Thermochemical study of the molecule (CsI)4

Surface

436

~ERMOCHEMICAL K. HILPERT

STUDY OF THE MOLECULE

and L. BENCIVENNI

Institute of Applied Physical Chemistry, GWWZtly

Received

Science 156 (1985) 436-443 North-Holland, Amsterdam

(Cd),

*

Nuclear Research Centre Jiilich, D - 5170 Jiilich, Fed. Rep. of

10 July 1984

The sublimation of CsI(s) was studied by the high-temperature mass spectrometric with a Knudsen cell. The (CsI), equilibrium partial pressure over CsI(s) was determined log{ p(Pa))

(748-813

= -(12748+278)/T(K)+(9.27~0.36)

method as

K).

Entropies and enthalpy increments of (CsI),(g) and (Csl),(g) resulted from estimated molecular parameters. The enthalpy changes of the reactions (CsI),(g) F? i Csl(g) and I CsIfs) F1 (CsI),(g) (i = 3, 4) were determined by the third-law method and discussed.

1. In~~uction Experimental thermochemical data are available for some metallic trimers and higher metal clusters [l]. while such data for ionic metal halide clusters are very scanty [2,3]. Hilpert [4] as well as Viswanathan and Hilpert [S] recently determined the dissociation enthalpies of (NaI),(g) and (CsI),(g), respectively. The first dissociation enthalpy of a transition metal halide trimer was obtained by Hilpert et al. [6]. Thermochemical data of metal halide clusters are for example necessary in order to check and to improve ionic model computations [3,4,7,81. New results from our thermochemical equilibrium studies of CsI microclusters are reported. Entropies and enthalpy increments of (CsI),(g) and (CsI),(g) were computed for the first time from estimated molecular parameters (geometries, main force constants) for these molecules. It thus also became possible to evaluate the thermodynamic properties for (CsI),(g), obtained by us earlier I.51 according to the second-law method, by the third-law method. Additionally, thermodynamic data for (CM),(g) were determined. Our results represent a further #nt~bution to the field of alkali halide clusters 171.

* On leave from:

Department

of Chemistry,

University

of Rome. 1-001X5 Rome, Italy.

0039~6028/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

K. Hilpert, L. Benciuenni / Thermochemical study oj(CsI),

437

2. Experimental The experiments were carried out with a single focusing mass spectrometer equipped with a molybdenum Knudsen cell. More details on the instrument are described in refs. [5,9]. The vapour species were ionized with an electronimpact energy of 3.4 al. The cesium iodide (E. Merck, Darmstadt) used for the investigation had a purity of more than 99.5%.

3. Results Upon

subliming

CsI(s) the gaseous species CsI(g) [Cs’, Csl+, I+], (CsI),(g) and (CsI),(g) [Cs,I:] were detected. F&I+, cs:, cs,1:1, PI),@) [w:I, The assignment of the ions given in brackets to the different neutral species has been described in ref. [5]. The partial pressures of (CsI),(g) (i = 1, 2, 3) are given in ref. [5]. In this work the partial pressure of (CsI),(g) was determined (see table 3) from the Cs,I: intensity as described in ref. [5]. The ionization cross section of the tetramer was estimated by the equation %sn4 = O-75( ecsi + ecs1+ %I + %I ). The partial pressures obtained from three independent runs agree very well. A least-squares treatment of the pressures in table 3 yields the equation log( p(Pa))

= - (12748 k 278)/T(K)

+ (9.27 f 0.36)

for the (W),(g) partial pressure in the temperature given errors are the standard deviations.

(1) range 748 to 813 K. The

4. Discussion 4.1. Entropies and enthalpy increments

of (CsI),(g)

and (CsI),(g)

Entropies and enthalpy increments of (CsI),(g) and (CsI),(g) (table 1) were computed from estimated molecular parameters (table 2) with the rigid-rotator-harmonic-oscillator approximation [lo]. No electronic contributions to the entropies and enthalpy increments of (CsI),(g) and (CsI),(g) were taken into account since a singlet ground state for these two molecules was assumed. The structures (table 2) follow from the results of ionic model computations for alkali halides [3,7,11]. The vibrational frequencies of (CsI),(g) and (CsI),(g) were computed by the F, G matrix method [12]. This method requires the estimation of geometries and force constants since no experimental data are available for these two molecules.

Table 1 Entropies and increments in enthalpy of (Csl),(g) with D ?,, symmetq and D,, symmetry computed from the estimated molecular parameters

29X 300 400 500 600 700 800 900 1000 Average uncertainty:

562.9 563.2 601.8 631.4 655.6 676.0 693.8 709.4 723.4

35.3 35.7 48.8 62.1 75.3 88.6 101.9 115.2 128.5

652.X 654.0 706.0 746.6 779.8 807.9 832.3 853.8 873.1

46.1 46.4 64.5 x2.7 100.9 119.2 137.4 155.7 174.0

f 5.4

kO.2

i 20.0

IO.9

and of ((‘51),(g) in table 2

with T<,

48.4 4x.x 67.0 x5.2 103.5 121.7 140.0 15x.3 176.6

704.9 706.0 758.4 799.1 832.3 X60.5 884.9 906.4 925.7

f 1.0

k31.4

If a planar ring of D,, symmetry is assumed for (CsI),(g) (see table 2) and the principal stretching and bending force constants of (Csl),(g). FR and F,/R’ respectively, are transferred to (CsI),(g). the 12 vibrational modes of

Table 2 Geometries.

force constants,

Fx. F,,. 6,/R’.

and vibrational

frequencies.

w, for (CsI),(g)

and

(Csl),(g)

Ffi ” (N mm’) F,] ‘) (N mm’) F,/R”’ (N m) w (cm-‘)

‘) h’ ‘) ”

R = 3.59 k .”

R = 3.714 Ah’

R = 3.583 Ah’

24.48

44.48 1.259

24.48

4.223 x 10 4 A; 81 57 A’? 98 A’; 38 E’ 90 75 E” 20

Ref. [19], Ref. ill]. See text. Doubly degenerate

mode

64

AI E TL T,

109 108 109 108

18 90 108

13

4.240 105 79 42

x 10 ’ 98 d’ 95 74 57 <‘) 38 25”’

81 I’) 52 21

44 11

(CsI),(g) can be computed from the symmetrized G and F matrices. The symmetry coordinates used in these computations are those reported by Anderson and Ogden for Si,O,(g) [13]. The 18 vibrational modes of (CsI),(g) with Td symmetry (see table 2) were estimated on the basis of a vibrational model similar to that used by Ogden and Ricks [14] for Sn,O,(g) by employing FR and FD as force constants where R and D are defined as for Sn,O,(g) [14]. It is assumed that these force constants equal those of cubic (NaI),(g), which were obtained from the frequencies of this molecule theoretically computed in ref. [lS]. The frequencies of planar (CsI),(g) (see table 2) were estimated by taking the same force constants as for (CsI),(g). The vibrational problem was solved by the use of unsymmetrized F and G matrices. The uncertainty of the entropies and enthalpy increments reported in table 1 was derived by assuming that the force constants of (CsI),(g) listed in table 2 might change within + 10%. In the case of (CsI),(g) with cubic and planar ring structure the given uncertainties resulted from a change of i10 cm-’ attributed to all vibrational frequencies (see table 2) with the exception of the two lowest modes which remained unchanged. 4.2. Thermociyamic With (CsI),(g)

properties

of (CsI),(g)

and (CsI),(g}

the estimated entropies and enthalpy increments it was possible to determine the enthalpy changes

i CsI(s) @ (CsI),(g)

of (C@,(g) and of the reactions

(i = 3,4)

(2)

(i= 3.4)

(3)

and i CsI(g)* according (CsI),(g), functions,

(CsI),(g)

to the third-law method [lo]. In addition, the partial pressures of i = 1, 3, 4, given in ref. [5] and eq. (1) were used. The Gibbs energy

employed in the computations were obtained from refs. [l&17] and table 1. As an example the results of a third-law evaluation are given in detail in table 3. Table 4 summarizes all enthalpy changes determined. The mean values together with the standard deviation (cf. table 3) are given in table 4 for the third-law enthalpies. The uncertainty of the Gibbs energy function for (CsI),(g) and (CsI),(g) was estimated in the same way as that of the entropies and enthalpy increments given in table 1 (see section 4.1). This uncertainty and the assumed uncertainty of a factor 1.5 for the (CsI), and (CsI), partial pressures give rise to the probable uncertainties for the third-law enthalpy changes of reactions (2) and (3) as listed in table 4.

440

Table 3 Third-law i = 41 Run

K. Hilpert, L. Benciuenni / Thermochemical

evaluation

of the enthalpy

T(K)

of sublimation

study

to (Csl),(g)

of(CsI),

with cubic structure

[cf. eq. (2)

K, = p,c~t,,,,,(Ra) (J mol-’ 1.507XlO~’ 6.333 x 10-s 2.028 x 10-s 3.682 x lo-’ 1.085 x lo-’ 2.287 x lo-” 3.028~10~’ 1.497x1o-7 7.752 x 10-s 3.962 x lOF* 1.496x 10-s

793 773 753 813 783 753 808 793 778 763 748

-

(kJ mol-‘)

K-‘)

134.27 134.87 135.46 132.83 134.57 135.46 133.30 134.27 134.72 135.16 135.61

286.0 284.9 285.1 286.0 284.8 284.3 286.0 286.1 285.3 284.4 285.2 285.3 +0.7

Mean:

Viswanathan and Hilpert [5] determined the enthalpy of sublimation to trimer [cf. eq. (2) i = 31 and the trimerization enthalpy [cf. eq. (3) i = 31 at 768 K according to the second-law method [lo] as given in table 4. By employing the enthalpy increments of CsI(s) [16], CsI(g) [18] and (CsI),(g) (table 1) these two enthalpy changes were converted to those corresponding to 298 K (see. table 4). Obviously, the data obtained according to the second- and third-law method agree well showing the accuracy of our investigations. Selected values resulted by taking the averages. Table 4 Summary

of the reaction

enthalpies

T* (K)

Reaction

determined

Second law

Third law

Selected

AH;* (kJ mall’)

A H,O,, (kJ mol-‘)

A Hb (kJ molt

A H&s (kJ mall’)

3 Csl(s) * (CsI),(g)

768

4 CsI(s) G (CsI),(g)

781

256.9+ 8.3 ‘) (244.0)

273.9* (265.2)

[cubic (CsI),(g)l 4 CA(s) P (CsI),(g)

781

(244.0)

(265.3)

[ring (CsI),(a)l 3 CsI(g) * (CsI),(g) 4 CsI(g) * (CsI),(g)

768

[cubic (CsI),(g)l 4 CsI(g) * (CsI),(g) [ring

8.3

~ 299.7 k 8.6

279.7 + + 0.x;, s ’ 285.3*n’ +07E’

276.8+_ 6.7 285 +16

326.0 ’*IxL’ ” ”

326

- 293.3 ‘,; ;;;t -479.1;::,L,

uncertainty

+26

- 296.5 + 6.8 -479 +16

_ 438.4 +-?_09C’ 26 h’ -438

(CsI),(g)l

‘) Ref. [5]. h) Estimated probable ‘i Standard deviation

- 289.9 f 8.6 *’

’)

h

+26

The second-law enthalpy for the sublimation to tetramer {see table 4) followed from the temperature dependence of the (CM), partial pressure given by eq. (1). This value has to be considered as very uncertain on account of the very small measured Cs,I: ion intensities representing (C@,(g) and the small temperature range of the measurements for (CsI),(g) which is smaller by a factor of about four than that for CsI(g). The second-law value for the enthalpy of sublimation to tetramer is, therefore, given in parentheses (table 4) and was not employed in the computation of selected values. From a comparison of the second- and third-law values one might expect that the cubic fCsI),(g) is the most abundant species in the equilibrium vapour at the temperature of our measurements. The enthalpy changes of the reactions (CsI)j(g)~(CSI),_~fgf+CSI(g)

(i-,2,3,4)

(4)

and the enthalpy of sublimation to monomer, which corresponds to the enthalpy change of reaction (4) with i --+co, were obtained from the selected sublimation enthalpies in ref. [5] as well as in table 4 and are plotted in fig. 1. The analogous enthalpy changes for NaI and FeI, computed from the sublima-

Fig. 1. Enthalpies of sublimation to monomer MX(g). d,,,W&,(MX), MX = NaI, Fel, (- - -). ): and enthalpy changes AH&, of the reactions (MX),(g) P (MX),_,(g)+MX(g). CSI (-----MX = NaI (0). CsI (v), FeI, (D); as well as dissociation enthalpies per molecule MX, AH&/i, for the reactions (MX),(g) e i MX(g), MX = Nal (O), Csl (I). Fel, (m). (The given error limits are probable uncertainties.)

K. Hilprrt,

442

L. Bencroennr

/ Thermochemicul

studv of (Cl),

tion enthalpies determined by Hilpert [4] and Hilpert et al. [6] are also given in fig. 1. In addition, the dissociation enthalpies per molecule MX of the polymers (MX),(g) (MX = NaI, CsI, FeIz) obtained from refs. [4-61 and table 4 are shown in the diagram. The enthalpy changes in fig. 1 of the reactions containing (CsI),(g) were computed by employing the data for the cubic structure. Obviously, the dissociation enthalpy per molecule increases on enlarging the polymers whereas the enthalpy to remove one MX molecule from an (MX), polymer shows a minimum for (MX)?. This agrees qualitatively with the results obtained by the theoretical computations in ref. [7] for the energy of NaCl clusters. The dissociation enthalpies per molecule at 298 K in fig. 1 can be converted into dissociation energies per molecule MX at 0 K for the reactions

(M%,(g) 2

iM+(g)

+ ix-(g)

(MX = NaI, Csl)

(5)

by using zero-point energies obtained from the vibrational frequencies in refs. [4,17,19] and table 2. In addition, the enthalpy changes in ref. [20], as well as the enthalpy increments in refs. [4,21] and computed by the rigidrotator-harmonic-oscillator approximation with the molecular parameters of refs. [17,19] and table 2, are employed in the conversion. The resulting energies are compared with the cohesive energies for the lattice dispersion of Nal(s) and CsI(s) into ions given as 659.8 and 680.4 kJ mol-‘. respectively [22]. The dissociation energies per molecule at 0 K for the reactions (5) with (MX),(g) as given in brackets are by 67 [cubic (CsI),(g)], 92 [(CsI),(g)], 118 [(CsI),(g)]. 101 [(NaI),(g)], and 119 kJ mol-’ [(NaI),(g)] smaller than the corresponding cohesive energies.

Acknowledgements

The authors wish to thank Professor Dr. H.W. Nurnberg for his kind support of this work and valuable discussions. They are also indebted to Mr. H. Gerads for the technical assistance in the measurements. Financial support by Deutsche Forschungsgemeinschaft is gratefully acknowledged.

References [l] K.A. Gingerich. in: Current Topics in Materials Science. Vol. 6, Ed. E. Kaldis (North-Holand. Amsterdam. 1980) p. 345. [2] H. Schafer. Angew. Chem. 88 (1976) 775. [3] D.H. Feather and A.W. Searcy. High Temp. Sci. 3 (1971) 155. [4] K. Hilpert. Ber. Bunsenges. Physik. Chem. 88 (1984) 132. [5] R. Viswanathan and K. Hilpert. Ber. Bunsenges. Physik. Chem. 8X (1984) 125. [6] K. Hilpert. R. Viswanathan. K.A. Gingerich. H. Gerads and D. Kobertr. J. Chem. Thcrmodyn. 17 (1985). in press.

R Hiiperf, L. Bencivenni

/ Therm~hemical

study 0f(Cs1)~

443

[7] T.P. Martin, Phys. Rept. 95 (1983) 169. [S] T.A. Mime and D. Cubicciotti, J. Chem. Phys. 30 (1959) 1625. [9] K. Hiipert, Habilitationsschrift, Technische Hochschule Darmstadt, Darmstadt (1981); Jiil1744, Report from the Nuclear Research Centre (KFA), Julich, Federal Republic of Germany (1981). [lo] D.R. Stull and H. Prophet, Eds., JANAF Thermochemical Tables, 2nd ed. (US Govt. Printing Office, Washington, DC, 1971). NSRDS-NBS-27. [l I] J. Diefenbach and T.P. Martin, Max-Planck-Institut fur Festkiirperforschung, Stuttgart, personal communication (1984). [12] E.B. Wilson, Jr.. J.C. Decius and P.C. Cross, Molecular Vibrations (McGraw-Hill, New York, 1955). [13] J.S. Anderson and J.S. Ogden, J. Chem. Phys. 51 (1969) 4189. [14] J.S. Ogden and M.J. Ricks, J. Chem. Phys. 53 (1970) 896. [IS] T.P. Martin and H. Schaber. J. Chem. Phys. 68 (1978) 4299. [16] 1. Barin and 0. Knacke, Therm~hemical Properties of Inorganic Substances (Springer, Berlin, 1973). 1171 M. Blander, in: Alkali Halide Vapors, Eds. P. Davidovits and D.L. McFadden (Academic Press, New York, 1979) p. 1. [18] K.K. Kelley, in: Contributions to the Data on Theoretical Metallurgy, XIII. High-Temperature Heat Content, Heat-Capacity, and Entropy Data for the Elements and Inorganic Compounds, Bureau of Mines, Bulletin 584 (US Govt. Printing Office, Washington, DC. 1960). [19] D.D. Welch, D.W. Lazareth, G.J. Dienes and R.D. Hatcher, J. Chem. Phys. 64 (1976) 835. [20] See Table 9 in: L. Brewer and E. Brackett, Chem. Rev. 61 (1961) 425. [21] R.L. Wilkins, J. Chem. Eng. Data 5 (1960) 337. [22] M. Born and K. Huang. Dynamical Theory of Crystal Lattices (Oxford Univ. Press, London, 1954) p. 26.