Pergamon Spectrochimica Acta, Vol. 51A, No. 4, pp. 643-651, 1995

Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved

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Infrared band strengths of B , H 6 from 2400 to 2800 c m -1 at room temperature

NGUYEN-VAN-THANH, t A . JEAN-LOUIS and C. BRODBECK

Laboratoire de Physique Mol6culaire et Applications, C.N.R.S., Universit6 Paris-Sud, B~timent 350, 91405 Orsay Cedex, France

(Received 24 May 1994; accepted 21 June 1994)

Abstract--Band strength measurements of the two infrared-active v16 and vs fundamental modes of B2H 6 are made at room temperature in the 2400-2800 cm -1 spectral range leading for the first time to the determination of the integrated absorption coefficient of the (v16,1'8) band system: S O = 1078 + 55 cm -2 atm -~ at T= 300 K. An analysis of hot bands, combination bands and isotopic transitions present in this absorption region is also given. These spectroscopic data will be useful for improving understanding the problem of boron in astrophysics.

INTRODUCTION

THE ORIGIN and evolut ion o f light e lements such as bo ron (l°B, nB) has long const i tuted a ma jo r p rob lem in astrophysics [1]. The diborane(6) (B2H6) molecule is known to be the simplest stable bo ron hydride [2] and since 1975 a concer ted spectroscopic s tudy on diborane(6) has been under t aken by D u n c a n and co-workers [3-8] in o rder to obtain precise values for vibrat ional assignment and molecular constants. Howeve r , there is still no data relative to the I R absorpt ion band strengths o f B2H6.

In o rder to comple te this spectroscopic analysis, we have under taken the measure- ments o f the strengths of the strongest bands o f d iborane which are relative to the B - H stretch in the 2400-2800 cm -1 spectral range more precisely. The aim of the present paper is to s tudy natural d iborane (a mixture containing UB and l°B in the ratio HB/I°B -- 4.06 [2], a value obta ined f rom bo ron measurements on Ear th) and particularly to present the evolut ion o f the spectral profiles and strengths o f the (v~6, Vs) band system at r o o m tempera tu re and for various densities o f B2H6. Since no value o f the total in tegrated band area has been repor ted in the li terature, we have measured the band system strengths using pure B2H6 gas and B2H6-inert gas mixture absorpt ion spectra in the 2400-2800 cm-~ region. The posit ions (wavenumbers ) o f the lines relative to the v~6 and vs bands for ~°B2H6 and 11B2H 6 have been de te rmined f rom spectra recorded with a resolut ion o f 0.04 cm -1 by Laffer ty et al. [9].

EXPERIMENTAL PROCEDURE

The IR absorption spectra were recorded on a Bruker IFS66V Fourier Transform spectrometer with a FWHM (full width at half maximum) of 0.12 cm -~. We used an optical filter to work in the frequency range from 1700 to 3500 cm -~. Except for the Q branch of the v~6 band which was about 14 times the spectral slit width, the ratio of the spectral slit width to the width of the band system is less than 1 x 10 -3. This is sufficiently small to avoid line shape corrections due to the finite slit width. The absolute calibration of the wavenumber scale was accomplished using the well-known positions of several lines in the 1 *-0 band of riCO [10]. Thirty-two scans were superimposed to yield each interferogram and the four-point apodization function was also used.

The experimental conditions are summarized in Table 1. The cell used was described previously [11]. About 15 values of the pressure were used and for each density two spectra at least were recorded. Experiments were conducted at room temperature which is kept constant at T= 302 + 1 K. The pathlength l = 4.78 cm was measured with a relative error equal to 2 x 10 -3.

The sample of B2H6 was obtained from Air Liquide in a supply tank under a pressure of 17 bar. The stated gas purity was 99%. Care has to be taken for the cooling of the tank containing B2I-I6

t Author to whom correspondence should be addressed.

643

644 NGUYEN-VAN-THANH et al.

Table 1. Experimental conditions for the study of the (v16, vs) band system of B~H6

Absorbing pathlength Gas pressure range Band Window / (cm) p (Torr)

(v~6, v8) sapphire 4.78 2-15

gas: in order to avoid the decomposition of B2 H6 into H2 and other boron compounds such as B4Ht0 and BsH9, it would be necessary to cool the supply tank in a deep freezer at -20°C during the experiments. At this temperature, only BEH6 is gaseous and the other boron hydrides are liquid or solid (see Table 2). Tetraborane(10) (B4HI0) was determined to be the chief decomposition product of diborane at room temperature [12].

Pressure measurements during the course of each spectroscopic observation were performed accurately by using two capacitive diaphragm type pressure transducers designed for 0-10 and 0- 100 Torr ranges with a relative error less than 2 x 10 -3. In order to compare the results of intensity measurements we used to consider the density of the gas, a physical quantity including information on pressure and temperature. Due to the lack of data relative to the density of diborane(6), we have assimilated B2H6 as an ideal gas, which is a valid approximation at the temperature and pressures used. Gas densities were also quoted in Amagat (1 Amagat of ideal gas = 0.0446148 mol dm-3), a unit of relative density.

Care was also taken for the pl product values not to reach saturation effects which become appreciable when the peak absorption ( /0- I t ) exceeds 0.4•o [13], where I0 and It are the background and gas spectral outputs, respectively. The background spectra are recorded with the empty cell. The saturation effects yield absorption coefficients which are lower than the extrapo- lated value of the Beer-Lambert law plot. These effects are shown in Fig. 1 for densities larger than 12 x 10 -3 Amagat.

RESULTS

Analysis of the spectra for v16 and v8 bands

The natural diborane contains three types of isotopic molecules: llBEH6, I~B~°BH6 and l°BEH 6 in the approximate proport ions 16, 8 and 1, respectively. 11B2H 6 and l°B2I-I 6 are asymmetric top molecules belonging to point group D2h. The llBl°lI-I6 molecule belongs to the lower point group D2. These molecules have 18 fundamental modes of vibration. Table I of Ref. [3] gives the distribution of fundamental vibrations of diboranes between symmetry species of the point group D2~ and associated gas phase band contour types.

We recorded the absorption profiles of the band system (V16 , V 8) in the 2400-2800 cm- 1 spectral range at T-- 302 K. These spectra are presented in Figs 1-3 for pure B2H6 gas and B2H6-X mixtures (X = At , N2). The v16 band (terminal B - H symmetric stretch) with symmetry species B3u is an A-type band which appears around 2520 cm-t . The Vs band

Table 2. Normal melting and boiling points for some simple volatile boron compounds [12]

m.p. b.p. Formula Name a (°C) (°C)

B2H6 diborane(6) - 165.5 -92.5 B4Hio tetraborane(10) -119.9 16.0 BsH9 pentaborane(9) -46.1 58.4

a The recommended nomenclature for boron hydrides is: diborane(6), tetraborane(10) and pen- taborane(9) for B2H 6, B4HI0 and BsH 9, respect- ively.

o

o

t ~ f-q

i

?

c~

24O0

I

2450

IR band strengths of B2H 6

I I I I I

(a)

V 1 6

V8

I I I I I

2500 2550 2600 2650 2?00 klavenumber crn -1

I

2750 2800

645

c 3 c¢3

O

i i i i i i i

V 1 6

V8

( b ) _

Lf3

C3

I I I I I I I

2400 2450 2500 2550 2600 2650 2700 2750 2800 Havenumber cm 4

Figure 1. Comparison of the (v~6, v8) band system spectra of pure B2H6 for two different values of B2H 6 density at ambient temperature: (a) p = 3 . 5 4 x 1 0 3 Amagat, T = 3 0 1 K, (b) p =

14.16 x 10 -3 Amagat, T = 301 K.

(terminal B-H antisymmetric stretch) with symmetry species B2, is a B-type band located near 2609 cm- 1. At first glance, the v16 and v8 bands appear to be respectively parallel and perpendicular bands of a symmetric top since diborane(6) is a very near prolate rotor ( ~ = - 0 . 9 5 ) [9].

In the 2400-2800 cm -1 atmospheric window, our spectra of natural diborane present two Q branches of v~6 bands centred at 2519.9 and 2521.7 cm -~ (Fig. 2) due to the isotopic molecules nB2H6 and ~°BnBH6. Only the very weak Q branch of the v16 band of l ° B 2 a 6 appears at 2525.0 cm -~. Figure 2 also shows portions of P and R branches of the v,6 band for the most abundant molecules "B2I-I6 and mB"BH6. In fact in the absorption

6 4 6 N G U Y E N - V A N - T H A N H et al.

I I

I I l I

0 'OT 5 Y 0 "g

O

Lc~

o

L~

C~

L~

L~

C~

L ~

L~

L~ C~

cD

o

Is]

CD

c ~

IS]

0 '0 TM

? _= X

JI

00

7,

E O

C~ o

o

~q

c D

I LO ! 0 3

i

CD CO

? o ~, cw

x, . .

CD

t_f3

I I

IR band strengths of BzH 6

I I

V 1 6 V 8

CD

2400 2450 2500 2550 2600 2650 2700 Havenurnber cm -1

I I I

(a)

I

2?50 2800

647

LO CO

O ( 'O

5"

CD

i i i i i

V 1 6

V8

C 3 I I I I I I

2400 2450 2500 2550 2600 2650 2200 14avenumber crn -I

I I

(b)

I

2750 2800

Figure 3. Comparison of the (Vl6, v8) band system spectra of B2H6-N 2 mixtures for two different values of total pressure P(B2H6-N2) at ambient temperature: (a)p(B2H6)=10.04Torr, P(B~H6-N2) = 100.0 Torr, T= 303 K; (b) p(B2H6) = 10.00 Torr, P(B2H6-N2) = 918.9 Torr, T=

303 K.

spectra of natural diborane the major contribution is due to UB2H6 and t°B"BH6 essentially. The isotopic species I°B2H 6 presents a much weaker contribution.

The isotopic frequency shift (in cm -t) is defined as

Avs --'= v s ( l ° l l l B H 6 ) - Vs(llB2H6) ( l a )

o r

Avs = vs(~°a2n6) - Vs(tIBEn6) (lb)

where vs is the band centre of the v ,= 1~-0 transition. Our Av,-values for s = 8, 16 measured at T-- 302 K (Table 3) are in good agreement with the values of Duncan et al. [7].

648 NGUYEN-VAN-THANH et al.

Table 3. Vibrational frequencies and isotopic frequency shifts of B2H 6

IIBNBH6 I°BHBH 6 IOBlOBH 6

v, (cm ~ ) Av, (cm t) Av~ (cm l)

8 2608.853" 8.7 h 13.if' 7.6"

16 2519.646" 2.2 b 5.36 b 2.1" 5.4"

° Ref. 191. b Ref. [7]. c Present work.

Many levels are significantly populated at 300 K. In addition to the v16 and v8 bands due to the three isotopic species, numerous combination bands and hot bands for each of the three isotopic species are present in the (v16, Vs) region. Only a few (vi+vj)-type combination bands are infrared active in the studies region: v2 + vlo, v7 + v17, v12 + v17, 1' 5 + 1)6, lP4 ÷ V13 , 1) 6 ÷ '1/14 , V 7 ÷ 1)13 a n d v 3 ÷ •17- I t is expected that their intensities a r e v e r y

weak and none o f t h e m were o b s e r v e d by Laf fe r ty et al. [9] who s tud ied this reg ion at high reso lu t ion .

In this spec t ra l reg ion there is no I R active ( v i - v j ) - t y p e hot band . On ly I R ( V s + V k - V k ) - t y p e hot bands with s = 16, 8 are presen t . The i r re la t ive in tens i t ies a re o b t a i n e d [14] by assuming the same value for the t rans i t ion m o m e n t of hot band and g r o u n d s ta te t rans i t ion and neglec t ing r e sonance effects:

l(vs + vk - vg)/ l (vs) = g~ exp ( - f l v i ) (2)

whe re f l = h c / k T and g , , the degene racy of the k th s ta te , is equa l to uni ty for all v ib ra t iona l s ta tes o f B2H6. Tab le 4 lists, for the m a j o r cons t i tuen t HB2H6, the f requen- cies, s y m m e t r y species and f rac t ional popu la t i ons Pg(T ) of the v ib ra t iona l levels conce rned with the ( v ~ + v ~ - v ~ ) - t y p e hot bands , the re la t ive in tens i t ies of which ( t abu l a t ed in the last co lumn) exceed 1%. The f rac t ional popu l a t i on P k ( T ) on the k th s ta te at t e m p e r a t u r e T is given [16] by

P,(T) = g, exp (-flv~)/Z~(T) (3)

where Zv(T) is the vibrational partition function defined [16] as

Z,(T) = H [1 - exp (-flvi)] -~' (4) i

Table 4. Fractional population of the most populated states and rela- tive intensities of the most intense hot bands of nB2H 6 at T= 300 K in

the spectral range 2400-2800 cm i

Vk

Frequency Symmetry Relative intensity of State (cm 1 )4 species Pk(300) (vs + Vk -- Vk ) bands c

vlo 368.6 B2,, 0.121 0.171 2Vto 759.0 b A~ 0.019 0.026 v4 790.0 A~ 0.016 0.023 v5 833.1 An 0.013 0.018 v7 860.0 B2g 0.011 0.016 v12 915.0 Big 0.009 0.012 v9 949.0 B2, 0.007 0.011

Ref. [7]. b Ref. [15]. CThe symmetry species of ( v s+v , -v , ) bands are that of the vs

band, i.e. B3, and B2u for s = 16, 8, respectively.

rJ)

• i • , •

2 4 6 8 10 12 14

p ( 1 0 .3 Ama g a t )

18 , = I I I I I I

16

14

12

10

! 0 _ ~

0

IR band strengths of B2I-t~ 649

|

16

Fig. 4. Integrated absorption coefficient Sv versus B2I-I6 density for (v~6, v8) band system at ambient temperature.

which is equal to 1.416 at T= 300 K. In the last formula, vi represents the energies of all the vibrational states from vl0 (~370 cm-1) to v4 + v5 + v~0 (~2000 cm-1). No harmonicity was taken into account to calculate these frequencies from the values of Duncan et al. [7]. The population of the ground state is 0.706 at T= 300 K. Analogous results are obtained for the isotopic species 1°B2H 6 (Zv(300) = 1.406).

Intensity results for the ('FI6 , V8) band system

The observed intensity is the integrated absorption coefficient Sv (in cm -2) defined as

Sv = ~ k(v) dv (5) J b a n d

where the measured absorption coefficient k(v) (in cm -1) is obtained from

k(v) = 1-' In [lo(v)/It(v)]. (6)

The background spectral output I0 is recorded with the empty cell or with the X-perturber gas alone. In Fig. 4 the values of the band system intensity Sv (Vl6, vs) are plotted as a function of p, the density of B2H6, expressed in Amagat. Within experimen- tal error, Sv is proportional to p. Using a least-squares technique the coefficient of proportionality S O is derived. S o is the integrated absorption coefficient per unit density (in cm -2 Amagat -1) defined as

S O = ( p l ) - ~ In [lo(v)/It(v)] dr. (7) J b a n d

The S O values of the (v~6, Vs) band system for natural diborane are given in Table 5 at T = 300 K. The relative error on the band area is considered as four times the standard deviation, i.e. about 1%. Since the storage conditions of B2H6 are unknown from its production to its delivery, we must take the slow thermal decomposition into account. Therefore, owing to the accuracy in pressure p, temperature T and absorbing pathlength

SA(A) 51:4-K

650 NGUYEN-VAN-THANH et al.

Table 5. Integrated absorption coef- ficient per unit density S o for (v]6, vs)

band system of natural B2H6

S O (cm 2Amaga t i) 1184 S O (cm 2 atm i at STP) 1184 S O (cm -2 a tm -~ at 300 K) 1078 S o (10 -~ cm 2 s-1 molecule 1 ) 132 S O (km mol-= l ) 265

l and the systematic error, the relative uncertainty in S O can be estimated to be about 5%. The final result obtained for natural B2H 6 g a s - - b y taking the stated gas purity into account - - i s S O= 1 1 8 4 + 6 0 c m -2 Amagat -1. The results for S O expressed in the usual units (cm -2 Amaga t -~, cm -2 atm -] at STP and at T = 300 K, cm 2 s -1 molecule -1 and km mol -~) are presented in Table 5.

In Fig. 5 the S O values of the (Vl6, vs) band system for B2H6-X mixtures (with X = Ar, N2) are plotted versus total pressure P(B2H6-X). Using a least-squares tech- nique and extrapolating at p ( X ) = 0, the S O value for pure B2H6 gas is deduced. The relative error in S O is about 9%. The final result obtained from B2H6-X mixtures is S O= 1191 + 105 cm -2 Amagat -~ which is in excellent agreement with the value obtained for pure B2H6.

Let us recall the following remarks about Table 5:

(i) the S O values in c m - 2 a t m -1 at STP are the same as those in cm -2 Amagat -1 since B2H 6 is considered as an ideal gas for the low pressures used;

(ii) the band strength measurements of natural diborane included not only v~6 and v8 bands but (Vs+Vk--Vk)-type hot bands, (vj+ vk)-type combination bands and isotopic transitions (essentially due to 11BzH 6 and HB~°BH6).

I I I I

1200 -

1 1 0 0 .

i ~ 1 0 0 0 - ¢d)

" ~ 900

E ' ~ 800

700

600 = I a I = I = I i I 0 1 O0 200 300 4 0 0 500

P (B2H6-X) (Torr) Fig. 5. Integrated absorption coefficient per unit density S O versus total pressure P(B2H6-inert

gas) for (vt6, Vs) band system at ambient temperature.

IR band strengths of B2H6

CONCLUSION

651

The present study on natural diborane has allowed us to determine for the first time the (v16, vs) band system strength at room temperature (T=300 K) with a reasonable relative acuracy better than 5%.

At room temperature, with the used resolution, the v16 and vs bands are not separated. Only spectra recorded at low temperature with isotopic species allowed us to determine S o values for individual v16 and v8 bands with a reduced contribution of hot bands.

The accurate laboratory spectroscopic data on boron hydrides and especially on band strengths of B2H 6 will be helpful both for the solar system and for the general problem of stellar origin and evolution [1].

We can point out that the study of intensities of B2H6 present also a stimulating interest relative to the valence structure of boron hydrides for which Eberhardt et al. [17] introduced the concept of the localized three-centre bond.

The present work will be followed by the synthesis and the spectroscopic study of the two isotopic molecules llB2H6 and ~°B2H6 at room and low temperatures in the same spectral range.

Acknowledgements--The support of the INSU (CNRS), grant 93/ATP/606, is gratefully acknowledged.

REFERENCES

[1] R. Beer, Icarus 29, 193-199 (1976). [2] E. L. Muetterties (Ed.), Boron Hydride Chemistry. Academic Press, New York (1975). [3] J. L. Duncan, D. C. McKean, I. Torto and G. D. Nivellini, J. Molec. Spectrosc. 85, 16-39 (1981). [4] E. Hamilton and J. L. Duncan, J. Molec. Spectrosc. 90, 129-138 (1981). [5] E. Hamilton and J. L. Duncan, J. Molec. Spectrosc. 90, 517-530 (1981). [6] J. Harper and J. L. Duncan, J. Molec. Spectrosc. 100, 343-357 (1983). [7] J. L. Duncan, J. Harper and E. Hamilton, J. Molec. Spectrosc. 102, 416-440 (1983). [8] J. L. Duncan, J. Molec. Spectrosc. 113, 63-76 (1985). [9] W. J. Lafferty, A. G. Maki and T. D. Coyle, J. Molec. Spectrosc. 33, 345-367 (1970).

[10] G. Guelachvili and K. N. Rao, Handbook of Infrared Standards, pp. 492-535. Academic Press, New York (1986).

[11] C. Brodbeck, J.-P. Bouanich, Nguyen-Van-Thanh and I. Rossi, J. Molec. Structure 80, 261-264 (1982). [12] R. M. Adams (Ed.), Boron, Metallo-Boron Compounds and Boranes, p. 573. lnterscience, New York

(1964). [13] H. J. Kostkowski and A. M. Bass, J. Opt. Soc. Am. 46, 1060-1064 (1956). [14] C. Brodbeck, I. Rossi, Nguyen-Van-Thanh and A. Ruoff, Compt. Rend. Acad. Sci. Paris C282, 659-662

(1976). [15] R. C. Lord and E. Nielsen, J. Chem. Phys. 19, 1-10 (1951). [16] G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 2. Van Nostrand, New York (1959). [17] W. H. Eberhardt, B. Crawford, Jr. and W. N. Lipscomb, J. Chem. Phys. 22, 989-1001 (1954).