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Simultaneous excitation of rotations and surface phonons in the scattering of D2 from a NaF crystal
647
Surface Science 126 (1983) 647-653 North-Holland Publishing Company
SIMULTANEOUS EXCITATION OF ROTATIONS AND SURFACE PHONONS IN THE SCATTERING OF D, FROM A NaF CRYSTAL G. BRUSDEYLINS
and J. Peter TOENNIES
Max - Planck - Institut fiir Strijmungsforschung,
B6ttingerstras.w
4 - 8, D - 3400 Giittingen, Fed. Rep. of
Germany Received
23 August
1982
Angular distributions and time-of-flight spectra have been measured for the scattering of n-D, from NaF(OO1) along the (100) direction at energies between 30 and 90 meV. The angular distributions reveal, in addition to the elastic diffraction peaks, additional sharp peaks due to the show rotational transitions 0 + 2, 1-+ 3, and 0 -+ 4. The relative rotational transition probabilities an anomalous behavior which can in part be explained by a kinematic rainbow. An enhancement of rotational transitions in grazing collisions (large ~9,) is also observed. The time of flight spectra confirm the assignments and reveal that phonon processes also are occurring simultaneously with the rotational transitions.
In collisions of a molecule with a surface the excitation or deexcitation of the rotational [l-5] or vibrational [6] degrees of freedom of the molecule have been observed. One of the problems in interpreting these experiments is to know to what extent phonons are involved in the energy transfer. Thus it is conceivable that phonon annihilation during a rotational excitation collision can considerably reduce the amount of energy transfer to the molecule and enhance the process. Rotational excitation of molecules on single crystal surfaces was first observed for H,-LiF by Boato, Cantini and Mattera [7] and for H,, D, and HD-MgO by Rowe and Ehrlich [8]. In these experiments only angular distributions were measured and rotational transitions were indirectly inferred from the observation of additional peaks. Allison and Feuerbacher [9] have recently carried out the first time-of-flight studies of D, and H, on LiF(OO1) (100) and were able to observe additional energy losses due to single acoustical Rayleigh surface phonons. In the present work we have used D, and not H,, because of its closer rotational level spacing. NaF crystals were chosen, since they were extensively studied previously using high resolution He nozzle beams, which revealed (compared to LiF) phonons of lower frequency which are more easily excited [lo]. By using a higher resolution than previously possible, we hope to be able to illucidate the mechanism of exchange between molecular rotations and 0039-6028/83/0000-0000/$03.00
0 1983 North-Holland
648
G. Brusdeylins, J.P. Tom&s
/ Excitation
of rotations and phonons
surface phonons. Moreover we had hoped to see optical phonons, which might be more probable for D, because of its greater polarizability compared to He and because of its quadrupole moment. The scattering apparatus is much the same as that used in previous surface phonon experiments [ 10,111. As previously, the angle between incident and outgoing beams is fixed at 90” and the incident angle f3i (with respect to the surface normal) is varied by rotating the crystal. Thus the final angle Bi is given by 8, = 90 - Bi. D, was expanded from a 9 pm diameter (effective) nozzle at a stagnation pressure of 200 bar and temperatures between 80 and 300 K. The velocity resolution was typically Au/v = 4% (FWHM) and beam energy was between 30 and 90 meV corresponding to wave vectors between 8 and 13 A-‘. At these temperatures the D, molecules are in the lowest rotational levels and for n-D, 66% are inj = 0 and 33% inj = 1. The air cleaved target crystals were cleaned by baking in vacuum. In some measurements the target was cooled down to about 120 K; at lower temperatures an adsorbate layer can effect the diffraction pattern. Fig. 1 shows two measurements of angular distributions for Ei = 89 meV and Ei = 31 meV. Above each peak we have listed the process involved as
Fig. 1. Measured angular distributions for scattering of D,-NaF(OO1) along the (100) azimuth. The assignments of the diffraction peaks are indicated above each peak. Below the spectrum we indicate the predicted locations of selective desorption features for an assumed well depth of 26.3 meV.
G. Brusdeylins,
J. P. Toennies / Excitation
of rotations and phonons
649
k: = I3 A-’
Fig. 2. Calculated final angles 6’, as a function of incident wave vector ki for D, -NaF(OOl) (100) azimuth. For certain processes 8, does not depend strongly on ki, leading to an enhancement. In general the peak intensities will be inversely proportional to the slope of the curves. Note that phonon processes have been neglected.
determined from the conservation equations. The (0, 0), (+ 1, + 1) and ( f 2, f 2) diffraction peaks are clearly seen, except at 3 1 meV where the (2, 2) diffraction peak is off the scale at smaller angles. At 31 meV only the 0 + 2 rotational transition (AE(0 + 2) = 22.2 meV) is allowed. Surprisingly, the - (1, 1) 0 + 2 peak is much greater than the (0, 0) 0 --j 2 peak, although we might have expected the reverse relationship. At 89 meV the j = 1 -+ 3 transition (AE( 1 + 3) = 36.9 meV) is also energetically accessible and leads to additional - diffraction peaks. We note once more that the (1, 1) 0 + -2 peak is particularly - strong and almost equal to the specular peak. Also, the (2, 2) 1 + 3 and (2, 2) 0 --, 2 maxima have nearly the same areas, although the 1 + 3 transition should be less probable because of the lower population of j = 1 molecules and greater energy transfer. - An explanation of the (1, 1) 0 + 2 enhancement at 89 meV is provided by a “rainbow” type of kinematic effect first pointed out by Rowe, Rathbun and Ehrlich [ 121. According to this effect certain processes may lead to nearly the same angle over a wide range of incident velocities. Thus, because of the finite velocity spread, these processes will appear as especially intense narrow maxima. Fig. 2 shows the result of calculated final angles versus incident wave vector for the conditions of our experiments. A rainbow occurs for (1, 1) 0 --, 2
G. Brusdeylins,
650
J. P. Toennies / Excitation
of rotations and phonons
D, - NaF K, =
13A-'
-73.6
-36.9 -2 2.2
Fig. 3. Some typical time-of-flight spectra are plotted at the bottom with the upward pointing flight time abscissa lined up with the corresponding angle in the angular distribution shown at the top. Note that the time-of-flight spectra have all been normalized to the same amplitude and that in fact the total intensities may be quite different as seen by comparison with the angular distributions.
at about ki = 13 A-’ corresponding to the observed enhancement. For the (2, ?) 0 -+ 2 and (2, 2) 1 -+ 3 processes at k, = 13 A-’ we do not expect a rainbow effect. Since, however, we have neglected phonons, these may shift the curves and explain the observed differences. Below each of the angular distributions in fig. 1 the brackets show the location where selective desorption [1 l] is expected to occur. The well depth was estimated, using a formula put forth by Hoinkes [ 131 to be D = 26.3 meV, and bound state levels were estimated by assuming a Morse potential (K = 1.23 A-‘). Since no maxima are observed, we conclude that there is no evidence for selective desorption. However, since the resolution and sensitivity in the case of D, are much worse than for the He experiments, we cannot rule out these processes altogether. For this system, over 100 time-of-flight (TOF) spectra have been measured. Only part of these extensive data has been evaluated. Fig. 3 shows some typical TOF spectra taken at angles corresponding to the peaks. In all cases the
G. Brusdey!im,
-8
-6
4
-2
J.P. Toennies / Excitation
0
2
4
6
of rotations and phonons
651
8
AK ItO'ollMl Fig. 4. Extended zone plot in which the observed energy transfer is plotted as ordinate versus the tota parallel momentum transfer. Both quantities can be extracted from the time of flight and angle at which a maximum in the TOF spectra are observed and are indicated by the black dots. The length of the diagonal flags are proportional to the logarithm of the intensities. The solid parabolas indicate the surface phonon dispersion curves for rotationally inelastic scattering and the horizontal lines the energy transfers for pure rotational transitions.
assignments made above have been confirmed by the TOF spectra. In addition, the TOF spectra help to make additional assignments where the angular distribution peaks are very weak. For example, the weak peak at about 57O is found to be due to the 0 + 4 excitation process (AE = 73.6 mev) which is just barely energetically possible at the collision energy of 88.8 meV. This indicates that rotational excitation is not strictly determined by the normal (z-direction) energy component, which is only about 28 meV in this case. Such a correlation has been inferred from data for NO on Ag( 111) [3]. Indeed, the observed enhancement for rotational excitation at large scattering angles suggests that the parallel momentum component may be more important, at least in our system. A detailed analysis of these and many other TOF spectra taken between the maxima in the angular distributions reveal the occurrence of phonon processes. The results of a preliminary analysis of the location of the peak maxima from
652
G. Brwdeylins,
J. P. Tommies / Excitation of rotations and phonons
the TOF spectra taken at different energies are indicated by black dots in the extended zone plot shown in fig. 4. In this diagram the overall energy transfer is plotted as the ordinate versus the total parallel momentum transfer. Thus the origin corresponds to specular scattering and points on the AK axis with AE = 0 and AK equal to an integral multiple of the reciprocal lattice vector correspond to elastic diffraction peaks. The sine curves show the location of inelastic scattering processes involving Rayleigh surface phonons but no rotational transitions. The horizontal lines indicate the locations of events due to rotational deexcitation and excitation. The diagonal bars next to some of the points roughly indicate the relative intensities. Examination of fig. 4 reveals that many events take place in which both phonon and rotational excitation take place. Simultaneously, in most cases, single phonons seem to be involved. The events with small phonon frequencies have a higher probability than the events with large phonon frequencies. From this preliminary analysis we find that phonon processes appear to take place with about the same probability, regardless of whether a rotational excitation takes place. A careful screening of all the data reveals a number of anomalous events in which the energy loss nearly corresponds to that for rotational excitation, but the parallel momentum transfer is noticeably greater or smaller than that corresponding to a diffraction peak. We attribute this to the conversion of parallel momentum into angular momentum. If this explanation is correct, then the observation of momentum shifts indicates that these molecules have been excited such that their final angular momentum is parallel to the surface but perpendicular to the scattering plane. Thus the different signs in the momentum shift correspond to angular momentum vectors with opposing directions. The occurrence of such processes apparently depends on the initial orientation of the molecule. We hope that a more systematic study of these anomalous events will tell us more about the conditions under which they occur. We are most grateful sions.
to A. Askar
(Istanbul)
for many
stimulating
discus-
References [l] F. Frankel, J. Hager, W. Krieger, H. Walther, C.T. Campbell, Segner, Phys. Rev. Letters 46 (1981) 152. [2] G. McClelland, G.D. Kubiak, H.G. Rennagel and R.N. Zare, 831. [3] A.W. Kleyn, A.C. Luntz and D.J. Auerbach, Phys. Rev. Letters [4] M. Asscher, W.L. Guthrie, T.-H. Lin and G.A. Somorjai, Phys. [5] D. Ettinger, K. Honma, M. Keil and J.C. Polanyi, Chem. Phys. (61 J. Fenn, S.P. Venkateshan and S.B. Ryali, to be published. [7] G. Boato, P. Cantini and C. Mattera, J. Chem. Phys. 65 (1976)
G. Ertl, H. Kuipers Phys. Rev. Letters
and K. 46 (1981)
47 (1981) 1169. Rev. Letters 49 (1982) 76. Letters 87 (1982) 413. 544
G. Brusdeylins,
J. P. Toennies / Excitation
of rotations and phonons
[8] R.G. Rowe and G. Ehrlich, J. Chem. Phys. 63 (1975) 4648. [9] W. Allison and B. Feuerbacher, Phys. Rev. Letters 45 (1981) 2040. [lo] R.B. Doak and J.P. Toennies, Surface Sci. 117 (1982) 1; G. Brusdeylins, R.B. Doak and J.P. Toennies, to be published. [I 1] G. Brusdeylins, R.B. Doak and J.P. Toennies, J. Chem. Phys. 75 (1981) 1784. [12] R.G. Rowe, L. Rathbun and G. Ehrlich, Phys. Rev. Letters 35 (1975) 1104. [13] H. Hoinkes, Rev. Mod. Phys. 52 (1980) 933.
653
Surface Science 126 (1983) 647-653 North-Holland Publishing Company
SIMULTANEOUS EXCITATION OF ROTATIONS AND SURFACE PHONONS IN THE SCATTERING OF D, FROM A NaF CRYSTAL G. BRUSDEYLINS
and J. Peter TOENNIES
Max - Planck - Institut fiir Strijmungsforschung,
B6ttingerstras.w
4 - 8, D - 3400 Giittingen, Fed. Rep. of
Germany Received
23 August
1982
Angular distributions and time-of-flight spectra have been measured for the scattering of n-D, from NaF(OO1) along the (100) direction at energies between 30 and 90 meV. The angular distributions reveal, in addition to the elastic diffraction peaks, additional sharp peaks due to the show rotational transitions 0 + 2, 1-+ 3, and 0 -+ 4. The relative rotational transition probabilities an anomalous behavior which can in part be explained by a kinematic rainbow. An enhancement of rotational transitions in grazing collisions (large ~9,) is also observed. The time of flight spectra confirm the assignments and reveal that phonon processes also are occurring simultaneously with the rotational transitions.
In collisions of a molecule with a surface the excitation or deexcitation of the rotational [l-5] or vibrational [6] degrees of freedom of the molecule have been observed. One of the problems in interpreting these experiments is to know to what extent phonons are involved in the energy transfer. Thus it is conceivable that phonon annihilation during a rotational excitation collision can considerably reduce the amount of energy transfer to the molecule and enhance the process. Rotational excitation of molecules on single crystal surfaces was first observed for H,-LiF by Boato, Cantini and Mattera [7] and for H,, D, and HD-MgO by Rowe and Ehrlich [8]. In these experiments only angular distributions were measured and rotational transitions were indirectly inferred from the observation of additional peaks. Allison and Feuerbacher [9] have recently carried out the first time-of-flight studies of D, and H, on LiF(OO1) (100) and were able to observe additional energy losses due to single acoustical Rayleigh surface phonons. In the present work we have used D, and not H,, because of its closer rotational level spacing. NaF crystals were chosen, since they were extensively studied previously using high resolution He nozzle beams, which revealed (compared to LiF) phonons of lower frequency which are more easily excited [lo]. By using a higher resolution than previously possible, we hope to be able to illucidate the mechanism of exchange between molecular rotations and 0039-6028/83/0000-0000/$03.00
0 1983 North-Holland
648
G. Brusdeylins, J.P. Tom&s
/ Excitation
of rotations and phonons
surface phonons. Moreover we had hoped to see optical phonons, which might be more probable for D, because of its greater polarizability compared to He and because of its quadrupole moment. The scattering apparatus is much the same as that used in previous surface phonon experiments [ 10,111. As previously, the angle between incident and outgoing beams is fixed at 90” and the incident angle f3i (with respect to the surface normal) is varied by rotating the crystal. Thus the final angle Bi is given by 8, = 90 - Bi. D, was expanded from a 9 pm diameter (effective) nozzle at a stagnation pressure of 200 bar and temperatures between 80 and 300 K. The velocity resolution was typically Au/v = 4% (FWHM) and beam energy was between 30 and 90 meV corresponding to wave vectors between 8 and 13 A-‘. At these temperatures the D, molecules are in the lowest rotational levels and for n-D, 66% are inj = 0 and 33% inj = 1. The air cleaved target crystals were cleaned by baking in vacuum. In some measurements the target was cooled down to about 120 K; at lower temperatures an adsorbate layer can effect the diffraction pattern. Fig. 1 shows two measurements of angular distributions for Ei = 89 meV and Ei = 31 meV. Above each peak we have listed the process involved as
Fig. 1. Measured angular distributions for scattering of D,-NaF(OO1) along the (100) azimuth. The assignments of the diffraction peaks are indicated above each peak. Below the spectrum we indicate the predicted locations of selective desorption features for an assumed well depth of 26.3 meV.
G. Brusdeylins,
J. P. Toennies / Excitation
of rotations and phonons
649
k: = I3 A-’
Fig. 2. Calculated final angles 6’, as a function of incident wave vector ki for D, -NaF(OOl) (100) azimuth. For certain processes 8, does not depend strongly on ki, leading to an enhancement. In general the peak intensities will be inversely proportional to the slope of the curves. Note that phonon processes have been neglected.
determined from the conservation equations. The (0, 0), (+ 1, + 1) and ( f 2, f 2) diffraction peaks are clearly seen, except at 3 1 meV where the (2, 2) diffraction peak is off the scale at smaller angles. At 31 meV only the 0 + 2 rotational transition (AE(0 + 2) = 22.2 meV) is allowed. Surprisingly, the - (1, 1) 0 + 2 peak is much greater than the (0, 0) 0 --j 2 peak, although we might have expected the reverse relationship. At 89 meV the j = 1 -+ 3 transition (AE( 1 + 3) = 36.9 meV) is also energetically accessible and leads to additional - diffraction peaks. We note once more that the (1, 1) 0 + -2 peak is particularly - strong and almost equal to the specular peak. Also, the (2, 2) 1 + 3 and (2, 2) 0 --, 2 maxima have nearly the same areas, although the 1 + 3 transition should be less probable because of the lower population of j = 1 molecules and greater energy transfer. - An explanation of the (1, 1) 0 + 2 enhancement at 89 meV is provided by a “rainbow” type of kinematic effect first pointed out by Rowe, Rathbun and Ehrlich [ 121. According to this effect certain processes may lead to nearly the same angle over a wide range of incident velocities. Thus, because of the finite velocity spread, these processes will appear as especially intense narrow maxima. Fig. 2 shows the result of calculated final angles versus incident wave vector for the conditions of our experiments. A rainbow occurs for (1, 1) 0 --, 2
G. Brusdeylins,
650
J. P. Toennies / Excitation
of rotations and phonons
D, - NaF K, =
13A-'
-73.6
-36.9 -2 2.2
Fig. 3. Some typical time-of-flight spectra are plotted at the bottom with the upward pointing flight time abscissa lined up with the corresponding angle in the angular distribution shown at the top. Note that the time-of-flight spectra have all been normalized to the same amplitude and that in fact the total intensities may be quite different as seen by comparison with the angular distributions.
at about ki = 13 A-’ corresponding to the observed enhancement. For the (2, ?) 0 -+ 2 and (2, 2) 1 -+ 3 processes at k, = 13 A-’ we do not expect a rainbow effect. Since, however, we have neglected phonons, these may shift the curves and explain the observed differences. Below each of the angular distributions in fig. 1 the brackets show the location where selective desorption [1 l] is expected to occur. The well depth was estimated, using a formula put forth by Hoinkes [ 131 to be D = 26.3 meV, and bound state levels were estimated by assuming a Morse potential (K = 1.23 A-‘). Since no maxima are observed, we conclude that there is no evidence for selective desorption. However, since the resolution and sensitivity in the case of D, are much worse than for the He experiments, we cannot rule out these processes altogether. For this system, over 100 time-of-flight (TOF) spectra have been measured. Only part of these extensive data has been evaluated. Fig. 3 shows some typical TOF spectra taken at angles corresponding to the peaks. In all cases the
G. Brusdey!im,
-8
-6
4
-2
J.P. Toennies / Excitation
0
2
4
6
of rotations and phonons
651
8
AK ItO'ollMl Fig. 4. Extended zone plot in which the observed energy transfer is plotted as ordinate versus the tota parallel momentum transfer. Both quantities can be extracted from the time of flight and angle at which a maximum in the TOF spectra are observed and are indicated by the black dots. The length of the diagonal flags are proportional to the logarithm of the intensities. The solid parabolas indicate the surface phonon dispersion curves for rotationally inelastic scattering and the horizontal lines the energy transfers for pure rotational transitions.
assignments made above have been confirmed by the TOF spectra. In addition, the TOF spectra help to make additional assignments where the angular distribution peaks are very weak. For example, the weak peak at about 57O is found to be due to the 0 + 4 excitation process (AE = 73.6 mev) which is just barely energetically possible at the collision energy of 88.8 meV. This indicates that rotational excitation is not strictly determined by the normal (z-direction) energy component, which is only about 28 meV in this case. Such a correlation has been inferred from data for NO on Ag( 111) [3]. Indeed, the observed enhancement for rotational excitation at large scattering angles suggests that the parallel momentum component may be more important, at least in our system. A detailed analysis of these and many other TOF spectra taken between the maxima in the angular distributions reveal the occurrence of phonon processes. The results of a preliminary analysis of the location of the peak maxima from
652
G. Brwdeylins,
J. P. Tommies / Excitation of rotations and phonons
the TOF spectra taken at different energies are indicated by black dots in the extended zone plot shown in fig. 4. In this diagram the overall energy transfer is plotted as the ordinate versus the total parallel momentum transfer. Thus the origin corresponds to specular scattering and points on the AK axis with AE = 0 and AK equal to an integral multiple of the reciprocal lattice vector correspond to elastic diffraction peaks. The sine curves show the location of inelastic scattering processes involving Rayleigh surface phonons but no rotational transitions. The horizontal lines indicate the locations of events due to rotational deexcitation and excitation. The diagonal bars next to some of the points roughly indicate the relative intensities. Examination of fig. 4 reveals that many events take place in which both phonon and rotational excitation take place. Simultaneously, in most cases, single phonons seem to be involved. The events with small phonon frequencies have a higher probability than the events with large phonon frequencies. From this preliminary analysis we find that phonon processes appear to take place with about the same probability, regardless of whether a rotational excitation takes place. A careful screening of all the data reveals a number of anomalous events in which the energy loss nearly corresponds to that for rotational excitation, but the parallel momentum transfer is noticeably greater or smaller than that corresponding to a diffraction peak. We attribute this to the conversion of parallel momentum into angular momentum. If this explanation is correct, then the observation of momentum shifts indicates that these molecules have been excited such that their final angular momentum is parallel to the surface but perpendicular to the scattering plane. Thus the different signs in the momentum shift correspond to angular momentum vectors with opposing directions. The occurrence of such processes apparently depends on the initial orientation of the molecule. We hope that a more systematic study of these anomalous events will tell us more about the conditions under which they occur. We are most grateful sions.
to A. Askar
(Istanbul)
for many
stimulating
discus-
References [l] F. Frankel, J. Hager, W. Krieger, H. Walther, C.T. Campbell, Segner, Phys. Rev. Letters 46 (1981) 152. [2] G. McClelland, G.D. Kubiak, H.G. Rennagel and R.N. Zare, 831. [3] A.W. Kleyn, A.C. Luntz and D.J. Auerbach, Phys. Rev. Letters [4] M. Asscher, W.L. Guthrie, T.-H. Lin and G.A. Somorjai, Phys. [5] D. Ettinger, K. Honma, M. Keil and J.C. Polanyi, Chem. Phys. (61 J. Fenn, S.P. Venkateshan and S.B. Ryali, to be published. [7] G. Boato, P. Cantini and C. Mattera, J. Chem. Phys. 65 (1976)
G. Ertl, H. Kuipers Phys. Rev. Letters
and K. 46 (1981)
47 (1981) 1169. Rev. Letters 49 (1982) 76. Letters 87 (1982) 413. 544
G. Brusdeylins,
J. P. Toennies / Excitation
of rotations and phonons
[8] R.G. Rowe and G. Ehrlich, J. Chem. Phys. 63 (1975) 4648. [9] W. Allison and B. Feuerbacher, Phys. Rev. Letters 45 (1981) 2040. [lo] R.B. Doak and J.P. Toennies, Surface Sci. 117 (1982) 1; G. Brusdeylins, R.B. Doak and J.P. Toennies, to be published. [I 1] G. Brusdeylins, R.B. Doak and J.P. Toennies, J. Chem. Phys. 75 (1981) 1784. [12] R.G. Rowe, L. Rathbun and G. Ehrlich, Phys. Rev. Letters 35 (1975) 1104. [13] H. Hoinkes, Rev. Mod. Phys. 52 (1980) 933.
653