Calorimetric studies of tunneling phenomena

ELSEVIER

Physica B 202 (1994) 325-331

Calorimetric studies of tunneling phenomena* Akira Inaba Department of Chemistry and Microcalorimetry Research Center, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan

Abstract

Calorimetric investigations have been performed for the molecules and ions that show tunneling in solids and adsorbed monolayers. A combination of heat capacity measurement and neutron scattering experiment yields valuable information about the energy scheme and the kinetic behavior such as spin conversion. Finding of a phase transition of those solids also gives us helpful information to understand the whole nature of tunneling phenomena. For ammonium ions diluted in a KBr crystal and for methane molecules adsorbed on the surface of graphite, the energy scheme of the rotational ground state was investigated. The rate of conversion between different spin species was determined for ammonium ions in KBr, methane molecules on graphite and solid 4-methylpyridine N-oxide. New phase transitions were found in 4-methylpyridine N-oxide, 1,3,5-tribromo-2,4,6-trimethylbenzene and 2,6-dimethylpyridine. A hydrogenbonded crystal Rb3 H(SeO4)2 has an excess contribution in heat capacity below 30 K, which may come from the proton tunneling.

1. Introduction

Calorimetric measurement is a macroscopic method that can be applied to investigation of rotational tunneling phenomena: The main interest is to explore the molecular and site symmetries and the strength of the intermolecular interaction [1]. While high resolution neutron scattering techniques allow us to see the rotational ground state directly [2], the calorimetry turns out to be useful and helpful to understand the whole nature of the tunneling system. For example, the rate of conversion between the nuclear spin symmetry species can be investigated by calorimetry [3].

*Contribution No. 75 from the Microcalorimetry Research Center, Faculty of Science, Osaka University.

The calorimetry is one of the easiest and most sensitive methods that can detect phase transition. One m a y discuss the dynamics of tunneling phenomena on the assumption that the crystal structure at low temperatures is the same as that at r o o m temperature. In some cases, however, the existence of a phase transition at low temperatures brings it to naught completely. The reason is that the intermolecular interactions are much more important in such systems rather than the intramolecular interactions. Finding of the phase transition by calorimetry therefore requests a detailed structural study at low temperatures. The purpose of the present paper is to demonstrate the usefulness of calorimetry for investigation of tunneling phenomena. The systems illustrated here are a m m o n i u m ions diluted in KBr crystal, 4-methylpyridine N-oxide, 1,3,5-trihalogeno-2,4,

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A. Inaba / Physica B 202 (1994) 325-331

6-trimethylbenzenes and 2,6-dimethylpyridine. More recently, the application of calorimetry has been extended to even diluted systems such as methane monolayers adsorbed on the surface of graphite, which are also described. An anomalous behavior of the low-temperature heat capacity in a hydrogen-bonded crystal Rb3H(SeO4)2 is illustrated, which may be relevant to proton tunneling.

2. Measurements

Two types of the calorimeters were employed to measure the heat capacity; one at 3 K < T < 300 K of adiabatic type [3,4] and the other at 0.3 K < T < 7 K of isoperibol type [5, 6]. With the adiabatic calorimeter, the time constant for reaching equilibrium gives the rate of conversion between different spin species in this particular case. The heat capacity of the adsorbed monolayers was determined from the difference between that of the calorimeter, adsorbent graphite, and gas, and that of the calorimeter and the adsorbent only [7]. The specific surface area of the graphite used, Grafoil MAT, was 24 mZ/g.

3. Results and discussion

3.1. Ammonium ions diluted in KBr crystal When a small amount of ammonium ions (say 0.5%) is substituted in KBr crystal, each ion feels an octahedral field given by the bromines [8]. The symmetry of the orientation of the ions and the energy scheme of the rotational ground states was investigated by combination of the neutron scattering and calorimetric studies [3]. According to a theory by Ozaki [9] the possible symmetry has a different energy scheme and the tunneling spectra favor the C3v model [3]. The heat capacity measurement proved the model as illustrated in Fig. 1, where only the contribution from the ions is plotted. The conversion between different spin species is forbidden in principle. However, the neutron scattering experiment showed that the conversion between the A and T is only forbidden or very slow at

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low temperatures [8]. The rate of spin conversion between them was obtained from the equilibration time during the heat capacity measurement. The results are plotted in Fig. 2 together with those obtained from the neutron scattering experiment [3]. The calorimetry turns out to be accessible when the rate of conversion is reasonably fast. 3.2. 4-Methylpyridine N-oxide The tunneling spectrum of solid 4-methylpyridine N-oxide has four pairs of the lines, almost equally spaced, which comes from the rotational tunneling of the methyl groups [-10]. It is then interesting to know whether the solid exhibits any phase transition at low temperatures, because solid 4-methylpyridine has a phase transition just below the melting point [11]. Moreover, the diffraction experiment at room temperature for 4-methylpyridine N-oxide indicates that the structure is very similar to that of 4-methtylpyridine at 4 K [12].

A. Inaba/ Physica B 202 (1994) 325-331

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Fig. 2. Temperature dependence of the characteristic time constant for the spin conversion in a m m o n i u m ions in a K B r crystal; the results obtained from neutron scattering experiment ( 0 ) and calorimetric measurement (0).

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The heat capacity showed that the solid 4methylpyridine N-oxide has two phase transitions; one at 97K and the other at 139K (Fig. 3). The former is of first order and the latter is of second order. The origin of the tunneling is probably due to the presence of four crystallographically nonequivalent methyl groups in the low-temperature structure. The site potentials are sufficiently different to yield the almost equally spaced spectrum, which is accidental. The time to reach equilibrium gave the rate of conversion between the spin species A and E, as shown in Fig. 4.

3.3. 1,3,5- Trihalogeno-2,4,6-trimethylbenzenes The compounds trichloro-(TCM), tribromo(TBM) and triiodo-(TIM)-trimethylbenzenes show three pairs of the tunneling lines with equal intensity [13], suggesting that there are three non-equivalent methyl groups of the molecules in the crystal. While they all crystallize in the same crystallo-

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Fig. 4. Temperature dependence of the characteristic time constant for the spin conversion in solid 4-methylpyridine N-oxide,

graphic group P I at room temperature, TCM has a phase transition around 160K [14]. It is thus interesting to know whether any phase transition occurs for TBM and TIM. The heat capacity showed that TBM has an anomaly around 30 K (Fig. 5). The anomaly is very broad and rather symmetrical as shown in Fig. 6 and the excess entropy amounts to approximately R In 2, suggesting that some order-disorder mechanism is pertinent: Two possible states per molecule may be expected in the high-temperature phase. In fact, a preliminary study by neutron diffraction indicated that the methyl groups are orientationally

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gion [16]. It is quite interesting to know the dynamics. Unfortunately, however, the crystal structure is unknown. As is often the case, it was suspected that the solid might have some phase transitions at low temperatures to settle the molecules in the crystal lattice. The heat capacity was measured between 3 and 300K. The melting point was determined to be 265.8K and three solid-solid phase transitions were found as shown in Fig. 7. The normal part of the heat capacity was subtracted to obtain the excess heat capacity (Fig. 8), where three peaks are discernible; a spike at 36K, a small anomaly at 53 K and a lambda-shaped anomaly peaked at 123 K. The time to reach equilibrium was rapid

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disordered at r o o m temperature [15]. Therefore, the methyl groups should be ordered at low temperatures. If, however, the methyl groups of the molecule are disordered independently from each other, then the entropy would be R In 8, rather than R In 2. The calorimetric result claims that the molecule has only two possibilities in the high-temperature phase, namely that the three methyl groups switch the orientation simultaneously. 3.4. 2 , 6 - D i m e t h y l p y r i d i n e

The rotational tunneling spectrum of methyl groups of solid 2,6-dimethylpridine was found to be so complicated, ranging over the wide energy-re-

Fig. 7. Heat capacity of solid 2,6-dimethylpyridine.

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Fig. 8. Excess heat capacity of solid 2,6-dimethylpyridine.

A. Inaba/ Physica B 202 (1994) 325-331

(within a few minutes) and normal over the whole temperature region except at the melting point. Hygroscopic water seemed to be the major impurity that significantly lowered the transition temperature of 36 K.

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Methane molecules sit on the graphite surface in such a way that every third of the hexagons of the graphite is occupied by the molecule, where every molecule feels a trigonal field. The energy scheme was worked out from the tunneling spectrum and the T level is split into two [17]. The heat capacity of the monolayer CH# was measured between 0.7 and 7 K. It showed that the spin conversion from the T to E would be rapid (Fig. 9), which is totally different from the bulk case [18]. When a small amount of oxygen was added, the equilibrium heat capacity of the whole system including the spin system was obtained (Fig. 9). The rate of spin conversion depends upon the temperature and the amount of oxygen as illustrated in Fig. 10.

3.6. CH3D Monolayer adsorbed on graphite For one of the isotopic methanes CHaD on graphite, the spin conversion becomes much faster [5]. The equilibrium heat capacity was obtained as illustrated in Fig. 11 1"6].A combination of the heat capacity measurement and the neutron scattering experiment determined the energy scheme (Fig. 12) [6], which is much more complicated than that for CH¢ on graphite. In this case, the heat capacity played an important role to determine the whole energy scheme.

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3.7. RbaH(SeO,02 Quite recently, an unusual isotope effect in some crystals containing hydrogen atoms has come into highlight: In some cases, a new phase transition appears when the hydrogen is replaced by deuterium [19]. A hydrogen-bonded crystal RbaH(SeO4)2 is an example. It has a symmetric short hydrogen bond which links two adjacent SeO 2- ions to form an H(SeO4)23- dimer. The

Fig. 10. Temperature dependence of the characteristic time constant for the spin conversion in the CH,t monolayer on graphite; with 0.42 tool % of 02 (A), 0.66 tool % of 02 (O) and 1.0 mol % of 02 (0).

hydrogenated crystal has no phase transition between 3 and 300 K, whereas the deuterated one has a phase transition at 95 K [20]. Moreover, the heat capacity becomes lower by deuteration below 30 K

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Fig. 12. Energy scheme ofthe rotational ground state obtained for the CH3D monolayer on graphite.

(Fig. 13), which is unusual. One of the possible explanations to this is that because of the tunneling of protons the hydrogenated crystal might have some relevant excitation: Assuming a two-level Schottky scheme, an excitation of 4.7meV is

Fig. 13. Comparison of the heat capacity at low temperatures between Rb3H(SeO4)2 ( 0 ) and RbaD(SeO4)2 (©).

expected [21]. The similar hebavior in heat capacity is also seen in a RbaH(SO4)2 crystal [22].

4. Summary Heat capacity measurements have been made for several systems that show tunneling. The calorimetry is a powerful method to detect phase transition. It also gives us useful information about the energy scheme and spin conversion. A combination of the calorimetric measurement, neutron scattering experiment and structural study is ideal to uncover the nature of tunneling phenomena. Fuller analysis of the heat capacities together with the experimental details will be reported elsewhere.

Acknowledgement The research was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture.

References I-1] W. Press, Single-Particle Rotations in Molecular Crystals, Springer Tracts of Modern Physics, Vol. 92 (Springer, Berlin, 1981).

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[2] Quantum Aspects of Molecular Motion in Solids, Springer Proceedings in Physics, Vol. 17, eds. A. Heidemann, A. Magerl, D. Richter, M. Prager and T. Springer (Springer, Berlin, 1987). [3] A. Inaba, H. Chihara, J.A. Morrison, H. Blank, A. Heidemann and J. Tomkinson, J. Phys. Soc. Japan 59 (1990) 522. [4] A. lnaba, T. Shirakami and H. Chihara, Chem. Phys. Lett. 146 (1988) 63. [5] A. Inaba and J.A. Morrison, Bull. Chem. Soc. Japan 61 (1988) 25. [6] P.C. Ball, A. lnaba, J.A. Morrison, M.V. SmaUey and R.K. Thomas, J. Chem. Phys. 92 (1990) 1372. [7] A. Inaba and H. Chihara, Can. J. Chem. 66 (1988) 703. [8] A. Heidemann, J. Howard, K.J. Lushinton, J.A. Morrison, W. Press and J. Tomkinson, J. Phys. Soc. Japan 52 (1983) 2401. [9] Y. Ozaki, J. Phys. Soc. Japan 56 (1987) 1017. [10] S. Ikeda, N. Watanabe, K. Inoue, Y. Kiyanagi, A. Inaba, S. Takeda, T. Kanaya, K. Shibata, T. Kamiyama, Y. Izumi, Y. Ozaki and C.J. Carlile, J. Phys. Soc. Japan 60 (1991) 3340.

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