Orientational states of C60 molecule in crystals

Local symmetry of orientational states of the C₆₀ molecule in crystals has been investigated. It was shown that the various orientational phase transitions in different crystals are related to different orientational orbits. The model of orientational phase transitions based on a sequence of orientational states with different symmetry properties has been suggested. We have found that both the local symmetry of C₆₀ molecule and the symmetry of its internal vibrations become higher after a reduction of crystal spatial symmetry at the phase transition. This effect is fairly common and can be observed in the orientational order-disorder phase transitions with wave vectors at the Brillouin zone boundary. Feasible manifestations of the predicted effect in various experiments are discussed. Zh. éksp. Teor. Fiz. 113, 1081–1093 (March 1998)     

Correlation between energy levels of linear and bent X2Y2 molecules

The permutation-inversion group developed by Longuet-Higgins is extended to a classification of the vibronic, torsional, and rotational wavefunctions of a nonrigid X₂Y₂ molecule by introducing a symmetry operation $\text{T}\text{?}$, which rotates the top half of the molecule by 2π and, accordingly, the molecule-fixed x axis by π. Since the energy levels of linear (D_∞h) and bent (C_2h, C_2h, and C₂) forms of X₂Y₂ are classified according to a set of common symmetry operations of this extended permutation-inversion group, their energy levels can be correlated, including those of nonrigid forms such as a quasilinear system or a free internal rotor. Nuclear spin weights and selection rules are derived.     

Deformation-induced changes in the structure of fullerites C60/70 during their mechanical activation

Structural changes occurring during the mechanical activation of fullerites C_60/70 have been investigated using X-ray diffraction, IR and UV spectroscopy, and scanning electron microscopy. The complete destruction modes of fullerite have been determined (3.5 h at the intensity of the mill of 4.3 W/g and 28 h at 2.2 W/g). The destruction of the crystal structure of fullerites is accompanied by the destruction of fullerene molecules. The residual solvent, which enters into the composition of C_60/70, is retained during the entire time of mechanical activation. In this case, the low-frequency shift of absorption bands of toluene (729 → 725 cm^?1), which is caused by the deformation of the solvent molecule in the composition of crystal solvates, has been observed. It has been shown that the deformation stability of graphite is substantially lower than in the case of fullerite.     

Isomorphous phase transition and orientational freezing in hexagonal mixed crystal C 70(1 - x) C60x. A pseudospin model

A four-state pseudospin model is constructed for the isomorphous phase transition hcp-2↦hcp-1 in pure C₇₀ and in C₇₀-rich mixed crystal C _{70(1 - x)} C_60x. With the specific anisotropic pseudospin interactions adapted to the C₇₀ crystal the model is equivalent to a two-state Ising model in a temperature-dependent field. Replica symmetric state of the model is shown to approach the critical point when the width of distribution of random fields and/or of random bonds increases. The temperature of the phase transition and the phase equilibrium temperature then are practically constant, whereas the experiment shows their strong decrease with x. The main effect of dilution resides in an x-dependence of the model parameters. Dilatometric data on the hexagonal C _{70(1 - x)} C_60x are used to fit these parameters. A metastable disordered phase subsisting below the phase transition is discovered in a range of the model parameters and is shown to be responsible for the macroscopic behaviour of the system. A good agreement with experimental data is obtained for the spontaneous strain and for the x-dependence of the hysteresis. Received 20 April 2001 and Received in final form 26 September 2001     

Anomalies in the microwave conductivity of a polycrystalline C60 membrane

A study is reported of an anomaly in the microwave conductivity of a polycrystalline C₆₀ membrane at T _c=260 K (the transition width is 30 K). Raman scattering measurements indicate that the sample is the C₆₀ fullerite without any signs of graphitization, amorphous phase, or the presence of C₇₀, and that the detected microwave conductivity jump can be unambiguously identified as due to the C₆₀ phase. Fiz. Tverd. Tela (St. Petersburg) 40, 577–579 (March 1998)     

Copper-oxygen substructures in carbon allotropes (graphite and fullerites)

A comparative study of crystalline graphite and copper-doped fullerite membranes is reported. It is assumed that C₆₀ clusters form complexes with oxygen and copper similar to those known to exist in graphite. Above room temperature, these complexes, first, change the symmetry of the fullerite lattice and, second, are responsible for the nonmonotonic temperature dependence of the electrical resistance. Fiz. Tverd. Tela (St. Petersburg) 41, 748–750 (April 1999) Deceased.     

Hamiltonian,symmetry group,and vibrational coordinates for the nonrigid molecule CXY2CCCXY2

A vibration-torsion-rotation Hamiltonian is derived for a molecule of the type CXY₂CCCXY₂ exhibiting nearly free internal rotation. The Hamiltonian obtained preserves many of the features of the ordinary Wilson-Howard vibration-rotation Hamiltonian and is based qualitatively on the idea of a slowly varying torsional reference configuration from which the atoms make rapid vibrational displacements. The appropriate molecular symmetry group for this molecule is found to be a double group of the simple Longuet-Higgins permutation-inversion symmetry group. The indeterminacy of symmetry species (single-valued vs double-valued) for coordinates used to describe the small amplitude vibrations is illustrated and clarified using a simple model for the skeletal bending vibrations.     

Mechanical, structural, and spectroscopic properties of C70 fullerite phases produced under high pressure and shear

X-ray diffraction patterns, Raman spectra, and the hardness of C₇₀ fullerite subjected to a high pressure with shear are investigated. It is shown that these conditions favor the phase transformation of molecular fullerite into the hard amorphous phase. The hardness of a specimen removed from a diamond anvil cell loaded up to 26 GPa under shear deformation applied is found to be equal to 30 GPa.     

Experimental study of the Grüneisen parameter of a fullerite C60 single crystal near phase transitions at 90 and 260 K by the photoacoustic method

The behavior of the Grüneisen parameter of single-crystal fullerite C₆₀ has been studied experimentally near orientational phase transitions at 90 and 260 K. The measurements have been performed by the photoacoustic method using an automated photoacoustic device with laser excitation (the intensity was modulated by a harmonic law) and shadow piezoelectric detection. The temperature dependence of the relative change in the Grüneisen parameter in the fullerite C₆₀ single crystal has been measured near the phase transitions at 90 and 260 K. The results have been analyzed.     

Electroconductivity and pressure–temperature states of step shocked C60 fullerite

A study of electrophysical and thermodynamic properties of C₆₀ single crystals under step shock loading has been carried out. The increase and the following reduction in specific electroconductivity of C₆₀ fullerite single crystals at step shock compression up to pressure 30 GPa have been measured. The equations of state for face centred cubic (fcc) C₆₀ fullerite as well as for two-dimensional polymer C₆₀ and for three-dimensional polymer C₆₀ (3D-C₆₀) were constructed. The pressure–temperature states of C₆₀ fullerite were calculated at step shock compression up to pressure 30 GPa and temperature 550 K. The X-ray diffraction studies of shock-recovered samples reveal a mixture of fcc C₆₀ and a X-ray amorphous component of fullerite C₆₀. The start of the formation of the X-ray amorphous component occurs at a pressure P _m≈ 19.8 GPa and a temperature T _m≈ 520 K. At pressures exceeding P _m and temperatures exceeding T _m, the shock compressed fullerite consist of a two-phase mixture of fcc C₆₀ fullerite and an X-ray amorphous component presumably consisting of the nucleators of polymer 3D-C₆₀ fullerite. The decrease in electroconductivity of fullerite can be explained by the percolation effect caused by the change of pressure, size and number of polymeric phase nuclei.     

Phase transformations in amorphous fullerite C60 under high pressure and high temperature

First phase transformations of amorphous fullerite C₆₀ at high temperatures (up to 1800 K) and high pressures (up to 8 GPa) have been investigated and compared with the previous studies on the crystalline fullerite. The study was conducted using neutron diffraction and Raman spectroscopy. The amorphous fullerite was obtained by ball-milling. We have shown that under thermobaric treatment no crystallization of amorphous fullerite into С₆₀ molecular modification is observed, and it transforms into amorphous-like or crystalline graphite. A kinetic diagram of phase transformation of amorphous fullerite in temperature–pressure coordinates was constructed for the first time. Unlike in crystalline fullerite, no crystalline polymerized phases were formed under thermobaric treatment on amorphous fullerite. We found that amorphous fullerite turned out to be less resistant to thermobaric treatment, and amorphous-like or crystalline graphite were formed at lower temperatures than in crystalline fullerite.     

1H-ENDOR investigations on gamma-irradiated betaine calcium chloride dihydrate at room temperature

The ENDOR technique is applied to study the structure of the free radical N(CH₃)₃, found in the high temperature phase in the incommensurate crystal BCCD after γ-irradiation. The radical possesses a planar structure with strong deviation from the C₃ symmetry. The hybridization of the nitrogen atom is sp². Each of the three methyl groups exhibits a single ENDOR line, indicating the rotation of groups at room temperature. The deviation of the¹H hyperfine tensors of the methyl groups from axial symmetry is not a hint as to a hindered rotation of the groups. This is predicted by the C₂ symmetry of the system consisting of a π orbital and a rotating CH₃ group.     

Neutron diffraction study of the interaction of iron with amorphous fullerite

The amorphous fullerite C₆₀ has been prepared by mechanical activation (grinding in a ball mill), and its interaction with iron during sintering of powders with 0–95 at % Fe has been studied. After sintering in the range 800–1200°C under a pressure of 70 MPa, the samples have nonequilibrium structures different from the structures of both annealed and quenched steels. In this case, the carbon phase, i.e., amorphous fullerite, undergoes a polyamorphous transition to amorphous graphite. It has also been shown that the interaction of amorphous fullerite with iron is weaker compared to crystalline fullerite or crystalline graphite.     

Calculation of thermodynamic properties for the high-temperature phase of C70 fullerene

An approach of calculating thermodynamic properties of the high-temperature modification of C₆₀ is extended to C₇₀. For the intermolecular forces we use the potential proposed by Verheijen et al. which has been derived by summing Girifalco potentials over the 25 pairs of interacting atomic shells in each pair of molecules. We have calculated the normal isobar of the fcc phase which is dominant at high temperatures and its spinodal point. Taking into account available information about the vibrational spectrum of the C₇₀ molecule, thermodynamic properties have been calculated, including components of the elastic tensor.     

Temperature-pressure phase diagram of CsHSO4

Abstract

On the basis of group theoretical analysis of phase transitions between the phases with known space symmetries the space symmetries of high pressure phases are theoretically predicted. A part of temperaturepressure phase diagram of CsHSO₄ in the region of high temperatures and pressures is theoretically constructed. It is shown that the new pahse of the C¹ _2h space symmetry can be observed at high pressures.     

Lattice dynamics and praphase in N-bensylanyline crystals

N-benzylanyline single crystals are grown, and X-ray diffraction probing of their structure allows their symmetry to be attributed to the C_2h.⁵ phase. Polarized Raman studies of these crystals allow the frequencies of lattice phonons to be estimated and their symmetry to be established. The abnormal behavior of the two lowest-frequency A_g symmetry soft modes, the condensation of which is not detected below the melting point (36–38°C), is noted. The possibility of a high-temperature virtual phase transition and praphase is discussed. Theory group consideration of the praphase allows determination of its symmetry and the symmetry of phonons related to the virtual phase transition.     

Incommensurate phases induced by an electric field

All magnetic symmetry classes for which the two-dimensional representations are physically irreducible are enumerated. These representations admit of the Lifshitz invariant induced by an external electric field aligned parallel to the principal axis of the crystal. In the majority of the cases, this field does not split two-dimensional representations into one-dimensional representations and, therefore, an incommensurate phase arises in an arbitrarily weak field. The representations of the magnetic classes C _4h and C′_4h are considered in close detail. The components of the toroidal momentum are chosen as the components of the order parameter.     

Energy spectrum and phase transitions in C70 fullerite crystals at high pressure

Measurements have been made of the Raman, optical absorption, and luminescence spectra of single crystals and pellets of the fullerite C₇₀ at T=300 K and at pressures up to 12 GPa. The baric shift dω/dP and the Grüneisen parameters of the Raman-active intramolecular phonon modes have been determined. It has been established that the d ω/dP value for certain phonon modes abruptly changes at pressures of P ₁≈2 GPa and P ₂≈5.5 GPa, as do the half-widths of the Raman lines. These features in the Raman spectrum are associated with phase transitions at high pressure. The baric shifts of the absorption and luminescence edges of C₇₀ crystals have been determined and are −0.12 eV/GPa and −0.11 eV/GPa, respectively, for absorption and luminescence. The baric shift of the absorption edge decreases significantly with increasing pressure and is −0.03 eV/GPa at 10 GPa. These data have been used to determine the deformation potential of the fullerite C₇₀, which is about 2.1±0.1 eV. Zh. éksp. Teor. Fiz. 111, 262–273 (January 1997)