Adsorption and desorption kinetics with regard for interaction among adatoms

Volume 22, number 1

CHEMICAL PHYSICS LETTERS

I5 September

1973

ADSORPTION AND DESORPTlON KINETICS WLTH REGARD FOR INTERACTION AMONG ADATOMS V.K. FEDJANIN 771~ Karpov

fnslifltte

ofP/~)~sical

Chertlistrv,

~lfoscow,

USSR

Received 5 April 1973

A new mctlmd of obtaining adsorption proposed

and desorption

Let us consider a homogeneous surface with IV active sites, N’ of which are “impurities”. An impurity is either a site, of which the properties (e.g., heat of adsorption, interaction of adatoms with its neighhours, E’ and so on) differ from the characteristic properties of the N-N* active sites, which may contain interacting adatoms; or it is a site which cannot be occupied by an adatom, i.e., an intersite, see ref. [ 11. The point character of the impurities and local changes of the properties of either neighbouring adatoms or the atoms on the impurity site are of considerable importance. Here we shall confine ourselves to the case when the impurity occupies oniy one site. The impurities are assumed to be randomiy distributed among the ,v sites of a regular structure. Impurities can be associated with a transition state of adsorption or desorption - their concentration (see below) determining the rate of the corresponding process. In accordance with refs. [1,2] let us write down the total energy of the system (adatoms +N* impurities).

F tot=Fg-BInvcB~lnj*+E*NC - 0 ln[Ni/@!(N-A+)!]

,

(1)

where v = (v(1) .,. v(p)) is the mean of the product of the operators y(i), 1 G i ,
rates on a uniform surlxe

with interacting

impurity formation energy. The averaging is carried out using the “adsorption hamiltonian” [3] Ha= --v c,r,-+

v = 13In{@

Zf,“[

2 1

exp[~(Eo+n~,)i~l/iorp)tl12

,

(3

i.e., u is expressed in terms of the adsorption coefficient in which the inter-electronic interaction is taken into account (see ref. [3]); the equilibrium characteristics of adsorption have been studied in detail with the help of (2). PO is the free enera of the “ideal” system F, = -0 InSp exp(-@f,), p = Ber. The last term in (1) originates in the entropy, andi* takes account of the internal degrees of freedom of the impurity. Minimizing (1) with respect to ,Y” we get I1* = N*/N for the impurity concentration II* =j* exp(-&*)

exp(dInv/&P)

.

(3)

It is quite natural to use correistion disintegration in order to calculate Y [I ,4]. Thus supposing full disintegration of correlations between impurity domains v + fl,(V(!-)> = tiy, where uI is fully determined by the properties of one impurity as well as by correlation functions of the “ideal” system [l-3]; using (3) we get n* =j*vl

exp(-De*) .

(4)

Expressing the correlation functions ofthe “ideaI” system to some approximation ES,41 one can calculate the rate OF adsorption and desorp tion of interact..‘. ,,

:

adatoms is

..

99

Volume 22, number 1

CHEMICAL PHYSICS LETTERS

ing adatoms on a homogeneous surface [ 51 with the help of (4). I am grateFu1 to Professor M-1. Temkin for his suggestion to use the results of refs. [ 1,2] in kinematic problems.

References S.V. Tjablikov and V.K. Fedjanin, Fis. Metall. i hletalloved. 23 (1967) 999; VKFedjanin, Dokl.Ahd. Nauk SSSR 19 (1971) 156.

15 September

1973

[Z] Y.K. Fedjanin, Report at the Conference on Statistical Physics, Lvov (19721, to be published. (3) V.K. Fedjanin, JFX 44 (1970) 495; 45 (1971)2867;,46 (1972) 119; ‘