An analysis of chemisorption in multicomponent systems
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9. C. Laird: Amer. Soc. Test Mater., Spec. Tech. Publ. 415, 1967, pp. 131-80.
10. G. T. Hahn, R. G. Hoagland, and A. R. Rosenfield: Met. Trans., 1972, vol. 3, pp. 1189-1202.
An Analysis of Chemisorption in Multicomponent Systems B. O Z T U R K A N D G. S I M K O V I C H The mechanical and corrosive properties of many polycrystalline materials frequently are influenced substantially by adsorption of minor solute components at grain boundaries and other interfaces. Unfortunately, because theoretical analyses have primarily been restricted to binary systems, most experimental efforts have necessarily interpreted results under restrictive theoretical foundations. Recently, Darken and Simkovich, ~following Wagner, 2 obtained theoretical relations for adsorption in ternary systems which may be utilized to predict either enhanced or reduced adsorption in such systems. This note is concerned with the extension of Darken and Simkovich's analysis of ternaries to multicomponent systems and indicates how the derived relations may be employed to indicate the course of adsorption as solutes are added or extracted from a solvent phase. Theorelical. For a binary system at equilibrium at constant temperature and pressure and where no strain energy is involved, e.g., at free interfaces or incoherent grain boundaries, the Gibbs adsorption equation is, r2
=
_ (i)o'~l,i)/t2]=
-
(i) i)oln,,2j /
[1]
where o is the surface free energy of the system,/,z is the chemical potential of component 2 (the solvent is taken as component 1), a z is the thermodynamic activity of component 2, R and T carry their normal connotation and F 2 is the excess concentration of component 2, with respect to c o m p o n e n t 1, adsorbed at the interface. Following Wagnerfl F 2 is defined explicitly as the difference between the concentration of component 2 in the surface region and the concentration of component 2 in the bulk phase where the concentrations are related only to the main component 1 (see Eq. 3). It should be noted that the Gibbs adsorption relation is not restrictive in terms of the amount of material adsorbed nor the spatial extent of adsorption?
B. OZTURK is Graduate Student, Metallurgy Section, Pennsylvania State University. G. S1MKOVICHis Professor of Metallurgy, Department of Materials Science and Engineering, Pennsylvania State University, University Park, PA 18802. Manuscript submitted February 4, 1980.
ISSN 0360-2133/80/1211-2032500.75/0 2032--VOLUME 1IA, DECEMBER 1980 9 1980 AMERICAN SOCIETY FOR METALS AND METALLURGICAL TRANSACTIONSA THE METALLURGICAL SOCIETY OF AIME
Utilizing, for a ternary system, the relation
and
do = - F2d/h - I'3d/-t3
[21
0 ln~y2 F2 "~ - RT(1 + ezv2)
and the definitions
Yi = ni/nl
bulk composition
[31
Yi = a/Yi
"activity coefficient"
[41
self-interaction coefficient
[51
Ei
- -
3 Oy In i7i 3 In,&
% -
Oy~-
3 In 7j -
interaction coefficient
3Yi
do = -F2d~2 - F3d~3 - I'4d/t 4
[61
Oo
3/.t2
3/~ 3
3/~ 4
[9]
for Yi = 2, 3 or 4 with the other y's held constant. Utilizing the relation
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