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Neutron inelastic scattering from ethylene: An unusual spectrum
Volume
CHEhflCAL
106, number 4
PHYSICS
LETTERS
NEUTRON MELASTIC SCATTERING FROM ETHYLENE: AN UNUSUAL SPECTRUM * H. JOBIC Itrstirur de Recherches sur Ia Cbtalyse. CNRS, 2 Avenue Albert Eirtstein. 69626 IWeurbarrne Cgdex. France Received
19 January 1984; in fmal form 17 February
I984
Neutron inelastic scatterin_e spectra of cry.taUiie ethylene have been measured at two temperatures. 1 and 80 K, between 80 and 250 meV. The spectra ore iound to consisr of weak and shifted peaks superimposed on 3 very broad background. This is accounted for by muiIi-phonon effects and Doppler broadening due 10 the small molecuIar mass of ethylene. A generaiization to neutron scattering from adsorbed molecules is made.
1. Introduction Much experimental
and theoretical
work
devoted recently to vibrational intensities
has been
by neutron inefastic scattering (NE) [l-6]. The new theories are based on a timescale separation between the low-frequency intermolecular (lattice)
modes within lattice
and the ~~-frequency
~tr~olecul~
measured
modes
a molecular crystal [3,6]. Tiie influence of the Debye-Wailer factor, which was originally thought to reduce the NlS intensities at large momentum (energy) transfers, was shown to be neghgible [3, 61. It was found that the lattice modes do not reduce the intensities of the high-frequency modes through a Debye-Wailer factor but that they produce a shift and a broade~g of the internal modes. The consequence is that the high-frequency vibrations (up to 500 meV) can be observed with hot neutrons, e.g. at the highflux reactor of the lnstitut Laue-Langevin or with pulsed sources. Most of the NIS studies have been made on hydrogenous materials with a heavy molecular mass (M), such as
hexamethylenetetramine
[ l] or polyethylene
121.
The importance of the ratio nr/M, where tn is the atomic mass of hydrogen, was clearly demonstrated in refs. [3,61: (a) When this ratio is small, the timescale separation * Experimental work performed at the institut Grenoble,
Laue-Langetin,
France.
0 009-~614184/S 03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
is realized and the Doppler broadening (recoil effect) is minimal. The intensities measured on a berylliumfilter spectrometer are found to correspond mainly to the calculated one-phonon disI~but~on functions [ 1, 2 1. although some structure can be observed near the transitions, with a high instrumental resolution [7]. (b) If the molecule in which the proton is bound is not heavy compared to the proton (e.g. ethylene), a different scattering is to be espected. lndeed, for a large rnjfif ratio. the situation becomes similar IO the case where there is no timescale separation [6].
2. Experimental
The NIS spectra reported in this paper were recorded with the new version of the beryllium-filter spectrometer IN 1B at the lnsritut Laue-Langevin. Only one monochromator plane, the Cu(220), is now necessary to cover the frequency range 30450 meV. However, because the instrumental alignment has not yet been fully tested
throughout
this frequency
range,
the preci-
sion of the measured transitions is only =4 meV. To record the NIS spectrum of crystalline C,H,, the temperature of the sample chamber of a He kyostar was set at 120 K (i.e. in the liquid phase for C2H4)_ The aluminium cell was placed inside the ciyostat and the gas was condensed in the cell through a heated tube. The condensed liquid was then solidified at a temperature below the freezing point (93 K). The scattering angle was taken as 90”. 321
Volume 106, number 4
CHEMICAL
3. Results and discussion The NlS spectra obtained at 4 and 80 K are shown in figs. la and lb, respectively. In ethylene, the observed infrared and Raman crystal frequencies are cIose to those in the gas. The lowestfrequency mode is found at 102 meV [S], so that all the internal modes, except the CH stretching modes situated above 370 meV, are present in fig. 1. The ver20
40
3.0
27 ApriI I984
PHYSlCS LETTERS
tical Sines indicate the frequencies of these modes, as measured using optical spectroscopy IS]. The spectra presented in fig. 1 are very unusual and it should be stressed that, even at 80 K, C2H4 is a solid. The structure of crystalline ethylene has been determined by neutron [9] and X-ray diffraction [lo]. The space group is F’2t /n and there are no phase transitions, at normal pressures, below the melting point (104 K). For heavier molecules, the differences observed be50
60 Eh?iz:
T
20
30
’ cc.
40
50
60 E(THr
Z
s 45cK+
3 0 z
0
XKJ
‘ 1!50
1
200
Fig. 1. NIS spectm of ethyfene obtained at (a) 4 K and(b)
322
I
250
80 K.
Eheu
Voiumc
106, number
4
CHEhfiCAL
PHYSiCS
tween
4 and 80 K are much less pronounced [ 11; the peaks obtained are more intense and a linear background due to multiphonon processes can be drawn (this background gradually increases with energy transfer). fn the spectrum obtained at 80 K (fig. I b), there is a very broad background and the oscillations corresponding to the internal modes are hardly discernible (at 90 K, the spectrum around 150 meV is fairly flat). According to the thermal parameters obtained at 85 K from a single-crystal X-ray diffraction study [ 101, the mean-square amplitude due to the lattice modes is very large for the hydrogen atoms. In this case, the lattice Debye-Wailer factor is very smal!, exp[-2WL(A’)j < 1, and the Gaussian approximation is well suited to describe the lineshape of a high-frequency internal mode at o,., 131:
sL(K,w)=
[7r*‘“IF]-‘exp[-(o’_
w h )2/4r3(w)f, (1)
where w’ = w [ I - (P?l/lii>] ,
(2)
and r’(a)
= a(kB T/h) m/M.
(3)
In these expressions, 3ik is the neutron momentum transfer (w 0: K>) and B the effective mass of the molecule obtained after averaging the Sachs-Teller inversemass tensor [ II]. The problem of defining the effective mass for a condensed phase has been discussed by Grant et al. 1121; there is no doubt, however, rhat the value for C,H, is much smaller than for hexamethylenetetra&ne [l] _ Using eq. (3) and the gas-phase value for R (5. j), the predicted linewidth for the modes around 150 meV is x45 meV (a fu!! normal-mode analysis might give a different value [6] but the order of magnitude is correct). The experimental value is found to be ~15 meV, which is still larger than the experimental resolution in this range (~8 meV). Since the two con-
tributions to the linewidth are convofuted, the result is that the different Gaussians cannot be resolved and this gives the broad background observed in fig. lb. At 4 K, the background is still very broad but a series of transitions becomes visible on top of it because the Debye-Waller factor, which affects the jntensi~ of the unshifted line at wh, has increased. The first
LETTERS
17 Aprrl
1984
three peaks at 102,118 and 128 meV are easily assignee At higher enerto vlr,, v8 + v7 and v3, respectively. gies, however, rhe assignment is less straightforward. The Gaussian nppro?rimation, eq. (I), is no longer valid and a numerical calculation similar to the one reported by Warner et al. [6] is necessary to explain the supplementary peaks due to multi-photon processes. In fig. la, some of these multiphonon peaks have an intensity comparable to the fundamentals (e.g. at 139 rwv). This example shows the limitations of NIS in studying the internal modes of molecules with a small molecular mass (at least on a beqllium-filter spectrometer which implies high momentum transfers). Some general considerations can be deduced from this example which apply to surface work 3s well as to molecular specrroscopy . For example, for the adsorption of sma!! molecules such as ethylene or acetylene onfo various.substrares: (a) For a we&interaction with the substrate (in a zeolite or on a hydrogen pre-covered nickel powder). we have obtained NIS spectra at 80 K which are intermediate between spectra 1a and 1b f 13 J _NIS results obtained for ethylene adsorbed on s!lser-A zeolite have been reported but this effect was not observed because the frequency range was limited to 85 mcV. so that only the hindered rotations and translations could be measured [ 141. (b) iiihen the interaction with the substrare is strong (e.g. on bare nickel powder). the effective mass of the “molecule” increases because of the bonding with the surface atoms. In this case, the linewidths are reduced [ISIIt can be generally recommended for these sytems to work at very low temperarure. because rhis produces a sharpening of the spectrum, as has already been reported [ 16).
References ( 11 H. Jobic. RE. Ghosh and A. Renouprez.
J. Chrm. Phys. 75 (1981) 4025. [?I H.Jobic,J.Chem.Phys.76(1981)2693. [ 31 A. Grifim and H. Jobic, J. Chem. Phys. 75 (1981) 5940. [4] J. Howard, B.C. Boland and J. Tomkinson,Chem. Phys. 77 (1983) 145. f.51 B. Domer and A. Griffin, J. Chem. Phys. 78 (1983) 890. (61 hf. Waxer, S.W. Lovesey and J. Smith. Z. Physilr 35 1 (1983) 109.
323
Volume 106, number 4 171 ii. Jobic and H. Lauter,Chem.
CHEMICAL PHYSICS LETTERS
Phys. Letters, to be submitted for publication. [S] J.L. Duncan and E. Hamilton. 1. hlol. Struct. Theochem. 76 (1981) 65. (91 W. Press and J. Eckert, J. Chem. Phys. 65 (1976) 4362. [lo] GJXVanNesand A.Vos.ActaCryst. B35 (1979) 2593. [ 111 TJ. Krieger and MS. Nelkin, Phys. Rev. 106 (1957) 290. [ 121 DM. Grant, R.J. Pugmire, R.C. Livingston, KA. Strong, HL. MchIurry and RM. Brugger, J. Chem. Phys. 52 (1970) 4424.
324
[ 13) H. Jobic and A. Renoup~, [ 141 J. Howard, K. Robson,T.C.
27 April 1984
unpublished Waddington
results. and ZA. Kadir.
Zeotites 2 (1982) 2.
[ 151 H. Jobic and A. Renouprez, Proc. ICSS4 and ECOSS3, SuppL Le Vide. Les Couches Minces, No. 201, Vol. 2 (1980) Q. 746. [ 161 H. Jobic and A. Renouprez.Surface Sci. lll(1981) 53.
CHEhflCAL
106, number 4
PHYSICS
LETTERS
NEUTRON MELASTIC SCATTERING FROM ETHYLENE: AN UNUSUAL SPECTRUM * H. JOBIC Itrstirur de Recherches sur Ia Cbtalyse. CNRS, 2 Avenue Albert Eirtstein. 69626 IWeurbarrne Cgdex. France Received
19 January 1984; in fmal form 17 February
I984
Neutron inelastic scatterin_e spectra of cry.taUiie ethylene have been measured at two temperatures. 1 and 80 K, between 80 and 250 meV. The spectra ore iound to consisr of weak and shifted peaks superimposed on 3 very broad background. This is accounted for by muiIi-phonon effects and Doppler broadening due 10 the small molecuIar mass of ethylene. A generaiization to neutron scattering from adsorbed molecules is made.
1. Introduction Much experimental
and theoretical
work
devoted recently to vibrational intensities
has been
by neutron inefastic scattering (NE) [l-6]. The new theories are based on a timescale separation between the low-frequency intermolecular (lattice)
modes within lattice
and the ~~-frequency
~tr~olecul~
measured
modes
a molecular crystal [3,6]. Tiie influence of the Debye-Wailer factor, which was originally thought to reduce the NlS intensities at large momentum (energy) transfers, was shown to be neghgible [3, 61. It was found that the lattice modes do not reduce the intensities of the high-frequency modes through a Debye-Wailer factor but that they produce a shift and a broade~g of the internal modes. The consequence is that the high-frequency vibrations (up to 500 meV) can be observed with hot neutrons, e.g. at the highflux reactor of the lnstitut Laue-Langevin or with pulsed sources. Most of the NIS studies have been made on hydrogenous materials with a heavy molecular mass (M), such as
hexamethylenetetramine
[ l] or polyethylene
121.
The importance of the ratio nr/M, where tn is the atomic mass of hydrogen, was clearly demonstrated in refs. [3,61: (a) When this ratio is small, the timescale separation * Experimental work performed at the institut Grenoble,
Laue-Langetin,
France.
0 009-~614184/S 03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
is realized and the Doppler broadening (recoil effect) is minimal. The intensities measured on a berylliumfilter spectrometer are found to correspond mainly to the calculated one-phonon disI~but~on functions [ 1, 2 1. although some structure can be observed near the transitions, with a high instrumental resolution [7]. (b) If the molecule in which the proton is bound is not heavy compared to the proton (e.g. ethylene), a different scattering is to be espected. lndeed, for a large rnjfif ratio. the situation becomes similar IO the case where there is no timescale separation [6].
2. Experimental
The NIS spectra reported in this paper were recorded with the new version of the beryllium-filter spectrometer IN 1B at the lnsritut Laue-Langevin. Only one monochromator plane, the Cu(220), is now necessary to cover the frequency range 30450 meV. However, because the instrumental alignment has not yet been fully tested
throughout
this frequency
range,
the preci-
sion of the measured transitions is only =4 meV. To record the NIS spectrum of crystalline C,H,, the temperature of the sample chamber of a He kyostar was set at 120 K (i.e. in the liquid phase for C2H4)_ The aluminium cell was placed inside the ciyostat and the gas was condensed in the cell through a heated tube. The condensed liquid was then solidified at a temperature below the freezing point (93 K). The scattering angle was taken as 90”. 321
Volume 106, number 4
CHEMICAL
3. Results and discussion The NlS spectra obtained at 4 and 80 K are shown in figs. la and lb, respectively. In ethylene, the observed infrared and Raman crystal frequencies are cIose to those in the gas. The lowestfrequency mode is found at 102 meV [S], so that all the internal modes, except the CH stretching modes situated above 370 meV, are present in fig. 1. The ver20
40
3.0
27 ApriI I984
PHYSlCS LETTERS
tical Sines indicate the frequencies of these modes, as measured using optical spectroscopy IS]. The spectra presented in fig. 1 are very unusual and it should be stressed that, even at 80 K, C2H4 is a solid. The structure of crystalline ethylene has been determined by neutron [9] and X-ray diffraction [lo]. The space group is F’2t /n and there are no phase transitions, at normal pressures, below the melting point (104 K). For heavier molecules, the differences observed be50
60 Eh?iz:
T
20
30
’ cc.
40
50
60 E(THr
Z
s 45cK+
3 0 z
0
XKJ
‘ 1!50
1
200
Fig. 1. NIS spectm of ethyfene obtained at (a) 4 K and(b)
322
I
250
80 K.
Eheu
Voiumc
106, number
4
CHEhfiCAL
PHYSiCS
tween
4 and 80 K are much less pronounced [ 11; the peaks obtained are more intense and a linear background due to multiphonon processes can be drawn (this background gradually increases with energy transfer). fn the spectrum obtained at 80 K (fig. I b), there is a very broad background and the oscillations corresponding to the internal modes are hardly discernible (at 90 K, the spectrum around 150 meV is fairly flat). According to the thermal parameters obtained at 85 K from a single-crystal X-ray diffraction study [ 101, the mean-square amplitude due to the lattice modes is very large for the hydrogen atoms. In this case, the lattice Debye-Wailer factor is very smal!, exp[-2WL(A’)j < 1, and the Gaussian approximation is well suited to describe the lineshape of a high-frequency internal mode at o,., 131:
sL(K,w)=
[7r*‘“IF]-‘exp[-(o’_
w h )2/4r3(w)f, (1)
where w’ = w [ I - (P?l/lii>] ,
(2)
and r’(a)
= a(kB T/h) m/M.
(3)
In these expressions, 3ik is the neutron momentum transfer (w 0: K>) and B the effective mass of the molecule obtained after averaging the Sachs-Teller inversemass tensor [ II]. The problem of defining the effective mass for a condensed phase has been discussed by Grant et al. 1121; there is no doubt, however, rhat the value for C,H, is much smaller than for hexamethylenetetra&ne [l] _ Using eq. (3) and the gas-phase value for R (5. j), the predicted linewidth for the modes around 150 meV is x45 meV (a fu!! normal-mode analysis might give a different value [6] but the order of magnitude is correct). The experimental value is found to be ~15 meV, which is still larger than the experimental resolution in this range (~8 meV). Since the two con-
tributions to the linewidth are convofuted, the result is that the different Gaussians cannot be resolved and this gives the broad background observed in fig. lb. At 4 K, the background is still very broad but a series of transitions becomes visible on top of it because the Debye-Waller factor, which affects the jntensi~ of the unshifted line at wh, has increased. The first
LETTERS
17 Aprrl
1984
three peaks at 102,118 and 128 meV are easily assignee At higher enerto vlr,, v8 + v7 and v3, respectively. gies, however, rhe assignment is less straightforward. The Gaussian nppro?rimation, eq. (I), is no longer valid and a numerical calculation similar to the one reported by Warner et al. [6] is necessary to explain the supplementary peaks due to multi-photon processes. In fig. la, some of these multiphonon peaks have an intensity comparable to the fundamentals (e.g. at 139 rwv). This example shows the limitations of NIS in studying the internal modes of molecules with a small molecular mass (at least on a beqllium-filter spectrometer which implies high momentum transfers). Some general considerations can be deduced from this example which apply to surface work 3s well as to molecular specrroscopy . For example, for the adsorption of sma!! molecules such as ethylene or acetylene onfo various.substrares: (a) For a we&interaction with the substrate (in a zeolite or on a hydrogen pre-covered nickel powder). we have obtained NIS spectra at 80 K which are intermediate between spectra 1a and 1b f 13 J _NIS results obtained for ethylene adsorbed on s!lser-A zeolite have been reported but this effect was not observed because the frequency range was limited to 85 mcV. so that only the hindered rotations and translations could be measured [ 141. (b) iiihen the interaction with the substrare is strong (e.g. on bare nickel powder). the effective mass of the “molecule” increases because of the bonding with the surface atoms. In this case, the linewidths are reduced [ISIIt can be generally recommended for these sytems to work at very low temperarure. because rhis produces a sharpening of the spectrum, as has already been reported [ 16).
References ( 11 H. Jobic. RE. Ghosh and A. Renouprez.
J. Chrm. Phys. 75 (1981) 4025. [?I H.Jobic,J.Chem.Phys.76(1981)2693. [ 31 A. Grifim and H. Jobic, J. Chem. Phys. 75 (1981) 5940. [4] J. Howard, B.C. Boland and J. Tomkinson,Chem. Phys. 77 (1983) 145. f.51 B. Domer and A. Griffin, J. Chem. Phys. 78 (1983) 890. (61 hf. Waxer, S.W. Lovesey and J. Smith. Z. Physilr 35 1 (1983) 109.
323
Volume 106, number 4 171 ii. Jobic and H. Lauter,Chem.
CHEMICAL PHYSICS LETTERS
Phys. Letters, to be submitted for publication. [S] J.L. Duncan and E. Hamilton. 1. hlol. Struct. Theochem. 76 (1981) 65. (91 W. Press and J. Eckert, J. Chem. Phys. 65 (1976) 4362. [lo] GJXVanNesand A.Vos.ActaCryst. B35 (1979) 2593. [ 111 TJ. Krieger and MS. Nelkin, Phys. Rev. 106 (1957) 290. [ 121 DM. Grant, R.J. Pugmire, R.C. Livingston, KA. Strong, HL. MchIurry and RM. Brugger, J. Chem. Phys. 52 (1970) 4424.
324
[ 13) H. Jobic and A. Renoup~, [ 141 J. Howard, K. Robson,T.C.
27 April 1984
unpublished Waddington
results. and ZA. Kadir.
Zeotites 2 (1982) 2.
[ 151 H. Jobic and A. Renouprez, Proc. ICSS4 and ECOSS3, SuppL Le Vide. Les Couches Minces, No. 201, Vol. 2 (1980) Q. 746. [ 161 H. Jobic and A. Renouprez.Surface Sci. lll(1981) 53.