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
Hall effect of epitaxial YBa2Cu3O7-x and Bi2Sr2CaCu2Oy films: Interpretation of the Hall effect on the basis of a renormalized tight-binding model.
The Hall effect of epitaxial YBa2Cu3O7−x and Bi2Sr2CaCu2O y films has been investigated experimentally and theoretically. In both compounds the normal state Hall coefficient R H (B || c-axis) is positive and exhibits a strong temperature dependence, which is more pronounced in YBa2Cu3O7−x than in Bi2Sr2CaCu2O y . The Hall coefficient R xyz H in the normal phase has been calculated on the basis of a renormalized two-dimensional tight binding model using the relaxation time approximation. Strong correlation effects are accounted for via doping dependent hopping terms leading to band narrowing. The influence of the choice of the relaxation time on the Hall coefficient is explored. The calculations have been performed for a wide range of parameters and are compared to experimental data.
Hygroscopic Expansion of some Casting Investments
CREDIT is generally given to Taggart1 for introducing the cast gold inlay to the dental profession. Although he realized that gold shrinks when cooled from molten state to solid state of room temperature, the investment available to him did not supply sufficient compensation. In 1910, Van Horn2 published a paper dealing with a method by which he obtained the compensation by means of wax expansion. The next major research in connection with this problem was the work of Coleman3 at the National Bureau of Standards. He determined the gold shrinkage to be 1.25 per cent and presented a casting technic with compensation values of quantitative nature. The total compensation for the gold shrinkage was obtained by the combination of the setting and thermal expansion of the mold. This procedure is the general practice followed at the present time for compensation. There are some disadvantages to this method. Skinner has indicated the difficulty of obtaining smooth castings and the improper compensation for the casting shrinkage.4 It has been found by Hollenback5 and Scheu6a that castings made at a high temperature are rougher than those made at a low temperature (450° C.), depending upon the great difference in thermal expansion between plaster of Paris and silica, which causes a poor union of the fine particles. This may also result in friability and there may be some warpage due to the differential expansion. A method which provides sufficient compensation at a low mold temperature is the hygroscopic casting technic.b Wilson7 showed that certain plasters expand as much as 0.0044 inch to the inch by taking up moisture from the air. With this information at hand, Scheula, b tested some commercial investment to determine what results the addition of moisture would have. He found6b: (1) All of the casting investments that were tested expanded. (2) The thicker the mix, the greater the expansion. (3) A mix with hot water expanded more than one with cold water. (4) The time at which the mix is placed in the water is of great importance. It was found that if the mix is placed in the water early, it would not expand so much as when placed in a little later. It was also found that if the mix was placed in the water after a certain time, it could not expand to the maximal amount. (5) The temperature of the water in which the mix is placed is important, for two reasons; (a) the temperature of the water controls slightly the expansion of the investment, and (b) water at a temperature of 1000 F. slightly softens the wax pattern so that the fine margins are not marred while expansion is taking place. The mix should remain in the water at least 20 minutes to obtain the full expansion, after which time no further expansion is obtained.