Hole concentrations, Hall number, and Tc relationships in substituted YBa2Cu3Oy.
One of the fundamental questions involving the high-temperature copper oxide containing superconductors is to understand the relationship between hole concentration and the superconducting transition temperature, T,. We help resolve this question by a study of Nd-, La-, Ga-, Ca-, and Zn-substituted YBa2Cu30~ with controlled oxygen stoichiometry. The total hole concentration is determined by a chemical method and trends in the mobile hole concentration by Hall measurements. By considering T, to be a function of the mobile sheet holes only, there is a maximum in T, (92 K) at a sheet-hole concentration of about 0.20-0.25 per Cu site. The importance of the hole concentration in Cu oxide containing superconductors is widely recognized and its relationship to the superconducting transition temperature (T, ) has been the object of numerous studies. ' '2 The hole concentration, which we call p, is an electron deficiency and can be determined chemically, as well as by Hall measurements. Although it is generally accepted that it is associated with the oxygen rather than the copper, i.e., 0, the chemistry of its determination is identical to that of Cu + or a hole in the copper-oxygen band. The Hall measurement is complimentary to the chemical measurement since it measures only the mobile holes. Previously, using both techniques we showed a rather linear relationship existed between T, and p in the La2 Sr„Cu04 system (for p &0.15) and discussed the possible T, vs p relationship in the 1:2:3-type materials, e.g. , YBa2Cu30». ' Our data suggested a possible relationship between the two systems if similar hole concentrations per sheet (CuOz), which we showed reached a maximum at about 0.15 in the one-sheet La2 „Sr,Cu04 system, could be produced in each of the two sheets of the 1:2:3 materials. Torrance et al. ' further studied the
Effects of Zn doping on YBaCuO superconductor
In this work we present a study of Zn impurity effects on the YBa2Cu3O7–δ high Tc superconducting ceramics prepared by the solid state reaction method. X-ray diffraction (XRD), scanning electron microscopy (SEM) and differential thermal analysis (DTA) techniques, and resistivity measurements are used to characterize the YBa(Cu1–xZnx)3O7–δ samples. The obtained results show that, for example, the value of the transition critical temperature is decreasing up to 80 K caused by the substitution of Zn for Cu in the interval 0 ≤ x ≤ 0.01. Also, the peritectic transformation of superconducting phase undergoes a displacement to lower temperatures compared with pure YBaCuO. On the basis of the obtained results, the effects of Zn doping on the structural and electronic properties are explained. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Effective long range order and phase transitions in finite, macroscopic one and two dimensional systems
Abstract The concept of long range order is discussed for finite macroscopic systems. It is shown that if the interaction range or strength, in units of kT , is of O (log N ), long range order is obtained in one dimensional systems. Short range and long range interactions are able to combine to cause long range order even when each of the two interactions by itself is much too weak to do so. A physical picture of the effects of the long range interactions is presented and supported by detailed calculations. We also show that the theorem stating that the two dimensional Heisenberg Model does not exhibit long range order is inapplicable when the interaction strength in units kT is of O (log N ), or when the range of the interaction is of O( log N) 1 4 . The two dimensional Bose gas will condense at temperatures of O( T 0 log N ) , where T 0 is the condensation temperature in three dimensions. The recent proof that superfluid long range order is impossible in two dimensions, is shown to be based, for finite N , on the analogous fact in the free gas, which is invalid according to the above. Consideration of thin Bose films shows that the transition from three dimensional (condensation at T 0 ) to two dimensional (condensation below T 0 ) behavior occurs at film thickness of order log N . This result can be of practical importance.