5G50.51 uperconductor uspension Abstract A superconductor is an object that, under certain conditions, has zero electrical resistance. A unique and interesting property of superconducting materials is the manner in which they interact with magnets. When a magnet attracts a typical magnetic object, the magnetic force causes the object to accelerate toward the magnet, and the two bodies will come into contact. When a magnet attracts a superconductor, the magnetic force causes attraction only up to a certain distance, at which point this magnetic force is balanced with other forces that result from the structure of the superconductor. Due to this balancing of forces, the superconductor can be suspended a short distance underneath the magnet. Picture etup etup is 0 minutes. Liquid nitrogen is required. afety Concerns Be careful when handling liquid nitrogen. Always use a dewar to contain the liquid nitrogen, and never use a tight-fitting lid. Do not spill liquid nitrogen on clothing. Do not immerse your hands or any body part in it. Use tongs to handle objects that have been immersed in liquid nitrogen, and wait for them to warm up before touching them directly. When handling the rare earth magnet, keep it away from small magnetic objects that it might abruptly attract. 1
Equipment uperconductor Meissner Effect Kit tyrofoam container and cup Liquid itrogen Procedure Of the two YBCO disks provided in the kit, the smaller one is the enhanced flux pinning (EFP) disk, and it is what should be used for this demonstration. It is instructive to first show that the superconductor disk is not magnetic at room temperature by placing it near the rare earth magnet and demonstrating that there is no attraction nor repulsion. ext, set the superconductor disk into the styrofoam dish. Fill the dish with liquid nitrogen until the liquid level is just above the surface of the disk. Wait for boiling to subside. Using non-magnetic tweezers, carefully move the cylindrical rare earth magnet over the superconductor, with the flat faces parallel to the table. lowly bring the magnet to the surface of the disk, so that the magnet just barely touches it. Try to center the axis of the cylindrical magnet above the center of the EFP disk. ote that the resistance felt during this step is a manifestation of the Meissner effect. lowly raise the magnet. The superconductor should follow close behind, and there will be a gap between the superconductor and the magnet. As the disk warms, the superconductivity of the EFP disk is lost, so the disk will eventually fall. Allow the disk to fall back into the liquid nitrogen bath. Do not lift the disk too high, as it may splash liquid nitrogen or become damaged. As time passes, the liquid nitrogen will boil away, so the dish should be topped up occasionally in order to keep the EFP disk completely immersed. Each time the superconductor is re-cooled, wait for the boiling to cease before again attempting to lift it with the magnet. The superconductor disk is very sensitive to moisture, so it should be kept as dry as possible while it warms. Frost will form on the superconductor when it is exposed to air. When the disk is removed from the liquid nitrogen bath remove frost with a clean wipe. Immediately place the disk under a desk lamp for a few minutes until it is completely dry and at room temperature. Any unused liquid nitrogen will boil away if it is left alone. It may also be spilled gently on the floor, where it will evaporate faster. Place all materials back in the storage box. The YBCO superconductor disk should be stored in a plastic bag with the drying agent. Theory An electrical conductor is an object through which electricity may flow. Although technically all materials permit current flow under certain conditions, in practice most objects are typified as either conductors (which permit current flow) or insulators (which prevent it). The factor that determines whether an object is a conductor or insulator is its resistance, which depends on both its geometry and the resistivity of its composite material. Resistivity, which varies from material to material, is a more general measure of opposition to current flow because it is independent of object geometry. In a given material, resistivity decreases as temperature decreases. In 1911, Heike Kamerlingh Onnes (1853-1926) discovered that certain metals exhibit zero resistivity at temperatures near liquid helium temperature (4.2 K). Metals that exhibit zero resistivity are called superconductors. It was found in 1986 that ceramics, from a class of materials called perovskites, exhibit superconductivity at much higher temperatures. These temperatures can sometimes reach as high as 90 K or even 140 K. These perovskite materials are classified as high-temperature superconductors, whereas those that require lower temperatures are appropriately known as low-temperature superconductors. The discovery of high-temperature superconductors was important because these temperatures are well above the boiling point of nitrogen (77 K). This meant that liquid nitrogen, which is both less expensive and easier to store than liquid helium, could be used to cool the perovskites sufficiently that they become superconductive. The temperature at which a material becomes a superconductor is known as its critical temperature, T c, and there are several factors that affect a superconductor s T c. The critical temperature of a given superconductor is not only a function of its material composition, but rather it is unique to that particular superconductor. The critical temperature also depends on whether or not any current is flowing through the sample, and whether a 2
magnetic field is present. For instance, a superconductor immersed in a magnetic field will have a lower critical temperature than one that is not. Finally, the critical temperature of a particular sample is also affected by whether or not the sample has many chemical impurities or structural defects. The high-temperature superconductor used in this demonstration is Y Ba 2 Cu 3 O 7 (YBCO). An experimental plot of its resistance as a function of temperature is shown in Figure 1. The sharp decline in resistance seen in the graph is characteristic of all superconductors, and also provides an estimate for the critical temperature of the superconductor. For a YBCO superconductor operating with a current of 0.3 A, the critical temperature is between about 85 K and 88 K. Figure 1: Graph of the experimental resistance of Y Ba 2 Cu 3 O 7 plotted as a function of temperature. For a given temperature of superconductor, there are also other critical values. One is the critical current density, J c, the maximum current density that can be applied through a superconductor before it loses its superconducting properties. It is important to never apply a current greater than J c through a superconductor, because the loss of superconductivity is permanent. Just as the critical temperature of a superconductor depends on the applied current and magnetic field, so too the critical current density is dependent upon the temperature and magnetic field of a superconductor at any given point in time. Finally, there is also a critical magnetic field strength, B c, associated with a superconductor in a given state. The exact value of B c depends on the temperature of, and current through, the superconductor. It also provides another means of classifying superconductors. In Type I superconductors there is only one value for B c. Above this field, the sample becomes quenched and loses its superconductive properties. ote that this loss of superconductivity is only temporary, and that superconductivity can be restored simply by removing the field. Type II superconductors are slightly more complex, and must be characterized by two critical magnetic field values, B c1 and B c2. Below B c1, the superconductor behaves as a Type I superconductor, resisting all magnetic flux due to a phenomenon called the Meissner effect. Above B c1, but below B c2, the superconductor enters what is known as a mixed state where there exist some regions in the superconductor that allow the presence of flux. In the mixed state the superconductor retains its overall zero resistivity. Above B c2, the superconductor loses its superconducting properties just like with Type I superconductors. The Meissner effect is a phenomenon unique to superconductors whereby they oppose all magnetic flux. When a superconductor is in the presence of an external magnetic field surface currents are induced in the superconductor that generate magnetic fields opposing the external field. The result is that the external magnetic field is cancelled in the superconductor. It is important to note that the Meissner effect is fundamentally different from Faraday s law of induction. The law of induction describes the opposition in a conductor to a change in magnetic flux, while the Meissner effect is an opposition in a superconductor to any magnetic flux. Figures 2a and 2b shows the YBCO disk in a magnetic field for instances when the YBCO is above and below critical temperature. The magnetic field is free to enter the disk when it is above the critical temperature, but no field can penetrate the disk once it is cooled below its critical temperature. Consider a Type II superconductor that is in a mixed state, i.e. subject to a magnetic field that is above B c1 3
B et External B et External uperconductor uperconductor (a) Above T c. (b) Below T c. Figure 2: Diagrams of a superconductor above and below the critical temperature, T c, within an external magnetic field. Grain Boundary Figure 3: Diagram showing the defects in superconductive material caused by the boundaries in adjacent grains. Forces acting on the superconductor F m : Meissner Force F b : Induced Magnetic Force F g : Force of Gravity F n : ormal Force of urface B F n F g + F m Figure 4: Diagram of a superconductor on a surface with a magnet being lowered onto it. The free body diagram for the superconductor is shown along with a list of the forces used in Figures 4, 5, 6 and 7. 4
but below B c2. In this state, there exist some regions in the superconductor that allow the presence of flux. If a superconductor in this mixed state interacts with an external magnetic field, then flux pinning can be observed. Flux pinning is the cause of the suspension effect highlighted in this demonstration. B F n F g + F m + F b Figure 5: Diagram showing the magnet being lowered onto the superconductor and the magnetic field starting to wrap around. The free body diagram for the superconductor is also shown. It is possible to model a mixed-state ceramic superconductor as having many different local values for T c and J c, which vary throughout the material as a result of the molecular composition. Perovskites, such as YBCO, have a crystalline structure that may appear uniform at the macroscopic scale, but that is actually composed of many small grains that together constitute a brittle solid. Each grain itself has a crystal lattice structure. At the microscopic scale, a superconductive material has defects, i.e. areas of structural nonhomogeneity, that arise at the boundaries of adjacent grains, as shown in Figure 3. Defects may also arise as a result of impurities in the sample. Each defect site has a local critical current density that is much lower than the typical critical current density in the superconductor, J c. uppose a permanent magnet is brought into the proximity of a superconductor, as in Figure 4. The magnet is slowly lowered down toward the superconductor, which effectively increases the magnetic field applied to the superconductor. The current at a region in the superconductor increases to oppose any change in flux. This current does not dissipate because the superconductor has no resistance. It is called a Meissner current, and it induces a Meissner force, F m, which is repulsive with respect to the permanent magnet. Unless the current density reaches J c, the induced current will be sufficiently high enough that all flux is negated, and so the magnetic field does not penetrate the superconductor. B F n + F b F g + F m Figure 6: Diagram showing the magnetic field wrapping around the superconductor as it is on the surface while the magnet starts to be pulled up. The free body diagram for the superconductor is also shown. When the magnet is lowered far enough, as in Figure 5, it reaches a point at which the superconductor starts to enter a mixed state. The Meissner currents throughout the sample are all increasing and remain below the critical current density J c, but recall that at the defect regions, the local critical current densities J c local are much lower than J c. ince the Meissner current continues to increase as the permanent magnet approaches, the number of defect regions that have reached J c local increases as well. There are thus various regions within the superconductor that act as regular conductors do, giving rise to the term mixed state. When a defect region reaches its J c local and reverts to a regular state, the magnetic field of the permanent magnet is able to temporarily penetrate that region, allowing flux to enter in that brief instant. As there is now a hole in the superconductivity, a current loop around the defect region is formed. This current loop is in a superconducting region and so it does not dissipate. It acts to oppose the change in flux through the defect region due to the permanent magnet, so the current loop induces a downward magnetic force, F b, on the superconductor. The closer the magnet moves, the more current is induced in order to negate the flux change. The flux at the defect region is thereby pinned. At the point that the permanent magnet changes direction, as in Figure 6, those current loops at defect regions again act to oppose the change in flux. ince the flux is now decreasing, the current loops decrease in 5
magnitude and then change direction, such that the induced magnetic force, F b, is now toward the permanent magnet. Flux pinning therefore creates the attractive force between the superconductor and the permanent magnet. When the magnet is lifted, as in Figure 7, the magnetic force by the miniature current loops acts upward, while the Meissner force and gravity continue to act downward. As long as the magnetic force resulting from the trapped flux is high enough to balance the downward forces, the superconductor will be suspended in a stable manner underneath the permanent B F b magnet. In the case of this demonstration, the superconductor will be lifted out of its liquid nitrogen bath as F g + a result of the attractive forces. When it is removed F m from the liquid nitrogen, it will begin to warm up. As it approaches its critical temperature, it begins to lose superconductive properties, so eventually stored currents will disappear, and then so will the upward magnetic force, causing the superconductor to fall. Theoreti- Figure 7: Diagram showing the magnetic field of the magnetic suspending the superconductor above the surface as well as the free body diagram for the superconductor. cally, if the superconductor were to remain sufficiently cold, this suspension effect could be prolonged indefinitely. The disk used in this experiment is referred to by the producers as an enhanced flux pinning (EFP) disk. It is different than typical Y Ba 2 Cu 3 O 7 (YBCO) superconductor disks in that it is made specifically to enhance the suspension effect. pecifically, there are more regions with defects at which the flux can be trapped. This particular EFP disk was created using a different temperature cycle than the manufacturers typical process, resulting in a higher number of grain boundaries. ote that it is also possible to create an EFP disk by doping a superconducting material with a small amount of silver oxide, which creates defect regions about the impurities. 6
References [1] Brant, E.H. Rigid levitation and suspension of high-temperature superconductors by magnets, American Journal of Physics, Vol 58, o. 1, January 1990. pg 43. [2] Colorado uperconductors Inc., Experiment Guide for uperconductor Demonstrations, Version 7.0, May 2007. pg 6-7, 16-18. [3] Freericks, J. K. Grain Boundaries: Guilty as charged, ature Physics, Vol 6, o. 8, August 2010. pg 559. [4] Peters, R. C. et al. Observation of enhanced properties in samples of silver oxide doped Y Ba 2 Cu 3 O x, Applied Physics Letters, Vol 52, o. 24, June 1988. pg 2066. 7