Chemisorption states of ionic lattices

J. Phvs. Chem.

Solids

Pergamon

Press 1968. Vol. 29, pp. 689-697.

CHEMISORPTION

STATES PETER

Department

of Electrical

Engineering,

OF IONIC

Britain.

LATTICES

MARK

Princeton

(Received

Printed in Great

University,

Princeton,

N.J. 08540.U.S.A

5 July 1967)

Abstract-A method for computing the chemisorption states of ionic lattices is presented in which the dominant interaction between the adsorbent and the adsorbate is a Madelung-type potential. The results describe quite well the chemisorption of oxygen on stable surfaces of ZnO and CdS. The same technique is used to establish a criterion for the stability of ionic surfaces. INTRODUCTION

MANY

PHYSICAL

involving

and

nonmetallic

fact that the Madelung

chemical

processes

lattice

surfaces rely on chemi-

action

sorption; that is, on the formation of adsorbed ions by the exchange of electrons between the adsorbate

and the band structure

adsorbent [ 11. sensitization[3]

Electrophotography and certain forms

of the

[2], dye of hetero-

geneous catalysis[4,5] are some well known examples. It is therefore desirable to have a direct potential

way of estimating the electronic energy level of a chemisorbed ion

relative sorbent.

to the band structure of the adThis paper proposes such a method

for the case where the adsorbent is dominantly ionic so that the principle interaction between adsorbate a Madelung-type covalency,

both

and adsorbent is through potential. Considerable in the

binding

of the

ad-

sorbent and in the chemisorption bond, may be accounted for with a fractional valence in the ionic theory. The results describe quite well the cases of oxygen ions adsorbed on CdS and ZnO. The same technique is applied to the co-adsorption of lattice constituents to yield a criterion for the stability of ionic surfaces. THE HC’l.K !\SI) SUKFACE STATES OF IONIC LATTICES The

proposed

method

is a direct extension

of the theory of intrinsic surface states of ionic lattices[6]. According to that theory, the

surface

states

follow

directly

from

the

site,

potential,

Madelung

constant C,sof a surface

and hence is

constant

also the ionic

always C

of

less

a lattice

removed from the surface. The magnitude of C depends

only on the

of the lattice.

It is computed

the

known

sum which

written

lattice

the

site far

geometry well

inter-

than

from

may

be

as [7]

where 4ij.k = -+l, depending on the sign of the ion located at the index position (i,.j,k) and

Rj,,,.

(0,O.O)

is

the

distance

to (i,.j, k) expressed

measured

from

in terms of the

nearest cation-anion distance. Each index runs from --3c to += with the point (0, 0, 0) excluded from the sum. In the classical limit (overlap binding

integrals sense),

neglected

the bulk

lattice are then obtained action potential

in

the

tight

states of the ionic by adding the inter-

AV = Ctcjr,,

(2)

to the ionization potential (-I,,) of the cationic lattice constituent and subtracting it from the electron affinity t-A,-) of anionic lattice constituent. Positive electron affinities are also possible. In equation (2), the valence Z may be fractional II) account for a covalent contribution to the binding, c is the magnitude

PETER MARK

690

of the electronic charge and r, is the lattice constant. For a surface terminating in an equal number of positive and negative ions, C, is computed from the relation [6] C,=

I: Q iP0,j,k

(3)

which is a sum over half-space; the index i is normal to the surface plane i = 0, and the j and k are projected parallel to the surface plane. Two assumptions are made in writing equation (3): there is no rearrangement of the surface lattice and no significant change in the lattice constant at the surface. Both assumptions are substantiated by low energy electron diffraction studies on the cleavage planes of many partially ionic crystals including the II-VI and III-V compounds with tetrahedral symmetry [8]. The computation of C, is facilitated by writing equation (1) as

C=EQ+C,Q+CQ i
=

i=O

THE

IONIC

OF

Ca= t&o Q. It is as if one atomic layer has been removed from the surface, laying bare the test site used to compute C,. By manipulating equations (5), (6) and (7), one obtains c, = c-c,.

(4)

STATE

LATTICES

Consider next an adsorbate ion. When the ion is near an ionic surface it experiences a shift in its potential (electron affinity or ionization potential) owing to the electrostatic interaction with the nearby ionic lattice. The magnitude of this effect can be estimated by computing the Madelung constant C, at the position of the adsorbed ion. For convenience, let the adsorbate site coincide with a virtual lattice site, one lattice constant distant from the surface. Then, C, is obtained from equation (5) by omitting the twodimensional lattice sum:

e-0

zoQ+2,F,Q.

CHEMISORPTION

(8)

The correction AV, to the free-space potentials of the adsorbate is

The second equality follows by symmetry. The summation indices j and k are implied. Similarly, equation (3) can be written as

%AV,, = Z,C,e/r,

resides atop a negative site and - if it sits on a positive site. The valence Z, may again be fractional in the event of a covalent contribution to the By combining the last two equations, chemisorption bond. The correction potential c,=tc+d,goQ. (6) can actually have any value between +AV,l depending on the exact location of the adThe computation of C, for a specific surface sorbed ion. For example, midway between index of a given lattice type amounts to com- two lattice sites, AL’, = 0. The development of the adsorption states puting the Madelung constant for the two dimensional surface plane (sum over O,j, k) from the free-space adsorbate potentials is illustrated schematically on Fig. 1. On the of that index since C is known. The cationic left is the energy band diagram of the ad(upper) and anionic (lower) surface state energies are then obtained by adding and sorbent. Two valence bands, the conduction subtracting equation (2) from ---I,,, and ---AX, band, the two intrinsic surface states of the respectively, but with C, substituted for C principle gap, and the Fermi level are shown. On the right are the potential energy diagrams in equation (2).

-&Q+i~oQ-

+ if the adsorbate

(9)

(5) lattice

CHE~ISOR~ION

INTRINSIC

STATES

OF IONIC

LATTICES

691

SURFACE

ADSORBENT

ELECTROPHOBIC

ELECTROPtilLlC

ADSORBATE

Fig. I. Potential energy diagram illustrating the evolution of the chemisorption states on an ionic surface. On the left side is the energy b and diagram of the adsorbent. Shown are two valence bands, the conduction band, the two intrinsic surface states of the principle gap, and the Fermi level. On the right are the potential energy diagrams of a donor-like electrophobic adsorbate fsmall ionization potential, positive electron affinity) and of an acceptorlike electrophjlic adsorbate (large ionization potential, negative electron affinity). The range of adsorbate levels on the surface is indicated by the shaded regions: the branches labelled - and f refer to the adsorbate situated on cationic and anionic lattice sites respectively.

of an electrophobic and of an electrophilic adsorbate. The former is characterized by a small ionization potential and a positive electron affinity while the latter has a large ionjzation potential and a negative electron affinity. The range of adsorbate levels on the surface is also indicated; the branches labelled - and + refer to the adsorbate situated on a cationic and anionic lattice site, respectively.

All states between these extremes are also possible+ An adsorbate is donor-like when its corrected ionization potential on the surface, -l&s) = --I,(m) +A V,I, lies near or above the Fermi level, and it is acceptor-like when its corrected electron affinity on the surface, -AA(s) = -A.4(m) 2 A V,,, lies near or below the Fermi levet. Accordingly, electrophobic adsorbates (hydrogen, alkalai metals

PETER MARK

692

191) tend to be donor-like while electrophilic adsorbates (oxygen, halogen [ IO]) tend to act as acceptors. To estimate the energy level of the adsorbate, consider the specific case of an acceptor-like adsorbate with a free-space electron affinity -AA more negative than that of the anionic lattice constituent (-AK), as shown in Fig. 2. This would hold for oxygen

AE, = 2AV-

(1,-A,)

(10)

and the depth AE, of the adsorbate below the conduction band is AE, = AVkAVm-

level

(Z,-A,4).

The depth AE, may be obtained ratio of equations ( 10) and ( 11):

(11) from the

ENERGY

(12)

t

where p = [ZM- A,] r,/2ZCe, and pu, = [~M--AAlro/2Z,Ce, and r = CJC. The ratio I, which is a purely geometric parameter, has been determined for several lattice types and surface indicies of surface terminating in an equal number of positive and negative ions[6]. Several of these Ivalues are reproduced in Table 1. Similarly, Table 1. r-values of several ionic surfaces Fig. 2. Potential energy diagram of an electrophilic, acceptor-like adsorbate on an ionic adsorbent. I, and Ax are, respectively, the free-space ionization potential of the cationic lattice component and the electron affinity of the anionic lattice component. A, is the free-space electron a.Rnity of the adsorbate assumed more negative than Ax.

chemisorbed on CdS. In the classical limit, the energies of the valence band and of the conduction band are -EC = --I.,, + AV and -E, = --A,-AV, respectively, and the energy of the adsorbate is -E, = -AA *AL’,; the upper and lower signs refer to the adsorbate located adjacent to a negative and to a positive lattice ion, respectively. The gap AE, between the valence band and the conduction band of the adsorbent is then

Lattice type NaCl NaCl NaCl NaCl CSCI Wurtzite Wurtzite Zincblende

Surface index (loo) (110) (210) (211) (110)

(1~70, (1010) (110)

r 0.96 0.86 0.11 0.60 0.90 0.88 0.79 0.85

p has been evaluated for 46 halides, oxides and sulfides [6]. Some representative values are reproduced in Table 2. Three values are listed for the II-VI compounds because of the uncertainty in the lattice valence Z.

CHEMISORPTION

STATES

Table 2. Values of p for several halides, oxides and sulfides

Material

Lattice type

Alkali Halides A@ A&l AgBr AgI MgO BaO NiO ZnO Cd0 ZnS CdS

(Z = 0.5) (Z = 1) (Z = 2) --

NaCl NaCl NaCl NaCl Zincblende Wurtzite NaCl NaCl Wurtzite NaCl Zincblende Wurtzite

693

LATTICES

taken (see below). Agreement is quite good when the chemisorption bond valence 2, is chosen close to the lattice valence. This is only reasonable. The Zn- and Cd-chalcogenide bonds are

partially covalent and one should not expect the ionicity of the chemisorption bond to differ greatly from that of the lattice bond. Thus, in analogy with the adsorbent bond,

<0.12 0.16 0.21 0.21 0.28 0.09

OF IONIC

0.06 0.17 0.15

0.23 0.16 0.23 0.30 0.31

0.50 0.52 0.57 0.56 0.60

0.33 0.33

0.41 0.41

0.57 0.58

According to Birman[ 111, who reviewed a variety of experimental results, the best estimates place 2 near 0.5 for the oxides and sulfides with wurzite and zincblende lattices, and somewhat larger than 0.5 for the cubic lattices owing to their greater ionicity. Consider the case of oxygen chemisorbed on the (1120) surface of CdS. The most suitable adsorbent valence is 2 = 0.5 (62.5 per cent ionicity). Also F,, is taken from the CdQ data of Table 1I. If Z,, = 0.5 also, AE,, ranges from 1.04eV to 1.47eV, the larger value corresponding to the oxygen residing on a Cd site. Since Cd0 is cubic, the Cdoxygen bond is probably more ionic than the Cd-sulfur bond so that the valence Z,, should be chosen larger than 2. Experiments[ 121 indicate that AE,, = 0.9eV, corresponding to Z,, = 0.75 (69 per cent ionicity) for the o*\ygen chemisorbed on a Cd site and to Z,, = 0.55 (63 per cent ionicity) for oxygen chemisorbed on an S site, the more likely value being the former since the adsorbate probably resides nearer a Cd lattice site. Similar estimates have also been made for oxygen chemisorbed on ZnO and ZnS, also with 2 = 0.5[ I I]. The results for four Z,,-values are summarized in Table 3 together with what experimental information is available. In each case, stable adsorbent surfaces are

the chemisorption bond should be viewed as one in which the lattice electron is only ‘partially’ transferred to the adsorbate. In particular the data shows that it is unlikley to have doubly negative oxygen chemisorbed on these II-VI compounds[5]; a negative AE,, locates the adsorption state above the conduction band edge. This is a direct consequence of the substantial covalent contribution to the binding in the adsorbent and in the chemisorption bond. ON THE STABILITY

OF IONIC SURFACES

It

is evident from Table 1 that the ratio r decreases with increasing surface index for a particular lattice type. Thus, from equa’tions (9) and (12), the low index surfaces generate the smallest shift of the adsorbate potential on chemisorption. This fact can be used to elicit a stability criterion for ionic surfaces. Consider the energy diagram of Fig. 3 which shows schematically the evolution of the lattice states from I,, and A,-, as well as of the states that represent the co-adsorption on the surface of the lattice constituents at their normal sites during growth of the lattice. The latter levels are labelled M,, and X,, for the adsorbed cationic and anionic components, respectively. The cationic component is raised in energy by +AV,, on adsorption while the anionic component is lowered by the same amount. Thus, the gap AC between the adsorption states is, by analogy with equation ( lo), AC = 2Al’,,where

AG

is negative

(/,,,--A.Y) when

work

(13) must

be

PETER MARK

694

Table 3. Chemisorption state of oxygen on C&S, ZnO and ZnS Lattice

valence

Z = 0.5’“)

1. CdS: A,!?, = 2.4 eV’*‘, ( 1 ITO) surface 2,

% ionicity

0.5 8.75 1.0 2.0

62.5 68.75 75 100

2. ZnO:

I.47 0.89 0.00 -5.96”’

AE, = 3.2 eV(*), (1120)

0.5 0.75 1.0 2.0

Experimental value 0.91 t 0.03’fi

surface

Chemisorbed on Zn site 1.50 0.91 0.08 -5.80

ElA

A& (eV) Chemisorbed on S site 1.04 0.24 -0.86 -7.67

Chemisorbed on Cd site

A& (cV) Chemisorbed on 0 site I .04 0.00 -0.85 -7.65

Experimental value

1.05-t 0.05Q

3. ZnS: AE, = 3.7 eV’*‘, (110) surface Chemisorbed on Zn site 2.23 1.43 0.28 -7.95

Z” 0.5 0.75 1.0 2.0

Chemisorbed on S site 1.41 0.19 -1.38 -11.3

Experimental(‘) value

(a). BIRMANJ. L.,Phys. Rev.109,810(1958). (6). Room temperature value. BUBE R. H., Photoconductiuity of Solids, Chap. 7, pp. 233-234. Wiley, New York (1960). (c). Negative A&-values locate the adsorption state above the conduction band edge. (d). MARK P., .I. Phys. Chem. Sol. 26,1767 (1965). (e). WATANABE H., WADA M. and TAKAHASHI T., Jap. J. appl. Phys. 4,945 (1965) (f) No data available.

expended to produce an ion pair; that is, when X, lies above M,. Since AL’, depends on T through equation (8), the amount of displacement on adsorption depends on the surface index; specifically, AV, increases with increasing surfaoe index so that AC becomes less negative accordingly. The ionic configuration of the co-adsorbed lattice constituents is stable when AG is positive: zll -&l--T) Thus,

co-adsorbed

> /_L.

ionic lattice constituents

are stabilized by those surfaces having sufficiently small r-values to invert the states M, and X,. Surfaces whose indecies provide sufficient stabilization to conform with this criterion must be growth surfaces, while those for which the inequality is reversed are the stable surfaces of the lattice. This model has been applied to a variety of surface indecies of several binary salts. The results are summarized in Table 4. Three values of the lattice valence are considered for the oxides and sulfides. Comparison with experiment is rather spotty. The alkali

CHEMISORPTION

-

-

-

-

-

s

‘2

i

m

STATES

OF IONIC

LATTICES

69.5

CHEMISORPTION

areas; hence the less prominently surfaces.

STATES

developed

( 100) macroscopic

REFERENCES

’I. WEISZ P. B., J. cl1en7. Phs.

20, 1483 (1952):

21.

1531(1953).

2.SCHAFFERT R. M. and OUGHTOh C. D.. ./. opt. Sec.Am. 38,991 (1948). AMICK J. A., KC‘,4 Hcv. 20,753.770(

1959).

3.WEST W. and CARROLL

B. H., In 7‘!1(, Theory c;f’ the, f’l~otogropl~ic~ PI-oc~c~s.~ (Edited by C. E. K. Meet and T. H. James), 3rd Edn.. Chap. 12. Macmillan. New York ( 1966). 4. HAUFFE K...~
OF

IONIC

LAvrTICES

8.

697

MAY J. W.. /,I(-(,.\.\(Edited h) C‘. E. K. hlee\ and ‘1‘. H. Jamc\). 31-d Edn.. Chap. 2. Macmill;in. New York (1966). IS. HURLBUT C. S.. JI-.. ~li~rc,ro/r~,q~. 17th Edn. Chap. 5. p. 3 19. Wiley. Ne\r j’ork (IOSY). J. and NAK.4\‘.4hlA I ., J. oppl. P/ry\. 16. CHIKAWA 35.2493(lY64,. 17. bl.AC RAF .A. U. .md
( I’)hhl. IX. HC:RI.BLI’~~‘.S..r~/~.,ir..p.“.~