Solid State Communications, Vol. 71, No. 8, pp. 693-696, 1989. Printed in Great Britain.

0038-1098/89 $3.00 + .00 Pergamon Press plc

SURFACE SEGREGATION IN MAGNETIC ALLOYS

S. Modak and B.C. Khanra*

Saha Institute of Nuclear Physics, 92, Acharya Prafulla Chandra Road, Calcutta 700 009, India

(Received 10 April 1989 by C.N.R. Rao)

A phenomenological model for surface segregation in magnetic alloys has been proposed. The magnetic interaction energy has been calculated and found to be small compared to the heat of segregation. The calculated results indicate that the component having higher magnetic moment segregates to the surface. This behaviour becomes more pro- minent in the presence of a magnetic field.

1. INTRODUCTION

THE STUDY of segregation properties of transition metal alloys is very important from the point of their utility as catalysts. Several theoretical models, phenomenological [ 1-10] as well as electronic [11-15], have been proposed to explain the segregation behav- iour of these alloys. The phenomenological models are usually based on several considerations like the relative bond strengths [1-2], the relative atomic sizes [4-6], the thermodynamic parameters of the alloy [7], the surface energies andL the elastic mismatch, etc. [8-10]. The segregation behaviour in the majority of the alloys may be explained by all the models, while in a few alloy systems the properties may be explained only by some specific models. The recent work by Ossi [16] gives a critical analysis of these models. However, it is found from the works of Mukherjee and Morfin-L6pez [15] and Ossi [I 6] that the segregation properties in the binary alloys, in whJLch one or both of the constituents are ferromagnetic in nature, could not be satisfactorily explained by the e, xisting models. It was felt that [15, 16] the effects of the magnetic interaction energy should be taken in'Lo account while formulating the theory of segregation for such alloys. But, to the best knowledge of the authors the problem is not yet studied seriously. It is the main purpose of the present work to study the effect of introducing ferromagnetic exchange interaction between two neighbouring atoms on the segregation characteristics of the magnetic alloys.

2. THE PHENOMENOLOGICAL MODEL

Let us consider the mechanisms that change the surface composition of an alloy AxB]_x, Depending

* To whom all cor:respondence should be addressed.

on the relative bond strengths E°A, E°n and E]B surface segregation may take place in an alloy. In the regular solution model the segregation equation may be expressed as [17]

X s X = - - e Q~/Rr, (1) 1 - x s 1 - x

where Qseg is the heat of segregation given by

Qso, = ½(z - Zs)(E°A -- E°~) 1 0 t - ~ A E [ Z ~ ( 1 - 2 x , ) - ( Z - Z~")(1 - 2 x ) ] .

(2)

In equation (2)

AE ° = 2E°n - E°A -- En°s. (3)

Z and Z~ are the co-ordination numbers of an atom in the bulk and surface respectively. Z~ may be further expressed as Z~ = Z~ + Z~" where Z~ and Z~" are the co-ordination number of a surface atom for contacts in the surface layer and with the second layer respectively.

Since spontaneous magnetization in a ferro- magnetic metal or alloy behaves as an order parameter this will further affect the segregation properties of ferromagnetic alloys. Let the A and B atom of a ferromagnetic alloy AxBl_x be characterised with spins SA and Sn and exchange interactions JaA and JBB respectively. The total magnetic interaction energy can then be written as (considering the nearest neigh- bour interactions only)

1 ~ ~ _ 2JijSi, Sj, ' (4) Emag = 2 i = | j ~ l

where Jjj is the exchange coupling constant for neigh- bouring atoms i and j ; N is the total number of atoms in the system; and n is the number of nearest neigh-

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694

bours. The factor 1/2 outside the summation ensures that no interaction is counted twice. Intuitively, we can guess that the interatomic exchange interactions would affect the pair-bond-energies E°A, E°~ and EA°B. The new expressions for these pair-bond-energies would then be

EAA = E ° ] ~,4 + J~S~; EBB = E°8 + J, BS~

E o o o 2E. . - (E~ + E ~ ) + 2J~.S~& . ( 5 )

2 2 - JAAS) -- JBBS~.

Please note, the magnetic interaction energy due to its origin in exchange is negative. But since the pair-bond energies are also negative hence the new pair-bond energies have been obtained by a simple summation of the two. Thus, in presence of a magnetic field the segregation behaviour may be predicted by equations (1) and (2) with the pair bond energies given by equation (5). Bond energies E°A and E°B of the alloy components can be calculated from the values of heat of vaporisation. AE ° can be calculated from the value of heat of solution. Exchange constants JAA, JBR, etc. can be calculated from the Curie temperature, Tc through the relation of the type

3kTc J~A = 2nSA(SA + 1)' etc. (6)

Again, since an alloy may undergo an order-disorder transition below a certain critical temperature, the segregation equation may be further modified by this alloy order-disorder transition. To understand this aspect of the alloy problem let p be a parameter such that it can vary from - 1 (pure B) to + 1 (pure A) [this amounts to replacing x by 1/2(1 + p)]. Further, let be an order parameter which is 1 - p or p - 1 for complete order and zero for complete disorder. Let the parameters p and • corresponding to surface be denoted by Ps and ~s. Then the segregation charac- teristics of an alloy in presence of a magnetic field and alloy order may be represented as [17]

k T In 1 + P____._2 = k T In 1 +_____pp 1 - P s 1 - p

+ ½(Z - Z,)(E~A -- Ess) 1 t + ~AE[psZ] - p ( Z - Z;)]

[p o~ °2 ~z~ l k T , (7) + 2 (1 - p2)2 P~ (1 - pZ)Z

where ~¢0 and ~0 are the equilibrium values of the bulk and surface order parameters. For a particular value of p we can calculate p~ by solving equation (7) numerically. From p~ we can calculate back our alloy

SURFACE SEGREGATION IN MAGNETIC ALLOYS Vol. 71, No. 8

surface concentration parameter x,. Please note, if we put c¢ ° = 0, ~ -- 0 the last term in equation (7) is zero indicating that the order-disorder effect is nil for the segregation characteristics. In addition to this, if JAA = O, JBB = 0 then EA.4 = E°AA and EBB -- Es°B, AE = AE ° and we recover the usual regular solution (RS) model for segregation [equations (1) and (2)]. Thus, from equation (7) we derive the segregation properties corresponding to three different situations; namely the regular solution results (RS), regular sol- ution results in presence of magnetic interactions [RS(M)] and lastly the regular solution results in present of magnetic interactions as well as alloy order parameter [RS(M, ~)]. There is further scope of study- ing the effect of applied magnetic field on the segre- gation properties of the ferromagnetic alloys. Intu- itively, we can feel that the applied field would be equivalent to an additional exchange interaction of appropriate strength. Or, in other words, we can understand the likely changes in the segregation properties due to applied magnetic field by using higher values for J. The results are presented in the next section.

3. RESULTS

The calculated results are shown in Tables 1, 2 and 3. The systems studied are such that at least one component of the alloys is ferromagnetic. The results presented are obtained for 5% of solute in the solvent. Qseg values presented in the tables have been calculated by recasting equation (7) to the form of equation (1). Let us first closely examine the results presented in Table 1. Please note, the effect of the ferromagnetic exchange interaction on the segregation properties is minimal. The magnetic interaction contributes to Qseg an energy of the order of 0.2-3.5 kJ mole -~. The general trend indicates that the ferromagnetic com- ponent experiences a force, however mild, towards the surface. And where both the components are ferro- magnetic, the component with larger magnetic moment segregates to the surface. Also note, except for the Co(Ni) system, the segregating component for all the systems remains unaltered due to the magnetic inter- action.

Table 2 shows the segregation behaviour of a few systems for various values of an effective exchange interaction, J ' (say). The results of this table would indicate how the segregation behaviour changes with applied field of various strengths. As mentioned in Section 2, the effect of applied field would be equivalent to taking higher value of the effective exchange inter- action J ' . Thus we calculate Qseg for values of J ' having strengths J ' = J, J ' = 5J and J ' = 10J

Vol. 71, No. 8 SURFACE SEGREGA TIO N IN MA G N ETIC ALLOYS

Table 1. Segregation results for some of the magnetic alloys

695

System: Oseg in (kJ mole- l ) solvent (solute) RS RS(M)

Segregating component

Theoretical prediction

RS RS(M)

Experimental observation (Reference]

Cu(Fe) - 41.6 - 41.2 Cu Cu Fe [18] Co(Fe) + 4.3 + 4.87 Fe Fe Fe [19] Co(Ni) + 0.03 - 0.39 Ni Co Ni [20] Fe(Pt) - 48.9 - 52.7 Fe Fe - Fe(Cu) + 12.4 8.67 Cu Cu Cu [21] Fe(Ni) - 4.7 - 6.37 Fe Fe Ni [22] Fe(Co) - 6.1 - 7.08 Fe Fe Fe [23] Ni(Fe) + 9.26 + 10.0 Fe Fe - Ni(Pt) - 39.54 - 40.7 Ni Ni Pt [24] Ni(Co) + 0.56 + 0.98 Ni Ni Ni [20] Pt(Ni) + 61.3 + 60.2 Ni Ni Pt [24, 25] Pt(Fe) + 94.0 + 90,5 Fe Fe Fe [25]

RS = Results calceLlated by simple regular solution model [equations (1) and (2)]. RS(M) = Results calculated by regular solution model including the effect of magnetic interaction,

where J is given by relation (6). Please note, Qseg changes significantly with J. However for the systems presented in Table 2, the sign of Qseg does not change indicating that the segregating component remains unaltered up to the field strength J ' -- 10J. To the best knowledge of the authors, no experimental results exist where the segregation behaviour of magnetic alloys has been studied as a function of applied mag- netic field. However, we suggest that such an exper- imental study would be of great importance from the point of view of their use as catalysts.

The effect of the alloy order-disorder process on the segregation characteristics is shown in Table 3. We have presented the results for three arbitrary systems. The values in column under RS(M, ~) indicate that they have been calculated with magnetic exchange as well as alloy order e. The values are for e = 0.1.

Table 2. Segregation characteristics of magnetic alloys for various J' values (J' includes the normal exchange interaction + additional exchange equivalent to applied magnetic field)

System: Qseg (kJ mole-~) Segregating solvent component (solute) J ' = J J ' = 5J J ' = lOJ

Ni(Cu) 9.8 7.27 4.47 Cu Co(Fe) 4.87 8.57 8.03 Fe Fe(Co) - 7 . 0 8 - 1 1 . 0 -15 .9 Fe

Please note, in case of Ni(Co) a segregation reversal is indicated in presence of the alloy order.

Finally, some typical segregation characteristics are shown in Fig. 1 where xs vs. x curves are plotted for the entire bulk concentration x = 0.0 to 1.0. The system chosen is CoxNi~_x. The effect of the magnetic field or the exchange interaction and alloy order on the segregation properties is illustrated by this figure.

4. CONCLUSIONS

Within the limit of accuracies of the regular sol- ution model (to predict the segregation properties of binary alloys) we have attempted to understand the role of exchange interaction, the applied magnetic field and the alloy order on the surface segregation in magnetic alloys. The following indications have been

Table 3. Segregation behaviour in presence of alloy order

System: Qseg (kJ mole 1 ) Segregating solvent component (solute) RS(M) RS(M, ~)

RS(M) RS(M, ~)

Ni(Co) + 0.98 - 0.27 Co Ni Co(Ni) - 0.39 - 1.62 Co Co Ni(Au) + 4.2 3.9 Au Au

RS(M, ~): regular solution model with exchange interaction and alloy order.

696 SURFACE SEGREGATION IN MAGNETIC ALLOYS Vol. 71, No. 8

1.c

COx Nil_ x ...'/ .... ../ D~ .." o.e " """ ..'/c ~ /

/..;U o , /.;"7"

Ill . ' " t

0.~

.°

• "~ ...i.../ 0.~ "/

J ~'..,.-.-'"i j I I I

0.0 0.2 0.4 0.6 0.8 1.0 Ni Co X

Fig. 1. Segregation behaviour of CoxNij x alloy as predicted by regular solution model. Curve A: No segregation line; Curve B: regular solution model (RS); Curve C: regular solution model with ferro- magnetic exchange interaction [RS(M)]; Curve D: regular solution model with ferromagnetic exchange interaction and alloy order [RS(M, ~)].

noted and pointed out in this work.

(i) The exchange energy is very small compared to the segregation energy otherwise coming from the different pair-bond energies. Thus, in most of the magnetic alloy systems the segregating component remains unaltered.

(ii) The exchange interaction lets the ferromagnetic atoms of the alloy to feel a pull towards the surface and this affects the effective segregation energy. In case of both the components being ferromagnetic, the component with higher magnetic moment segregates to the surface.

(iii) In presence of an applied magnetic field the effective exchange interaction increases and the segre- gation behaviour may be greatly perturbed due to this field.

(iv) The effect of alloy order on the segregation characteristics of magnetic alloys is dependent on the strength of the order parameter - the higher the value of the order parameter the larger is the effect on segregation.

We believe, the importance of this work lies in its relevance to catalysis research where the catalytic

activity in presence of a magnetic field is of interest. A suggestion has also been made for studying exper- imentally the surface composition of a ferromagnetic alloy in presence of a magnetic field. That would help us to have a better theoretical understanding of the problem.

REFERENCES

1. F.L. Williams & D. Nason, Surf Sci. 45, 377 (1978).

2. J.L. Morfin-L6pez & L.M. Falicov, Phys. Rev. B18, 2542, 2549 (1978).

3. D. Kumar, A. Mookherjee & V. Kumar, J. Phys. F6, 725 (1976).

4. D. McLean, Grain Boundaries in Metals, Oxford University Press, Oxford (1957).

5. P. Wynblatt & R.C. Ku, Surf Sci. 65, 511 (1977).

6. F.F. Abraham, Phys. Rev. Lett. 46, 546 (1981); F.F. Abraham & C.R. Brundle, J. Vac. Sci. Technol. 18, 506 (1981).

7. J.J. Burton & E.S. Machlin, Phys. Rev. Lett. 37, 1433 (1976).

8. A.R. Miedema, Z. Metallk. 69, 455 (1978). 9. J.C. Hamilton, Phys. Rev. Lett. 42, 989 (1979).

10. J.R. Chelikowski, Surf Sci. 139, L197 (1984); M.P. Seah, J. Catal. 57, 450 (1979).

11. G. Kerker, J.L. Mor~n-L6pez & K.H. Benne- mann, Phys. Rev. B15, 638 (1977).

12. Ph. Lambin & J.P. Gaspard, J. Phys. F10, 2413 (1980).

13. S. Mukherjee, J.L. Mor~n-L6pez, V. Kumar & K.H. Bennemann, Phys. Rev. B25, 730 (1982).

14. C.A. Balseiro & J.L. Morfin-L6pez, Phys. Rev. B21, 349 (1980).

15. S. Mukherjee & J.L. Morfin-L6pez, Surf Sci. 188, L702 (1987).

16. P.M. Ossi, Surf. Sci. 201, L519 (1988). 17. M.J. Sparnaay, Surf Sci. Rep. 4, 101 (1984). 18. J. Bernardini & J. Carbone, Acta Met. 21, 1561

(1973). 19. R. Herschitz & D.N. Seidman, Acta Met. 33,

1547 (1985). 20. E.E. Hajesar, P.T. Dawson & W.W. Smeltzet,

Surf. Interface Anal. 10, 343 (1983), 21. B.E. Sundquist, Acta Met. 12, 585 (1964). 22. K. Wandelt & G. Ertl, J. Phys. F6, 1607 (1976). 23. G. Allie, C. Lauroz & P. ViUemain, Surf Sci.

104, 583 (1981). 24. L. de Temmerman, C. Creemers, H. Van Hove

& A. Neyens, Surf Sci. 183, 565 (1987). 25. J.J. Burton & R.S. Polizzoti, Surf Sci. 66, 1

(1977).