SURFACE AND INTERFACE ANALYSISSurf. Interface Anal. 28, 73–76 (1999)

Equilibrium Surface Segregation of Silver to theLow-index Surfaces of a Copper Single Crystal

J. Y. Wang, J. du Plessis,* J. J. Terblans and G. N. van WykDepartment of Physics, UOFS, 9300 Bloemfontein, Republic of South Africa

The equilibrium surface segregation of Ag to the low-index surfaces of Cu single crystals is presented. It isfound that the close-packed surface of the (111) orientation allows a high interaction parameter resultingin a discontinuous transition in the surface concentration against temperature, as well as a step in thesegregation kinetics. In contrast, the rougher surfaces of the (110) and (100) orientations yield smallerinteraction parameter values and a smooth transition in surface coverage against temperature is observed.Copyright 1999 John Wiley & Sons, Ltd.

KEYWORDS: models of surface kinetics; Auger electron spectroscopy; surface segregation; copper; silver; low-index single-crystal surfaces;bulk diffusion

INTRODUCTION

The copper matrix provides a suitable substrate for surfacestudies. It is easily cleaned, compared to other metalssuch as iron, and the low-index surfaces vary from aclose-packed surface (111) to an open row-like structurefor the (110) surface. The different surface structureslead to quite different behaviour for phenomena such assurface segregation. Both the equilibrium coverage andthe kinetics of the segregation process are affected by thespecific surface structure.

The segregation of silver to the low-index surfaces ofcopper was studied by various groups in the past, boththeoretically1 – 9 and experimentally.10 – 24 An aspect thatwas studied in greater detail in this laboratory is thediscontinuous transition that is observed in the surfaceconcentration as the temperature is increased above acertain critical value.25,26 This type of transition is foundon the (111) surface and has been reported.37 Although apredicted hysteresis was not found, a complex segregationkinetic curve could be fitted using only three parameters:the segregation energyG, the interaction parameter�and the diffusion coefficientD.38 The investigation hasnow been extended to the other two low-index surfacesand the results are reported here. It will be shown that the(111) surface allows a closer approach of the segregatingAg atoms than the other two surfaces, resulting in a higherinteraction energy. The effect of the interaction energyon both the equilibrium coverage and the kinetics of thesegregation process will be discussed in detail.

EXPERIMENTAL

The three single crystals (5 N) were doped to 0.2 at.%silver by evaporating a predetermined thickness of silver

* Correspondence to: J. du Plessis, Department of Physics, UOFS,9300 Bloemfontein, Republic of South Africa.E-mail: duplessj@fsk.nw.uovs.ac.za

Contract/grant sponsor: FRD, South Africa.

onto the back of the crystals. The thickness of the evap-orated layer depended on the required bulk concentra-tion and the thickness of the single crystal itself. Forthese samples, an evaporated thickness of¾10 µm wasneeded to dope the crystals to 0.2 at.% silver. It should beemphasized that crystal doping and preparation took placeoutside the analysing vacuum chamber. After thin-filmdeposition, the samples were transferred to an argon-filledquartz tube and placed in an outside vacuum furnace at920°C for 25 days. After this long anneal, the sampleswere taken from the argon tubes and mounted on the resis-tance heaters inside the analysing vacuum chamber. Theanneal at 920°C is required to homogenize the sampleand both calculations and experiments on dummy samplesshowed that a homogeneity of 99.999% is achieved after25 days. This means that the concentration at the oppositeface is 99.999% of the concentration at the deposited face(or, in other words, that the concentration profile varieswith only 0.001% in the bulk). This dopant level is belowthe solubility limit of Ag in Cu at the segregating temper-atures, i.e. 0.3 at.% at 400°C.

Although great care was taken to maximize experimen-tal accuracy, the placement of the thermocouple prob-ably presented the largest source of uncertainty. Thethermocouple was spot-welded to a thin stainless-steeldisc, which was then inserted between the heater andthe crystal. Calibration of the thermocouple in terms ofthe true surface temperature was done using a dummysample. This eliminated most of the systematic temper-ature errors but the mechanical set-up (placement of thethermocouple on the disc and thermal contact betweenheater–disc–sample) could not be expected to be identicalfor all set-ups.

The silver segregated to the three surfaces in the tem-perature region 400–600°C. The surface concentrationwas measured by Auger electron spectroscopy and nearlyone monolayer of surface coverage was observed in allthree cases. The experimental detail is given elsewhere37

but the important points are given here again. Before anysegregation run, the sample was homogenized at 610°Cfor several hours to restore any depletion from previousruns. The sample temperature was then lowered to the

CCC 0142–2421/99/130073–04 $17.50 Received 30 November 1998Copyright 1999 John Wiley & Sons, Ltd. Accepted 31 December 1998

74 J. Y. WANGET AL.

segregation temperature and the surface was cleaned byargon ion sputtering. These regimes ensured that the initialcondition was as close to homogeneous bulk concentrationas possible.

RESULTS AND DISCUSSION

The results for the equilibrium segregation of silver tothe low-index surfaces are given in Figs 1–3. It is clearthat the segregation behaviour differs from the (111) to the(110/111) surfaces. A discontinuous transition is observedfor the (111) surface, but the transition from high to lowcoverage occurs smoothly for the other two surfaces. Thesegregation parameters may be obtained from a fit of theequilibrium segregation equation.27

XS

1� X� DXB

1� XBexp

[GC 2�.X� � XB/

RT

].1/

where X� is the equilibrium surface concentration,XB

is the bulk concentration,G is the segregation energyand� is the interaction parameter defined in the regularsolution model.27 The best fits of Eqn (1) are given by thesolid lines in Figs 1–3 and the only parameters fitted areG and�. From the numerical values of the segregationenergy and interaction parameter it is also clear that the

Figure 1. Equilibrium segregation of silver to the (111) surfaceof a copper single crystal.

Figure 2. Equilibrium segregation of silver to the (110) surfaceof a copper single crystal.

Figure 3. Equilibrium segregation of silver to the (100) surfaceof a copper single crystal.

two surfaces (110) and (100) behave similarly: the fittedvalues areG110 D 29.6š 0.6 kJ mol�1, �110 D 8.7š0.6 kJ mol�1, G100 D 29.2š 0.6 kJ mol�1 and�100 D8.7š 0.6 kJ mol�1. The discontinuous transition may befitted byG111D 24.6š0.6 kJ mol�1 and�111D 13.8š0.36 kJ mol�1 for a slightly lower segregation energy buta significantly higher interaction parameter�. In termsof surface miscibility gaps, the transition temperature of450°C is lower than the critical temperatureTc D �/2R28

in the case of the (111) surface but higher than this criticaltemperature for the other two surfaces:Tc.111/ D 557°Cand Tc.110/100/ D 250°C. However, it was shown inRef. 27 that this is not a sufficient condition to observea discontinuous transition and that the bulk concentrationshould be lower than a critical bulk concentrationXBC,which is given by the solution of

lnXBC

1� XBCC 2

(G

�� 2XBC

)C 2D 0 .2/

Both of these conditions are met for the (111) surfacebut not for the (110) and (100) surfaces. The high interac-tion parameter� for the (111) orientation also influencesthe kinetic behaviour. The kinetic results for a tempera-ture close to the transition temperature are given in Fig. 4.The solid line is the fit from the solution of the system ofcoupled rate equations

∂X�

∂tD[MXB1

d2�B1,S

].3/

∂XB1

∂tD[MXB2

d2�B2,B1 � MX

B1

d2�B1,S

].4/

...

∂X.j/

∂tD[MX.jC1/

d2�.jC1,j/ � MX

.j/

d2�.j,j�1/

].5/

...

whereX� is the surface concentration of the segregant andXB1 is the first bulk layer concentration of the segregant,etc. The rest of the bulk therefore consists ofN � 1layers and the interlayer distance is given byd. ThequantityM is the mobility of the segregant. Fordilute

Surf. Interface Anal. 28, 73–76 (1999) Copyright 1999 John Wiley & Sons, Ltd.

Ag SEGREGATION TO LOW-INDEX Cu SURFACE 75

Figure 4. Kinetics of the segregation of silver to the (111) surfaceof a copper single crystal at 447 °C.

alloys the mobility is related to the diffusion coefficientvia D D MRT, whereR is the universal gas constant andT is the temperature. Furthermore,�.jC1,j/ D �.jC1/ ��.j/��.jC1/

m C�.j/m , where�.j/ is the chemical potential ofthe segregant in layerj and�.j/m is the chemical potentialof the solvent in layerj.

The only additional parameter in these equations com-pared to Eqn (1) is the diffusion parameterD, and it isclear from the fit that the complex segregation behaviouris described excellently by the rate equations. The rate-limiting step is the surface energy, which is lowered bythe attractive interaction between the segregating silveratoms. Once the surface concentration reaches a criticalvalue the surface energy becomes much lower than thebulk energy of the segregating atom, and the driving forcefor segregation increases sharply. At the same time, thedepleted layer below the surface has been replenished andthe diffusion flux is also high. These two terms contributeto a sharp increase in the surface concentration at 30 000 s.

Not only do the equilibrium and kinetic results agreevery well, but the value of the interaction parameter for the(111) surface may be linked to the bulk value of the inter-action parameter calculated from bulk phase diagrams. Itis found that the bulk interaction parameter for the Cu–Agbinary eutectic phase diagram is�B D 29.2 kJ mol�1.37

The coordination number of an atom in the fcc struc-ture is 12, yielding an atom–atom interaction potential of2.4 kJ mol�1. For the (111) surface, the segregated layeris only two-dimensional and the coordination number fora silver atom on the (111) surface is 6. From the fittedvalue of the interaction energy, the atom–atom interactionis 13.8/6 D 2.3 kJ mol�1, which also agrees excellentlywith the bulk value.

The only remaining point that may be addressed isthe lower value of the interaction energies on the (110)and (100) surfaces. For the low-index surfaces, low-energy electron diffraction (LEED) studies were carriedout in other laboratories.29 – 36 The LEED picture foundfor the (100) surface was ac.10ð 2/ structure.29 – 32 TheAg overlayer is compressed by 1.7% in the Cu[110]direction and expanded by 2.1% in the Cu[110] direction,and the close-packed two-dimensional structure is notreproduced as on the (111) surface. The effect is evenmore pronounced on the (110) surface, where ap.8ð 4/surface structure was observed.36 The surface structurefor the (110) surface is given in Fig. 5. The troughs

Figure 5

Figure 6. Overlayer mesh according to literature low-energyelection diffraction results,36 indicating the alignment of thesegregated rows along the troughs in the (110) surface.

are readily distinguished in this, the roughest surface ofthe three low-index surfaces. Thep.8 ð 4/ overlayerstructure can be meshed onto this surface if every fourthrow of segregated Ag atoms is placed in a trough, asis indicated in Fig. 6. The substrate therefore destroysthe close-packed structure that was found on the (111)surface. The interatom distances are therefore differentfrom those found on the (111) surface and the interactionenergy is therefore also lower. It is, however, not clearwhy the (110) and (100) surfaces present with the sameinteraction energies.

CONCLUSIONS

It was shown in a separate paper39 that the rough sur-face of the (110) orientation would result in a lower bulkvacancy formation energy and a consequently lower totalactivation energy for diffusion near these orientations. Thesurface structure therefore influences the surface segrega-tion in three aspects: it determines the segregation energyand the equilibrium coverage; it determines the interactionparameter for segregation of interacting species, whichmay result in a discontinuous transition in the equilib-rium coverage versus temperature and a step-like kineticcurve; and it determines the bulk vacancy concentrationto influence the bulk diffusion coefficient.

Acknowledgements

Financial support from the FRD, South Africa, and stimulating dis-cussions with P. J. K. Paterson of RMIT, Melbourne, Australia, aregratefully acknowledged.

Copyright 1999 John Wiley & Sons, Ltd. Surf. Interface Anal. 28, 73 76 (1999)

76 J. Y. WANGET AL.

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Surf. Interface Anal. 28, 73–76 (1999) Copyright 1999 John Wiley & Sons, Ltd.