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.     

非晶态超导体转变温度Tc的经验公式

本文提出一个非晶态非过渡金属超导体的T_c经验公式,T_c=Aλ<ω>^1/2/(<ω>/ω₀+(1+λ)/20),式中A=(1/5)^(K1/2)。计算值和实验值,以及和Garland理论值的比较表明,T_c经验公式能很好地描述非晶态超导体的T_c值。 关键词：     

X-ray study of [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> at low temperatures

The unit cell parameters a, b, and c of [N(CH₃)₄]₂ZnCl₄ have been measured by x-ray diffraction in the temperature range 80–293 K. Temperature dependences of the thermal expansion coefficients α_a, α_b, and α_c along the principal crystallographic axes and of the unit cell thermal expansion coefficient α_V were determined. It is shown that the a=f(T), b=f(T), and c=f(T) curves exhibit anomalies in the form of jumps at phase transition temperatures T₁=161 K and T₂=181 K and that the phase transition occurring at T₃=276 K manifests itself in the a=f(T) and b=f(T) curves as a break. A slight anisotropy in the coefficient of thermal expansion of the crystal was revealed. The phase transitions occurring at T₁=161 K and T₂=181 K in [N(CH₃)₄]₂ZnCl₄ were established to be first-order.     

The contribution of color-octet current color-octet current toD decays

Bauer and Stech pointed out that inD decaysa ₁ anda ₂ are approximately equal toc ₁ andc ₂ obtained from the renormalization group equation. This means that the non-leading 1/N _c term in the formulation vanishes. Many authors conjecture that there is a cancellation between the 1/N _c term and an extra <λ ^a λ λ ^a > term emerging from the analysis of non-factorizable matrix elements. We employ the hybrid MIT bag model to estimate the cancellation effects and find that the ratio of <λ ^a λ λ ^a > over the 1/N _c term is about ?0.16～?0.24 which is 2～3 times smaller than the value from data fitting.     

Low-temperature x-ray diffraction studies of the crystallographic parameters and thermal expansion of (CH3)2NH2Al(SO4)2 · 6H2O crystals

The a, b, c, and β crystallographic parameters of the (CH₃)₂NH₂Al(SO₄)₂ · 6H₂O crystal (DMAAS) have been measured by x-ray diffraction in the 90–300-K temperature range. The thermal expansion coefficients along the principal crystallographic axes α_a, α_b, and α_c have been determined. It was shown that, as the temperature is increased, the parameter α decreases and b increases, whereas c decreases for T<T _c (where T _c is the transition temperature) and increases for T>T _c, so that one observes a minimum in the c=f(T) curve in the region of the phase transition (PT) temperature T _c ～ 152 K. The thermal expansion coefficients α_a, α_b, and α_c vary in a complicated manner with increasing temperature, more specifically, α_a and α_c assume negative values at low temperatures, and the α_a=f(T), α_b=f(T), and α_c=f(T) curves exhibit anomalies at the PT point. The crystal has been found to be substantially anisotropic in thermal expansion.     

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.     

Coupled KdV equations with multi-Hamiltonian structures

We present a large class of systems of N-equations which possess (N+1) purely differential, compatible Hamiltonian structures. Our generic equations are isospectral to [(Σ^N−1₀ε_iλ²ⁱ)∂²+Σ^N−1₀υ_iλ²ⁱ]ψ=λ^2Nψ, but our class also includes degenerate, nondispersive systems which are unrelated to this linear problem. Embedded in this class, for each N, there are N distinct coupled KdV systems. When N = 2 our class includes 3 known equations: dispersive water waves, Ito's equation and reduced Benney's equations. These equations are thus tri-Hamiltonian. We also present 2 examples of 3-component quadri-Hamiltonian systems, which generalise the above mentioned dispersive and nondispersive water waves.     

M-Zentrenbildung in röntgenbestrahlten KCl-Kristallen

The production of F- and M-centres in KCl by X-irradiation has been studied at temperatures between ?20 °C and 50 °C. The optical absorption measurements could be conducted without interrupting the X-irradiation. The results can be summarized as follows: 1. In Harshaw KCl crystals the number of F-centres created by the so-called fast coloration process was proportional to the height of the absorption band at 204 mμ prior to the irradiation. 2. The F-centres formed by the fast process did not contribute to the formation of M-centres. 3. In crystals with a strong absorption band at 204 mμ unstable M-centres were observed, which decayed rapidly after the cessation of the X-irradiation. Their concentration was found to be independent of the F-centre concentration. 4. At temperatures below 0 °C the relation between the concentration of the stable M-centres and the F-centre concentration could not any longer be represented by [M]=k ₁₂·[F₁]·[F₂]+k ₂₂·[F₂]², F₁ and F₂ referring to the F-centres created respectively by the fast and the slow coloration process. Except at very low F₂-centre concentrations however the relationship [M]=k ₀+k ₂·[F₂]² represented the experimental data at all temperatures between ?20 °C and 50 °C. At constant temperaturek ₂ varied withL, the X-ray energy absorbed per unit time and unit volume, according to 1/k ₂=a+bL+cL ². The temperature dependence ofa ^?1 b ^?1 andc ^?1 could be approximated by Boltzmann factors. The corresponding activation energies wereE _a=0.12 eV,E _b=0.53 eV,E _c=0.97 eV.     

McMillan Tc公式的解析推导(Ⅰ)——μ*=0情形

作者在μ^*=0情形,从Eliashberg方程解析地导出如下的T_c公式:T_c=αω_logexp{-b((1+cλ)/λ)},式中α=2γ/π,b=c=1;Inγ=C=0.5772是Euler常数。这个T_c公式只有在T_c=0.36/α(k)以下才是正确的,α是个大于1并随材料而异的常数。我们推测,当T_c超过上述范围后,T_c公式的函数结构很可能不同于McMillan T_c公式,至少α,b和c等参量不再是些不依赖于材料的常数了。 关键词：     

McMillan Tc公式的解析推导(Ⅲ)

本文把作者在前面两篇文章导出的T_c公式推广成下面形式:T_c=αω_log(ω_log/ω_c)^{(μ*/(λ-μ*))exp{-(1+λ)/(λ-μ*)},并从线性Eliashberg方程出发,导出了计算α的方程组。α一般是λ和μ*的函数。在弱耦合极限下,由上述方程组解得,α=2γ/π,其中lnγ=C=0.5772是Euler常数。这个结果表明了,前面两篇文章得到的T_c公式在弱耦合极限下是正确的。作者进而在Einstein谱和μ*=0情形,用数值计算方法从定α的方程组算出当λ=0.23,0.25,0.38和0.48时,a的数值。结果表明,至少在0.23≤λ≤0.45区间中,α变化很小,近似等于1/1.30。此时,本文的T_c公式实际上就是Allen及Dynes修改后的经验的McMillan T_c公式。 关键词：}     

X-ray diffraction analysis and occurrence of multiple phases in Bi-Sr-Ca-Cu-O superconductors

Starting composition 1112 for Bi-Sr-Ca-Cu-oxide yields multiphase super-conductors with the proportion of constituent phases depending sensitively on the annealing temperature. The R-T curves show zero resistivity and the transition corresponding toT _c = 80 K phase prominently. However, indexing of X-ray diffraction peaks reveals presence of 80 K (lowT _c) as well as 108 K (highT _c) phase. The lowT _c phase thus corresponds to the orthorhombic structure with a unit cell ofa = 5.4Å,b = 27 Å andc = 30.56 Å. This is further understood to be composed of a pseudotetragonal cell ofa =b = 5.41 Å. The highT _c phase similarly pertains to the orthorhombic structure withc = 36 Å.     

非晶态超导体的2△0/(kBTc)和声子谱参量

提出了能够很好地描述非过渡金属无序和非晶态超导体的2Δ₀/(k_BT_c)与声子谱参量之间关系的一个公式:2Δ₀(k_BT_c=4.95[1-(T₀<ω>^1/2)/A(1/(λω₀)+1/(20λ<ω>)+1/(20<ω>))]。计算了大量已知声子谱的非晶和无序超导体的能隙2Δ₀对T_c的比,结果表明在百分之几的范围内与实验值符合。指出了非过渡金属和合金的非晶态超导体,既可以是一个2Δ₀/(k_BT_c)值远大于BCS理论值(3.53)的强耦合超导体,也可以是一个2Δ₀/(k_BT_c)值比BCS理论值还要小得多的弱耦合超导体。 关键词：     

Synthesis and excess conductivity analysis of TlBa2(Ca3−y Be y )Cu4O12−δ superconductors

TlBa₂(Ca_3?y Be _y )Cu₄O_12?δ (y = 0, 0.5, 1.0, 1.5, 2) samples are synthesized at normal pressure and the influence of doped Be-atoms on the superconductivity parameters at the microscopic level is investigated by carrying out excess conductivity analyses of conductivity data. The samples have shown tetragonal structure and the unit cell volume decreases with increased Be-doping. The onset temperature of superconductivity [T _c(onset)] and zero resistivity critical temperature [T _c(R = 0)] decrease with increased Be, however, the magnitude of diamagnetism is enhanced with Be (except for Be-doping of y = 1.0). The apical oxygen mode of the type Tl–O_A–Cu(2) and CuO₂ planar oxygen mode are softened as observed in FTIR absorption measurements. The FIC analyses of conductivity data have shown an increase in the coherence length along the c-axis and inter-plane coupling. The values of B _c0(T), B _c1(T), J _c(0), τ _φ are improved with the doping of Be. These observations suggested that due to the proximity effect there is less suppression in the value of the order parameter of the Cooper pairs from |ψ|² = 1 value in the CuO₂ planes in Be-doped samples that maintains the density of carriers in the conducting CuO₂ planes [since the |ψ|² = n/2] which promotes enhancement in the magnitude of superconductivity.     

Stoichiometry of the chevrel phase SnMo6S8

The phase field of the Chevrel phase Sn_xMo_yS₈ was investigated by metallographic methods. A shift of the phase field away from the “ideal” compound SnMo₆S₈ towards the molybdenum-rich side of the phase diagram was observed. The degree of off-stoichiometry could not yet be determined, however, the c/a ratio of the hexagonal lattice parameters can be used to characterize the samples. Measurements of the superconducting transition temperature indicate two superconducting “phases”, which differ in the c/a ratio of the lattice parameters. While phase A showed a linear variation of T^a_c with c/a in the region from 11.0 to 13.0 K phase B was independent of the c/a ratio with a T^b_c = 10.8 ± 0.2 K.     

McMillan Tc公式的解析推导(Ⅱ)——μ*≠0情形

本文把文献[1]的理论以及所得到的T_c公式推广到μ^*≠0情形,得到T_c=(2γ)/πω_log·(ω_log/ω_c)^{(μ*/(λ-μ*))}·exp{-(1+λ)/(λ-μ^*)}. Inγ=C=0.5772是Euler常数。 关键词：     

Anisotropy in the length change of gallium single crystals at their superconducting transition

The magnetostriction of gallium single crystals has been measured for the three principal axes between 0.3K and 1.1 K. It is found that the length change at the transition from the superconducting to the normal state is given approximately by (Δl/l)_a = − 3.10⁻⁹, (Δl/l)_b = + 4.4 · 10⁻⁹ and (Δl/l)_c = + 1.8 · 10⁻⁹, for the a, b and c axes at T = 0 K. A short discussion of the results with respect to microscopic theory is presented.     

Structure and magnetotransport properties of the new quasi-two-dimensional molecular metal β″-(BEDT-TTF)4H3O[Fe(C2O4)3] · C6H4Cl2

The β″-(BEDT-TTF)₄A^I[M^III(C₂O₄)₃] · G(A^I=NH ₄ ⁺ , H₃O⁺, K⁺, Rb⁺; M^III=Fe, Cr; G = “guest” solvent molecule) family of layered molecular conductors with magnetic metal oxalate anions exhibits a pronounced dependence of the conducting properties on the type of neutral solvent molecules introduced into the complex anion layer. A new organic dichlorobenzene (C₆H₄Cl₂)-containing conductor of this family, namely, β″-(BEDT-TTF)₄H₃O[Fe(C₂O₄)₃] · C₆H₄Cl₂, is synthesized. The structure of the synthesized single crystals studied by X-ray diffraction is characterized by the following parameters: a = 10.421(1) Å, b= 19.991(2) Å, c= 35.441(3) Å, β = 92.87(1)°, V= 7374(1) ų, space groupC2/c, and Z = 4. In the temperature range 0.5&;2-300 K, the conductivity of the crystals is metallic without changing into a superconducting state. The magnetotransport properties of the crystals are examined in magnetic fields up to 17 T at T = 0.5 K. In fields higher than 10 T, Shubnikov-de Haas oscillations are detected, and the Fourier spectrum of these oscillations contains two frequencies with maximum amplitudes of about 80 and 375 T. The experimental results are compared with the related data obtained for other phases of this family. The possible structural mechanisms of the effect of a guest solvent molecule on the transport properties of the β″-(BEDT-TTF)₄A^I[M^III(C₂O₄)₃] · G crystals are analyzed.     

Elastic constants of solid krypton at T = 77 K determined by inelastic neutron scattering

Long-wavelength acoustic phonons have been studied for each of the [ζ00]T, [ζ00]L, [ζζ0]L and [ζζ0]T₁ branches in solid Kr at T = 77 K by means of inelastic neutron scattering utilizing ‘cold neutrons’ as they are available in the long-wave length tail of the pile spectrum. The raw data have been corrected for resolution effects taking into account the curvature of the dispersion surface and variation of mode eigenvectors. It has turned out, that this yields appreciable shifts of the raw data. The results of our experiment give c₁₁ = 4·25 ± 0·10, c₄₄ = 2·04 ± 0·03, c₁₂ = 2·82 ± 0·12 and a value for B = (c₁₁ + 2c₁₂)/3 = 3·30 ± 0·09 × 10¹⁰ dyne/cm². Available thermodynamic data for Kr gives a derived value for B^ad = 2·58 ± 0·06 × 10¹⁰ dyne/cm² indicating a large difference between zero sound and first sound in solid Kr at high temperatures.     

X-ray determination of the linear compressibilities of (SN)x

The linear compressibilities of (SN)_x have been determined up to 22 kbar using a hydrostatic-pressure X-ray cell: at 1 bar, k_a = 5.5;k_b = 2.2; k_c = 5.0; k_[201] = 3.8 —; all in units of 10^-12cm²/dyne. The results are compared with other chain-like solids and confirm the anisotropic three-dimensional bonding character of (SN)_x. Pressure dependence of the electrical conductivity is discussed.     

Effect of doping with iron on the charge ordering in La0.33Ca0.67Mn1−y Fe y O3 (y = 0, 0.05) manganites

The formation and specific features of the superstructure in La_0.33Ca_0.67Mn_1?y Fe _y O₃ (y = 0, 0.05) manganites doped with iron are investigated using transmission electron microscopy. The electron diffraction patterns of the manganites are studied in the temperature range 90–300 K, and the high-resolution electron microscope images recorded at temperatures of 91–92 K are analyzed. In both manganites, the structural transition that is accompanied by the formation of the superstructure and which is directly observed from the appearance of additional peaks in the electron diffraction patterns occurs at a temperature that is in close agreement with the charge ordering temperature T _CO determined from the temperature dependences of the magnetization M(T). In the temperature range 90 < T < 200 K, the undoped compound has a commensurate superstructure characterized by the vector q = 1/3a* and triple the unit cell «3a × b × c» (where a ≈ b ≈ √2a _c , c ≈ 2a _c , and a _c ～ 3.9 Å is the lattice parameter of a simple perovskite). The doping with iron (5 at. %) brings about a decrease in the charge ordering temperature T _CO by 50 K and the formation of an incommensurate structure for which the magnitude of the vector q is smaller by approximately 15%. The unit cell of the superstructure in the iron-doped compound is not triple the unit cell but involves defects of ordering, such as quadrupling of the unit cell, numerous translations by a _c √2 along the a direction, and dislocation-type defects in the stripe structure of the charge ordering. These pseudoperiodic defects lead to a decrease in the magnitude of the vector q and are responsible for the incommensurability of the structure. A decrease in the charge ordering temperature T _CO due to the doping with iron and the incommensurability of the superstructure correlate with the change in the concentration of Mn³⁺ Jahn-Teller ions as a result of their replacement by Fe³⁺ non-Jahn-Teller ions.