7082
J. Phys. Chem. B 1997, 101, 7082-7086
Calculations of Vibrational Energy Relaxation Rates of C-H,D,T Stretching Modes on Hydrogen-, Deuterium-, and Tritium-Terminated H,D,T/C(111)1×1 Diamond Surfaces Ying-Chieh Sun* and Jiunn-Ming Chen Department of Chemistry, National Taiwan Normal UniVersity, 88 Tingchow Road, Sec. 4, Taipei 11718, Taiwan, ROC ReceiVed: March 3, 1997; In Final Form: May 23, 1997X
The vibrational energy relaxation rates of excited C-H,D,T stretching modes on hydrogen, deuterium, and tritium-terminated H,D,T/C(111)1×1 diamond surfaces, respectively, are calculated using the Bloch-Redfield theory combined with classical molecular dynamics simulation. A valence force field is used to model the interactions between carbon atoms in the bulk. The calculated lifetimes of 30 and 0.2 ps for the first excited states of the C-H and C-D stretching modes agree well with the experimental results of 19 and 0.2 ps, respectively. The lifetime of the first excited state for the C-T stretching mode on the tritium-terminated T/C(111)1×1 diamond surface is predicted to be 0.3 ps. Analysis of the power spectra of the fluctuating force along the C-H,D,T bonds suggests that the vibrational energy relaxation of 1:3 resonance for the first excited state of the C-H stretching mode and 1:2 resonance for C-D and C-T stretching modes results in a difference of lifetimes by an order of 2 between the C-H stretching mode and C-D and C-T stretching modes on the hydrogen, deuterium, and tritium-terminated H,D,T/C(111)1×1 diamond surfaces. Calculations of the relaxation rates for the V ) 2 states of C-H, C-D, and C-T stretches give lifetimes of 0.1, 0.2, and 0.4 ps, respectively, all on the time scale of tenths of a picosecond.
I. Introduction Hydrogen on diamond surfaces has received a great deal of attention recently because of its role in chemical vapor deposition of diamond thin films.1-3 The growth mechanism is substantially influenced by energy transfer between the vibrational modes on the surface and in the bulk. Many experiments have been carried out to probe the vibrational modes and the interactions between the adsorbates and surfaces on various surfaces.4-25 Because of the development of the sum-frequency generation (SFG) spectroscopy,26 the vibrational modes on the surface can be resolved in the frequency domain as well as the time domain. On hydrogen-covered H/C(111) diamond surface, the C-H stretching mode was measured to be 2835.5 cm-1 using Infrared (IR) spectroscopy.21 The C-C-H bending mode was found to be 1290 cm-1 using low-energy electron energy loss spectroscopy (EELS).27 Recently, Chin et al. have used the SFG spectroscopy to probe the vibrational modes on the H/C(111) surface and observed resonance peaks for the C-H stretching and C-C-H wagging at 2838 and 1331 cm-1, respectively.22 The anharmonicity of the C-H stretching mode was found to be 110 cm-1,23 which a recent calculated anharmonity of 113 cm-1 28 using ab initio calculation agrees with. In addition to the frequency domain measurement, a lifetime of 19 ps for the first excited state of the C-H stretching mode was found from the time domain measurement.23 The lifetime is much shorter than the lifetime of 0.95 ns for the Si-H stretching mode on the H/Si(111)1×1 surface.6 In addition to the hydrogen-terminated H/C(111)1×1 diamond surface, the vibrational modes on the deuterium-terminated D/C(111)1×1 surface were investigated as well. Measurements using the SFG and IR spectroscopies in the frequency domain21,22 give C-D stretching frequencies of 2115 and 2110 cm-1, respectively. The width of the resonance peak in the IR spectrum gives a lifetime of 0.2 ps for the first excited state of the C-D stretch on the D/C(111)1×1 surface.21 X
Abstract published in AdVance ACS Abstracts, August 1, 1997.
S1089-5647(97)00791-8 CCC: $14.00
A number of theoretical calculations have been carried out to examine the vibrational energy relaxation dynamics of a signal mode in complicated molecular systems based on theoretical approaches.29-55 To our knowledge, theoretical calculation of energy relaxation rates of vibrational modes on surfaces using Bloch-Redfield theory29-32 was first carried out by Gai and Voth in their work on vibrational energy relaxation rate calculations of Si-H stretching modes on the H/Si(111)1×1 surface.43 The calculated lifetime of 1.7 ns for the first excited state of Si-H stretches on the H/Si(111)1×1 surface at 300 K agrees well with the experimental result of 0.95 ns.6 In addition to the calculation for the Si-H stretching modes on the H/Si(111)1×1 silicon surface, the vibrational energy relaxation rate of C-H stretches on the H/C(111)1×1 diamond surface was carried out using the same theory and calculational method as well.56 This prior calculation for the C-H stretching mode on the H/C(111)1×1 surface,56 in which an earlier observed stretching frequency of 2830 cm-1 20 and a frequency of 1290 cm-1 for the C-C-H bend27 were used, gave a lifetime of 60 ps, which is about 3 times longer than the experimental result of 19 ps in the recent SFG real time measurement.23 Since the C-C-H bending modes couple significantly with the C-H stretching modes, the use of the newly found C-C-H bending frequency of 1331 cm-1 in the calculation may give better computational results of the relaxation rate for C-H stretching modes. In the present calculation, we recalculate the lifetime of the C-H stretching mode on the hydrogen-terminated H/C(111)1×1 surface using the bending frequency of 1331 cm-1 found by SFG spectroscopy22 instead of 1290 cm-1 used in the previous calculation56 in the EELS experiment.27 In addition, The lifetimes of C-D and C-T stretching modes on the D/C(111)1×1 and T/C(111)1×1 surfaces, respectively, are calculated as well. The following sections are organized as follows. Section II describes the method used in the present calculations, including a description of carbon-carbon interactions in the bulk of diamond substrate used in the previous calculation of © 1997 American Chemical Society
H,D,T/C(111)1×1 Diamond Surfaces
J. Phys. Chem. B, Vol. 101, No. 36, 1997 7083
H/C(111)1×1 surface,56 since it is particularly of interest in the present calculations of C-H,D,T stretches on the H,D,T/ C(111)1×1 diamond surfaces, respectively. The results and discussion are given in section III. Concluding remarks are given in section IV. II. Method The description of the Bloch-Redfield relaxation theory has been given in the previous calculations for H/Si(111)1×1 and H/C(111)1×1 surfaces.43,56 Briefly, the lifetime of the first excited state of C-H stretches on the H/C(111)1× 1 surface is determined by the dominant coupling term43,56
2|〈0|q|1〉|2 2
p (1 + e
-βpω10
-∞ dt e-iω ∫ +∞ )
〈δF(0) δF(t)〉cl
10t
(2.1)
where the 〈0|q|1〉 is the transition matrix element between C-H stretching states |0〉 and |1〉, q is the vibrational coordinate of the C-H oscillator of interest, and ω10 is the transition frequency between states |0〉 and |1〉. 〈δF(0) δF(t)〉cl is the classical fluctuating force autocorrelation function for the C-H bond. The inverse of this term gives the lifetime of the V ) 1 state. The decay of the V ) 2 state is determined by a term that has the same form as eq 2.1, except the indices 1 and 0 are replaced by 2 and 1, respectively. The lifetimes of C-D and C-T stretching modes on D,T/C(111)1×1 surfaces are determined in the same way at their transition frequencies. The simulation system and procedure are the same with the previous calculation of H/C(111)1×1 surface56 except the C-C-H bending frequency is changed to a newly measured bending frequency of 1331 cm-1 23 instead of 1290 cm-1 27 measured earlier. Since the carbon-carbon interactions in the bulk of diamond substrate used in the previous calculation of H/C(111)1×1 surface56 are particularly of interest in the present calculations of vibrational energy relaxation rates of C-H,D,T stretches on H,D,T/C(111)1×1 surfaces, the employed valence force field potential57 in the simulations for the interactions between the carbon atoms of diamond substrate is described at length below. The potential energy, which is given by
V)
1
H†(l′)Fl′,lH(l) ∑ 2 l,l′
(2.2)
is the summation of all the interactions between the smallest unit cells of the diamond-like structure, which contain two carbon atoms in each cell. l and l′ denote the indices for unit cells. H(l) is the internal coordinate vector which contains four bond lengths and 12 bond angles in the lth unit cell, and H† is the transpose of H. Fl,l′ is the force constant matrix between the unit cells l and l′. The force constant parameters for a lattice crystal were optimized to fit the phonon dispersion curves which can be obtained by finding the eigenvalues of the dynamical matrix.58 The optimized interaction coefficients Fl,l′ are given in ref 57. Note that, although the potential expression in terms of the bond lengths and angles in eq 2.2 is in a linear form, the transform from internal coordinates to the Cartesian coordinates gives nonlinear couplings between vibrational modes. The calculated phonon dispersion curves of diamond crystal in the direction Γ f χ of k-space are shown in Figure 1. The C-H bond potentials were described with Morse functions with the stretching frequency and the anharmonicity fit to the experimental result of 2838 and 110 cm-1, respectively.23 The bending force constant for the C-C-H angles was obtained by multiplying the ratio of the square of the newly found bending frequency of 1331 cm-1 22 to the bending frequency
Figure 1. Phonon dispersion curves of diamond lattice in the direction of Γ f χ in k-space. The filled circles are the calculated eigenfrequencies of the dynamical matrix for diamond crystal. ∆ are depicted experimental data obtained from ref 57.
Figure 2. Fourier transform of the fluctuating force autocorrelation function (eq 2.1) along a C-H bond at 300 K. The solid line is the position of the V ) 1 f 0 fundamental transition frequency ω10 ) 2838 cm-1. The dashed line is the position of the V ) 2 f 1 transition frequency ω21 ) 2728 cm-1.
of 1290 cm-1 used in the previous calculation,56 since the energy transfer between the vibration of adsorbates and electronic excitation of nonmetal substrates is usually far less efficient than for the metal substrates. The C-H dipole-dipole interactions are not included in the present simulations. In the present calculations, the akma unit system, in which the units for length, mass, time and energy are angstroms, atomic mass units, 4.888821 × 10-14 s, and kcal/mol, respectively, is used. The simulations for D/C(111)1×1 and T/C(111)1×1 surfaces were carried out in the same way except the hydrogen mass was replaced by the masses of deuterium and tritium atoms, respectively. III. Results and Discussion The calculated power spectra of fluctuating force on C-H,D,T stretching modes on H,D,T/C(111)1×1 diamond surfaces, respectively, are shown in Figures 2-4. The magnitudes of the power spectra at their resonance frequencies are input into eq 2.1 to calculate lifetimes of the V ) 1 and V ) 2 states of the C-H,D,T stretches on the H,D,T/C(111)1×1 surfaces, respectively. For the first excited state, the lifetime of the C-H stretching modes is calculated to be 30 ps, which agrees well with the experiment result of 19 ps.23 The lifetime of the present
7084 J. Phys. Chem. B, Vol. 101, No. 36, 1997
Figure 3. Fourier transform of the fluctuating force autocorrelation function (eq 2.1) along a C-D bond at 300 K. The solid line is the position of the V ) 1 f 0 fundamental transition frequency ω10 ) 2110 cm-1. The dashed line is the position of the V ) 2 f 1 transition frequency ω21 ) 2050 cm-1.
Figure 4. Fourier transform of the fluctuating force autocorrelation function (eq 2.1) along a C-T bond at 300 K. The solid line is the position of the V ) 1 f 0 fundamental transition frequency ω10) 1788 cm-1. The dashed line is the position of the V ) 2 f 1 transition frequency ω21 ) 1748 cm-1.
calculation is one-half shorter than the previous calculation of 60 ps56 since the bending frequency of 1331 cm-1 22 is used instead of 1290 cm-1 measured earlier.27 The higher bending frequency used in the present calculation results in the calculated lifetime closer to the experimental result of 19 ps than the lifetime of 60 ps in the previous calculation.56 The difference between the present result and the experiment result may arise from the inadequacy of an accurate description of the interactions between atoms using empirical potential functions in the simulation. For the deuterium-terminated D/C(111)1×1 surface, the magnitude of the force power spectrum on the C-D bond at the resonance frequency of 2110 cm-1 for the C-D stretching mode is higher than the C-H on the H/C(111)1×1 surface by about an order of 2. With this number in hand, the calculation of the lifetime of the first excited state for the C-D stretching mode on the D/C(111)1×1 surface gives a lifetime of 0.2 ps, which is in good agreement with the experimental result of 0.2 ps using IR spectroscopy.21 The lifetime of the first excited state for the C-D stretching mode is shorter than the lifetime of the C-H stretching mode by an order of 2. For the C-T stretching mode of the T/C(111)1×1 surface, the frequency of the C-T stretch is estimated to be 1788 cm-1 by multiplying the square root of the reduced mass ratios of the C-T bond to the C-H bond with the C-H stretching frequency of 2838 cm-1. The strength of the fluctuating force power spectrum at
Sun and Chen the resonance frequency gives a lifetime of 0.3 ps for the C-T stretch on the T/C(111)1×1 surface. The magnitude of the fluctuating force power spectrum curves in Figure 2, Figure 3, and Figure 4 reflects the coupling strength between the C-H,D,T stretching modes and the bath modes, which are comprised of the C-C-H,D,T bends and phonons of diamond substrate on the H/C(111)1×1, D/C(111)1×1, and T/C(111)1×1 surfaces, respectively. By multiplying the square root of the mass ratios of the deuterium and tritium atoms to hydrogen atom with the C-C-H bending frequency of 1331 cm-1, the frequencies of C-C-D and C-C-T bends are estimated to be 941 and 768 cm-1, respectively. Owing to the high Debye frequency of ∼ 1400 cm-1 27,58 for diamond crystal, the C-C-D and C-C-T bends couple with the bulk phonons where C-C-H bends couple rather loosely with the bulk phonons on the H/C(111)1×1 surface. For the H/C(111)1×1 surface, the relaxation of a C-H stretch avoids the massive 1:2 resonance with the bath phonons. In contrast, the frequencies of 2110 and 1788 cm-1 for the C-D and C-T stretching modes locate in the 1:2 resonance region. The strength of the fluctuating force power spectra at the resonance frequencies of C-D and C-T stretch give lifetimes on the time scale of tenths of a picosecond. The difference of 1:3 and 1:2 resonance for the energy relaxation of C-H and C-D,T stretches on the H/C(111)1×1 and D,T/C(111)1×1 surfaces, respectively, results in a difference of lifetimes by an order of 2. Interestingly, the power spectrum curve of C-H in Figure 2 differs significantly from those of C-D and C-T stretches in Figure 3 and Figure 4, which are similar both in magnitude and shape. Since the high bending frequency of 1331 cm-1 for the C-C-H bend is rather decoupled from the phonons of diamond crystal comparing with C-C-D and C-C-T bends, “a peak” at ∼2600 cm-1, about the doublet of the C-C-H bending frequency, emerges in the curve of the force power spectrum for C-H stretch. The strong resonance around this frequency results in a fast relaxation rate for the V ) 2 state of the C-H stretching mode (see below). These findings are the same as the results in the earlier calculation of the H/C(111)1×1 surface56 using the earlier measured C-C-H bending frequency of 1290 cm-1.27 The present analysis based on the force power spectra suggests that, in the case where the bending modes couple with other bath modes strongly, since the bending modes mix with other bath modes, the bending modes do not give significant enhancement in the force power spectrum. When the bending mode couples with other bath modes weakly, strong resonance occurs at the doublet of the bending frequency. The vibrational energy relaxation assisted by two phonons in the vibrational energy relaxation shortens the lifetime of an excited state of a stretching mode significantly. Similar results of the vibrational energy relaxation rates were observed and analyzed in terms of the kinetic coupling expressed by G -matrix elements59 for the molecules in gas phase60 and prior calculation of Si-H and C-H stretching modes on H/Si(111)1×1 and H/C(111)1×1 respectively.43,56 The difference of force power spectra between C-H and C-D,T may arise from the couplings between the C-C-H and C-C-D,T bending modes with the bulk phonons, which is not clear in the present study. In addition to the first excited state, the lifetime of the V ) 2 state for the C-H,D,T stretches were calculated as well. Based on the experimental result of anharmonicity of 110 cm-1 for the C-H stretch and the stretching frequencies of 2838, 2110, and 1788 cm-1 for the C-H, C-D, and C-T stretches, respectively, in the Morse potential function used in the simulation, the anharmoncities of C-D and C-T are estimated to be 60 and 40 cm-1, respectively. The magnitude of the power
H,D,T/C(111)1×1 Diamond Surfaces spectra at the resonance frequency of the V ) 2 f 1 transition gives lifetimes of 0.1, 0.2, and 0.4 ps for the V ) 2 states of the C-H, C-D, and C-T stretches, respectively. In contrast to the first excited state of the C-H stretch, the V ) 2 state of the C-H stretch relaxes its energy on the same time scale of tenths of a picosecond with the C-D and C-T stretches. The redshift of 110 cm-1 for the V ) 2 f 1 transition of the C-H stretch falls in the 1:2 resonance region. The lifetime of the V ) 2 state of the C-H stretch is shorter than the first excited state by an order of 2, as found in the previous calculation of the H/C(111)1×1 surface.56 In the cases of C-D and C-T stretches, the red-shifts of the anharmonicities of 60 and 40 cm-1 for C-D and C-T stretches, respectively, do not give a significant difference in the strength of the fluctuating force power spectra between the V ) 2 f 1 and V ) 1 f 0 transitions and the resulting lifetimes for the V ) 2 and V ) 1 states. The present calculations of the force power spectra for C-H, C-D, and C-T stretch on the H/C(111)1×1, D/C(111)1×1, and T/C(111)1×1 surfaces, respectively, suggest that the energy relaxation of the first excited state employs a 1:3 resonance for C-H stretch and a 1:2 resonance for V ) 1 f 0 transitions of the C-D and C-T stretches and V ) 2 f 1 transitions of C-H, C-D, and C-T stretches. Good agreements of the present results of the first excited states for the C-H and C-D stretches with the experimental results are encouraging. The calculated results of the relaxation rates for the first excited state for C-T stretch and the V ) 2 states of C-H,D,T stretches may be of aid in the observation of the vibrational energy relaxation dynamics for the C-H,D,T stretching mode on the H,D,T/ C(111)1×1 diamond surfaces. In all of the present calculations, the forces on C-H,D,T bonds arising from the couplings between C-H,D,T stretching modes and bath modes in the autocorrelation function of eq 2.1 were calculated in classical approximation using classical molecular dynamics simulation. Because of the high bending frequencies of C-C-H,D,T bends and surface phonons of diamond substrate of a Debye frequency of ∼1400 cm-1, the quantum effect of the bath phonons in the vibrational energy relaxation of C-H,D,T stretches may be substantial. Important development has been made in investigating quantum dynamics in complicated condensed matter systems using molecular dynamics simulation.44-50,52,53,61-66 On the basis of a linear model in which the bath modes couple with the system mode bilinearly, Bader and Berne found that the lifetime of the vibrational mode should be multiplied by a factor of 2kB T/pωtanh(pω/2kBT), where kB, T, and ω are Boltzmann constant, temperature, and the vibrational frequency, respectively, to account for the quantum effect arising from the couplings between the system mode and bath modes when a quantum solute-classical solvent model is used in the calculation.51,52 In addition to this development in quantum dynamics using a linear model, a generalized quantum dynamics theory based on the Feynman path centroid formalism which includes nonlinear couplings between the system mode and bath modes was developed by Cao and Voth.45-50 Following Bader and Berne’s findings of quantum effect in the calculation of relaxation dynamics using molecular dynamics simulation,52 multiplication of the factors of 2kBT/pωtanh(pω/2kBT) at their transition frequencies to the calculated lifetimes above at 300 K gives lifetimes of 5, 0.04, and 0.07 ps for the V ) 1 states and 0.02, 0.04, and 0.1 ps for the V ) 2 states, which are about 4-6 times shorter than the calculated lifetimes above, for the C-H,D,T stretches on H,D,T/C(111)1×1 surfaces, respectively. The results for the V ) 1 states of C-H and C-D stretches are about 4 and 5 times shorter than the experimental results
J. Phys. Chem. B, Vol. 101, No. 36, 1997 7085 respectively. While the significant difference between these two calculated and experimental lifetimes, after multiplication of the factor 2kB T/pωtanh(pω/2kBT) based on the linear model,52 may be in part due to the inadequacy of an accurate description of molecular interactions in the calculational model, the effect of nonlinear couplings between the stretching modes and bath modes in the vibrational energy relaxation of stretching modes may be important as commented by Voth52 in ref 52 for the case of Si-H stretches on H/Si(111)1×1 surface.43 Investigation of this effect using quantum dynamics theory which includes nonlinear effects in simulation, for instance, the newly developed quantum dynamics theory based on the Feynman path centroid,44-50,61-66 should be the focus of future study. IV. Concluding Remarks In the present report, the Bloch-Redfield relaxation theory combined with classical molecular dynamics simulation and the model of the H/C(111)1×1 surface in a prior calculation of the vibrational energy relaxation rate of the C-H stretching modes on H/C(111)1×1 surface56 were used, except the earlier measured C-C-H bending frequency of 1290 cm-1 27 was replaced with the newly measured frequency of 1331 cm-1,22 to calculate the vibrational energy relaxation rates of C-H,D,T stretches on H,D,T/C(111)1×1 surfaces, respectively. Use of the newly found C-C-H bending frequency of 1331 cm-1 in the calculation of the C-H stretch on the H/C(111)1×1 surface results in a lifetime of 30 ps, which is in better agreement with the experimental result of 19 ps, than the previous result of 60 ps56 using the earlier measured C-C-H bending frequency of 1290 cm-1. The calculated lifetime of 0.1 ps for the V ) 2 state of the C-H stretch is on the same time scale as the lifetime of 0.3 ps found in the previous calculation56 as well. Because of strong resonance at around the doublet of the C-C-H bending frequency, the red-shift of V ) 2 f 1 from the V ) 1 f 0 transition frequency due to the anharmonicity of 110 cm-1 for the C-H stretch locates in the 1:2 resonance region and shortens the lifetime to the time scale of tenths of a picosecond. These results based on the analysis of the calculated force power spectrum in the present calculation for C-H stretches reach the same conclusion in the previous calculation of the H/C(111)1×1 surface.56 For the C-D and C-T stretches on D,T/C(111)1×1 surfaces, respectively, the calculated lifetimes of 0.2 ps for the first excited states of C-D stretching modes agree well with the experimental results of 0.2 ps as well. The lifetime of the C-T stretches on the T/C(111)1×1 surface is predicted to be 0.3 ps, on the same time scale with the lifetime of the C-D stretch on the D/C(111)1×1 surface. The longer lifetime of the C-H stretching modes in the tens of picoseconds than the lifetimes of C-D and C-T stretching modes in the tenths of a picosecond by an order of 2 is due to the 1:3 and 1:2 resonance relaxation pathways for the C-H and C-D,T stretches on the H/C(111)1×1 and D,T/C(111)1×1 surfaces, respectively. In addition to the first excited state, the calculations of the relaxation rates for the V ) 2 states of the C-H, C-D, and C-T stretches gave lifetimes of 0.1, 0.2, and 0.4 ps, respectively, all on the same time scale of tenths of a picosecond. The calculated force power spectrum of the C-H stretch differs significantly from the power spectra of C-D and C-T stretches. Since the C-C-H bend on the H/C(111)1×1 surface couples with the bulk phonons rather weaker than the C-C-D and C-C-T bends on the D/C(111)1×1 and T/C(111)1×1 surfaces, respectively, strong resonance for the C-H stretch at around the doublet of the C-C-H bending frequency exists, while the doublets of C-C-D and C-C-T bending frequencies do not give such
7086 J. Phys. Chem. B, Vol. 101, No. 36, 1997 significant resonance enhancement in the power spectra of the C-D and C-T stretches. The present calculated lifetimes and the analysis based on the calculated force power spectra on the H,D,T/C(111)1×1 diamond surfaces may be used to understand the vibrational energy relaxation dynamics of the C-H,D,T stretching modes on other monohydride-terminated diamond surfaces. The investigation of the effect of nonlinear couplings between the stretching modes and bath modes in vibrational energy relaxation dynamics discussed in section III and use of more accurate potential functions to describe molecular interactions should be the topics of future study in order to obtain better results and insight in theoretical calculations of vibrational energy relaxation dynamics. Acknowledgment. We are indebted to Prof. G. A. Voth for helpful discussion on energy relaxation theory. We also thank Prof. Y. R. Shen and Drs. J. S. Cao, H. C. Chang, J. C. Lin, C. L. Cheng, and J. K. Wang for helpful discussions. Y.C.S. thanks Prof. W. K. Liu for getting him interested in this study. This research is supported by the National Science Council under Grant No. NSC 86-2113-M-003-011 and NSC 86-2732-M-003004. National Center of High-Performance Computing is acknowledged for providing computer time on SGI Power Challenge. References and Notes (1) DeVries, R. C. Annu. ReV. Mater. Sci. 1987, 17, 161. (2) Spear, K. E. J. Am. Ceram. Soc. 1989, 72, 171. (3) Angus, J. C.; Hayman, C. C. Science 1988, 241, 913. (4) Chabal, Y. J. Surf. Sci. Rep. 1988, 8, 211. (5) Chabal, Y. J.; Higashi, G. S.; Raghavachari, K. J. Vac. Sci. Technol. A 1989, 7, 2104. (6) Guyot-Sionnest, P.; Dumas, P.; Chabal, Y. J.; Higashi, G. S. Phys. ReV. Lett. 1990, 64, 2156. (7) Guyot-Sionnest, P.; Dumas, P.; Chabal, Y. J. J. Electron Spectrosc. Relat. Phenom 1990, 54/55:27. (8) Guyot-Sionnest, P. Phys. ReV. Lett. 1991, 66, 1489. (9) Guyot-Sionnest, P. Phys. ReV. Lett. 1991, 67, 2323. (10) Dumas, P.; Chabal, Y. J.; Higashi, G. S. Phys. ReV. Lett. 1990, 65, 1124. (11) Jakob, P.; Chabal, Y. J. J. Chem. Phys. 1991, 95, 2897. (12) Jakob, P.; Chabal, Y. J.; Raghavachari, K.; Dumas, P.; Christman, S. B. Surf. Sci. 1993, 285, 251. (13) Jakob, P.; Chabal, Y. J.; Raghavachari, K.; Christman, S. B. Phys. ReV. B 1993, 47, 6839. (14) Jakob, P.; Chabal, Y.; Raghavachari, K.; Becker, R. S.; Becker, A. J. Surf. Sci. 1992, 275, 407. (15) Chabal, Y. J. Mol. Struct. 1993, 292, 65. (16) Hines, M. A.; Chabal, Y. J.; Harris, T. D.; Harris, A. L. Phys. ReV. Lett. 1993, 71, 2280. (17) Morin, M.; Jakob, P.; Levions, N. J.; Chabal, Y. J.; Harris, A. L. J. Chem. Phys. 1992, 96, 6203. (18) Kuhnke, K.; Morin, M.; Jakob, P.; Levions, N. J.; Chabal, Y. J.; Harris, A. L. J. Chem. Phys. 1993, 99, 6114. (19) Mitsuda, Y.; Yamada, T.; Chuang, T. J.; Seki, H.; Chin, R. P.; Huang, J. Y.; Shen, Y. R. Surf. Sci. Lett. 1991, 257, L633--L641. (20) Chin, R. P.; Huang, J. Y.; Shen, Y. R.; Chuang, T. J.; Seki, H.; Buck, M. Phys. ReV. B 1992, 45, 1522--1524.
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