1702
J . Phys. Chem. 1990, 94, 1702-1705
itself no kinetic intermediate acceptor. The Hamiltonian has the form
Allthough the three-level system can be solved analytically by means of the Cardan formula, a more indirect way leads to less complicated results. It is assumed that the energy level Ep. of IP*) differs form the level EHL-of vibronically excited IHL-) in the order of the coupling of these levels t p H i IEp. - EHL-l c ~ H . On the other hand the level EEL-of the intermediate BL lies considerably above Epr and EHL-and this difference is larger than all transfer matrix elements: ( ~ E B ,-- E H ~ - ~IEB~- Ep.1) >> Itpel,ItpHI,ItBHI.In the resulting expressions only the lowest order 1, IcBHI/IEB~-E H ~ tpBand c >> eBH one obtains Iq = llBl - 1.111.
Observation of ESR Spin Flip Satellite Lines of Trapped Hydrogen Atoms in Solid H2 at 4.2 K Tetsuo Miyazaki,* Nobuchika Iwata, Kenji Fueki, Department of Synthetic Chemistry, Faculty of Engineering, Nagoya University, Chikusa- ku. Nagoya 464-01, Japan
and Hirotomo Hase Research Reactor Institute, Kyoto University, Kumatori-cho, Sennan-gun, Osaka 590-04, Japan (Received: March 20, 1989; In Final Form: August 30, 1989)
ESR spectra of H atoms, produced in y-irradiated solid H2, were studied at 4.2 K. Two main lines of the ESR spectra of H atoms that are separated by about 500 G accompanied two weak satellite lines. Both satellite lines and main lines decrease with the same decay rate. In the D2-H2 mixtures, the satellite-line intensity depends upon the number of matrix protons. The spacing of the satellites from the main lines is equal to that of the NMR proton resonance frequency. It was concluded that the satellite lines were not ascribable to paired atoms but to spin flip lines due to an interaction of H atoms with matrix protons. The analysis of the spin flip lines and the main lines suggests that H atoms in solid H,are trapped in the substitutional site.
Introduction The role of quantum mechanical tunneling in reactions H~ (D,HD) + H (D) has been one of the important problems in the ‘Author to whom correspondence should be addressed.
0022-3654/90/2094-1702%02.50/0
theory of chemical kinetics. When hydrogen atoms are produced by ?’-radiolysis of solid hydrogen at an ultralow temperature, the hydrogen atoms react with hydrogen molecules by tunneling. Miyazaki et have obtained the following results on the (1)
Miyazaki, T.; Lee, K. P. J. Phys. Chem. 1985, 90, 400.
0 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 4 , 1990 1703
ESR Satellite Lines of Trapped H Atoms in Solid H2
5 G
tunneling reactions at 4.2 and 1.9 K by ESR spectroscopy. (1) Direct evidence was obtained for a tunneling reaction H D D H D2.1.2 (2) A marked-isotope effect was observed on the tunneling reactions H2 (D2,HD) H (D).4 (3) The absolute rate constants for the tunneling reactions were measured3v5and compared with the theoretical rate c o n ~ t a n t s . ~ (4) * ~ *H~atoms in solid H2 migrate through solid H2 by repetition of the tunneling reaction H2 + H H H2.395 Information of trapping sites of H atoms in solid H2, which reflect a distance between a H atom and neighboring H2 molecules, is very important for elucidating of the tunneling reactions. However, no experimental study on trapping sites of H atoms in solid hydrogen has been reported yet. Since solid hydrogen is a well-known quantum solid, H atoms in solid H2 can be considered as quantum particles in a quantum solid. Thus, trapping of H atoms in solid H2 invokes interesting problems in low-temperature physics. It is well-known that ESR spectra of trapped hydrogen atoms, produced by the radiolysis of acid ice at low temperatures, show spin flip satellite lines. Knowledge on the trapping site of the H atoms was obtained in terms of the analyses of the ESR spin flip satellite The previous studies on ESR spin flip lines of trapped H atoms, however, are limited only to a matrix of acid ice. In the present study, we have observed the ESR spin flip satellite lines of H atoms in solid hydrogen at 4.2 K. This observation will give us new information on trapping sites of H atoms in solid hydrogen.
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H-
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Experimental Section H2 and D2 were more than 99.999 and 99.5 mol % pure, respectively. Hydrogen was sealed in a sample tube and solidified by rapid cooling of the sample tube from room temperature to 4.2 K. The sample in a cryostat was irradiated at 4.2 K with y-rays from a @Cosource. Irradiation doses were 0.1 Mrad for H2 and a D2-H2 (50 mol %) mixture and 0.4 Mrad for a D2-H2 ( 1 mol %) mixture. The details of the experimental procedure were described in the previous papera3 In the previous study, a sample tube and a cryostat were made of fused silica “Spectrosil”, which contains O H bonds, as many as 4000 ppm. When the sample is y-irradiated at 4.2 K, H atoms are produced in significant amounts, both in the sample tube and the cryostat. ESR spectra of the H atoms in silica and satellite lines of the ESR spectra of the H atoms in solid H2 overlap each other. In order to suppress the formation of H atoms in silica, in the present work a sample tube and a cryostat were made of special fused silica ”T2230”, obtained from the Toshiba Ceramic Co., which contains OH bonds at 5 ppm. The yield of H atoms in the radiolysis of silica T2230 was of that in silica Spectrosil.16 Thus, we have succeeded in diminishing the H atom yield due to the irradiated silica and obtained a clear ESR spectrum of H atoms produced in solid hydrogen. The trapped H atoms, produced by y-radiolysis of hydrogen, were measured at 4.2 K by a JES-FE2XG ESR spectrometer that (2) Lee, K. P.; Miyazaki, T.; Fueki, K.; Gotoh, K. J. Phys. Chem. 1987,
91, 180. (3) Miyazaki, T.; Lee, K. P.; Fueki, K.; Takeuchi, A. J. Phys. Chem. 1984, 88. 4959. (4) (a) Tsuruta, H.; Miyazaki, T.; Fueki, K.; Azuma, N. J. Phys. Chem. 1983, 87, 5422. (b) Miyazaki, T. Bull. Chem. Soc. Jpn. 1985, 58, 2413. (5) Miyazaki, T.; Iwata, N.; Lee, K. P.; Fueki, K. J . Phys. Chem. 1989, 93, 3352. (6) Takayanagi, T.; Masaki, N.; Nakamura, K.; Okamoto, M.; Sato, S.; Schatz, G.C. J. Chem. Phys. 1987,86, 6133. (7) Trammell, G. T.; &Ides, H.; Livingston, R. Phys. Reo. 1958,110,630. ( 8 ) Kohnlein, W.; Venable, J. H. Nature 1967, 215, 619. (9) Sprague, E. D.; Schulte-Frohlinde, D. J . Phys. Chem. 1973,77,1222. (IO) Bowman, M.;Kevan, L.; Schwartz, R. N. Chem. Phys. Lett. 1975, 30, 208. ( I I ) Bales, B. L.; Lesin, E. S. J . Chem. Phys. 1976, 65, 1299. (12) Kevan, L.; Plonka, A. J . Phys. Chem. 1977, 81, 963. (13) Ohno, K. Radiat. Phys. Chem. 1978, 12, 83. (14) Plonka, A.; Bogus, W. Radiat. Phys. Chem. 1980, 16, 365. (15) Hase, H.; Higashimura, T. Radiat. Phys. Chem. 1986, 27, 385. (16) Miyazaki. T.; Azuma, N.; Yoshida, S.; Fueki, K. Radiat. Phys. Chem. 1988, 32, 695.
i x 1110
I I
Figure 1. Low-field component of ESR spectra of H atoms, produced by y-radiolysis of solid hydrogen at 4.2 K: (a) H atoms in the irradiated H 2 measured at a microwave power level of 1 FW; (b) H atoms in the irradiated D2-H2 (50 mol %) mixture (the central main peak and the satellite peaks were measured at 0.001 and 1 pW, respectively); (c) H atoms in the irradiated D2-H2 (1 mol %) mixture (the central main peak and the satellite peaks were measured at 0.001 and 1 p W , respectively).
was modified for measurement at such a low microwave power as 0.0001 pW by use of a rotary attenuator and a special electric circuit. The amounts of H atoms were obtained by double integration of the signals with a personal computer. Results The ESR spectrum of H atoms, produced by y-radiolysis of solid H2, consists of the low- and high-field main spectra separated by about 500 G . Each main line accompanied two satellite lines that were able to be observed at high-microwave-power levels above 0.4 pW. Figure 1 shows the low-field components of the ESR spectra of H atoms produced in y-irradiated H2 (a), D2-H2 (50 mol 7%) mixture (b), and D2-H2 (1 mol %) mixture (c) matrices at 4.2 K. Since ESR spectrum of H atoms in solid hydrogen is very sharp, the spectrum can be observed clearly a t a low microwave power of 0,001 pW.” The line shapes of the main
1704 The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1 5 0 7 -
0
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’
O
15
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Figure 2. Microwave power saturation behavior of H atoms produced main peak (Hmin);(A) satellite peak by y-radiolysis of H2 at 4.2 K: (0) (Hra,clllle).
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Figure 3. Decay of H atoms caused by a tungsten (W) lamp illumination of y-irradiated H2at 4.2 K. The initial amounts of a main peak (0) and are normalized to 1.0. A is the ratio of the amounts a satellite peak (0)
of a satellite peak to those of a main peak.
and the satellite spectra of H atoms in solid H2were computeranalyzed by the method similar to the one reported previ0us1y.l~ It turned out that the observed line shapes of both main and satellite spectra fitted Lonrentzian rather than Gaussian shapes. Figure 2 shows the microwave power saturation behavior of trapped H atoms produced by y-radiolysis of H2 at 4.2 K. The main lines (Hmain),denoted by circles, begin to saturate at a microwave power of about 0.005 pW, while the satellite lines (Hsalellite), denoted by triangles, begin to saturate at a power of about 2 pW. When the sample of y-irradiated solid H2 was illuminated with a tungsten lamp, the amounts of H atoms decreased. This is probably due to a slight increase of the temperature of the sample by the ill~mination.~ The decay of the main and the satellite lines caused by the illumination and the intensity ratios of the satellite line to that of the main line are plotted in Figure 3.
Discussion Identijkation of the Satellite Lines. It was reported previouslyl* that ESR spectra of H (or D) atoms in the y-irradiated solid CH4 (or CD4) at 4.2 K showed the satellite structure that was interpreted in terms of paired radicals. There are two possibilities for interpretation of the satellite lines in Figure la: One is that the satellite lines are due to paired H atoms, while the main line is due to isolated H atoms. The other is that the satellite lines are the spin flip lines due to a dipole-dipole interaction of H atoms with matrix protons as observed in the y-irradiated acid The latter interpretation is more plausible for the satellite lines observed for H atoms in solid H2 by the following reasons. First, when the y-irradiated solid H2 is illuminated by a tungsten lamp, the amounts of H atoms decrease by a recombination reaction, caused probably by a slight increase of temperature. Figure 3 shows the amounts of the H atoms upon the illumination. Both (1 7) A line width, a peak-to-peak width, of the ESR spectrum of H atoms in H2is 0.43 G, while that of H atoms in a D2-H2 ( 1 mol 9%) mixture is 1.2 G. The reason for the different line widths in the two matrices is not elucidated as yet. One possible explanation is as follows. It was reported previously that H atoms cannot migrate through solid D2,whereas H atoms migrate through solid H2by repetition of a tunneling reaction H2 + H H + H2(cf. ref 3 and 5 ) . The tunneling diffusion of H atoms in H2may cause the motional narrowing of ESR spectrum of H atoms in H2.
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Miyazaki et al. satellite peaks and a main peak decrease with the same decay rate. If the main and satellite spectra are due to different H atoms, that is, isolated H atoms and paired H atoms, the decay rates of the two H atoms must be different upon illumination. This may result in a change of the Hsatellite/Hmain ratio during the decay of H atoms. The constant ratio in Figure 3 indicates that the ESR spectrum is due to the same kind of H atoms that accompanies spin flip lines. Second, the intensity of spin flip lines depends upon the number of matrix protons (cf. eq 1 in the next section). The main and satellite lines of H atoms in the D2-H2 (50 mol %) mixture and the D2-H2 (1 mol %) mixture, shown in parts b and c of Figure 1, do not show any microwave power saturation at the microwave power levels of 0.001 pW for Hminand 1 pW for Hsatellite. Thus, one can directly compare the intensity of the satellite lines. It follows that the satellite lines appear clearly in the D2-H2 (50 mol 7%)mixture but that their intensity is very weak in the D2-H2 (1 mol %) mixture. The remarkable dependence of the satellite-line intensity upon the number of matrix protons indicates that the satellite peaks are due to matrix proton spin flip lines. Third, if the satellite lines are due to the spin flip of matrix protons, the separation between the main and satellite lines is approximately given by gN/&H where g N and BN are nuclear g factor and magneton, respectively, and H i s the applied magnetic field. Thus, the separation between the main and satellite lines for H atoms in solid H2 is expected as about 5.0 G, while the separation for D atoms in solid D2 is about 0.76 G. As shown in Figure la, an experimental value of the separation between the main and satellite lines for H atoms in solid H2 is about 5 G, which coincides with the theoretical value (5.0 G). This is about a fifth of the separation for the radical pairs reported in CH4 a t 4 K.18 In the ESR spectra of D atoms in the y-irradiated solid D2 at 4.2 K, satellite lines could not be observed. Since the separation between the main and satellite lines for D atoms in solid D2 is expected as only 0.76 G, the main and satellite lines of D atoms may overlap each other, making observation of satellite lines impossible. This is contrary to the result that both ESR spectra of H atoms in irradiated CH4 and those of D atoms in irradiated CD4 showed satellite lines that are ascribed to paired radicals.Is Fourth, spin flip lines due to matrix protons are caused by a spin-forbidden transition, while the main line is caused by the allowed transition. Thus, if the satellite lines are spin flip lines, the microwave saturation behavior of the satellite lines may be different from that of the main peaks. As shown in Figure 2, the satellite lines begin to saturate at 2 pW, while the main lines have already saturated above 0.005 pW. This different saturation behavior may be relevant to the different type of transitions between the satellite lines and the main lines. Fifth, if paired atoms exist in the y-irradiated solid H2, ESR spectra of AMs = f 2 transition should be observed at a half-field resonance position. The AM, = f 2 transition signals from the paired atoms, however, could not be detected under the condition of high sensitivity of the spectrometer. Therefore, it is concluded that the satellite lines shown in Figure 1 are the spin flip lines due to the interaction of H atoms with nearby matrix protons. Since ESR spin flip lines of trapped H atoms have been reported only in acid ice, the present observation of spin flip lines of H atoms in solid H2 is a new example in addition to the acid ice matrix. Trapping Site of H Atoms in Solid H2. Knowledge on the trapping site of the H atoms has been obtained in terms of the analyses of the ESR spin flip satellite line^.^-^^ The analyses are classified as three main types: (1) method of Trammel1 et al.,’ in which the intensity ratio of the satellite to the main line is used to estimate an average distance to the nearest-neighbor matrix protons once a number of them is assumed; (2) method of Bowman et a1.,I0 in which energy separation of the satellite from the main line is analyzed to determine an unique distance to the nearestneighbor matrix protons; and (3) method of Bales et al.,”*’9 in (18) Toriyama, K.; iwasaki, M.; Nunome, K. J . Chem. Phys. 1979, 71, 1698.
ESR Satellite Lines of Trapped H Atoms in Solid H2 which the second” and the first momentI9 of the spin flip satellite with respect to the main line is analyzed by combining the other methods. This allows one to independently determine the number of the nearest-neighbor protons and the distance to them. In both methods 2 and 3, the key quantity is energy deviation ( d - N/2), where d is the energy separation of the satellite from the main line and N/2 = gN/?NH in which gN is the nuclear spectroscopic splitting factor and ON is the nuclear magneton. A typical value of ( d - N/2) is ca. 8 X erg for trapped H atom^.^*'^*^^ In order to get a value of this order of magnitude, one should measure the resonance field strength with an accuracy of 0.01 G. Furthermore, the applied microwave frequency must be measured with an accuracy of at least 10 kHz in the X-band in order to get a reliable g value. In this context, it is not easy to perform experiments at 4.2 K so that one cannot use methods 2 and 3, although these methods are theoretically superior to method 1. In the case of H atoms in acid ice, the effective distance between trapped H atoms and neighboring protons, estimated by method 1, coincides within errors of about 20% with the distance estimated by methods 2 and 3.7-15 In the present study, we have used method 1 to obtain qualitative information on the structure of H atoms in solid H2. When n matrix protons exist at an average distance ( ( r ) , )away from a trapped H atom, ( r ) ,can be calculated from the ratio of the satellite line intensity (Z,) to the main line intensity (2Zm),by the following relation given by Trammel1 et ala7 where g is the electron g factor, /? is the Bohr magneton, and H is the applied magnetic field. Since the microwave saturation behaviors of the main and satellite peaks are different, the ratio (Is/21m)was obtained from the slopes of the straight line, which expresses the linear relation between the peak intensities and roots of the microwave power (cf. Figure 2). The average distance ( ( r ) , ) ,obtained from eq 1 by use of the experimental ratio Is/21m, are 3.6-4.0 A, if the effective number of protons (n) is taken as 1 and 2. The crystalline structure of solid H2 at 4.2 K is a hexagonal closest packed (hcp) structure.20 If it is assumed that H atoms are trapped in the crystal, the distance between the nearest protons and a trapped H atom can be calculated from the structure. The distances for three trapping sites are 3.4 A for a substitutional site, 2.3 A for an interstitial octahedral site, and 1.9 8, for an interstitial tetrahedral site. The effective distances (3.6-4.0 A), obtained experimentally, are roughly similar to the distance (3.4 A) for the substitutional site. This work is the first study of (19) Bales, B. L.; Bowman, M. K.; Kevan, L.; Schwartz, R. N. J . Chem. Phys. 1975,63, 3008. (20) (a) Silvera, 1. F. Rev. Mod. Phys. 1980, 52, 393. (b) Bostanjoglo, 0.; Kleinschmidt, R . J . Chem. Phys. 1967, 46, 2004.
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1705 trapping sites of H atoms in solid hydrogen, and thus information on trapping sites of H atoms in solid hydrogen is too scanty to decide the precise structure of the trapping sites. Lastly, we will point out several problems for elucidation of the trapping sites of H atoms in solid hydrogen. First, normal H2 used here consists of 25% para H2, whose rotational quantum number is zero at 4.2 K, and 75% ortho H2, whose rotational quantum number is 1. When a H2 molecule orients its molecular axis to a trapped H atom, the distance between the trapped H atom and the proton of the H2 molecule becomes the nearest. It is tentatively assumed here that only one or two H2 molecules orient their molecular axes to the trapped H atom. The orientation of para H2 and ortho H2 molecules near the trapping site may be an important factor for analysis of ESR spin flip lines. Second, solid hydrogen, a well-known quantum solid, is highly compressible and as a consequence causes substantial change in density.20a Thus, a solid hydrogen is a very soft matrix. It is assumed here that one or two hydrogen molecules are found near a trapped H atom and the rest of the hydrogen molecules are pushed away, resulting in the distortion of the lattice. The possibility of local distortion near the trapped H atom must be studied in the future. Third, a H atom in a H2 molecule changes its sition by about 30% of its equilibrium atomic separation (0.74 ) because of its high zero-point energy of vibration. The large variation of its position must be considered for analysis of ESR spin flip lines. Fourth, it is necessary to determine independently the number and distance of adjacent protons by the methods 2 and 3, described in the first paragraph of this section. Fifth, recently a G value of trapped H atoms in the radiolysis of solid H2 at 4.2 K has been measured as 6.2.21 H atoms, produced by decomposition of H2, may be trapped initially in both interstitial and substitutional sites. According to the previous studies,15 H atoms migrate through solid hydrogen by repetition of the tunneling reaction H2 + H H + H2. A H atom, produced initially by decomposition, reacts fast with a neighboring H2 molecule in a lattice by quantum mechanical tunneling. Then, the tunneling reaction H2 + H H + H2 leaves the product H atom in the lattice site, which is a substitutional site. If the tunneling reaction H2 + H H + H2 is repeated, almost all of H atoms may be found in the substitutional site. It is an interesting problem to correlate the trapping site of H atoms with the tunneling reaction in the solid hydrogen.
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Acknowledgment. We thank Prof. Horst Meyer of Duke University, USA, for his fruitful discussion. This work was supported in part by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Science, and Culture. Registry No. H, 12385-13-6; H2,1333-74-0. (21) Miyazaki, T.; Fueki, K.; Kato, M. Rudiut. Phys. Chem., in press.
