Concurrent changes of crystallographic and Mössbauer effect parameters at the high-spin(5T2) ⤥ low-spin(1A1) transition in compounds of iron (II)

Distinct and different X-ray diffraction patterns are found for the ⁵T₂ and ¹A₁ phases at the high-spin(⁵T₂) ? low-spin(¹A₁) transition in Fe(bt)₂(NCS)₂ (I) and Fe(phy)₂(ClO₄)₂ (II) (bt = 2,2′-bi-2-thiazoline; phy = 1,10-phenanthroline-2-carbaldehydephenylhydrazone). The peak profiles show the same temperature dependence and the same hysteresis behaviour as the ⁵T₂ and ¹A₁ fractions determined on the basis of Mössbauer effect or magnetism. At the transition temperature T_c, both phases are coexistent.     

Change in the polarizability of MBBA molecules upon the nematic-isotropic liquid transition and physical consequences

The Lorentz tensor components L _j and the polarizability tensor components γ _j of 4-methoxyben-zylidene-4′-butylaniline (MBBA) liquid crystal molecules in nematic and isotropic phases have been determined experimentally. The quadratic dependences of the mean value $\bar \gamma $ (S) and anisotropy Δγ(S) of the polarizability in the nematic phase on the orientational order parameter S of molecules have been established. Within the phenomenological approach, the dependences $\bar \gamma $ (S) and Δγ(S) have been derived, and their features for MBBA and other known objects have been interpreted. The relation of the dependences $\bar \gamma $ (S) and Δγ(S) to the features of the nematic-isotropic liquid phase transition has been found.     

Influence of nematic and smectic orders on polarizability of molecules of ethyl-p-(4-ethoxybenzylideneamino-)α-methyl cinnamate liquid crystals

Experimental values of the polarizability tensor γ components of molecules of ethyl-p-(4-ethoxybenzylideneamino-)α-methyl cinnamate liquid crystals in the nematic and smectic A phases have been obtained. Quadratic dependences of the longitudinal, γ _l , and transverse, γ _t , components, the mean value $\bar \gamma $ , and anisotropy Δγ in both phases have been established as functions of the orientational order parameter S of molecules in a maximally wide range of S. The nematic-smectic A phase transition with a continuous variation of S manifests itself as kinks in the linear dependences of $\bar \gamma $ , Δγ, and γ _l on S ² and does not influence the dependence γ _t (S ²). The observed dependences have been derived in the framework of the theory of the nematic-smectic A phase transition. The factors responsible for different influences of the orientational and positional orderings of molecules on the polarizability parameters have been determined.     

X-ray diffraction of the smectic phases of N-(p-n-heptyloxybenzylidene)-p′-n-pentylaniline

Using X-ray diffraction the various smectic phases of N-($\text{p}$-$\text{n}$-heptyloxybenzylidene)-$\text{p}$′-$\text{n}$-pentylaniline can be classified (with increasing temperature) as S_H, S_B, S_C and S_A, respectively. The long molecular axes are probably tilted with respect to the normal to the layers in the S_A, S_C and S_H phases, and perpendicular to the layers in the S_B phase.     

Polarized Fluorescence of Jet-Cooled indole and Carbazole and Their Complexes with Water

The spectra of the fluorescence excitation within the rotational contours of the bands of the pure electronic long-wavelength S ₀-S ₁ transitions of jet-cooled indole and carbazole molecules and their complexes with water are measured. For the carbazole-water complex, a contour with three maxima is registered, which is possibly related to the occurrence of two isomers, differing in a slight displacement of hydrogen between the nitrogen atom of the imine group of carbazole and the oxygen atom of the water molecule. The degrees of polarization of integral fluorescence upon excitation within the rotational contours of the S ₀-S ₁ electronic transition bands of the above molecules and their complexes with water are determined for the first time. The coincidence of the calculated (7.7%) and measured (7.3%) values of the degree of polarization upon excitation in the rotational Q branch of the ^b L ₁-A electronic transition of indole confirms the accepted intramolecular orientation of the transition dipole moment at an angle of 38.3° with respect to the principal axis of inertia A. Upon excitation of indole, its complex with water, and carbazole into the P and R branches, the measured and calculated degrees of polarization are also close to each other and amount to 2–3%. This confirms the occurrence of contributions to the fluorescence polarization due to the rotations of the indole molecules around the principal axes of inertia A and C.     

Functional properties of quantum logics

A quantum logic is defined as a setL of functions from the set of all statesS into [0, 1] satisfying the orthogonality postulate: for any sequencea ₁,a ₂, ... of members ofL satisfyinga _i+a _j≤1 fori≠j there isb∈L such thatb+a ₁+a ₂+...=1. Every logicL is in a natural way an orthomodular σ-orthocomplemented partially ordered set (L, ≤, ′) with members ofS inducing a full set of measures onL. It is shown that a logicL is quite full if and only if (L,≤,′) is isomorphic to an orthocomplemented set lattice of subsets ofS. Sufficient conditions are given in order that a quite full logic be representable in the set of projection quadratic formsf(u)=(Pu, u) on a complex Hilbert space, or in the set of trace functionsf(A)=Trace (AP) generated by projectionsP, where the domain off is the set of non-negative self-adjoint trace operators of trace 1 in a complex Hilbert space.     

The number of independent traces and supertraces on symplectic reflection algebras

It is shown that A:= H₁, _η (G), the sympectic reflection algebra over ?, has T_G independent traces, where T_G is the number of conjugacy classes of elements without eigenvalue 1 belonging to the finite group G ? Sp(2N) ? End(?^2N) generated by the system of symplectic reflections.

Simultaneously, we show that the algebra A, considered as a superalgebra with a natural parity, has S_G independent supertraces, where S_G is the number of conjugacy classes of elements without eigenvalue -1 belonging to G.

We consider also A as a Lie algebra A^L and as a Lie superalgebra A^S.

It is shown that if A is a simple associative algebra, then the supercommutant [A^S, A^S] is a simple Lie superalgebra having at least S_G independent supersymmetric invariant non-degenerate bilinear forms, and the quotient [A^L, A^L]/([A^L, A^L] ∩ ?) is a simple Lie algebra having at least T_G independent symmetric invariant non-degenerate bilinear forms.     

Superfluid-to-normal phase transition and extreme regularity of superdeformed bands

We derive an exact semiclassical expression for the second inertial parameter B for superfluid and normal phases. Interpolation between these limiting values shows that the function B(I) changes sign at the spin I _c that is critical for the rotational spectrum. The quantity B proves to be a sensitive measure of the change in static pairing correlations. The superfluid-to-normal transition reveals itself in a specific variation of the ratio B/A versus the spin I with a plateau characteristic of the normal phase. We find this dependence to be universal for normal deformed and superdeformed bands. A long plateau with a small value of B/A ～ A ^?8/3 explains the extreme regularity of superdeformed bands.     

Quenching of SO2 phosphorescence by a magnetic field

Phosphorescence excitation spectra of the ã³B₁← [Xtilde]¹A₁ transition of SO₂ were measured in the absence and presence of a magnetic field (B = 0?44 T², P(SO₂) = 0?7 Torr). The absorption and phosphorescence excitation spectra of the ã³B₁← [Xtilde]¹A₁ transition of SO₂ measured in the absence of a magnetic field show that the relative intensity of the bands of the phosphorescence excitation spectrum is smaller than the relative intensity of the corresponding bands of the absorption spectrum beginning with the (0, 2, 0) band. In the presence of a magnetic field, the intensity of the phosphorescence excitation band falls, for ν_exc> 26400 cm^-1. Under the direct excitation of the ã³B₁← [Xtilde]¹A₁ transition, the dependence of the magnetic quenching of the SO₂ phosphorescence on the excitation frequency (ν_exc) was studied at P(SO₂) = 0?7 Torr and B = 0?44 T. The dependence of the magnetic field effect on ν_excshows that only the vibrationally excited levels of the ã³B₁ state are sensitive to an external magnetic field. The magnetic field strength and the pressure dependence of the magnetic field effects were studied under indirect excitation of the ã³B₁← [Xtilde]¹A₁ transition at λ_exc = 308 nm. The magnetic field and the pressure dependence were investigated for pure SO₂ and for SO₂ + RH (RH n-C₅H₁₂) mixtures. It was found that the magnetic field effect was saturated at B ? 0?25 T. The saturation value (Gr = l(0?3 T)/l(0)) increases with increasing gas pressure. The magnetic field, the pressure and the excess vibrational energy (ν_excess) dependence of the magnetic quenching of SO2 phosphorescence show that the data observed can be explained by an indirect mechanism within the framework of a low level density approximation.     

Franck-Condon factors and absolute transition probabilities for the if (B3Π0+-X1Σ+) transition

Improved spectroscopic constants have been used to calculate Rydberg-Klein-Rees (RKR) potentials and Franck-Condon factors for the IF(B³Π₀₊-X¹Σ⁺) transition. The Franck-Condon factors are generally in good agreement with previously calculated values, but differ by as much as 30% for transitions from higher levels of the B-state. Several experimentally measured relative transition moment functions have been evaluated and the best scaled, so that the total transition probability calculated for each B-state vibrational level, A(v'), matched measured values. The scaled function was then used to calculate individual transition probabilities, A(v',v), for the vibronic transitions.     

Spectroscopic studies of the sulphur afterglow

The afterglow emission spectrum of sulphur and argon mixture is found to consist of (a) the main band system of S₂(B³Σ^-_u?X³Σ^-_g) in the region 3200–6600 Å and (b) the atomic spectrum of argon in the 7500–9000 Å region. Although B?X bands of S₂ obtained by ordinary excitation extends from 2829 to 7100 Å, the lower wavelength limit of these bands from the afterglow is only 3200Å. It is proposed that the S₂ molecules are formed in the B³Σ^-_u state through inverse predissociation when two S atoms approach each other along the potential curve of the predissociating electronic state 1_u.     

Anomalous temperature dependence of magnetic relaxation in YBa<Subscript>2</Subscript>Cu<Subscript>2</Subscript>O<Subscript>7 − δ</Subscript> oxygen-deficient single crystals

The dependence of the magnetization relaxation rate S = ?d lnM/dlnt on temperature T is measured in YBa₂Cu₃O_{7 ? δ} samples with various oxygen concentrations. It is found that the S(T) curve changes qualitatively when oxygen deficit δ exceeds the threshold value δ_th = 0.37. For δ < δ_th (T _c > 60 K, where T _c is the superconducting transition temperature), function S(T) has the well-known peak at T/T _c = 0.4. For δ > δ_th (at T _c < 51 K), this peak transforms into a plateau and a new sharp peak appears at T/T _c = 0.1. The threshold value δ_th of the oxygen deficit corresponds to the transition of the sample from the disordered state into the ordered state of oxygen vacancies. We consider the change in the shape of the S(T) curve as a macroscopic manifestation of this transition.     

Transition Probabilities in the BΣ-XΣ and the BΣ-AΠ Electronic Systems of MgO

Transition probabilities for the B¹Σ⁺-X¹Σ⁺ and the B¹Σ⁺-A¹Π electronic systems are presented for v=0-4 and J=0-150 in each electronic state. The functional form of the electronic transition moment for the B-X transition is taken from published ab initio results. The B-A moment is assumed to have the same form and is scaled using empirical branching ratio data. The R_e(r) are used with Rydberg-Klein-Rees (RKR) wavefunctions to calculate transition probabilities for v=0-4 and J=0-150. The RKR potentials were calculated based on empirical spectroscopic constants.     

The correlation function of the Ising model in the MFA and their sum rule

It is shown that in the correctly performed molecular field approximation the correlation function 〈S(q) S(-q)〉 fulfills the sum rule N^-1Σ_q〈S(q) S(-q)〉 = 1. This can be proved for ferro- and antiferromagnets and the disordered phases of o-hydrogen.     

On the time and cell dependence of the coarse-grained entropy. I

We consider a finite, thermally isolated, classical system which passes from an equilibrium state $\text{A}$ by the removal of an internal constraint to another equilibrium state $\text{B}$ after an empirical relaxation time. In the phase space of the system, cells are introduced according to the set of measuring instruments used and their experimental inaccuracies. It is shown that the coarse-grained entropy S_cg(t) tends to its new equilibrium value in general faster than the expectation values of the macroscopic variables to their new equilibrium values. We then investigate the dependence of S_cg(t) on the size of the phase cells. For fixed t, we find a lower bound on S_cg(t) by doing to the limit of infinite accuracy of the measuring instruments. In the limit t → ∞, this lower bound on S_cg(t) also converges to the equilibrium entropy of $\text{B}$. These properties strongly support the opinion that S_cg(t) is a proper microscopic expression for the entropy for equilibrium and nonequilibrium. Finally, explicit calculations of S_cg(t) for the model of a point particle enclosed in a one-dimensional box are presented which confirm the general results.     

Monte Carlo simulation of film growth in a phase separating binary alloy model

Using a kinetic Monte Carlo method, we simulate binary film (A_0.5B_0.5/A) growth on an L×L square lattice with the focus on the domain growth behaviour. We compute the average domain area, A(t), as a measure of domain size. For a sufficiently large system, we find that A(t) grows with a power law in time with A(t)∼t^2/3 after the initial transient time. This implies that the dynamic exponent for domain growth with non-conserved order parameter is z=3, a value which was theoretically predicted for the conserved order parameter case. Further analysis reveals that such a power-law behaviour emerges because the order parameter is approximately conserved after the early stage of growth.     

Fluctuations of orientational order in a uniaxial nematic liquid crystal with biaxial molecules and its response to an external field

Homogeneous thermal fluctuations of the orientational order parameters S and G of biaxial molecules in a uniaxial nematic liquid crystal are investigated in the framework of the molecular-statistical theory. It is demonstrated that the molecular biaxiality significantly affects the order parameters S and G, their temperature dependences in the nematic phase, the amplitude and the temperature dependence of the order parameter fluctuations in the nematic and isotropic phases, and the character of the transition from the nematic phase to the isotropic liquid phase. It is established that the fluctuations of the parameters S and G in the nematic phase are related to the temperature dependences of S and G and the susceptibilities χ_S and χ_G of the nematic liquid crystal to external fields, which leads to a change in the parameters S and G at a fixed director orientation. Explanations are offered for the known experimental data on the orientational ordering of biaxial molecules under the action of external fields in the isotropic phase of nematic liquid crystals.     

Structure-mediated transition in the behavior of elastic and inelastic properties of beach tree bio-carbon

Microstructural characteristics and amplitude dependences of the Young modulus E and of internal friction (logarithmic decrement δ) of bio-carbon matrices prepared from beech tree wood at different carbonization temperatures T _carb ranging from 600 to 1600°C have been studied. The dependences E(T _carb) and δ(T _carb) thus obtained revealed two linear regions of increase of the Young modulus and of decrease of the decrement with increasing carbonization temperature, namely, ΔE ～ AΔT _carb and Δδ ～ BΔT _carb, with A ≈ 13.4 MPa/K and B ≈ ?2.2 × 10^?6 K^?1 for T _carb < 1000°C and A ≈ 2.5 MPa/K and B ≈ ?3.0 × 10^?7 K^?1 for T _carb > 1000°C. The transition observed in the behavior of E(T _carb) and δ(T _carb) at T _carb = 900–1000°C can be assigned to a change of sample microstructure, more specifically, a change in the ratio of the fractions of the amorphous matrix and of the nanocrystalline phase. For T _carb < 1000°C, the elastic properties are governed primarily by the amorphous matrix, whereas for T _carb > 1000°C the nanocrystalline phase plays the dominant part. The structurally induced transition in the behavior of the elastic and microplastic characteristics at a temperature close to 1000°C correlates with the variation of the physical properties, such as electrical conductivity, thermal conductivity, and thermopower, reported in the literature.     

Relation of the 2S + 1 states per site potts model to a nonlinear spin-S ising model

The interaction energy of the Potts model with 2S + 1 states per site is of the form ∑_〈i,j〉δS_iS_j where δS_iS_j is the Kronecker delta symbol. The expansion of δS_iS_j in a finite power series in S_j and S_j is explicitly given.     

Nonisotropic L-conversion-electron — X-ray directional correlations in160Dy

The directional correlations betweenL-conversion electrons andL x-rays have been measured. The electrons were emitted in the 86.78keV 2⁺→0⁺ transition in¹⁶⁰Dy, in the decay of¹⁶⁰Tb. The experimental results areA ₂₂(e _L -x _Li )=0.085 (22),A ₂₂(e _L -x _Lα )=0.0066 (29),A ₂₂(e _L -x _Lβ )=0.0000 (27), andA ₂₂(e _L -x _Lγ )=0.0096 78). These results are in disagreement with published theoretical values. It is suggested that the discrepancy is due to a phase inconsistency in the internal conversion matrix elements and there is good agreement withA ₂₂ values calculated in this work.