Low-temperature elastic constants and piezoelectric coefficients of langasite (La3Ga5SiO14)

A complete set of elastic constants C _ij and piezoelectric coefficients e _ij of a La₃Ga₅SiO₁₄ (langasite) single crystal was determined from 5.5 to 275.5?K by resonant ultrasound spectroscopy. Unlike a conventional crystal, the elastic constants C _ij of the langasite crystal showed three types of temperature dependence: (i) monotonic elastic stiffening upon cooling (C ₄₄ and C ₁₄); (ii) monotonic elastic softening (C ₆₆); and (iii) a stiffening-to-softening transition below 150?K (C ₁₁, C ₁₂, C ₁₃ and C ₃₃). In addition, a strong correlation between C ₆₆ and the piezoelectric coefficient e ₁₁ was confirmed. Group theoretical lattice dynamics analysis revealed that the novel phenomena of elastic softening and strong correlation are explained on the basis of two types of optical mode internal displacements which have the totally symmetric A ₁ and doubly degenerated E symmetries in the point group D ₃.     

Differential Geometry from Differential Equations

We first show how, from the general 3rd order ODE of the form , one can construct a natural Lorentzian conformal metric on the four-dimensional space . When the function satisfies a special differential condition the conformal metric possesses a conformal Killing field, , which in turn, allows the conformal metric to be mapped into a three dimensional Lorentzian metric on the space ) or equivalently, on the space of solutions of the original differential equation. This construction is then generalized to the pair of differential equations, z _ss =S(z,z _s ,z _t ,z _st ,s,t) and z _tt =T(z,z _s ,z _t ,z _st ,s,t), with z _s and z _t the derivatives of z with respect to s and t. In this case, from S and T, one can again, in a natural manner, construct a Lorentzian conformal metric on the six dimensional space (z,z _s ,z _t ,z _st ,s,t). When the S and T satisfy differential conditions analogous to those of the 3^rd order ode, the 6-space then possesses a pair of conformal Killing fields, and which allows, via the mapping to the four-space of (z,z _s ,z _t ,z _st ) and a choice of conformal factor, the construction of a four-dimensional Lorentzian metric. In fact all four-dimensional Lorentzian metrics can be constructed in this manner. This construction, with further conditions on S and T, thus includes all (local) solutions of the Einstein equations. Received: 10 October 2000 / Accepted: 26 June 2001     

Electron-vibration effects in Cs2SiF6 : Mn4+

We report a study of the ⁴ A _2g →² T _1g absorption band of Mn⁴⁺ in Cs₂SiF₆. The band shows several lines or groups of lines associated with transitions from the ⁴ A _2g ground state to the spin-orbit components (² T _1g )Γ₈ and (² T _1g )Γ₆ coupled to the three odd-parity vibrations v ₆(t _2u ), v ₄(t _1u ) and v ₃(t _1u ). The absorptions associated with the (² T _1g )Γ₈ electronic state have structure whereas those associated with the (² T _1g )Γ₆ do not. It is shown that the structure is a consequence of splitting of the Γ₈ × v vibronic multiplets by electron-vibration interaction. The intensity of the ⁴ A _2g →(² T _1g )Γ _i + v_j vibronic transitions are expressed in terms of a small number of parameters; two parameters for v(t _1u ) modes and three for v(t _2u ) modes. Plausible but not good fits to the low temperature Zeeman data and vibronic splitting patterns are obtained. The excitation spectrum of the Cs₂SiF₆ : Mn⁴⁺ in the region of the ⁴ A _2g →² E_g and ⁴ A _2g →² T _1g is recorded using a c.w. dye laser. This reveals numerous weaker lines involving combinational modes and even-parity modes v₅ (t _2g ), v ₂(e_g ) and v ₁(a _1g ). Several interesting electron-vibrational effects are observed. These are illustrated and discussed qualitatively.     

Rotational analysis of the v 2 + v 6 ±1, v 5 ∓1 + v 6 ∓1 and v 5 ∓1 + v 6 ±1 interacting infrared bands of methyl bromide

The rotational analysis of the infrared absorption spectrum of CH₃ ⁷⁹Br and CH₃ ⁸¹Br between 2150 and 2510 cm^-1 was performed on a Fourier transform spectrum with a resolution of 0·007 cm^-1. The bands v ₂ + v ₆(E) and v ₅ + v ₆(A ₁ + A ₂ + E) occur in this region, giving rise to several perturbations as in the corresponding system of methyl chloride [3]. Forbidden transitions, observed in correspondence of the level crossing of the x-y Coriolis coupling between v ₂ + v ₆ and v ₅ + v ₆(E), enabled us to estimate the value of A″ - 225D″_K at 5·16186 cm^-1 for CH₃ ⁷⁹Br and 5·16173 cm^-1 for CH₃ ⁸¹Br. The parallel system of v ₅ + v ₆ exhibits a perpendicular structure, and an l-type resonance couples those levels of the parallel and perpendicular components of v ₅ + v ₆ involved in transitions from the K″ = 0 levels of the ground state. The ^QQ ₀ branches of the A ₂ component of v ₅ + v ₆, made active by this resonance, are observed for both isotopic species.     

Generalized Linear Mixing Rule for Classical Coulomb Mixtures

It is shown that the Coulomb energy U of fully ionized ionic mixture can be written as a sum over partial contributions of ion species j: U = T Σ_j N_ju (Γ_j, y_j) (generalized linear mixing rule). In contrast to the traditional linear mixing rule U_LM = T Σ_j N_ju_OCP(Γ_j), applicable for strong coupling, the partial contribution function u depends not only on Γ_j, but on an additional parameter y_j = (r_D/r_D^OCP)² also. Here r_D and r_DOCP are Debye radiuses in the mixture and in the one component plasma at coupling parameter Γ_j, correspondingly. The parameter y_j does not depend on a specific composition of the mixture, but on the Debye radius r_D only, making function u (Γ_j, y_j) universal. The generalized linear mixing rule can be applied at any coupling parameter, if ionic mixture is not crystallized. It reproduces results of the Debye‐Hückel theory at weak coupling and traditional linear mixing rule at strong coupling. It can be easily applied to the complicated mixtures, composed of a large number of ion species. Since y_j is temperature independent, the Coulomb contribution to Helmholtz free energy of the mixture can also be presented in a form of generalized linear mixing rule (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The orientation of porphins in n-alkane Shpolskii hosts

When a solution of a porphin in n-octane is slowly frozen the guests predominantly occupy a single site (A) in which the porphin has been shown to replace a number of host molecules displaced along the b-direction; if the solution is quickly frozen the optical spectra reveal the presence of a second site (B). In the present paper it is shown that the occurrence of these two types of sites, A and B, is a common phenomenon throughout the series from n-heptane (C₇) to n-decane (C ₁₀) as hosts and phenomenological criteria are formulated to distinguish between the two kinds of sites.

The orientation of palladiumporphin (PdP) in the A and B sites of a C₇ host is determined from Zeeman experiments on the S ₁← S ₀ and T ₀ →S ₀ transitions in a single crystal of C₇ doped with PdP. The porphin nuclei in the B sites replace a number of alkanes displaced along the a-axis. In the course of the experiments signals related to a third type of site, B', grew in intensity in the spectra. This site is coplanar with the B site and it differs from the latter by an in-plane rotation of the trapped molecule over 20°. The origins of the S ₁ ←S ₀ transition for the two types of site are assigned for H₂P, ZnP and PdP as solutes in C₇, C₈, C₉ and C₁₀ as hosts.

Finally, the Zeeman shifts observed in the S ₁ ←S ₀ transition of PdP in the three sites of C₇ yield an effective orbital angular momentum for PdP in the state S ₁ of (4·4 ± 0·1)?, in excellent agreement with previous determinations.     

Screened potential of a test charge in a two-dimensional Bose condensate

We calculate the screening properties of a boson superlattice with distanced between the planes at temperature zero. The screened Coulomb potentialV _s (r,d) of a test charge located in one plane is calculated in the neighboring plane. It is found that this interplane potential is attractive with a maximal atraction at the intraplane distancer _m:V _s (r _m ,d)<0.V _s (r _m ,d) versusd shows a minimum atd _m , indicating a maximal attraction for anoptimal superlattice period d_m. The attraction could give rise topairing of bosons between different planes.     

典型随机信号特征参数统计分布的分形特性

建立了一种能够描述随机信号结构基本特征的双参数脉冲信号统计模型.基于此模型,脉冲信号群幅度计数分布q(l_V),宽度计数分布p(l_τ)及给定宽度信号子集的幅度计数分布ε_lτ(l_V),给定幅度信号子集的宽度计数分布δ_lV(l_τ)均能很稳定的服从以序列自然数为自变量的对数正态分布.且计数分布的统计特征量μ_lnV,μ_lnτ,σ_lnV,σ_lnτ与信号的特征参数l_V,l_τ之间存在内在联系,这种联系的形式即随机信号分形特性的表现,表明随机信号特征参数的统计分布之间具有非整数维分形特征. 关键词： 分形 随机信号 双参数 统计     

Linear low-temperature dependence of the surface impedance of a Ba0.6K0.4BiO3 single crystal

The temperature dependences of the real part R _s and the imaginary part X _s of the surface impedance Z _s =R _s +iX _s of the superconductor Ba_0.6K_0.4BiO₃ (T _c ≃30 K) are measured at a frequency of 9.4 GHz. Its temperature dependence _{Z s} (T) and that of the complex conductivity σ _s (T) can be described on the basis of a two-fluid model under two assumptions: The density of superconducting carriers increases linearly, and the relaxation time increases as a power law (∝1/T ⁵), with decreasing temperature T<T _c . This model also describes well the curves Z _s (T) and σs (T) recently measured for YBa₂Cu₃O_6.95 and Bi₂Sr₂CaCu₂O₈ single crystals. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 783–788 (10 December 1996)     

Quantum BRST charge for quadratically nonlinear Lie algebras

We consider the construction of a nilpotent BRST charge for extensions of the Virasoro algebra of the form {T _a ,T _b }=f _ab ^c T _c +V _ab ^cd T _c T _d , (classical algebras in terms of Poisson brackets) and [T _a ,T _b ]=h _ab I+f _ab ^c T _c +V _ab ^cd (T _c T _d )(quantum algebras in terms of commutator brackets; normal ordering of the product (T _c T _d ) is understood). In both cases we assume that the set of generators {T _a } splits into a set {H _i } generating an ordinary Lie algebra and remaining generators {S }, such that only theV _ij are nonvanishing. In the classical case a nilpotent BRST charge can always be constructed; for the quantum case we derive a condition which is necessary and sufficient for the existence of a nilpotent BRST charge. Non-trivial examples are the spin-3 algebra with central chargec=100 and theso(N)-extended superconformal algebras with levelS=–2(N–3).     

The action-angle coordinates for particle motion in magnetic mirror systems

In this paper the problem of the possibility of determining the cyclic Hamiltonian function of a particle moving about a magnetic vessel of the mirror type is discussed. From the Hamiltonian of the typeH=H(P ₁,P ₂,P ₃,Q ₃), derived by the author in a previous paper, the Hamiltonian functionH=H(J₁,J ₂,J ₃,w ₃) was determined whereP _i ,Q _i are the generalized impulses and coordinates andJ _i ,w _k is the action-angle coordinate system. The determination of the form H=H(J₁,J ₂,J ₃) depends on the possibility of solving the quadrature of the Hamilton-Jacobi equation leading to an open form in the general case. Some approximative expressions, suitably replacing the mirror system, are discussed. The solution has been extended to the range of relativistic velocities. The question of the uniqueness of the expression of the Hamiltonian function in cyclic variables is analyzed; it follows from this that the class of canonical transformations leaving the Hamiltonian in a cyclic form does not allow any great simplification of the relatively complicated transformation expressions.     

Approximate solution of the Percus-Yevick equation for a binary mixture of hard spheres with non-additive diameters

We present an approximate solution of the Percus-Yevick integral equation for a binary mixture of hard spheres with non-additive diameters. Defining R_ij the distance of closest approach between particles of species i and j by R ₁₂ = ½(R ₁₁ + R ₂₂) + α, we obtain a closed set of equations for the direct correlation functions c_ij (r) when 0 < α ? min [½(R ₂₂ - R ₁₁), ½R ₁₁]. Our expressions for c_ii (r), and for c ₁₂(r) in the range 0 < r ? ½[R ₂₂ - R ₁₁] - α, agree with those previously obtained by Lebowitz and Zomick.     

Growth of Ba2−x Sr x NaNb5O15 thin film on La0.05Sr0.95TiO3 substrate by pulsed laser deposition

Ba_2−x Sr _x NaNb₅O₁₅ thin films were prepared on La_0.05Sr_0.95TiO₃ substrates by pulsed laser deposition. The structural and ferroelectric properties of the thin films depended on substrate temperature (T _sub) and Sr concentration. When T _sub was fixed at 700 °C, the Ba_2−x Sr _x NaNb₅O₁₅ (x = 0, 0.6, 1.0, and 1.4) thin films exhibited a high c-axis orientation. The thin films consisted of well-developed grains and exhibited a smooth surface. The c-axis-oriented Ba_0.6Sr_1.4NaNb₅O₁₅ thin film with the lowest Curie temperature also exhibited a high c-axis orientation and a P-E hysteresis loop with a high ferroelectricity at T _sub 650 °C. Thus, its remanent polarization (P _r) and coercive field (E _c) were 2P _r 24.9 μC/cm² and 2E _c 107 kV/cm, respectively. These values indicate that Ba_2−x Sr _x NaNb₅O₁₅ has ferroelectricity in the thin film form.     

The Thermodynamic Evolution of the Cosmological Event Horizon

By manipulating the integral expression for the proper radius R _e of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe we obtain an analytical expression for the change δR _e in response to a uniform fluctuation δρ in the average cosmic background density ρ. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately stationary, and evolves subsequently such that δρ/ρ is constant. The respective variations 2πR _e δR _e and δE _e in the horizon entropy S _e and enclosed energy E _e should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature T _e of the CEH at an arbitrary time in a flat FRW universe is E _e /S _e , which recovers asymptotically the usual static de Sitter temperature. Furthermore it is proven that during radiation-dominance and in late times the CEH conforms to the fully dynamical First Law T _e dS _e =PdV _e −dE _e , where V _e is the enclosed volume and P is the average cosmic pressure.     

Influence of ignition condition on the growth of silicon thin films using plasma enhanced chemical vapour deposition

The influences of the plasma ignition condition in plasma enhanced chemical vapour deposition (PECVD) on the interfaces and the microstructures of hydrogenated microcrystalline Si (μc-Si:H) thin films are investigated. The plasma ignition condition is modified by varying the ratio of SiH₄ to H₂ (R_H). For plasma ignited with a constant gas ratio, the time-resolved optical emission spectroscopy presents a low value of the emission intensity ratio of Hα to SiH^* (I_Hα/I_SiH^*) at the initial stage, which leads to a thick amorphous incubation layer. For the ignition condition with a profiling R_H, the higher I_Hα/I_SiH^* values are realized. By optimizing the R_H modulation, a uniform crystallinity along the growth direction and a denser μ c-Si:H film can be obtained. However, an excessively high I_Hα/I_SiH^* may damage the interface properties, which is indicated by capacitance-voltage (C-V) measurements. Well controlling the ignition condition is critically important for the applications of Si thin films.     

Contribution of superconducting grains and grain boundaries to the magnetoresistance of ceramic YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − δ</Subscript> high-temperature superconductors in weak magnetic fields

The current-voltage characteristics of granular YBa₂Cu₃O_6.95 high-temperature superconductor samples have been measured at a temperature of 77.3 K in external transverse magnetic fields H _ext with a strength of up to H _ext ≈ 500 Oe for low transport current densities (0.1 A/cm² ≤ j ≤ 0.6 A/cm²). The current-voltage characteristics obtained have been used to construct dependences of the magnetoresistance ρ on the quantities j (ρ(j) _Hext=const) and H _ext(ρ(H _ext) _{j = const}). It has been revealed that the current and field dependences of the magnetoresistance exhibit anomalies at H _ext ≥ H _c1g , where H _c1g is the lower critical field of superconducting grains. A comparative analysis of the dependences ρ(j)H _{ext = const} and ρ(H _ext) _{j = const} has made it possible to develop concepts regarding the influence of the processes of redistribution of the magnetic field between grain boundaries and superconducting grains on the transport and galvanomagnetic properties of granular high-temperature superconductors. It has been established that the field dependences of the magnetoresistance exhibit specific features associated with the beginning of penetration of Josephson vortices into grain boundaries in the magnetic field H _c1J and with the breaking of a continuous chain of Josephson junctions in the magnetic field H _c2J .     

Lifting <Emphasis Type="Italic">q</Emphasis>-difference operators for Askey-Wilson polynomials and their weight function

We determine an explicit form of a q-difference operator that transforms the continuous q-Hermite polynomials H _n (x|q) of Rogers into the Askey-Wilson polynomials p _n (x; a, b, c, d|q) on the top level in the Askey q-scheme. This operator represents a special convolution-type product of four one-parameter q-difference operators of the form ɛ _q (c _q D _q ) (where c _q are some constants), defined as Exton’s q-exponential function ɛ _q (z) in terms of the Askey-Wilson divided q-difference operator D _q . We also determine another q-difference operator that lifts the orthogonality weight function for the continuous q-Hermite polynomialsH _n (x|q) up to the weight function, associated with the Askey-Wilson polynomials p _n (x; a, b, c, d|q).     

Raman microscopy of a small uniaxial crystal: Tetragonal aspartame

A general method is presented for determining the shape and orientation of the Raman tensor of a molecule in a uniaxial crystal using a Raman microscope. First, equations are derived to connect the Raman tensor components (α_xx, α_yy, etc.) of a molecule to the Raman tensor components (α_aa, α_cc, etc.) of a crystal that is composed of molecules in a uniaxial arrangement, with an orientation specified by the two angles χ and θ. Next, a method is presented to obtain a correct set of values of the intensity ratios I_ac/I_aa and I_cc/I_aa from observed values of the intensity ratios measured with a Raman microscope. To augment the experimental data, the depolarization ratio ρ (for a completely random molecular orientation) is plotted as a function of r₁ = α_xx/α_zz and r₂ = α_yy/α_zz, so that a possible set of r₁ and r₂ values can be found from an observed value of ρ. The method has been applied to an aspartame IIA crystal (P4₁). A set of values of r₁, r₂, χ and θ has been determined for each of the following Raman fundamentals: 1741 cm⁻¹ (ester CO stretch), 1667 cm⁻¹ (amide I), 1275 cm⁻¹ (amide III) and 1204 cm⁻¹ (C C_phenyl stretch), excited at 488.0 nm.     

Relaxation of post-illumination electric fields in strongly biased high-resistance structures with a single deep impurity level

This paper examines how an electric field relaxes when a discontinuous large carrier-depleting voltage applied to high-resistance symmetric metal-semiconductor-metal (MSM) and metal-insulator-semiconductor-insulator-metal (MISIM) structures having a single impurity level, and how its energy level ɛ _t=E _c−E _t and the tunneling transparency T _n,p of the metal-semiconductor or metal-insulator boundary affect the relaxation. It is shown that the relaxation of the field and the form of its steady-state distribution depend on the ratio of the time constant t _p in the majority-carrier (hole) region to the ionization time τ _t ⁻¹ =α _n (n _*+n ₁)+α _p (p _*+p ₁) of a deep trap in the bulk. This ratio determines the relative contributions of free ρ _p,n and bound charge dnsities ρ _t (where α _n,p is the coefficient for capture by an impurity, and p _*, n _*, p ₁, n ₁ are equilibrium concentrations and Shockley-Read constants in the bulk). For τ _t ≈(τ _t )_max≫t _p ,ρ _t ≫ it is found that ρ _p,n and ρ _t ≫ρ _p,n , which corresponds to a trap energy close to , independent of the value of T _n,p , decaying oscillations arise in the concentration distribution, bulk charge, and field appear in the bulk. The amplitude of these oscillations reaches a maximum at time t≈0.4τ _t. Decreasing the ratio α _p/α_n causes τ _t to deviate from (τ _t)_max. When this happens, the field no longer oscillates; instead, it increases with positive curvature in the cathode portion of the bulk. The quantity T _n,p determines the behavior of the field in the neighborhood of the anode. The value of (dE/dx)₀ is positive for MSM structures (T _n,p ≈1), and negative for MISIM structures (T _n,p ≈0). For transparencies close to a critical value T _n,p ⁰ , the field in the structure remains almost uniform over an impurity ionization time. Fiz. Tverd. Tela (St. Petersburg) 39, 1775–1782 (October 1997)