Electronic structure of C60 fullerite

The complete systems of fundamental optical functions of single crystals and polycrystalline films of fullerite (C₆₀) are calculated on the basis of known reflection spectra and the imaginary and real parts of the permittivity. The integrated permittivity spectra are decomposed into elementary components. The three basic parameters of each component (the energy of the maximum, the half-width, and the oscillator strength) are determined. The nature of these components of the permittivity is discussed on the basis of existing theoretical calculations of fullerite bands. Fiz. Tverd. Tela (St. Petersburg) 41, 1124–1125 (June 1999)     

Thermal conductivity of pressure polymerized C60

60 polymerization in the temperature interval at pressures below by measurements of the time dependence of the thermal conductivity. It has been found at that the polymerization process at is slower than the reverse transformation from “polymeric” to “monomeric” phase at . The thermal conductivity of polymerized C₆₀ was measured in the temperature range and found to increase with increasing temperature, which reflects strong phonon scattering. Both the presence of non-bonded C₆₀ molecules and a high degree of structural disorder in the crystalline lattice of the polymeric phase might be responsible for the behaviour of . The results for are qualitatively similar to those reported previously for C₆₀ polymerized at higher , but an order of magnitude smaller. Received: 20 September 1996/Accepted: 11 November 1996     

On the spectral frequency distribution of translational vibrations in a face-centered cubic lattice of the C60 fullerite

The spectral frequency distribution g(ω) of translational lattice vibrations in the face-centered cubic phase of the C₆₀ fullerite at T = 300 K is calculated by the superposition method. The contribution from the translational vibrations to the heat capacity C _V of the C₆₀ fullerite and the x-ray characteristic temperature gJ_R entering into the exponent of the Debye-Waller factor are determined using the calculated frequency distribution g(ω). The results of the calculations are in good agreement with experimental data. It is noted that the librational and intramolecular lattice vibrations observed in the C₆₀ fullerite do not contribute significantly to the temperature-induced decrease in the x-ray diffraction intensity at T = 300 K. The Grüneisen parameters γ_mod calculated from the x-ray diffraction data are consistent with the thermodynamic Grüneisen parameters γ_lat at temperatures T ≤ 80 K but substantially exceed those at T ≈ 300 K. New x-ray diffraction experiments are proposed for independently determining the anomalously large negative values of the parameter γ₀, which is actually an orientational analog of the Grüneisen parameter.     

Structure of “cubic graphite”: Simple cubic fullerite C24

Physics of the Solid State - The structure of an intermediate carbon phase, the so-called “cubic graphite,” is determined. Close agreement between the calculated and experimental...     

Thermal conductivity of C60 and C70 crystals

We have performed thermal conductivity measurements on C₆₀ and C₇₀ crystals grown by sublimation. For single crystal C₆₀, the thermal conductivity k is 0.4 W/m K at room temperature and is nearly temperature independent down to 260K. We observed a sharp orientational phase transition at 260K, indicated by a 25% jump in k. Below 90K, k is time dependent, which manifests itself as a shoulder-like structure at 85K. The temperature and time dependence of k below 260K can be described by a simple model which accounts for the thermally activated hopping of C₆₀ molecules between two nearly degenerate orientations, separated by an energy barrier of 240 meV. It is found that solvents have a strong influence on the physical properties of C₇₀ crystals. For solvent-free C₇₀ crystal, k is about constant above 300K. There is a broad first-order phase transition in k at 300K with a 25% jump. We associate this transition with the aligning of the fivefold axes of the C₇₀ molecules along the c-axis of the hexagonal lattice. Upon further cooling, k increases and is time independent.     

Equation of state for fullerite C60

A new equation of state for fullerite C₆₀ is derived in the framework of the quantum-statistical method. This equation includes two Grüneisen parameters responsible for vibration–rotational and intramolecular contributions of fullerene molecules, which are represented in the form of isotropic quantum oscillators. The intramolecular vibrations of carbon atoms are described by the Debye heat capacity theory, and the cold contribution to the free energy is calculated using the Lennard–Jones pair potential for fullerene molecules. The theory is in a very good agreement with the experiment.

     

Electronic structure and elastic moduli of the simple cubic fullerite C24—A new allotropic carbon modification

The energy band structure, equation of state, density of states, and elastic moduli of a new allotropic carbon modification, namely, fullerite C₂₄ with a simple cubic lattice (known previously as cubic graphite), are calculated by the full-potential linearized augmented-plane-wave (FLAPW) method with geometry optimization for the first time. The dependence of the total energy on the lattice constant exhibits a minimum for a ₀ = 0.60546 nm. In this case, the lengths of the C-C bonds between fullerene molecules, the lengths of the 6,6-bonds shared by hexagons, and the lengths of the 4,6-bonds shared by a square and a hexagon are equal to 0.1614, 0.1503, and 0.1637 nm, respectively. An analysis of the energy band structure and the density of states demonstrates that the simple cubic fullerite C₂₄ is a direct-band-gap insulator or a semiconductor with a band gap of 1.6 eV. The calculated bulk modulus B ₀ = 196 GPa and the elastic moduli C ₁₁ = 338 GPa, C ₁₂ = 139 GPa, and C ₄₄ = 30 GPa indicate that the fullerite under investigation is a mechanically stable material. The inference is made that the simple cubic fullerite C₂₄ is a new diamond-like molecular zeolite with a unique combination of properties, such as the porosity and nonpolarizability, on the one hand, and the mechanical strength, chemical inertness, and high thermal conductivity, on the other hand. The simple cubic fullerite C₂₄ can be considered a promising low-dielectric-constant (low-k) material (?₀ < 5.7) for use in fabricating interconnections and substrates intended for integrated circuits and nanoelectronics.     

Fluorination of the cubic and hexagonal C60 modifications by crystalline manganese trifluoride

This paper reports on a comparative study of the solid-state fluorination of the cubic and hexagonal fullerene C₆₀ modifications by crystalline manganese trifluoride. It is shown that the variation of the fullerene crystal structure does not noticeably affect the composition of the fluorination products. The enthalpy and entropy of sublimation of the C₆₀ hexagonal phase are experimentally determined for the first time.     

On the mechanical properties of C60 fullerite crystals

First experimental data on the plasticity, strength and microhardness of C₆₀ fullerite crystals are reported. It is concluded that the mechanical properties of the crystals studied are isotropic, and the values of their breaking point are low. The obtained results are compared with those for other materials (graphite, indium etc.).     

On the effective Debye temperatures of the C60 fullerite

The effective Debye temperatures Θ_eff determined for solids by different physical methods have been analyzed and compared. Attention has been focused on the original parameter of the Debye theory of heat capacity, i.e., the translational calorimetric Debye temperature Θ _c ^t (0), and the X-ray Debye temperature Θ _x in the framework of the Debye-Waller theory for the C₆₀ fullerite. It has been established that the true Debye law T ³ is satisfied for the C₆₀ fullerite over a very narrow range of temperatures: 0.4 K ≤ T ≤ 1.8 K. For this reason, the experimental Debye temperatures Θ _c ^t (0) obtained for the C₆₀ fullerite by different authors in the range T > 4.2 K are characterized by a large scatter (by a factor of ∼5). It has been revealed that the value Θ _c ^t (0) = 77.12 K calculated in this paper with the use of the six-term Betts formula from the harmonic elastic constants $ \tilde C_{ijkl} $ \tilde C_{ijkl} of the C₆₀ single crystal in the limit T = 0 K is closest to the true Debye temperature. It has been demonstrated using the method of equivalent moments that the real spectral frequency distribution of translational lattice vibrations g(ω) for the C₆₀ fullerite deviates from a parabolic distribution. The effective Debye temperatures Θ_eff involved in applied problems of thermodynamics of crystals and elastic scattering of different radiations from lattice vibrations have been determined. The quantitative measure of anharmonicity of translational and librational lattice vibrations of the C₆₀ fullerite has been determined. This has made it possible to empirically evaluate the lattice thermal conductivity κ of the C₆₀ fullerite at T ≈ 300 K: κ(300) = 0.80 W (m/K), which is in good agreement with the experimental thermal conductivity κ_exp = 0.78 W (m/K) at T ≈ 250 K.     

Permutation-inversion symmetry of C70 fullerite in the high-temperature phase

The permutation-inversion symmetry group of C₇₀ fullerite in its high-temperature phase is constructed with allowance for the rotation of its constituent molecules, and the local symmetry group of a rotating molecule in the crystal is identified. Irreducible representations of these groups are constructed that are compatible with the principle of wave-function symmetry with respect to permutations of identical nuclei. A group-theoretic classification is made of the quantum states of a rotating molecule and of the crystal in the high-temperature phase of C₇₀ fullerite. Selection rules are derived for electronic, vibrational, and rotational spectra in terms of irreducible representations of the permutation-inversion symmetry group of the crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1895–1901 (October 1997)     

Thermal conductivity of crystalline chrysotile asbestos

The thermal conductivity of crystalline chrysotile asbestos made up of hollow tubular Mg₃Si₂O₅(OH)₄ filaments is measured in the range 5–300 K. The paper discusses the possibility of using this material in studies of the thermal conductivity of thin filaments of metals and semiconductors incorporated into the channels of crystalline chrysotile asbestos tubes.     

Electron energy-loss spectroscopy studies on C60 and C70 fullerite

The electronic structure of the crystalline fullerites C₆₀ and C₇₀ has been investigated by high-energy electron energy-loss spectroscopy in transmission. From valence band excitations and from core-level excitations of the C 1s level information on occupied and unoccupied and bands has been obtained.     

Properties of the microhardness of single-crystal C60 fullerite in sclerometric tests

The mechanical properties of single-crystal fcc C₆₀ fullerite are investigated by sclerometry and precision contact profilometry. Quantitative estimates are obtained for the microhardness anisotropy on the (100) and (111) planes. Polarity of the mechanical properties is observed in the (111) plane. The mechanisms considered for the orientational deformation of C₆₀ single crystals by a moving indentor confirm existing data showing that plastic deformation in solid C₆₀ occurs along the [011] (111) systems. Fiz. Tverd. Tela (St. Petersburg) 41, 1119–1123 (June 1999)     

Relaxation model of the orientational phase transition in fullerite C60

The model of thermal behavior of a thermoelastic medium is developed in the context of the Landau theory of phase transitions. In the framework of this model, two different problems are considered with allowance for order parameter relaxation: the problem of relatively slow uniform heating (cooling) of the medium under external hydrostatic pressure and the problem of order parameter relaxation at thermal isolation. A finite value of the relaxation constant τ of the order parameter is demonstrated to bring about the heating (cooling) rate dependence of the physical quantities, such as specific heat. The relaxation time of the order parameter is shown to be twice larger than the temperature relaxation time, as a consequence of the Landau expansion of the free energy.     

On the thermal decomposition of the C60D19 deuterium fullerite

The gas-phase products of thermal decomposition of the C₆₀D₁₉ deuterium fullerite are studied by mass spectrometry. It is found that, in addition to D₂ molecules, the gas phase over the deuterium fullerite sample heated to a temperature of 773 K contains CD₄ methane and C₆D₆ benzene molecules. The deuterocarbon molecules are revealed in the gas phase even at 673 K.