On the role of Gibbsian segregation in causing preferential sputtering

REVIEW PAPER

On the Role of Gibbsian Segregation in Causing Preferential Sputtering t

Roger Kelly IBM Thomas J. Watson Research Center, Yorktown Heights, N e w York 10598, USA

It is well known that preferential sputtering with binary alloys correlates significantly with chemical binding, but only the sense and not the magnitude of the effect can be understood in these terms. It is argued here that the correlation is, in fact, an indirect one due to bombardment-induced Gibbsian (or similar) segregation. The preferentially removed component is characterized by a composition profile consisting of a one atom-layer-thick spike at the surface; this is the depth from which most sputtered atoms originate so the spike must have near-bulk composition. There is then a severely depleted subsurface region in accordance with Gibbsian segregation equilibrium (or an equivalent effect) and a final return to bulk composition. The reason for the marked correlation with chemical binding is that segregation is governed significantly more often by binding than by the alternatives of size, surface chemistry, an interstitial flux, or long-range ordering.

INTRODUCTION

We are here concerned with bombardment-induced compositional changes with alloys, also termed preferential sputtering. Such changes are of very wide occurrence and have been the subject of numerous experimental works, theoretical descriptions, and reviews. It is the object of the present work to complete arguments begun elsewhere’*’ and outline briefly what is proposed to be the correct description, namely that preferential sputtering, except when it is mass-correlating, is identical with bombardment-induced Gibbsian (or similar) segregation. The overriding importance of segregation in this context has been proposed recently also by Swartzfager et al.? Nalcamura et al.,3A Li et a1,4 and Holloway and Bhattacharya.’ We give here no lists of systems but leave this for companion works in which the greater part of the literature on preferential sputtering and segregation is analy~ed.~.’

The history of preferential sputtering has been tur- bulent. The earliest view was that it correlated with mass, such that the lighter species was lost preferentially [e.g. References 8- 1 11. The geometry and composition profile at the surface of a bombarded binary alloy were therefore believed to appear as in Figs. l(a) and (b). We recognize a steady-state (‘03’) bombardment-induced surface (‘2’) composition of component A labelled x:(~,, a steady- state altered layer due to bombardment-enhanced diffusion which shows an ever increasing composition up to that labelled x F ( ~ ~ , a freeze-in depth, L, at which the enhanced diffusion is assumed to cease, and finally the bulk (‘3’) composition labelled x ~ ( ~ ) . ’ ’ , ’ ~ The assumption that the enhanced diffusion terminates abruptly is obviously a simplification but little is gained (provided x:cL) is similar to x * ( ~ ) ) in making a more realistic, therefore more complicated, model.

t Invited paper presented at the Third International Conference on Quantitative Surface Analysis held at the National Physical Labora- tory, Teddington, UK, 22-24 November 1983.

CCC-0142-242 I/SS/

@ Wiley Heyden Ltd, 1985

Analytically this problem can be described in terms of the one-dimensional diffusion equation for a system with a uniform enhanced diffusion coefficient D and with the surface receding at velocity v :

a X A / d t = D d 2 X A / a Z 2 + V d X A l a Z (1)

I t i I p-MOBILE-t-FROZEN+-

I I

I I I I I t I I I I 1 ! I + 0 1 2 3 L /X

DEPTH (atom layers)

- 1 I I I I I I ’ * + 0 1 2 3 L /X

DEPTH (atom layers)

Figure 1. (a) Sketch of a possible geometry for analysing mass- correlating preferential sputtering. The target up to depth L / A , where A is the mean atomic spacing, shows a uniform bombardment-enhanced diffusion coefficient but beyond L is assumed to be diffusionally ‘frozen’. (b) Composition profile such as would arise from mass-correlating preferential sputtering for a geometry as in Fig. l(a). x‘&_ the steady-state (‘a’) surface (‘2’) composition of component A in the binary alloy A-B, is followed by a diffusion- limited depletion of A, and then at depth L by x ~ ( ~ ) , the bulk (’3’) composition.

‘0007-0001 $03.50

SURFACE AND INTERFACE ANALYSIS, VOL. 7, NO. 1, 1985 1

R. KELLY

The steady-state boundary condition at z = 0 is xA = x:(~), as determined by the mass-correlating preferential sputtering, and that at z = L is not X T < ~ ) = xA(3)'2*13 but rather

D(dxz/dz)L+uxz(L)= uxA(3) (2) The steady-state solution to ( 1 ) and (2) follows as

XA=XA(3)-(XA(3)-Xz((2)) exp ( - u z / D ) for z < L ; x, = xA(3) for z > L

(3)

The fact that the first line of (3) reduces to xA=x& for large D may be taken as proof that the boundary condition of (2) is correct.*

The view that preferential sputtering was in general a mass-dependent effect appearing as in Fig. l(a) and (b) and described by ( 1 -3) persisted for some time, being still sustained in some contemporary work. Such a description is, however, easily shown to be inadequate in most of the situations to which it was applied: there are about as many examples known where alloys lose a lighter component as where they lose a heavier or equal- mass Exceptions, which probably show true mass-correlating preferential sputtering, include systems bombarded under near-threshold condi- t i0ns,6,~, '~ systems consisting of two or more isotope^,^,^,"*'^ together with a limited number of alloys provided that they are studied by ISS.3,6*7,17-'7B

The next view chronologically was that preferential sputtering could be attributed to chemical binding differ- ences. One approach of this type was to assume the relevance of cascade sputtering, so that the yield of component A, SA, scaled as

S A xA/ uA

where UA, the surface binding energy, depends explicitly on chemical binding.' Such an approach was shown to be successful in predicting trends and still remains as the best single indicator of the sense of preferential

Unfortunately it was, at the same time, quite unable to explain the extent of preferential A second approach based on chemical binding differ- ences was to assume the relevance of thermal sputtering. In view of recent evidence, however, that thermal sputtering is virtually non-existent with metals, even with volatile systems such as Zn'' or Ag,I9 it need not be considered further.

More recently, it was suggested that what is conventionally termed preferential sputtering may often be identical with bombardment-induced Gibbsian segregation or an equivalent The correlation with chemical binding would thus be indirect: segregation is governed significantly more often by binding than by alternative effects, and, if induced by bombardment, would cause major compositional changes just beneath the surface.

The main problem with the argument is that it pre- supposes that a subtle thermodynamic effect will occur within the volume affected by a violent collision cascade where the average particle energy is 2 to 3 orders of magnitude greater than thermal energy. It is therefore

* The solution for z < L for the boundary condition x:(~) = xA(3) i s xA = x:(~,+ ( x ~ ( ~ , -x:(*))( 1 -exp [ -uz /D] ) ( 1 - exp [ - u L / D ) ] - ' . For large D it reduces to xA = x:(~) + ( xA(3) - x:(~,)( z / L ) instead of the expected xA = x:(~).

0.682 4 I 1 I I I 1 ,I!,., Ar++Cu0.44 AU0.56 1.

(-120°C) 4 ANNEALED (300°C)

ANNEALED (25") 0.58

t 0.50 I I I I I I

0 10 20 30 BOMBARDMENT TIME (min)

Figure 2. Composition profiles for Cuo,Auo, as obtained by first bombarding to steady state with a 24 pA/cm2 beam of 2 keV Ar+ at -120°C. then either not annealing or heating to 25 "C for 12 h or heating to 300 "C for 1 h, then cooling again to -120 "C, and finally profiling with a 0.4 pA/cmZ beam of 2 keV Ar+. Compositions were obtained with low-energy AES, using the 60 eV signal for Cu and the 69 eV signal for Au. The authors showed that the bombardment- enhanced diffusion needed for creating the profiles during the initial bombardment occurs only for high current densities and, accordingly, that a 0.4 pA/cmZ beam accomplishes a true profiling. Due to Li, Koshikawa, and Goto4

important that new evidence for the role of Gibbsian segregation with bombarded alloys now exists. For example, it is seen in Fig. 24 how a profile appropriate to nearly pure segregation ('annealed (300 "C)') evolves to one showing the preferential loss of subsurface atoms ('annealed (25 "C)' and 'not annealed (-120 "C)') when the post-bombardment annealing temperature is 1owered.t Figure 33 gives a further example of a bombarded alloy showing profiles in which there is a characteristic subsurface loss, while similar profiles can be found also in Refs. 17, 20-26.

It is our contention that subsurface loss, i.e. loss which suggests the occurrence of mass transport against the concentration gradient combined with sputtering, is an explicit proof that Gibbsian (or similar) segregation occurs within the volume affected by a collision cascade. It is further contended that the reason why the violence of the cascade does not prevent this, including why cascade mixing does not completely eliminate the surface spikes seen in Figs. 2 and 3, is one of timescale: a cascade ends at 0.1-1 ps,27 the recrystallization (i.e. elimination of grossly misplaced atoms) ends at roughly

the thermal spike ends at roughly

? T h e surface compositions in Fig. 2, thence the height of the composition spikes, were probably somewhat underestimated because of the use of AES. Kang e? o L , " ~ . ' ' ~ using ISS, find that x2u(2) for bombarded Cu, 4 3 A ~ 0 57 is 0.70-0.73.

2 SURFACE AND INTERFACE ANALYSIS, VOL. 7, NO. 1, 1985

ON THE ROLE OF GIBBSIAN SEGREGATION IN CAUSING PREFERENTIAL SPUTTERING

2

0 k 0.2

2

Q 8

0 10 20 30 40 50 “.I

ARGON DOSE (io’x ions/cm2)

Figure 3. Composition profiles for Ago 2 7 A ~ 0 as obtained by first bombarding to steady state with 2 keV Ne at the indicated temperatures, then quenching to -90°C. and finally profiling with 2 keV Ne. Compositions were obtained with ISS using the same 2 keV Ne+astheprobeion. DuetoSwartzfager,Ziemecki,and Kelley3

whereas bombardment-induced segregation can take many seconds to reach completion (Fig. 5).30 The segregation is thus occurring subsequent to the thermalization of the cascade atoms, thence in a lattice which is normal except for residual defects.

SEGREGATION MODELS

Van Santen and Boersma3’ have presented a standard thermodynamic argument, involving the minimization of free energy, which relates the steady-state (‘co’) surface composition of component A in a binary system, x:(~), to the bulk composition, x ~ ( ~ ) . It is assumed that segregation alters only the outer monolayer on the grounds that generalizations to several monolayers change neither the trends nor the general magnitudes. It is assumed further that an alloy can be described as a random (‘regular’) solution, i.e. it has an arbitrary heat of mixing, AH,,,, but an ideal entropy of mixing. The assumption regard- ing the entropy is equivalent to proposing that the con- stituent atoms are located randomly, a situation equivalent to the disordered state which develops when alloys are bombarded at low enough temperature^.^^

The final result is2

(4)

where Q, the heat of segregation, is the enthalpy change when A atoms are transferred from the bulk to the surface and B atoms make the converse change. The changes are normally confined to the outermost atomic

but this is precisely the layer from which 80- 100% of sputtered atoms originate.35736 The corre- sponding geometry and composition profile are therefore as in Figs. 5(a) and (b).

Q can be evaluated in terms of either chemical binding or strain energy, though in principle other considerations (such as ordering37338 or change of bond-type) also apply. We first consider binding. If Z3 is the bulk coordination number, 2,(-0.25 Z,) is the vertical part of Z3 (i.e. the

part in the direction of the surface normal), and Z, 1 (-0.5 5) is the lateral part of Z,, then the final result is2

for an ideal solution and a similar relation but with the additional factor ( yA/ Y ~ ) ~ on the right-hand side for a regular solution. Here yi is the thermodynamic activity ~oe f f i c i en t~~ and s stands for

It follows from actual values of yi that ( 5 ) , without the additional factor (?A/ Ye)’, is an adequate description of the problem.6

The alternative is to evaluate Q in terms of strain energy. Recent summaries of the arguments are made by40-42 and lead to the result that ( 5 ) should be multi- plied, for xA<< xB, by still a further factor,

Here ri is an appropriate atomic radius, KA is the bulk modulus of the minority species, and GB is the shear modulus of the majority species. The form of ( 6 ) will be noted to always favor the segregation of the minority species, a result which is not correct. Also, it neglects the fact that part of the energy released by a misfitted atom moving to the surface is offset by the creation of surface defects such as d i s l o ~ a t i o n s ~ ~ , ~ ~ or an altered lattice spacingu and the further fact that metal surfaces are slightly e~panded.~’

We therefore offer the following qualifications to (6 ) : (a) Equation ( 6 ) is applicable only to an oversized

species, since an undersized species is like a vacancy and there is no significant relaxation of atomic positions around a vacancy in a meta1.4”42’46

(b) If a metal surface involves a very slight expan~ion,~’ it follows that oversized atoms would still be drawn to a surface but undersized atoms might be rejected.2

(c) In any case ( 6 ) is probably too large numerically since it neglects surface

The result of this argument is that segregation will most often correlate with chemical binding, with the weaker bonded species segregating. But in those in- stances where the more strongly bonded species is significantly larger it may segregate instead. Examples included A 1 - c ~ ; ~ CU-AU,~’ and In-Ga,36 together with Au-Cr, Gd-Co, and Gd-Fe which have not been studied explicitly but show composition change^^^-^' as if the larger species was segregating. A surface showing segregation would tend, when bombarded, to lose the segregated component preferentially provided the necessary mass transport could occur at the bombardment temperature. Such mass transport is well documented: as seen, for example, in Fig. 4.,O

The form of the composition profile that would occur if preferential sputtering were consequent to Gibbsian (or similar) segregation is easily deduced. The loss of material at the surface leads, when steady state is achieved, to the boundary condition in the outermost


R. KELLY

i Ar+4Ag0.20 Ni0.80

0 500 1000 1500

TIME AFTER BOMBARDMENT (s)

Figure 4. Relaxation of surface composition of a thin film sandwich consisting of 1Onm of Ag between 50nm thick Ni films. The sandwich was first bombarded (and any surface layer of Ag thus removed) with 1 keVAr+, the beam was then turned off, and the segregation of Ag to the surface was followed in real time at 20°C. Whether the diffusion was through the bulk, consequent to ion- beam mixing, or along grain boundaries is unclear in our opinion, but it is fairly certain to have been bombardment-enhanced. Compositions were obtained with medium-energy AES, using the 353 eV signal for Ag. Due to Fine, Andreadis, and Da~arya.~'

layer,

xA = x F ( 2 ) (7)

The quantity x:((,) is to be evaluated from the conservation relation,52

i.e.

xz(2) = [1 + xB(3) yAB/xA(3)1-I (8) where Y, is the sputtering yield defined in terms of ions incident on one component of the target and the ratio YAB takes into account all possible preferential effects, whether due to mass, chemical binding, or other causes. It is known that such preferential sputtering is normally unimportant with alloys,lz2 and that when it does occur (as under near-threshold ~ o n d i t i o n s , 6 ~ ~ ~ ~ ~ with isotope^,^*^*'^,'^ and with certain alloys studied by ISS3.6*7*'7-'7B) it is often a small effect. It follows that Y A B

approaches unity, thence that x& 4 xA13) as in Fig. 3. The existence of Gibbsian (or similar) segregation, here assumed to extend over only one atom layer and to be in steady state (cf. also Ref. 3a), introduces a subsidiary boundary condition for the second atom layer,

a xA = XA(2')

where for true Gibbsian segregation xz(2s) would be evaluated from (4) rewritten in the following way:

(9)

a

i Q c

*

rn

I 0 0

2

i i (a)

DEPTH (atom layers)

0 1 2 3 DEPTH (atom layers)

Figure 5. (a) Sketch of the usual geometry for analysing Gibbsian segregation. The segregation is assumed to occur only in the outer atom layer and the bulk of the solid is taken as having a uniform diffusional mobility. (b) Steady-state composition profile such as arises from thermally activated Gibbsian segregation for a geometry as in Fig. 5(a).

The diffusion equation is the same as ( l ) , L is, as before, the depth of assumed diffusional 'freezing' (Fig. 6(a)), and the boundary condition at z = L remains as in (2). The steady-state solution follows as

X A = x:((,) = [ 1 + xg(3) YAB/XA(3)]- ' for z = 0;

XA=XA(3)-(XA(3)-X:((Z'))exp(-vz/D) forO<z<L;

(10) X A = xA(3) for z > L

This result, shown schematically in Fig. 6(b), is of the form shown previously in Figs. 2 and 3.4*3 As already noted, the characteristic surface spike can be expected to appear in spite of cascade mixing (and similar effects) since it forms subsequent to the thermalization of the cascade atoms, thence in a nearly normal lattice.

Treatments of the same problem exist also in other work though none is fully correct. For example, Refs. 12 and 13 used a boundary condition at z = L different from (2) and Ref. 53 assumed that both sputtering and segregation occur beneath the outermost atomic layer. We propose that (10) is the only correct steady-state solution within the approximation of (2).

The profile types to be expected with bombarded or heated alloys are accordingly the following:

(a) Preferential sputtering correlating with either mass or chemical binding alone would be described by Figs. l (a) and (b), based on (3). They are probably always irrelevant with alloys, but can be expected to play a role


ON THE ROLE OF GIBBSIAN SEGREGATION IN CAUSING PREFERENTIAL SPUTTERING

(a)

DEPTH (atom layers)

1 I I I 1 I 1 1 I I I>>

DEPTH (atom layers) 0 1 2 3 L / X

Figure 6. (a) Sketch of a possible geometry for analysing bombardment-induced Gibbsian segregation. The segregation is assumed to occur only in the outer atom layer and is followed by a region of uniform diffusional mobility and finally a 'frozen' bulk as in Fig. l(a). (b) Composition profile such as would arise from bombardment-induced Gibbsian segregation for a geometry as in Fig. 6(a). The steady-state surface composition of component A, x&, is shown as being similar to the bulk composition, xq(,), as is appropriate when mass-correlating effects are absent or unimportant. Deple- tion occurs only beneath the surface, with the numerical value of the steady-state subsurface ('2") composition, x:(~), being established by segregation equilibrium as in (9). The position of L, as in Fig. l(b), is determined by the depth a t which bombardment- enhanced diffusion is assumed to cease.

with the limited number of non-alloy systems showing mass-correlating effects (e.g. Refs. 6, 7, 14-17). They would also play a role with oxides and halides when the preferential sputtering arose from chemical changes at the outer surface54 provided segregation effects were absent.

(b) Thermally activated Gibbsian segregation is described by Figs. 5(a) and (b), based on (4) or (5). It is the well known result when alloys are heated but not bombarded and the surface is analysed with essentially any surface-sensitive technique.

(c) Bombardment-induced Gibbsian (or similar) segregation, described by Figs. 6(a) and (b) and by Eqn. (lo), shows a characteristic concentration 'spike' at the surface. It is here proposed to be the result obtained when alloys are bombarded but not heated, mass-correlating effects are absent or unimportant, and the surface is profiled on the atomic scale. Such profiles are seldom reported, in principle owing to the use of techniques like high-energy AES which lack the necessary depth resolution. Occasionally, however, they have been observed explicitly, especially when ISS or low-energy AES is used (Figs. 2 and 34*3). The depletion would be in the same sense as thermally activated Gibbsian segregation when the mass transport was caused by bombardment-induced vacancies, though could be in the reversed

I .o

0

N 8 3 0.8

x

i 0 0.6 I- cn 0 a

0

-

5 0.4

W V

K 3 v)

0.2 i?

I I I (a) 0.0 0.2 0.4 0.6 0.8 0.0

Ni BULK COMPOSITION, xcU(3)

i 0 k v) 0 a z 0 V

0.6

0.4 W V

K v)

2 3 0.2

nn

t

0 U

v.v 0.0 0.2 0.4 0.6 0.8 I .o Ni cu

BULK COMPOSITION, xcu(3)

Figure 7. (a) Steady-state surface compositions expressed as atom fraction of Cu. ~2"~~). for Cu-Ni specimens which were either annealed (i.e. segregated) or bombarded (i.e. preferentially sputtered). O=ISS study after annealing at 600 T: A=ISS study after annealing at 500 'C3' (revised with respect to Ref. 3). M=AES study after annealing at 650"CBo (revised with respect to Ref. 3). +=AES study after annealing at 600 T.6' O=ISS study after bombarding at 25 "C with 2 keV Ne3 The AES signals were obtained a t low energy, namely, 106 eVforCuand 101 eVforNi.Thediagonallinecorresponds to no surface alteration. Due to Swartzfager, Ziemecki, and Kelley3 (b) Steady-state surface compositions, ~2"~~). for Cu-Ni specimens which were bombarded with 500eVAr+ to steady state a t the indicated temperatures and then analysed a t room temperature. Compositions were obtained by high-energy AES, using the 920 eV signal for Cu and the 710eV signal for Ni. Due to Shimizu. Ono. and Nakayama.s8

sense if the mass transport was caused by surface chemistry (as with Fe-Ti55,6) or an interstitial flux (as with B e - c ~ ~ ~ , ~ ' ) .

(d) An intermediate situation also exists where alloys are both bombarded and heated. This possibility has not yet been explicitly taken into account here, but would lead, it is clear, to a situation where there is no freezing-in


R. KELLY

1.20 t - 1 cu0.!50 '+0.50

1.10

p 0.90 a 0.80

0 15 30 45 60 75 90 EJECTION ANGLE (degrees)

Figure 8. Angular variation of the sputtered-particle yield ratio, S,/Scu, for 20 and 160 keV Ar+ bombardment of C ~ ~ , ~ p t o . ~ as determined by RBS analysis of sputter deposits. The distributions have been normalized to the average composition of the material sputtered into the entire hemisphere. Due to Andersen, Chernysh, Stenum, S~rensen, and whit lo^.^'

at z = L (as in Fig. 6(a)) and a macroscopic subsurface depletion therefore occurs. Segregation, an effect conventionally attributed to a single atom layer, should thus be able to trigger a compositional change of macroscopic dimensions. It is easily seen that the first two lines of (10) remain valid but with L+ a.

EXPERIMENTAL EVIDENCE

Insofar as profiles as in Fig. 6(b) or Eqn. ( 10) occur, then there are a number of experimental consequences.

(a) A concentration 'spike' showing near-bulk composition in accordance with (8) will be seen explicitly if a sensitive enough analytical technque is used (Figs. 2 and

(b) The existence of a concentration spike will often be inferrred by a conflict between results for, for example, ISS and AES (Figs. 7(a) and (b)3958). In par- ticular, ISS will tend to reproduce a near bulk composition as given by (8) whereas AES will give a strongly depleted (or enhanced) composition, often approaching zero or unity. The ISS results can even be in a different sense from the AES.3*17-17B

34,3).

(c) The existence of a concentration spike will often be inferred by the tendency for the non-segregating species to be sputtered more nearIy normal to the surface (Fig. 859). This can lead to a reversal in the sense of the angular eff ect between low and high incident ion energy.I5

(d) The segregating species will be depleted starting at the second atom layer and will therefore be reported, when techniques such as XPS or high-energy AES are used, as being preferentially sputtered (Fig. 7(b)58).

(e) Since Gibbsian segregation correlates most often with chemical binding, less frequently with size, and never with mass, the sense of the preferential sputtering will be that the species which is lost tends to be that with the weaker binding whether this is the lighter or heavier species. Mass will enter only in special cases where binding is i r r e l e ~ a n t . ~ * ~ , ' ~ - ' ~

(f) Although bond-correlating Gibbsian segregation explains most examples of preferential sputtering, there are a few examples of size-correlating Gibbsian segregation,36,38,47 of segregation induced by surface chemistry,55s6 of segregation consequent to an interstitial flu^,'^,'^ and of segregation arising from long- range ~rdering.~' Conservation of matter still requires that the profile be as in Figs. 6(a) and (b), while angular emission effects as in Fig. 8 will still occur.59

(g) Macroscopic specimens which are both bombarded and heated will show a macroscopic subsurface depletion as in Fig. 3.3

CONCLUSIONS

What is conventionally called preferential sputtering and is assumed to lead to a profile as in Figs. l(a) and (b) is often identical with bombardment-induced Gibbsian (or similar) segregation and leads to a profile as in Figs. 6(a) and (b). Of 40 systems for which information is available: the segregation in 30 cases is bond-correlating Gibbsian, in five cases is size-correlating Gibbsian, in three cases is induced by surface chemistry, in one case can be understood both in terms of surface chemistry and an interstitial flux, and in one case shows the effects both of size and of long-range ordering.

Mass-dependent effects are less important than once thought. Nevertheless, they play a well-defined role under certain condition^^*^*^^'^-'^-^^^ and may be of even wider occurrence but normally unreported because of experimental problems. The main problem is that they would often be confined to the concentration spike seen in the outermost atom layer as in Figs. 6(a) and (b) and would be detected only by ISS and not by AES, XPS, RBS, etc.

Acknowledgements

The author is grateful to Joseph Fine (National Bureau of Standards, Washington) for commenting on the manuscript.

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ON THE ROLE OF GlBBSlAN SEGREGATION IN CAUSING PREFERENTIAL SPUTTERING

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On the role of Gibbsian segregation in causing preferential sputtering

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