Thermodynamic and dilatometric properties of the dimerized phase of a C<Subscript>60</Subscript> fullerene

This paper reports on the results of complex investigations into the structural, thermodynamic, and dilatometric properties of the C₆₀ dimerized phase prepared under compression of a C₆₀ fullerite at a pressure up to 8 GPa and a temperature of 290 K. It is demonstrated that the dimerized phase has a face-centered cubic structure with a lattice parameter a=14.02±0.05 Å. The dimeric structure of the studied sample is confirmed by x-ray diffraction analysis. According to the dilatometric data, the volume jump observed in the vicinity of the orientational transition for the dimerized phase is estimated to be approximately 30 times less than that for the C₆₀ fullerite. The temperature dependence of the heat capacity of the (C₆₀)₂ crystalline dimer is examined using precision adiabatic vacuum calorimetry under normal pressure in the temperature range from T → 0 K to 340 K. The results obtained are used in the calculations of thermodynamic functions, namely, the heat capacity C _p ⁰ (T), the enthalpy H⁰(T)-H⁰(0), the entropy S⁰(T), and the Gibbs function G⁰(T)-H⁰(0). The fractal dimension D is determined as a function of the heat capacity. The standard entropy of the formation of the (C₆₀)₂ crystalline dimer from a simple compound (graphite) at T=298.15 K and normal pressure is calculated.     

Thermodynamic Study of Formamidinium Lead Iodide (CH5N2PbI3) from 5 to 357 K

In the present study, the molar heat capacity of solid formamidinium lead iodide (CH₅N₂PbI₃) was measured over the temperature range from 5 to 357 K using a precise automated adiabatic calorimeter. In the above temperature interval, three distinct phase transitions were found in ranges from 49 to 56 K, from 110 to 178 K, and from 264 to 277 K. The standard thermodynamic functions of the studied perovskite, namely the heat capacity C°_p(T), enthalpy [H⁰(T) − H⁰(0)], entropy S⁰(T), and [G°(T) − H°(0)]/T, were calculated for the temperature range from 0 to 345 K based on the experimental data. Herein, the results are discussed and compared with those available in the literature as measured by nonclassical methods.     

Stoichiometric synthesis of fullerene compounds with lithium and sodium and analysis of their IR and EPR spectra

A modified method is proposed for preparing fullerene compounds with alkali metals in a solution. The compounds synthesized have the general formula Me _n C₆₀(THF)_x, where Me = Li or Na; n=1–4, 6, 8, or 12; and THF = tetrahydrofuran. The use of preliminarily synthesized additives MeC₁₀H₈ makes it possible to prepare fullerene compounds with an exact stoichiometric ratio between C ₆₀ ^n? and Me ⁺. The IR and EPR spectra of the compounds prepared are analyzed and compared with the spectra of their analogs available in the literature. The intramolecular modes T _u (1)-T _u (4) for the C ₆₀ ^n? anion are assigned. The splitting of the T _u (1) mode into a doublet at room temperature for Me _n C₆₀(THF)_x (n=1, 2, 4) compounds indicates that the fullerene anion has a distorted structure. An increase in the intensity of the T _u (2) mode, a noticeable shift of the T _u (4) mode toward the long-wavelength range, and an anomalous increase in the intensity of the latter mode for the Li₃C₆₀(THF)_x complex suggest that, in the fullerene anion, the coupling of vibrational modes occurs through the charge-phonon mechanism. The measured EPR spectra of lithium-and sodium-containing fullerene compounds are characteristic of C ₆₀ ^? anions. The g factors for these compounds are almost identical and do not depend on temperature. The g factor for the C ₆₀ ^n? anion depends on the nature of the metal and differs from the g factor for the C ₆₀ ^? anion.     

Thermodynamic properties of (NH4)2KGaF6 elpasolite

The heat capacity of (NH₄)₂KGaF₆ elpasolite is measured in the temperature range from 80 to 350 K. A sequence of three phase transitions at T ₁=288.5 K, T ₂=250 K, and T ₃=244.5 K is revealed, and the thermodynamic characteristics of these transitions are determined. The influence of hydrostatic pressure on the phase transition temperature is investigated. The results obtained are discussed within the model of orientational ordering of NH ₄ ⁺ and GaF ₆ ^3? ionic groups.     

A computational study of entropy rules for charged fullerenes

Thermochemical data on fullerenes are relatively scarce. However, some thermochemical information can be derived from gas-phase experiments using the Knudsen cell mass spectrometry method. The third-law treatment can be carried out on the observed data, though one has to make the crucial presumption that the change in the thermodynamic potential ΔΦ _T ^o in the course of the reactions considered is negligible: ΔΦ _T ^o =0. It would be difficult to check the presumption directly in the experiment, but it can be checked computationally. Model reactions like C₆₀+ ₇₀ ^? = ₆₀ ^? +₇₀ are selected. The change in the thermodynamic potential ΔΦ _T ^o and the change in the standard entropy ΔS _T ^o are computed. For example, at a temperature of T=1000 K, the standard changes for the reaction evaluated using the SAM1 method are ΔΦ _T ^o =1.513 cal/(mol K) and ΔS _T ^o =?0.054 cal/(mol K). Overall, the computations support the critical thermodynamic presumption.     

Electronic properties of charged fullerenes characterized by EPR and Vis-NIR spectroscopy

EPR and Vis-NIR absorption spectra have both been measured for clarification of contradictory statements about the para-and diamagnetic states of fullerenes. Thereby identification of one sharp EPR signal in solution at room temperature to C ₆₀ ^? (g=2.000±4.0001; ΔB=0.07±0.01 mT) could be made upon using different fullerene sources (TechnoCarbo, Hoechst) and methods of anion generation (chemically, electrochemically, and photochemically). This fact is also supported by the similar observation for a monosubstituted derivative (g=1.9999; ΔB=0.10 mT), in which a small broadening of this sharp signal is found originating from additional¹H hyperfine interactions. Furthermore theg-values of the radical anions of C₆₀ increase with charge (g(C ₆₀ ^? <g(C ₆₀ ^2? ) < <g(C ₆₀ ^3? ) <g(C ₆₀ ^5? )) indicating largest contributions from spin-orbit coupling for the monoanion. No diamagnetic states for the dianions of [60]- and [70]- fullerenes could be found so far but biradical species with largest zero field splittingsD=2.7 mT (C ₆₀ ^2? ), andD=3.1 mT (C ₇₀ ^2? ), respectively. The cation formation of C₆₀ (g=2.0023-2.0029; ΔB=0.15-0.20 mT) with antimony pentachloride was controlled by mass spectrometry. Stable cations were found only in methylenechloride. In other solvents like toluene addition reactions seem to occur.     

Study of spin-wave dynamics in Fe65Ni35 ferromagnetic via small-angle polarized-neutron scattering

The results of studying the spin dynamics of a classical Fe₆₅Ni₃₅ invar alloy are presented and analyzed. The investigations are performed via small-angle polarized-neutron scattering in the oblique geometry of a magnetic field at various temperatures (T < T _C). This approach is based on the analysis of left-right asymmetry in the magnetic scattering of polarized neutrons. The asymmetry effect arises when the magnetization direction of a sample is inclined with respect to the wave vector of the incident beam. The spin-wave scattering is concentrated within a range bounded by the cutoff angle θ_c determined by the magnetic field: θ _c ² (H) = θ ₀ ² ?(gμ_B H)θ₀/E, where \(\theta _0 = \hbar ^2 \frac{1} {{2Dm_n }}\) , H is the external magnetic field, E is the initial neutron energy, D is the spin-wave stiffness constant, and m _n is the neutron mass. The scattering is blurred by spinwave damping in the vicinity of the cutoff angle. The spin-wave stiffness constant can be obtained from a comparison of the asymmetric contribution to scattering and a model function. The temperature dependence D = D(T) is well defined by the expression D = D ₀ |τ| ^x , where \(\tau = 1 - \frac{T} {{T_C }}\) , x = 0.47 ± 0.01, D ₀ = 137 ± 3 meVŲ, and τ > 0.1 in the entire temperature range. The given method enables us to construct the temperature dependence of the spin-wave stiffness constant with a high accuracy and a small step.     

Optical Properties of Solid Pseudoisocyanine Films Doped with Cluster Derivatives of Boron Hydrides

The formation and optical properties of J aggregates of pseudoisocyanine iodide in solid films in the presence of cluster anionic derivatives of boron hydrides and carboranes (B₁₀H ₁₀ ^2- , B₁₂H ₁₂ ^2- , B₂₀H ₁₈ ^2- , [Ni^IV(1,2-B₉C₂H₁₁)₂]⁰, 1,2-B₉C₂H ₁₂ ^- , [Co(1,2-B₉C₂H₁₁)₂]^-, [Ni(1,2-B₉C₂H₁₁)₂]^-, B₁₀H₈I ₂ ^2- , [Sn(1,2-B₉C₂H₁₁)]⁰) are studied. It is shown that the addition of anions B₁₀H ₁₀ ^2- or B₁₀H₈I ₂ ^2- leads to an efficient formation of stable J aggregates. The addition of carborane complex of nickel [Ni^IV (1,2-B₉C₂H₁₁)₂]⁰ also leads to the formation of J aggregates, although less stable ones. Carborane complex of tin [Sn^II(1,2-B₉C₂H₁₁)]⁰ facilitates the formation of a monomeric form of the dye. The remaining compounds yield no distinct pattern of formation of a certain monomeric or J-aggregated film structure. With the aid of the semiempirical AM1 method, the charge distributions in the cation of the dye and anionic derivatives of the boron hydrides are calculated. It is supposed that the bipolar distribution of a negative charge in the B₁₀H ₁₀ ^2- anion facilitates the formation of a J aggregate. By addition of salts of organic cations to a film of pseudoisocyanine-closo-hydrodecaborate (PCG), J aggregates with a narrow width of the J peak are obtained. The thermal decay of J aggregates in these films is studied. On the basis of the data obtained (the presence of an isosbestic point upon thermal decomposition of J aggregates and their reaggregation; the narrowing and increasing of the J absorption peak, as well as increasing of luminescence, upon dilution of a J-aggregated PCG film with organic cations; and the bipolar character of the electrostatic interaction of the B₁₀H ₁₀ ^2- anion with the dye), it is assumed that the J peak of pseudoisocyanine in the films studied corresponds to the absorption of a dimeric form of the dye.     

Scaling behavior of the Hall coefficient of Si:P at the metal-insulator transition

Measurements of the Hall coefficient R _H (T, B) of Si:P with P concentration N between 3.54 and 7.0·10¹⁸ cm^?3 are reported for the temperature range 0.04 K ≤ T ≤ 4K and in magnetic fields up to 7 T. Even far above the metal-insulator transition (MIT), a sign change of the temperature coefficient similar to the behavior of the conductivity σ(T) in moderate fields is not observed in R _H (T). Field and temperature dependence of R _H both increase as the MIT (at the critical concentration N _c = 3.52 · 10¹⁸ cm^?3) is approached. A careful extrapolation to T → 0 and B → 0 indicates that R _H ^?1 scales to zero as R _H ^?1 ～| N ? N _c ^μH with μ _H = (0.44 ± 0.04) in agreement with previous results.     

Continuous measures in one dimension

Families of unimodal maps satisfying

1. T _λ: [?1,1]?[?1,1] withT(±1)=?1 and |T _λ ^′ (1)|>1.
2. T _λ(x) isC ² inx ² and λ, and symmetric inx.
3. T ₀(0)=0,T ₁(0)=1 with \(\frac{d}{{d\lambda }}\) T _λ(0)>0

are considered. The results of Guckenheimer (1982) are extended to show that there is a positive measure of λ for whichT _λ has a finite absolutely continuous invariant measure. The appendix contains general theorems for the existence of such measures for some markov maps of the interval.     

On the signatures of the canonical and the metrical energy densities of vector fields

The energy-density components Θ ₀ ⁰ andT ₀ ⁰ of the canonical and of the metrical energy-momentum tensors Θ _k ⁱ andT _k ⁱ for a statical field of vector mesons have opposite signatures: Θ ₀ ⁰ =H=?T ₀ ⁰ =?L. From this property some relativistic and field-theoretical theorems can be deduced in an elementary way.     

Effect of γ irradiation on the structural and thermal properties of [N(C2H5)4]2ZnBr4 in the vicinity of a first-order phase transition

The unit cell parameters a and c of nonirradiated [N(C₂H₅)₄]₂ZnBr₄ crystals in the temperature region 90–300 K and of samples irradiated with γ rays to doses of 10⁶ and 5 × 10⁶ R in the 270-to 300-K interval were measured using x-ray diffraction. The data obtained were used to derive the thermal expansion coefficients α_a and α_c. It is shown that the parameter a increases and the parameter c decreases with increasing temperature. In the vicinity of the phase transition (PT) at T = 285 K, the temperature dependences of a(T) and c(T) reveal anomalies in the form of jumps and the α_a(T) and α_c(T) curves have a maximum and a minimum, respectively. The heat capacity of nonirradiated and irradiated [N(C₂H₅)₄]₂ZnBr₄ samples was measured by adiabatic calorimetry. A maximum was found in the C _p(T) curve at T = 285 K. Both x-ray diffraction and heat capacity measurements showed that the PT temperature decreased after γ irradiation.     

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to lights d-shell nuclei. The key ingredients of our approach are:a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure;b) two successive unitary transformations that extract the “maximally decoupled” collective bosons with angular momentaJ=0(s _ππ ⁺ ,s _νν ⁺ ,s _πν ⁺ ) andJ =2(d _ππ ⁺ ,d _νν ⁺ ,d _πν ⁺ (T=0),d _πν ⁺ (T=1)). The method is applied to obtain the low-energy spectra and the electron scattering form factors for the 0 ₁ ⁺ →2 ₁ ⁺ transitions in²⁰Ne and²⁴Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s _πν ⁺ ,d _πν ⁺ (T=1),d _πν ⁺ (T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.     

Computable upper bounds for the adiabatic approximation errors

For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.     

Thermodynamic study of compounds of the Nd-Ba-Cu-O system

Standard enthalpies of formation for solid solutions of composition Nd_{1 + x} Ba_{2 ? x} Cu₃O _y (x = 0–0.8, y = 6.65–7.24) from oxides were determined by solution calorimetry. The heat capacity of NdBa₂Cu₃O_6.87 phase was measured in the range 5–320 K by low-temperature adiabatic calorimetry. The absolute entropy S ^o(T), the difference of enthalpies H ^o(T)-H ^o(0 K), and the reduced Gibbs energy Φ^o(T) = S ^o(T)–[H ^o(T)–H ^o(0)]/T were calculated on the basis of smoothed dependence C _p (T) in the 0–320 K range. An assessment was made for the heat capacities and the absolute entropies of solid solutions Nd_1+x Ba_2?x Cu₃O _y . The obtained set of thermodynamic parameters can be used for the calculation of phase equilibria in the Nd-Ba-Cu-O system.     

Effect of γ irradiation on the heat capacity of (CH3)2NH2Al(SO4)2 · 6H2O crystals near the ferroelectric phase transition

The heat capacity of dimethyl ammonium-aluminum sulfate crystals (DMAAS), both nonirradiated and γ-irradiated to fluences of 10⁷, 5×10⁷, and 10⁸ R, has been measured by the adiabatic method near the ferroelectric phase transition (PT) within the 80–300 K temperature range. The C _p =f(T) curve exhibits a λ-shaped anomaly near the phase-transition point T _C =152 K. The PT temperature and the magnitude of the anomaly are shown to decrease with increasing γ-irradiation fluence. It has been established that the ferroelectric PT at T _C =152 K, which lies close to the tricritical point, shifts progressively more under γ irradiation toward the second-order PT, and that the behavior of the anomalous part of the heat capacity in the ferroelectric phase is described by the thermodynamic theory of Landau. The experimental heat-capacity data have been used to calculate the variation of the thermodynamic functions of the DMAAS crystal.     

Search forββ decay of76Ge to the excited states in76Se

Lower limits on the half-life of theββ(2v+0v) decay of⁷⁶Ge to the excited states in⁷⁶Se have been obtained using the results of low-background measurements with a HPGe detector surrounded by passive germanium shielding: T_1/2(0⁺ → 2 ₁ ⁺ ) >1.1 · 10²¹ y, T_1/2(0⁺ → 0 ₁ ⁺ ) > 1.7 · 10²¹ y, T_1/2(0⁺ → 2^2/+) > 1.4 ·10²¹ y.     

IR spectroscopy of rare-earth aluminum borates RAl3(BO3)4 (R = Y,Pr-Yb)

Rare-earth aluminum borates RAl₃(BO₃)₄ (R = Y, Nd-Yb) obtained by spontaneous high-temperature flux crystallization form two polytype modifications described by the space groups R32 (D ₃ ⁷ ) and C2/c (C _2h ⁶ ). They differ in the symmetry versions in mutual arrangement of layers. These borates have been investigated by mid- and far-IR spectroscopy in combination with factor-group analysis of the vibrations of BO ₃ ^3? ions; translational motions of Al³⁺, R³⁺ (Y, Nd-Yb), and BO ₃ ^3? ions; and BO ₃ ^3? rotations. Rare-earth aluminum borates are assigned to different space groups according to their IR spectra. Borates with large rare-earth Nd and Pr cations are crystallized into the space group C2/c (C _2h ⁶ ), while borates with smaller (Y, Sm-Yb) ions are crystallized into the space group R32 (D ₃ ⁷ ). The rhombohedral structure of the latter compounds includes monoclinically ordered domains, as is evidenced by the presence of monoclinic-phase bands in the IR spectrum. NdAl₃(BO₃)₄ and SmAl₃(BO₃)₄ can form both monoclinic and rhombohedral polytypes. The IR spectrum of the monoclinic SmAl₃(BO₃)₄ phase contains bands due to the rhombohedral phase, while the IR spectrum of NdAl₃(BO₃)₄ (which is described by the space group R32) contains bands due to the monoclinic polytype. The presence of domains with another arrangement of layers in the polytype structure is a characteristic sign that corresponds to the order-disorder theory; this theory explains the structure of polytypes.     

Simultaneous electrochemical and electron paramagnetic resonance studies of fullerene anion radicals C 60 1− and C 60 3−

Simultaneous electrochemical and electron paramagnetic resonance experiments have been carried out on the reduced C₆₀ fullerene to examine theg-factor assignment of the radical species. C ₆₀ ^1? and C ₆₀ ^3? show the following EPR characteristics at room temperature: C ₆₀ ^1? :g _1?=2.0002±0.0001, 2ΔB _1s=0.17 mT, and C ₆₀ ^3? :g _{3?=2.0008±0.0002}, 2ΔB _1s=0.07 mT. EPR linewidths are apparently narrower compared to those in most of the spectra previously reported. Variable temperature EPR study on solution containing C ₆₀ ^1? has shown thatg _1? value is not while the linewidth is only slightly temperature dependent.