We attempted to increase the flux pinning capabilities of YBCO by doping it with the rare earths Sm, Nd, Eu, Dy, Ho, and Gd. Bulk samples of rare earth doped yttrium superconductors were made by annealing pellets at various temperatures and in various gases through four sinters.  We then measured and compared the samples using x-ray diffractometry and magnetic susceptibility tests. We have found that the samarium-doped sample had the best flux-pinning and that there is a correlation between the strain in a sample and its flux-pinning capabilities. We will continue to study samarium-doped YBCO, and if we find that one sample has substantially improved flux pinning properties, we will produce a film by pulsed-laser-deposition and test its superconductivity properties.

1.  Introduction
Rare earth barium copper oxide superconductors are useful because of their low resistance, good flux pinning capabilities, high transition temperature of 93 K, and stable nature.  These properties make high temperature superconductors such as YBa₂Cu₃O₇ (YBCO) excellent candidates for AC power and high magnetic field applications.  The problem with YBCO is that it is difficult to align the grains in powder form to make long lengths of this material.  The Superconductivity Technology Center at Los Alamos National Laboratory now has the capability to make one-meter length tapes composed of superconducting YBCO film, with very well aligned grains on hasteloy substrates. Our goal was to increase the flux pinning capabilities of the YBCO film by doping it with the other rare earths Sm, Nd, Eu, Dy, Ho, and Gd.
We measured a YBCO sample and studied similar rare earth superconductors REBa₂Cu₃O₇  (RE = Sm, Nd, Dy, Eu, Gd, or Ho).  We then made bulk samples of rare earth doped yttrium superconductors (RE_0.5Y_0.5Ba₂Cu₃O₇ where RE= Sm, Nd, Dy, Eu, Gd, or Ho). We characterized the samples using x-ray diffractometry and magnetic susceptibility measurements. It was our hope that because the flux-pinning capabilities of some of the other rare earth superconductors are better than the YBCO (SmBa₂Cu₃O₇ for example), the dopant would improve the flux pinning capability of our sample.

2.   Experimental Processing
    The process of preparing the samples for testing is one of mixing and sintering powders. For each sample, stoichiometric amounts of rare earth oxide, barium carbonate, copper oxide, and yttrium oxide needed to achieve the desired stoichiometry and sample mass of about 30 g were mixed. Each of the constituent compounds was mixed and ground in an agate vial with Spex Mill 8000 and then pressed into a one-inch diameter pellet. Each pellet was then placed in a 920 o C furnace for between three and seven days. After annealing, the pellet was crushed, reground, pressed, and resintered at 920 o C.  This process was repeated three times. For the fourth and final sintering, the pellet was annealed in pure oxygen at temperatures from 420 o C to 920 o C for 42 hours. We then left the sample in the oxygen at 420 o C for 25 to 50 more hours. Most of these superconductors absorb oxygen at 420 o C and expel it around 920 o C, so cycling the temperature allows the sample to acquire more oxygen. Each grinding and sintering allows each of the compounds to react more with each other, thus making a more homogenous sample. After each sintering, some material was taken from each pellet and measured.

3.    Measurements
    We measured three properties of each material: the magnetic susceptibility as a function of temperature, the lattice parameters, and the magnetization as a function of field. The susceptibility can indicate the quality of a superconductor- how homogenous, without impurities our secondary phases, the sample is. We use a SQUID (superconducting quantum interference device) magnetometer to measure magnetization, which is the response of a solid from an applied field, from each sample at temperatures from 1 K to 100 K.  From the temperature dependence of the susceptibility, we determined the onset and ending temperatures of the superconducting transition. The narrower the transition is in temperature, the more homogenous. Wide transitions suggest that there is a variation among unit cells- some cells may be better oxygenated or some cells may have atoms on the wrong sites. This is important because some of our samples are more difficult to make and may need special conditions to optimize their properties. Flux pinning properties are somewhat independent of transition widths, so even if the susceptibility suggests that a sample is inhomogeneous, we can still draw meaningful conclusions about flux-pinning.
Finding the lattice parameters of a sample is a daunting task. First, x-ray diffractometer measurements must be done on the sample. This is where a x-ray scan of the sample is done at various angles and the counts per second are measured at each angle or fraction thereof. This graph then has a line fit to it. The up to 35 variables used in the equation of the fit represent every aspect of the unit cell from atom positions to concentrations of atoms at sites.
Measurement of the lattice parameters using Rietveld analysis allows us to determine how the unit cell of our samples varied in size from that of pure YBCO. The unit cell of a crystal is the smallest repeating unit of atoms in the crystal. Lattice parameters are the sizes of each of the lengths of the unit cell (length, width, and height). Thus, viewing the change in size of the unit cell can allow us to see whether or not a site has been occupied by another atom. This is important because that can change in position will change the properties of the crystal. Finding lattice parameters allows me to correlate unit cell size to flux-pinning capability.
Using a SQUID magnetometer, we were able to measure the magnetic moment of each superconducting sample as a function of field at 75 K, and from that, derive relative flux-pinning capabilities. A hysterisis loop is a measurement of the magnetization versus field, typically from positive field, to negative field, and back to positive field, thus producing a loop. Our samples were tested from 7 T to 7 T. Each point in this plot represents the amount of flux trapped inside of the sample, and we can derive the flux-pinning capabilities of a sample by measuring the average width from the corresponding points of field. For example, one measurement would be the width between the magnetization at 2G in decreasing field and the magnetization at 2G in increasing field. In a normal metal, such as aluminum, a hysterisis loop would be a straight line because flux would be able to enter and exit the sample freely. However, superconductors are resistant to a changes in their flux density, thus there is a difference in the flux density of the sample when pushing flux in and pulling flux out. The bigger this difference is the better flux-pinning capabilities the sample has. Since this is a direct measurement of what wefor, this is the most important measurement. At 75 K, we found the average width of the hysterisis loop between 3000 G to 20000 G for each of the samples.

4.   Analysis
We are looking for better flux-pinning superconductors and trends that might lead to a better understanding of flux-pinning. Since we are comparing the reaction of YBCO to dopants of different sizes, our analysis is done with respect to ionic size. Some trends were confirmations of already know properties of superconductors and YBCO in particular. The midpoint of a superconductordopant increased in all of our samples. This is because as the ionic size of the dopant increases, the unit cells with the dopant are larger than the unit cells with the yttrium. This non-uniformity causes a lower Tc for the sample. Looking at the lattice parameters, we also see that as the ionic size of the dopant increases, the average size of the sampleunit cell increases as well. The interesting, and possibly unknown, discovery that we made was that there is a correlation between the strain in the sample and the flux-pinning capabilities. Strain is caused in the sample structure because there are unit cells of different sized connected to each other, this a smaller adjacent unit cell will cause compression on a larger one, or a larger unit cell will cause an expansive tension on another unit cell. The strain percentage of the sample can be found in the difference between the x-ray peak of the pure sample and the x-ray peak of the doped sample. We have found that as the strain in a sample increases, via increasing the ionic size of the dopant, that the flux-pinning capabilities of the sample also increase. This is supported by the fact that the samarium-doped sample had the greatest strain and the best flux-pinning capabilities. Also, the sample doped with neodymium, which has a larger ionic size than samarium, has a much smaller strain than samarium and is also a much worse flux-pinner.  We believe this to be because the neodymium atoms in the unit cell are switching place with the barium atoms. We believe this is a common occurrence in the unit cell of a doped yttrium superconductor where the dopant is almost the ionic size of barium. If this is the case, strain can be greatly relieved by the switching of the barium and the dopant atoms. Although, that was well known, the correlation between strain and flux-pinning capabilities is one that may be relatively new, thus further studies will be done on samarium-doped YBCO, and the correlation between strain and flux-pinning.