Energy Scales in the High-Tc Superconductor YBa2Cu3O6+x

The optical conductivity sum rule is used to examine the evolution of the spectral weight N() in both the normal and superconducting states of optimally and underdoped YBa₂Cu₃O_6+x along the a axis. Differences in N() above and below T _c allow the strength of the superconducting condensate _s to be determined. In the optimally-doped material, _s is fully formed at energies comparable to the full superconducting gap maximum (0.1 eV), while in the underdoped material the energy scale for convergence is considerably higher (0.6 eV). This difference is discussed in terms of normal-state properties.     

Comparison of Superconductivity and Structure for Lanthanum Replacing for Barium and Copper in YBa2Cu3Od

X-ray diffraction studies and the resistivity measurements are used to characterize the structure and the superconductivity of the nominal composition of YBa₂Cu_{3 – x} La _x O _d (YBCLO) cuprates with x 0.30. There was a BaCuO₂ impurity phase detected with x 0.10. The structure of the main phase (123) has the orthorhombic form with Pmmm symmetry in the whole doping range. With increasing content of lanthanum, x, the lattice constants increase for x < 0.04, and decrease for x 0.04. Rietveld refinements for X-ray diffraction show that the dopant of lanthanum substitutes for copper in the lower doping level, and replaces for both barium and copper in the high doping level. The zero-resistance temperature T _c0 first increases with the increase of the content of lanthanum in YBCLO as x 0.04 and then decreases with x as x 0.04. We compared the results with those of La-doped YBa_{2 – z} La _z Cu₃O _y cuprates. The different relationship in superconductivity dependence of lanthanum content may result from the strains due to the different occupancy of lanthanum in the unit cell of YBa₂Cu₃O _d .     

AC electrical conductivity of electron beam evaporated Cu-GeO2 thin cermet films

AC electrical properties of 410 nm think 30 at.wt% Cu-70 at.wt% GeO₂ thin films are reported for the frequency range 10⁴ to 10⁶ Hz and temperature range 150 to 425 K. The loss tangent (tan ) and the dielectric loss (/₀) are found to show striking minima around a cut-off frequency 10⁵ Hz. In the lower frequency range (10⁵ Hz), ₁() ^s T ⁿ is obeyed with s (0 to 0.51) increasing as a function of temperature and n (0.10 to 0.14) showing a very weak temperature dependence. In the higher frequency region (10⁵ Hz), ₁() and /₀ increase sharply leading to the quadratic behavior of ₁() with s equal to 2. These processes are discussed by analyzing an equivalent circuit which shows that at lower frequencies, the effects of series resistance in leads and contacts can be neglected, while at higher frequencies such effect give rise to spurious ² dependance for the conductance. A weakly activated AC conductivity and a frequency exponent s that increases with increasing temperature suggest that the low frequency behavior originates from carrier migration by tunneling process.     

Magnetic Phase Diagram of Ca1?xMnxO

Alternating current susceptibility and direct current magnetization have been studied for polycrystalline Ca_1–x Mn _x O. On increasing the Mn content, magnetic ordering changes from spin glass behavior for 0.25 x 0.4 to antiferromagnetic order. The paramagnetic/antiferromagnetic transition is of second order for 0.5 x 0.65 and of first order for x 0.7. For low Mn concentrations, the high-temperature alternating current susceptibility can be described by a diluted Heisenberg magnet model developed for diluted magnetic semiconductors.     

Chemical Control of Underdoped and Overdoped States in Y(Ba2 ? ySry)Cu3O6 + δ

The chemical control of underdoped and overdoped states in the Y(Ba_{2 – y} Sr _y )Cu₃O_{6 +} (0.1 and 0.9) compounds has been observed by high-resolution O K-edge X-ray-absorption near-edge-structure spectra. The chemical substitution of Sr for Ba in the fully-oxygenated Y(Ba_2–y Sr _y )Cu₃O_{6 +} (0.9) compounds gives rise to high hole concentrations within both the CuO₂ planes and the out-of-plane sites, leading to the overdoped state and the decrease in the superconducting transition temperature from 92 K for y=0 to 84 K for y=0.8. In contrast, an increase in the Sr content in the oxygen-deficient Y(Ba_{2 – y} Sr _y )Cu₃O_{6 +} (0.1) compounds did not indicate superconductivity. The oxygen-deficient compounds exhibit the underdoped state due to the low hole concentration.     

On the number of term orders

By an admissible order on a finite subsetQ of ⁿ we mean the restriction toQ of a linear order on ⁿ compatible with the group structure of ⁿ and such that ⁿ is contained in the positive cone of the order. We first derive upper and lower bounds on the number of admissible orders on a given setQ in terms of the dimensionn and the cardinality ofQ. Better estimates are possible if the setQ enjoys symmetry properties and in the case whereQ is a discrete hyperbox of the form In the latter case, we also give asymptotic results as d _k for fixedn. We finally present algorithms which compute the set of admissible orders that extend a given binary relation onQ and their number. The algorithms are useful in connection with the construction of universal Gröbner bases.AMS Classification: primary 06F20 secondary 06-04, 11N25     

Sr2YRu1?uCuuO6: Evidence for SrO-Layer Superconductivity

Sr₂YRuO₆ doped on its Ru site by Cu superconducts at the below 45 K, although its Ru and Cu are magnetically ordered at 23 K and 86 K, respectively. The SrO layers superconduct. Ba₂GdRuO₆, when doped with Cu, does not superconduct, because L = 0 Gd is not crystal-field split, and so induces Cooper pair-breaking.     

Low-Field microwave measurements of YBa2Cu3O7?x near the superconducting transition temperature

Novel microwave absorption and dispersion measurements have been performed on well-characterized single-crystal platelets of the high-T _c superconductor YBa₂Cu₃O_7–x . The results are explained in terms of the rapid variation of the penetration depth near and belowT _c . Since EPR measurements are very sensitive to small changes in absorption and dispersion, this technique should be very useful in the understanding of the transition temperature region in both new and old superconducting materials.     

Effect of magnesium content on the stress exponent and effective stress in the steady state creep of Al-Mg alloys

The stress exponent of steady state creep,n, and the internal ( _i) and effective stresses ( _e) have been determined using the strain transient dip test for a series of polycrystalline Al-Mg alloys creep tested at 300° C and compared with previously published data. The internal or dislocation back stress, _i, varied with applied stress,, but was insensitive to magnesium content of the alloy, being represented by the empirical equation _i=1.084 ^1.802. Such an applied stress dependence of _i can be explained by using an equation for _i of the form _i (dislocation density)^1/2 and published values for the stress dependence of dislocation density. Values of the friction stress, _f, derived using the equation _e/=(1–c) (1– _f/), indicate that _f is not dependent on the magnesium content. A constant value of _f can best be rationalized by postulating that the creep dislocation structure is relatively insensitive to the magnesium content of the alloy.On leave from Engineering Materials Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

Bounds for traces in complete intersections and degrees in the Nullstellensatz

In this paper we obtain an effective Nullstellensatz using quantitative considerations of the classical duality theory in complete intersections. Letk be an infinite perfect field and let f₁,...,f n–rk[X₁,...,X_n] be a regular sequence with d:=max_j deg f_j. Denote byA the polynomial ringk [X₁,..., X_r] and byB the factor ring k[X₁,...,X_n]/(f₁,...,f_n r); assume that the canonical morphism AB is injective and integral and that the Jacobian determinant with respect to the variables X_r+1,...,X_n is not a zero divisor inB. Let finally B^*:=Hom_A(B, A) be the generator of B^* associated to the regular sequence.We show that for each polynomialf the inequality deg (¯f) dⁿ r(+1) holds (¯fdenotes the class off inB and is an upper bound for (n–r)d and degf). For the usual trace associated to the (free) extensionA B we obtain a somewhat more precise bound: deg Tr(¯f) dⁿ r degf. From these bounds and Bertini's theorem we deduce an elementary proof of the following effective Nullstellensatz: let f₁,..., f_s be polynomials in k[X₁,...,X_n] with degrees bounded by a constant d2; then 1 (f₁,..., f_s) if and only if there exist polynomials p₁,..., p_sk[X₁,..., X_n] with degrees bounded by 4n(d+ 1)ⁿ such that 1=_ip_if_i. in the particular cases when the characteristic of the base fieldk is zero ord=2 the sharper bound 4ndⁿ is obtained.Partially supported by UBACYT and CONICET (Argentina)