Laboratory Report Materials Physics Laboratory
The determination of the Superconducting Transition Temperature Yufei Chang • Group H
Abstract The experiment was set out to determine the superconducting transition temperature at which the resistance becomes zero,of YBa₂Cu₃O₇₋ᵩ using the four-point probe method. There were two parts to the experiment; cooling and warming. The sample was cooled using liquid nitrogen until it reached a contant temperature. The sample was then slowly taken out of the liquid nitrogen and warmed up by a controlled heater. Reading of voltage and temperature were recorded for both the cooling down and warming up processes. two graphs were plotted for both the processes, and from these graphs, the Tⅽ values were obtained.
Introduction Superconductivity is a phenomenon displayed by some materials when they are cooled below a certain temperature, known as the superconducting transition temperature, Tⅽ. Below Tⅽ, these superconducting materials experiences no electrical resistance and perfect diamagnetism. In this experiment, however we will only be focussing on the zero resistance of the superconducting material YBa₂Cu₃O₇₋ᵩ. Superconductivity was discovered in 1911 by Kamerlingh Onnes at the University of Leiden when mercury was cooled down to helium temperatures.❶ Its Tⅽ was found to be about 4K, which is a very low temperature and difficult to achieve. it was not until 76 years later that scientists succeeded to find a material whose Tⅽ was higher than that of the boiling point of liquid nitrogen(77K). Nitrogen is abundant and relatively easy to liquefy, and thus inexpensive. In 1957, J Bardeen, L.N.Cooper, and J.R.Schrieffer proposed a theory which explained the phenomenon of superconductivity . This theory is known as the BCS theory. The BCS theory states that electrons with opposite spin can become paired, forming Cooper pair. Cooper pairs are formed by electron-phonon interactions.❷ An electron in the cation will distort the lattice around it, creating an area of greater positive charge density around itself. This deformation of the lattice(phonon) causes another electron with opposite spin to be attracted into this region. The electrons are indirectly attracted to each other and form a Cooper pair. The Cooper pairs within the superconductors are what carry the supercurrent. A Cooper pair is more stable than a single electron within the lattice, therefore it experiences less resistance. However, the superconducting state cannot be made up entirely of Cooper pair as this would lead to the collapse of the state. Physically, the Cooper pair is more resistant to vibrations within the lattice as the attraction to its partner will keep it on course, therefore, Cooper pairs move through the lattice relatively unaffected by thermal vibrations. The electrons are held together with a certain binding energy. If this binding energy is higher
than the energy provided by kicks from oscillating atom in the conductor, then the electron pair will stick together and resist all kicks, thus not experiencing resistance.
Experimental A sample of YBa₂Cu₃O₇₋ᵩ was provided in the form of a bar. Before the sample was placed into the cooling system, its measurements were taken. On the sample were four contacts, two at the ends of the bar which served as current leads, two which ere wrapped round the middle of the bar and served as voltage probes. This four-point geometry was used to overcome the problems of contact resistances at the current leads. A constant current ( I is 10mA) was passed through the sample and the voltage generated was sensed at the two probes and measured on a digital voltmeter. A thermocouple was connected to the system, allowing the temperature to be monitored. The sample holder was placed in a vacuum flask, and the sample was slowly immersed into the flask containing liquid nitrogen. The temperature and voltage were then recorded as the tube was lowered and the temperature started to decrease. The tube was slowly lowered as to prevent inaccurate results which might had been caused by rapid fall in temperature. The reading were taken in the intervals of approximately 10 degrees. The sample was continued to be cooled until a constant temperature was achieved. At this point, the voltage became zero. The next part of the experiment was the warming up process. The sample was slowly taken out of the liquid nitrogen and warmed up using a controlled heater. The temperature and the voltage were again recorded for the heating cycle.
Experimental Dimensions of the sample DIA= 0.95mm Length= 7.5mm Cross sectional area=∏×0.475²=0.709mm² Constant current=10mA The resistance of the sample R is given by the equation R = ρl/A ① R is the resistance of the material Ω ρ is the specific resistivity of the material J/kg l is length of the sample cm A is cross sectional area of the sample cm² And as V=IR ② V is voltage mV I is current mA R is resistance Ω So, by substituting R into equation① and rearranging the equation to find resistivity gives
ρ=VA/Il ③ A/Il can be taken as a constant which is 9.45×10⁻⁴ cm mA⁻¹
Discussion and Conclusion The data that got from this experiment was not accurate and that cause the graphs above look not as theoretical shapes( not linear relation). And the Tⅽ is not correct neither. The ideal temperature for cooling should drops rapidly at around 90K and goes to zero at 85K. For warming, it should be 95K and 105K. And the temperature difference between these two process should around 10K, that due to the gap of the electron energy states. This means a small amount of energy is not sufficient to disturb the Cooper pairs and so cause electrical resistivity. The major reason for the fail is from taking results. The temperature changed to fast and had not enough time to copy them down.( actually not for man to copy) And the equipments used were so like RUBBISH !! In this experiment, a four point geometry was chosen rather than a two point geometry. This is as the two point geometry can only record one parameter at a time, whereas the four point parameter can record two at the same time, in this case, voltage and temperature. The BSC theory explained in the introduction only predicted a theoretical maximum of Tⅽ of around 30-40K, as above this, thermal energy would cause electron-phonon interactions of an energy too high to allow formation of or sustain Cooper pairs. The Tⅽobtained in this experiment is higher than the theoretical limit imposed by the theory. An explanation for this is that there are holes within the superconductors. Metal ions in compounds such as YBa₂Cu₃O₇₋ᵩ are partially oxidized. This means that there are holes of positive charge within the lattice. Although the positive holes are usually stabilized by surrounding counter-ions, the highly charged ions will still ideally want to reduce. However, they cannot gain an electron from neighboring ions . When a current is applied to the material, electrons travel along the ions planes in the lattice. As an electron passes a hole in a neighboring plane, it will push negative charge from orbitals on a reduced cation towards the hole by distorting the lattice. The oxidized cation then reduces, and the reduced ion oxidizes, moving the hole backwards as an electron moves forwards. This extra current caused by the normal current is the supercurrent.❸
Reference MSE 205 notes ❶❷lab script ❸http://www.gamry.com/App_Notes/EIS_Primer/EIS_Primer.htm#Impedance%20Definition