Vibrational relaxation by metal atoms

CHEMICALPHYSICSLETTERS

Volume 6, number 5

1 September 1970 1 .’.-._

VIBRATIONAL

RELAXATION

BY

METAL

ATOMS

EDWARD R: FISHER and GEOFFFEY K. SMITH Research ZnsCitufe fin- Engineering Sci&ces and

Department of Chemical Engineerirrg and Material Sciemces, Wayne State University, Detroit, Michigan 48202, USA

Received 14 July 1970 Estimates have been made on the vibrational relaxation of Nz in collision %
Na, K. Rb, Cs and Al using an ionic curve crossing model. calculations and to beam experiments are ixxiic~ted~

The relationship of these restits

During recent studies on the quenching of electronically excited alkali atoms by diatomic molecules [i, 21, it has been noted that the assutied ionic curve crossing mechanism provides a means by which vibrational energy in the diatomic c&n be relaxed in collisions with metal atoms. The process may be represented as

X+.N2@ = I) + {x’ - N$v_))

Polurizabilities Intermediate

Li+ -Ns Na+- Ns

where X denotes a metal atom. The purpose of this communication is to indicate the magnitude of the vibrational relaxation cross sections expected from reaction (1) and to suggest molecular beam experiments which will not only collaborate these cakulafions but provide important information for the further verification of the electronic quenching model. The metal atoms investigated include Li, Na; K, Rb, Cs and Al. For collisions between metal atoms possessing low ‘ionization potentials and simple diatomic molec$.es such as N2, 02, CO., etc., the potential energy curves correspondjng to the ionic system, .i.e. p -Nz, become energetically favorable at .rather large intermolecular distances, This fact not only provides a ctirve crossing mechanism for characterizing the quenching of electronically excited alkali atoms but also provides a, mechanis‘m for the relaxatiqn of vibrational energy in N2 and simiiar diatomics. By,u@ng the polarjzability of the ionic intermediate as a parameter, good’agreement has been obtained between measured tid calculated ,total quenching crpsti sections. for all_ the alkali ‘atqms [2]. The pola_rizabilities‘ thus obtained are showxi in table 1 and have be&x used in the present- CalculatiQn~. -. .433 _-.,_ ., -, . I.:._ -_ : .._ -, I . . .

Polarizability

(A3)

40 20

50

Rb+ - Ns

(1)

Table 1 for the ionic intermediates

40 a)

Ki - N2

+ X+ N2(” = 0) + K.E. ,

to earlier

Cs+ - Nz Al+-Nz

100

40

a) Note the polarizsbility for the Na+ - Ni sy?ems is considkably larger than previously used 111agreement with experimental data [ 3.41.

The alkali -N2 neutral interaction potentials have been calculated from the 0 - N2 interaction 1% V(eV) = 35i exp{-2.6@(i) -Ro(i)]) , where R, is obtained from the relative displacement of the repulgive core of the alkali atomargon curves of Baylis [6], with R,=O for Na. The details of the estimates of these potential curves will be published shortly [2]. The potential .curveti for Al have been estimated by cornparing the Lennard-Jones u for Na with that esti‘,mated for Al following the. method of Hirschfelder [?I and using the form as given by eq. (2). The curve .crpgsing probabilities have been assumed to be of the-landau-Zener form [l] in which the-interactidn matrix eletient.is-a product of an &ctronic component ‘(giyen by the ‘Hasted-Chong corkelation [a]) and a viblrational :over@p (ki.ti@ate-d frdm.the Fran&-Condon:fgc, tors fbr.thp NO “GAMMA” system [9]. .. ‘..., _,. ‘_’ -. -. _ -, .I -.- -. --. _’ -..__. -_ . __.

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Yolume 6, number 5

CHEMICAL PfntsI69 LETTERS

1 September1910

Table 2 Rate coefficients for the relamtiarr of N~{u = 11 by metal atoms Metal atom

10°

‘i-=2500OK

Li

1.o-ll a)

3.0-11

6.0-=

Na

1.0-12 8.rJ’15 4.0’11 1 B-10 6.0’13

4.0-12 2 S-13 t3.w~~

1x11 1_0-~~ Lo-=0 4.0-10 7_0-12

K Rb cs Al

CROSS ZXCZION

T=300 GK T=LOOO9(

3.0-10 2.0-12

s) l.O-x1 = 1.0xlO-lf cm3/moleculesec.

(f”)

ccoss

SECTION I

I

.l

.P

RELATWE

.3

lCtNETiC

ENElGY

I

I

.4

.5

I-4

Fig. 1. Cross sections versus relative kinetic energy for the relaxation of N@ = 1) by metal atoms. The results obtained for the vibrational deactivation cross sections are displayed in fig. 1. FolIowing integration of these cross sections over a Boltmann velocity distriIwtioo the rate coefficients shown in table 2 are found. These rate coefficients are very IarFe compared to any other known vibration-translation processes in X2; or in other similar diatomics. Further, the weak temperature dependence is a reflection of the attractive nature of the potential energy cprves due to the ionic cume crossing. The absolute values of the’cross secticns are, however, sensitive to the assumed pohrizabilities of the idnic intermediate as shown in fig. 2 for the Li reaction. This sensitivity stres%es the qualitative character of these calculations but simultaneously suggests that mqlecular bea& expeSiments (such as those performed on H2 [IO]) wiU provide an alternative method for verificatitixi of tile polarizabilities obtain6d via :&e &e&hing cdculations.

I

.l

I

t

I

.3 .a .t RELATIVEKINETIC ENEIGY WI

‘

.s

Fig. 2. Variation of the cress section for the r&.xation Gf N2@ = 1) by Li with polarlzshifity of the ionic intermediate. The prediction that the v&ratio& relaxation of 32 and similar diatomics is very k&e in collision with certain metal atoms is in itself interesting but these results may also be fmportant to some upper atmospheric problems in which metal atoms arc present ;in.relatively high concentrations. The usefulness of these results 439

CHEMICALPHYSICSLETTEBS

Volume 6, number 5

.to. l&o&tory applications such as the N+ line Feversal method [ll] are precluded due‘to the

1 September 1970

REF’EREN&S

very iOwconcentrations of alkali atoms normally

[l] E.Baier. E.R.Fjsber and F.GiImore. J. Chem. Phy~. 51 (1969) 4173. [2] E_.k. Fish& &d G. K. Smith, in preparation. [3] B.P.Kippl& G.Co$ey and L;Krause. Phys. Rev. 159 (1965) 11. [4J V.Kempter, W.Meckl&brauck. M.Menzinger, G.ScbuIXer. D.R.Herschbach and Ch.ScbIier. Chem. Phys. Letters -6 (1970) 97. [5] Ya.N.Belyaev and V.G.Leonas. Zh. Tekb. Fiz.

&xotitered. It sho@d also be noted that not all metal atoms are‘expected to have large vibrational relaxation cross sections on N2.. Bar&m, for example, has a rebtively low ionization potential (5.19 eV) but due to the large effective “size” of the barium atom, thherepulsive core of the potential is moved to sufficiently large intermolecular distances that an appreciable activation enez$y is associated with tpe curve crossing making the cross section for vibrational relaxation negligibly small. A similar activation energy associated with the crossing of the ionic and neutral potential curves has been proposed to explati the very large difference observed in the quenching of Tl(62P& by N2 and 02 [12].

11 (1965) 353. English transl. Soviet Phys. Tech. Phys. 11 (1966) 257. [S] W.Baylis, J.Chem. Phys. 51 (1969) 2665. [7J J.O.Hirschfelder and M.A.Eliason, Ann. Acad. Sci. N.Y. 67 (1957) 451. [a] J. B. Hasted and A.Y. J.Chong, Proc. Phys. Sot. (London) 80 (1962) 441. [S] R. W. Nicholls, J. Res. Natl. Bur. Std. 68A (1964) 535. [lo] P.F.Dittner and S.Datz, Abstracts of Sixth Intern. Co&. Phys. Electr. aqd Atomic Collisions (196!3) p. 469. [ll] I.R. Kurle. J. @hem. Phys. 41 (1964) 3911. [12] J. A. Bellisio and P. Davidovits. to be published.

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