Volume 11, number .4 CHEMICAL PHYSICS LETTERS 1 November 1971

SCATdtIN@ MEASUWMENTS, SECOND,VHtIAL COEFFI&IENTS; AND.THE ~TE~TO~i~ PBTENTUL FOR ARGON

Division of Chemistry, Nationai Research Council of Conada, U ftm, CDnadu

Received 27 August 1971

Second virid coeffitients for argon are calculated using a pair potentM’det&mined from scattetiigand spcctro- swpic data by Parson and Lee. Agreement with experiment is poor. A potential due to Basker, Fisher end Watts agrees about as well as that of Parson and Lee with the scattering and spectroscopic data, and also gives second virial coefficients in excellen: a@vement with experiment.

Accurate measurements of molecular beam differ- ential scattering cross sections have recently provided

Fig. 1. Second virial coeffhieuts expressed as differen& from 6: 12 potential values. Dashed curve, potential of Parson and Lee [ 11; solid curve, potential of Barker et aI: [ 101, ~kxpcri- mental data: o Weir et at [5]; CJ Byrne et al. 161; &Fender and

Halsey /?I; v Michels et at l8] ; *W&&y et + [9j. ’ . . . .

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@uabk information on interatomic forces in km-t gases [l; 21. hen and Lee [II determ&ed a pair potential which was consistent with their scitteriq me&wements and also with f&e spectroscopic data on the A.r, rn~~ec~e of Taaka mind Yoshino [3,4]. We haire calculated second vi&l coefficients for argon using this potential, and the resuIts are shown &I fig, 1 I T&e cakuiations included a quantum correction (the term af order h2 in the Wigner-Xir~wood expansion). This correction is smafl, amounting to about t3 cm3/mole at 80% znd t 1.7 cm3/mole at 30r3%, To provide a convenienf scale we have plotted the dS ference between tie computed and experimentat [S-9] secolnd viriai coefficients and those calculated with *the traditional 6:12 potent&I function, with depth e/k = 119.8% and diameter a= 3.405 &It will be seen that the agreement wi& experiment is un- satisfktory, ~~‘de~~o~s as large as 30 cm3/mole .ti the low temL;erature r;urge where the most recent measurements of Weir et at. [SI and Byrne et al, [6f are in excelIetit agreement with otie another, and only slightly worse agreement with the measurements of Fender-and Haisey f7f. ‘l%is disagreement is sufficient to discjuaN& th~‘potentiaf qf Parson aitd Lee a.5 an ac-

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Fig. 2. ~oiec&r.be&‘differe’ntM scatt&ng intensities of Parson and Lee [ I]. In the upper curves thi points axe exp~r~~e~~, the dashed,and &d CIUWS Were calculatedby Parson and Lee for t+e potent&& of Barker and Pompe [ 121 and Bobetic and Barker

; [Ill respectively,.and the dash-dotted cur~,e represents intexpolited values for the potential of Barker et al. [IO]. The lower cmve was calculated for the poteniial of Dymond and Alder 1141 by Parson and Lee.

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Volume 11, number 4’ CHEMICAL PHYSICS LETTERS I November 1971

curate pair. potential for argon. There is no ambiguity arising from many-body interactions because the second virial coefficients, like the scattering and spectroscopic data, depend only on pair interactions.

uniquely td give a precise pair potantS, and that other data, in particular second viriai coefficients, should also be used.

Also shown in fig. 1, are second virial coefficients We are grateful to Dr. Y.T. Lee, Dr. G. Soles, Dr. calculated using the potential due to Barker et aI. [IO] , 1.J: McGee, and Dr. H3.M. H+Iey for communicath?g which has the form their results prior to pubtication.

where UBB and Use are the potentials of Bobetic and Barker [ 1 I] and Barker and Pompe [ 121 respectively.

These three potentials represent successive refme- ments in a process in which potentials having correct short-range and long-range behavior were fitted to ex- perimental data on gaseous, solid [ 111 and liqcid [lo] argon, with the assumption that many-body interac- tions other than the three-body Axilrod-Teller inter- action could be nelgected. -Although the latter assump tion is not beyond criticism it is nevertheless true that the successive refinements bring the potentials into closer and closer agreement with the scattering data of Parson and Lee and the spectroscopic data of Tanaka L&d Yoshino (see figs. 2 and 3). In fact the final po- tential of Barker et al. agrees with these data about as well as the potential of Parson and Lee, and gives

second virial coefficients in excellent agreement with experiment. A recent careful determination of a po- tential for argon from second virial coefficients and gas viscosities alone by Klein and Hanley [ 131 led to a result very close to the potentials of Bobetic and Barker and of Barker et al. All this suggests that the latter potential is very close to the truth. On the basis of the scattering results (fig. 2) and spectroscopic data (fig. 3) the potential of Dymond and Alder [ 141 ap- pears to be less satisfactory.

It appears that present scattering data, even when combined with spectroscopic data, cannot be inverted

,.;.

References

t11

121

t31

141

ISI

161

[71

[81

191

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illI iI21

[I31

1141

J.hf.Parson and Y.TLee, Third Intern. Symp. on Molec- ular beams, Cannes (1971):private communication. This paper will be submitted ior publication to the J. Chem. Phys. M.Cwallini, M.A.Dondi. G.ScoIes and U.Valbusa, Third Intern. Symp. on hfolecukr beams, Cannes (1971). Y-Tanaka and K.Yoshino. I. Cbem. Phyr 53 (1970) 2012. L.W.Bruchand Y.J.McGee, J. Chem. Phys. 53 (1970) 4711; private communication. R.D.Weir, l.Wynn Jones, J.S.RowLmon and GSaville, Trans. Faraday Sot. 63 (1967) 1320. M.A.Byme, M.R.Jones and L.A.K.Staveley, Trans. Faraday Sac. 64 (1968) 1747. B.E.F.Fender and G.D.Halsey Jr.. I. Chem. Phys. 36 (1962) 1881. AMicheLs, J.M.Levelt and W.de Graaf. Physiu 24 (1958) 659. E.Whalley, Y.Lucien and WGSchneider, Can. 1. Chem. 31 (1953) 722. J.A.Barker, R.A.FiBer and R.O.Wat?s. Mol. Phys., to be published. M.V_Bobetic and J.A.Barker, whys. Rev. B2 (1970) 4169. J.A.Barker and A.Pompe, Australian J. Chem. 21 (1968) 1683. M.Klein and H.J.M.HanIey, I. Chem. Phyr 53 (i970) 4722; private communiation. J.H.Dymond and BJ.Alder. I. Chem. Phys. 5 I (1969) 309.

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