This problem can be solved if one of the species in the binary alloy system has isotopes. For example, if we just look at the Fe signals in Stainless Steel 410 and ignore the Cr signals for the moment, then the system can be considered to be a binary system with two com- ponents, Fes4 and non-Fe++ With eq. (A.3) and the known isotopic abundance of Fes4, e&i can be calculated. Now with the value of e&6 known, one can go back to Fe-Cr binary system and find out the real concentration of Cr, for, from the apparent concentration Fcr. The technique has been extended to multi-component systems [44]. Its validity is confirmed here with Pt-8% W, Pt-5% RU whose bulk minority concentrations were known as well as the deep bulk of Stainless Steel 410 system whose Fe isotopic abundance is known.

For example, in fig, 5b, the true average concentration of Cr in the bulk was calculated to be -12% which is comparable to the true value of 11% within the statistical fluctuation. Since the percentage of Cr in the bulk is already small, the number of Crs4 isotope ions will be much smaller than the number of Fes4 ions. So that Crs4 was ignored in this calculation. This procedure would not be accurate in the Cr rich first layer (see Appendix B).


In surface segregation, the near surface layers are usually depleted with the segregated species. If the isotopic abundance is used as a calibrator, then even the assumption of constant field evaporation rate of all layers can be relaxed. The data can still provide the true concentration as has been shown above.

The statistical uncertainty involved in a binary system is derived as follows

fA = NA/@A + NB) , (A.4)

whereas NA is the actual number of A ions detected, Nu is the actual number of B ions detected. Then the uncertainty AfA is

AfA = [(NA + NB) AN.4 - NA W~A + NB)I WA + NBY . (A-5)

If we assume that the uncertainty &VA in detecting NA is +3x2, then A(NA + Nu) is +(NA t Nu)l12 and eq. (A.5) becomes

(‘4.6)

Positive sign in the bracket is chosen to assume a maximum uncertainty. There- fore

AfA = (fAjN)1’2(1 + fA’2), (A.7)

where

N=NA +Nn (A.8)

is the real total number of atoms field evaporated and subsequently successfully detected. Also

N = e,eJiNe , (A.9)

where N,, is the total number of pulses.

Appendix B

Derivation of the absolute composition of dilute alloys without a calibrator

We have also developed a technique for analyzing binary alloy systems when a calibrator is unavailable. It can be applied to species with a single isotope, or to a system with small number of atoms detected, therefore the calibrator even if it exists can not be used due to large statistical fluctuation.

Since ij~ = 1 xxp(-6G?&ifA) = %,/NO whereas % A is the apparent total number of A atoms detected and NO is the total number of pulses, and a similar equa- tion applies for fiu, we have

fdfB = h(l - ?i,&)/h(l - aB) . @.I)

436 Y.S. Ng, T.T. Tsong / ToF atom-probe FM investigation

For a two component system fA + fB = 1, thus

fA = ln(1 - %Jln[(l - R&(1 - tiu)] .

For a multicomponent system,

fi= ln(1 - Ci)

9

In L,fJ (1 - 511

$=l.

03.2)

(B.3)

The method can also be benefited by using the isotope abundance of a species. Assuming there are two isotopes in B, Br and Ba with their relative abundance

given by o1 and 02, crl t cr2 = 1, thus fB1 = ctlfB, then

fA= a1 ln(1 - fi&

ln(1 - %n,) + (Yl ln(1 - HA)

(B.4)

(B.5)

This method is found to be less accurate than the previous method described in (A). However, if no second isotope exists or its abundance is too small, then eq. (B.2) can be conveniently used. The uncertainty AfA in this case can be calculated from eq. (BS) and

fA=+EAthB . A a%,, ’

With a few manipulations, one gets

AfA = {I$" [ln(l - %n,) + o1 ln(1 - AA)] 1-l

(B-6)

(B.7)

For the case where B has only a single isotope, err = 1, and eq. (B.7) reduces to

AfA = {&‘2 [h(l - &) + h(l - ff,d I-’

@3-8)

Since Are, %A, and %n are all known, both fA and AfA can be calculated. This method usually gives a higher uncertainty than that given by eq. (A.7).

It is useful when no second isotope is available. We also want to point out here that when two charge states exist for the ions of one species, they can be treated in a


similar fashion as isotopes. This technique was used in the calculation of the first

layer concentration of Cr in Stainless Steel 410 since only a small number of mass 54 signals were detected, and also since the number of Cr+, in the signals might be comparable to that of Fes4 in the Cr rich first layers.

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ToF atom-probe fim investigation of surface segregation in dilute alloys