Eu@C86 isomers: Calculated relative populations

Abstract

Relative populations of four energy-lowest IPR (isolated-pentagon-rule) isomers of Eu@C₈₆ are computed using the Gibbs energy based on characteristics from density functional theory calculations (M06-2X/3-21G?～?SDD entropy term, M06-2X/6-31G*～SDD or B2PLYP(D)/6-31G*～SDD energetics). The calculations confirm that the recently isolated Eu@C₁(7)-C₈₆ species is a major isomer in a relevant temperature region. Relationship to the empty C₈₆ cages is discussed, too.     

Evaluation of the relative stabilities of two non-IPR isomers of Sm@C76

Density-functional theory calculations are presented for two low-energy Sm@C₇₆ isomers with the isolated-pentagon rule (IPR) violating cages. The relative isomeric populations at high temperatures are evaluated using the calculated molecular terms and relationships to observations are discussed. It is shown that the observed Sm@C_2v(19138)-C₇₆ species can be computed as the major isomer if the encapsulate motions are treated as relatively restricted. With the restriction conjecture, the major isomer is about two times more populated than the minor Sm@C₁(17459)-C₇₆ endohedral. The study points out the importance of symmetry considerations in stability evaluations for general nanocarbons.     

Computations on Metallofullerenes Derivatized during Extraction: La@C80-C6H3Cl2 and La@C82-C6H3Cl2

Recently, an extraction of la metallofullerenes from soot using 1,2,4-trichlorobenzene has been reported for La@C₈₀ and La@C₈₂. In both cases, the cages were derivatized by the solvent (forming La@C₈₀-C₆H₃Cl₂ and La@C₈₂-C₆H₃Cl₂) and the following X-ray analysis disclosed rather unexpected cages: C₈₀(C _2v ;3) and C₈₂(C _3v ;7). In order to explain the challenging observations, a two-step computational treatment is presented. The first step deals with the high-temperature gas-phase formation of the underivatized endohedrals while the second step models the reaction with the solvent. The Gibbs free energies were evaluated for representative temperatures and the computational scheme was able to confirm high relative populations for the observed derivatized cages.     

Calculations of the water-dimer encapsulations into C84

The water-dimer formation and its encapsulation into D₂(22)-C₈₄ and D_2d(23)-C₈₄ fullerenes is evaluated. The water-dimer populations are computed using the potential-energy change from the G3 theory and anharmonic partition functions from the MP2/AUG-cc-pVQZ approach. The encapsulation energetics is treated at the M06-2X/6-31++G** level and it is found that the water-dimer storage in C₈₄ is attractive, yielding an energy gain of more than 10 kcal mol^?1. This substantial encapsulation energy together with the computed temperature increase of the water-dimer population in the saturated steam suggests that the (H₂O)₂@C₈₄ endohedrals could be produced in a high-temperature/high-pressure approach similarly to encapsulation of rare gases in fullerenes.     

Sc2O@C78: Calculations of the yield ratio for two observed isomers

The very recently observed production ratio 3:1 between Sc₂O@C₇₈(C_2v/3) and Sc₂O@C₇₈(D_3h/5) endohedrals can be reproduced in quantum-chemical calculations though only after a transition from the DFT to MP2 approach. It is concluded that the C_2v/3-cage-based species should be lower in the potential energy by about 1.5 kcal/mol.     

A Bent Tb2C2 Cluster Encaged in a CS (6)-C82 Cage: Synthesis,Isolation and X-ray Crystallographic Study

Terbium (Tb)-based dimetallofullerene, Tb₂C₈₄, has been synthesized and isolated by multistep HPLC. According to the UV-vis-NIR spectroscopic characterization and comparison with the reported analogous M₂C₈₄ (M = Sc, Y) metallofullerenes, the molecular structure of Tb₂C₈₄ is proposed to be Tb₂C₂@C_s (6)-C₈₂ featuring a metal carbide clusterfullerene (CCF) structure, which is unambiguously confirmed by X-ray crystallographic study. A detailed analysis of the crystal structure of a cocrystal of Tb₂C₂@C_s (6)-C₈₂·Ni^II(OEP)·2C₆H₆ (Ni^II(OEP) = nickel (II) octaethylporphyrin) reveals that a bent Tb₂C₂ carbide cluster is encaged rigidly inside a C_s (6)-C₈₂ cage. The C-C bond within the encaged Tb₂C₂ carbide cluster behaves as a typical C-C triple bond. The asymmetric unit in Tb₂C₂@C_s (6)-C₈₂·Ni^II(OEP)·2C₆H₆ contains two fullerene sites, for which the encaged Tb₂C₂ carbide cluster however locates at nearly the same position with one Tb atom being beneath a hexagon and another Tb atom pointing to the conjunction of two adjacent hexagons.     

A methyl parathion electrochemical sensor based on Nano-TiO2, graphene composite film modified electrode

A methyl parathion electrochemical sensor based on nano-TiO₂ and graphene composite film modified glassy carbon electrode has been developed. The electrochemical behavior of MP at the sensor was investigated by cyclic voltammetry and linear sweep voltammetry. Scanning electron microscopy was used to characterize the surface morphology of nano-TiO₂ and graphene composite film. Compared with a bare glassy carbon electrode or a mono-film modified electrode, the redox peak currents of methyl parathion on the composite film modified electrode improved greatly, indicating that the sensor showed good catalytic effects. The optimal experimental condition was obtained. The results indicated that the linear sweep voltammetry responses of methyl parathion, in pH 5.2 acetate buffer solution with open-circuit accumulation for 2 min, were linear with concentrations of methyl parathion in two ranges of 0.002～5 μM and 5～100 μM. The linear equations were i_Pc(μA) = 0.0136 + 4.965c_MP(μM) (R₁² = 0.9911) and i_Pc(μA) = 21.87 + 0.8206c_MP(μM) (R₂² = 0.9914), respectively. The detection limit was 1.0 nM (S/N = 3). The sensor exhibited high sensitivity and good reproducibility as well as certain anti-interference ability. It was applied to the determination of residual MP in fresh apple sample with the recovery of 92%～102%. The result was satisfactory.     

Two-gap superconductivity in R2Fe3Si5 (R=Lu,Sc) and Sc5Ir4Si10

Abstract

R₂Fe₃Si₅ (R= Sc, Y, Lu) contains nonmagnetic iron and has a relatively high superconducting transition temperature T_c among iron-containing superconductors. An anomalous temperature dependence of specific heat C(T) has been reported for polycrystalline samples down to 1 K. We have grown R₂Fe₃Si₅ single crystals, confirmed the anomalous C(T) dependence, and found a second drop in specific heat below 1 K. In Lu₂Fe₃Si₅, we can reproduce C(T) below T_c, assuming two distinct energy gaps 2Δ ₁/k_BT_c = 4.4 and 2Δ ₂/k_BT_c = 1.1, with nearly equal weights, indicating that Lu₂Fe₃Si₅ is a two-gap superconductor similar to MgB₂. Hall coefficient measurements and band structure calculation also support the multiband contributions to the normal-state properties. The specific heat in the Sc₂Fe₃Si₅ single crystals also shows the two-gap feature. R₅Ir₄Si₁₀ (R = Sc, rare earth) is also a superconductor where competition between superconductivity and the charge-density wave is known for rare earths but not for Sc. We have performed detailed specific heat measurements on Sc₅Ir₄Si₁₀ single crystals and found that C(T) deviates slightly from the behavior expected for weak-coupling superconductors. C(T) for these superconductors can also be reproduced well by assuming two superconducting gaps.     

Hot hardness of (Fe,Cr)3C and (Fe,Cr)7C3 carbides

Hot hardness was measured on the primary carbides, (Fe, Cr)₃C and (Fe, Cr)₇C₃, in unidirectionally solidified iron-carbon-chromium hypereutectic alloys with chromium more than 4.8 wt %. The hardness-temperature relation was represented by two Ito-Shishokin formulae,H _v =A(— BT), and thus was drawn by two lines on a semilogarithmic graph. The inflection temperature where the two lines intersected was found at 730 to 860 K for (Fe, Cr)₃C carbide containing 0 to 14 wt % Cr, increasing with an increase in the chromium concentration in the carbide, and at about 910 K for (Fe, Cr)₇C₃ carbide containing 36 to 76 wt % Cr. With increasing chromium concentration in each carbide, the hardness of the carbide increased and the thermal softening coefficients decreased. The effect of chromium on the hardness, the inflection temperature and the thermal softening coefficients was more pronounced for (Fe, Cr)₃C carbide than for (Fe, Cr)₇C₃ carbide. Each of the thermal softening coefficients,B ₁(T<T _t),B ₂(T>T _t), the inflection temperature,T _t, room-temperature hardness,H _v(T _RT), and the hardness atT _t,H _v(T _t), related linearly to the chromium concentration in the carbides, and hence the hot hardness of the carbides could be expressed as functions of temperature and chromium concentration in the carbides. The relationships betweenH _v(T _RT) andH _v(T _t) and between the thermal softening coefficient,B ₂, and the activation energy for creep,Q _c(kJ mol^–1), were represented by the following equations:H _v(T _t)0.7H _v(T _RT),B ₂=1.26/Q _c.     

Anharmonic effects in the specific heat of aluminum

The specific heat at constant pressure, C _p , of aluminum has been measured by Leadbetter between 300 and 772 K and by Brooks and Bingham between 330 and 893 K. Both sets of data are converted to the specific heat at constant 0 K volume, C _v0, by the Slater-Overton method, based on the equation of state and not the Debye type of theory. Corrections to the work of Overton are given. Our analysis shows that the C _v0 obtained from Leadbetter's data remains below 3R up to 750 K, whereas it becomes >3R for the Brooks and Bingham data in the temperature range 650–850 K. Calculations of C _v0 (harmonic + anharmonic) from three pseudopotentials are reported for (a) Harrison modified point ion potential with Hubbard exchange and correlation factor in the dielectric function, (q); (b) Ashcroft pseudopotential with the same (q) as in (a); and (c) Dagens-Rasolt-Taylor (DRT) M2 pseudopotential with Geldart-Taylor (q). The shape of the C _v0 curve is found to be similar for all three potentials. For DRT potential, C _v0 reaches 3R at 700 K, whereas the other two barely approach 3R about 900 K. The anharmonic contribution to C _v0 is a factor of two larger for the Dagens et al. compared to the other two potentials. There is a marked difference between the C _v0 curve from the analysis of the Brooks and Bingham data and the theoretical curves. It appears that the experimental points are too high from about 500 K up. The C _v0 curve from Leadbetter's data is very similar to the three theoretical curves, but the results appear to be too low. A remeasurement of the specific heat from 500 K to the melting point is needed.     

Extraction of Critical Current Density and Flux Creep Exponent in the Magnetic Superconductor Ru-1212 Using the ac Magnetic Susceptibility Measurements

The ac susceptibility data was employed to extract the temperature dependence of the critical current density, J _c(T), as well as the variation of flux-creep exponent n(T,H _ac) with temperature and ac field amplitude in bulk samples of polycrystalline magnetic superconductor RuSr₂GdCu₂O₈ (Ru-1212). The critical state models and the collective flux-creep approximation model were successfully accounted to describe such behavior below the transition temperature. The calculated values of n(T,H) are well fitted to a power law of the following form: n(T,H)=n ₀(H)T ^−s(H), where s is field dependent exponent whose values varied from −2.4, −1.01 for field amplitudes ranging from 0.5 G and 3.8 G. The power law describing the frequency dependence of χ′ is found to be consistent with the results of the current-dependent effective activation energy of the form U(J)=U ₀ln (J _c/J). Additionally, the dependence of the current density is found to scale according as: J _c(T)=J _c0(1−T/T _c) ⁿ , where the exponent n values varied from 1.05 to 1.25. Such dependence is an indication of intergrain coupling that could be ascribed in terms of superconductor–insulator–superconductor junctions. The derived temperature dependence of J _c(T) is in good agreement with the data obtained from the measurements using the traditional “loss-maximum” approach. Furthermore, the flux-creep effect increased with increasing both ac fields and temperatures except at about 15–25 K below the onset of T _c, where a slowing down of the flux creep was observed.     

Molar Heat Capacity at Constant Volume of Trifluoromethane (R23) from the Triple-Point Temperature to 342 K at Pressures to 33 MPa

Molar heat capacities at constant volume (C _v) of trifluoromethane (R23) have been measured with an adiabatic calorimeter. Temperatures ranged from the triple point to 342 K, and pressures up to 33.5 MPa. Measurements were conducted on the liquid in equilibrium with its vapor and on compressed liquid and gaseous samples. The samples were of high purity, as verified by chemical analysis. Calorimetric quantities are reported for the two-phase (C ⁽²⁾ _v), saturated-liquid (C or C_x), and single-phase (C _v) molar heat capacities. The C ⁽²⁾ _v data were used to estimate vapor pressures for values less than 100 kPa by applying a thermodynamic relationship between the two-phase internal energy U ⁽²⁾ and the temperature derivatives of the vapor pressure. The triple-point temperature and the enthalpy of fusion were also measured. The principal sources of uncertainty are the temperature rise measurement and the change-of-volume work adjustment. The expanded relative uncertainty (with a coverage factor k=2 and thus a two-standard deviation estimate) is estimated to be 0.7% for C _v, 0.5% for C ⁽²⁾ _v, and 0.7% for C .     

Pseudogap Behavior in the Electronic Specific Heat of La2−xSrxCuO4

In La214, the electronic specific heat coefficient (=C _el /T) is gradually suppressed with lowering T below a certain temperature T* (> T _c ), where the in-plane resistivity and magnetic susceptibility also tend to be suppressed slightly. Temperature T*, increasing with lowering x, is in qualitative agreement with the mean field T _c (T _co ), estimated from the superconducting gap amplitude 2 _o at T T _c , as the onset temperature T* of a pseudogap in Bi2212. The gradual suppression of below T _co implies that a pseudogap will also open up below T _co in La214 as in Bi2212. In underdoped samples, whose pseudogap-like behaviors in C _el(T) become marked, the anomaly of C _el around T _c is rather different from the BCS expectation.     

Mixed-State Specific Heat of the Type-II Superconductor Nb0.77Zr0.23 in Magnetic Fields up toB c2

In order to document the behavior of the mean-field mixed-state specific heat of an isotropic. strongly type-II superconductor (i.e., with a large value of the Ginzburg parameterk), and to provide a basis for comparison with high-temperature superconductors, we measured the specific heatC of the alloy Nb_0.77Zr_0.23 withT _c = 10.8K, B _c2 (0) = 7.9T, in magnetic fieldsB = 0, 0.2, 1.0, 12, 2.0, 2.4. 3.0, 3.3. 4.0. 4.4, 4.8, 5.2, 6.0. 6.6, 7.2 and 10 T. The values of the upper critical fieldB _c2 ( T), thermodynamic critical fieldB _c (T), Ginzburg parameterk(T), and coefficient γ(B) = lim_{T0(C(T. B)/T)} are derived from the specific heat data and found to be in agreement with the GLAG theory in the dirty limit. The behavior of the mixed-state specific heat is analyzed in terms ofC _el /T,∂(C _el /T)/∂B, and∂(C _el /T)/∂T vs. Tcurves, whereC _el is the electronic contribution to the specific heat.     

Inelastic neutron scattering results on pure and doped fullerenes

Via inelastic neutron scattering (INS) generalized phonon densities of states are obtained for C₆₀ and superconducting A₃C₆₀ (A=K, Rb). Changes in the intramolecular modes agree with and augment recent Raman (RA), infrared (IR), and INS measurements, i.e., in the vicinity of the high-frequency modes of C₆₀ [H _g (8),A _g (2),H _g (7)] we find a pronounced shift of about 10 meV toward smaller energy transfers upon intercalating with potassium. Separated from these vibrations by a gap are the intermolecular spectra which for the doped samples display well-defined optic modes at 11 and 14 meV due to the vibrations of Rb and K ions. Indications of a weak anomalous temperature dependence of low-energy phonons ( <3 meV) nearT _c are observed for K₃C₆₀.     

Depression of the superfluid transition in4He

We study superfluid⁴He near T in a homogeneous metastable state where a finite superfluid velocity v_s is present. Neglecting vortices we perform a renormalization-group calculation of the critical velocity v_sc(T) at which the superfluid state becomes unstable. We apply this result to the situation where the superfluid velocity is induced by a finite heat current Q. A critical heat current Q_c(T) corresponding to v_sc(T) is found which implies a transition temperature T (Q)=T[1–A_oQ^x]. We determine the exact exponent x=[(d–1)v] ^–1 0.744 in d=3 dimensions and calculate A_o in one-loop order. Our results for A_o and x are compared with recent experimental data.     

Thermal and magnetic measurements on YBa2Cu3O7−y

Specific heat measurements in zero and7T magnetic fields from 0·4 to 100 K, and magnetic susceptibility measurements aboveT _c on a series of polycrystalline samples of YBa₂Cu₃O_7−y (YBCO) reveal a number of regularities. The size of ΔC(T _c )/T _c for the samples [ΔC(T _c ) is the jump in the specific heat atT _c ] appears to vary linearly with the low-temperature value of the Debye Θ, with the entropy change between ≈ 85 K andT _c induced by the application of a 7 ^Г magnetic field, and with the variation of the observed low temperatureγ with magnetic field, dγ/dH. On the other hand the temperature-independent part of the magnetic susceptibility aboveT _c appears to be essentially independent of ΔC(T _c )/T _c . These results are consistent with the idea that samples of YBCO belowT _c are a mixture of superconducting and normal phases. Supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S. Dept. of Energy under Contract DE-AC03-76SF00098, and by an EXXON Education Grant from the Research Corporation.     

Thermodynamic functions for the formation of isomeric CF3 adducts of C70 and C84

Gas-phase formation enthalpies and Gibbs energies of formation (Δ_fH°_m; Δ_fG°_m) of trifluoromethylderivatives of fullerenes C₇₀ and C₈₄ are calculated at the DFT (density functional theory) level of theory. The approach employs homodesmic (HD) transtrifluoromethylation reactions and experimental thermochemical data on C₆₀, C₇₀, C₈₄ and S₆-C₆₀(CF₃)₁₂.     

Intrinsic and extrinsic mechanisms of vortex formation in superfluid3He-B

We report on the first comprehensive measurements of critical superflow velocities in³He-B which allow different mechanisms of vortex formation to be identified. As a function of temperatureT and pressureP, we measure the critical angular velocity Ω_c(T, P) at which vortices start to form in slowly accelerating rotation in a cylindrical container filled with³He-B. Owing to the long coherence length ξ(T, P)∼10–100 nm, either trapped remanent vorticity or intrinsic nucleation may dominate vortex formation, depending on the roughness of the container wall and the presence of loaded traps. NMR measurement with a resolution of one single vortex line allows us to distinguish between different processes: (1) Three extrinsic mechanisms of vortex formation have been observed. One of them is the vortex mill, a continuous periodic source which is activated in a rough-walled container well below the limit for intrinsic nucleation. (2) In a closed smooth-walled container intrinsic nucleation is the only mechanism available, with a critical velocity v_c(T, P)=Ω_c(T, P), whereR is the radius of the container. We findv _c (T, P) to be related to the calculated intrinsic stability limitv _ch (T, P) of homogeneous superflow. The existence of this connection in the form of a scaling law implies that nucleation takes place at an instability, rather than by thermal activation or quantum tunneling which become impossible because of an inaccessibly high energy barrier.