THE TRANSITION OF MAGNETIC SUSCEPTIBILITY OF THE SUPERCONDUCTING YBa 2 Cu 3 O 7

Transcription

1 THE TRANSITION OF MAGNETIC SUSCEPTIBILITY OF THE SUPERCONDUCTING YBa 2 Cu 3 O 7 Nyamjav, Dorjderem Abstract. It is the known fact that a magnetic susceptibility of the superconductor, χ=-1. A theory shows that the transition of the material to superconducting should occur at certain critical temperature, thus causing the resistivity of the material fall as a step function. In this experiment we observed the transition behavior of 123 superconductor and did qualitative analysis. 1. Introduction The superconducting YBa 2 Cu 3 O 7 -the superconductor [1], found by Paul Chu and his colleagues in 1987 [2], achieves its superconducting behavior at the temperature of about 90û K. [3] At this critical temperature a resistance of the material should drop to zero according to the theory. The perfect diamagnetism has magnetic susceptibility, χ, of negative unit. Then, MaxwellsÕ equation for magnetic field becomes, B= µ o H( 1 + χ) = µ 0 ( H + M ) = 0, which implies that there will be no magnetic field inside of the perfect diamagnetism. Therefore, if the superconductor is placed in a magnetic field the external magnetic field will expelled out of the material.(in both FC and ZFC cases) [3] If the material is field cooled, in the presence of the external field, the field will be expelled from the material. This effect is called Meisner effect [5] and this is the idea of our experiment. The goal of our experiment was to observe the transition behavior of YBa 2 Cu 3 O 7 material and give qualitative analysis. 2. Measurement and procedure Let us look at the following standard problem: two circular rings with YBa 2 Cu 3 O 7 sample placed between them and the one of the rings carries a current. Then above the critical temperature, T c, the magnetic field will penetrate through the sample. Although it will not be able to do so when the temperature drops below T c. Hence there will be change in pick-up voltage of the second coil. Therefore we can take advantage of this B vs T behavior and investigate χ.

2 First of all we estimated the pick-up voltage of the second ring using on axis trick [4]. µ 0I z 2 2 B = [ 1 3 ( ) ( 3cos θ 1)] 2R 4 R 1 1 max 2 z V R NNI t 1 3 z z = R + R µπ ωsin( ω) ( ) 1 ( ) 3 cosθ 1 cos θ where, N 1, N 2 - number of turns of rings, I- current flowing through driving coil, z-distance counted from the center of the driving coil, ϑ-angle counted from the center of the driving coil. R 1 -radius of the driving coil. Using this expression we estimated the appropriate number of turns of coils, current and distance between coils and the measured pick-up voltage agreed to our expression in error range of 15% or less. As mentioned above we used field cooled superconductor. We had placed our sample and coils inside of the cryostat, whose inside was pumped into vacuum of the order of thousandth of torr. The set up for the experiment as follows. We measured the pick-up voltage on the second coil. The value for the pick up voltage should have decreased dramatically below the transition temperature. Because the field will be expelled, making magnetic flux through the second coil much less than it was. Moreover, the inductive EMF on the pick up coil will decrease in its turn. θ 3. Results and discussion Fig.1. Circuit scheme. We did measure the pick-up voltage in different frequencies of the current and the 2 sets are shown below. Feedback current was changing during

3 measurement. But this effect had been removed by normalizing the voltage into VT ( ) the current at the critical temperature: V T IT IT nor( ) = ( c) ( ) Also the plot V/I will give us some information regarding to the induction influence on the measured voltage value. V/I vs T V/I vs T Fig.2. (V/I) vs T plot at the frequency of 32Khz. V(nor) vs T V(nor) vs T Fig. 3. V nor vs. T plot at the frequency of 32Khz.

4 8000 V vs T V (e-6 V) V vs T V(nor) vs T T, 'K Fig.4. V vs. T plot at the frequency of 1.2Khz. 72 V/I vs T V/I, (e-3 ohm) V/I T Fig. 5. (V/I) vs. T plot at the frequency of 1.2Khz. In all of the measurements we observed the following behaviors: 1. change occurring at temperature of 85ûK 2. distortion in the shape of the output signal 3. exponential type of decrease.

5 Though he critical temperature for our sample is about 90K, we had value of 85K. However, we need to consider the temperature gradient: q = k A T A x, where q-heat transferred, A-area of the sample, k A -specific heat. In our case, we had q=7mw, x=4mm, A=625mm 2 and k A =30x10-3 J/(m*K). Using these values the equation gives us T~(1-3)K. Therefore, our value for T C seem to be quite reliable. The slight bump in plot is due to the purity of the sample and this can be explained in terms of the purity of the sample, [3] which causes electron-phonon scattering to be dominant than the freezing out of electrons. [5] Bayot had similar result as ours and he concluded it is evidence for strong electron-phonon coupling. Also J.C.Phillips gives us the response of the resistivity to the Fig. 6. Resitivity in YBa 2 Cu 3 O x sintered samples. doping and it is shown in Fig.6. [6] The one interesting observation is at lower frequency Òthe resistanceó, i.e. V/I ratio being dramatically less than it were at higher frequencies. We think, it is because of the fact that coil has some inductance which makes V/I ratio less. Also it explains why output voltage was not leading input signal by π/2. Rather it was 4π/5. Although we did not really find χ we were able to observe the change related to it and our obtained plot looks similar to the one obtained Bednorz and Miller in [3] Finally we can conclude We saw transition behavior of the superconductor YBa 2 Cu 3 O 7. T C for the YBa 2 Cu 3 O 7 superconductor is (85±3)K. There can be slight increase in resistivity at the range of T C.

6 4. References 1. Onnes (note 19), P.F.Dahl, ÒSuperconductivityÓ, Charles P.Poole. Jr., ÒSuperconductivityÓ, D.Jackson, ÒClassical electrodynamicsó, ÒPhysical properties of high temperature superconductorsó by Donald M.Ginsberg, J.C.Phillips, ÒPhysics of High-T C superconductorsó, 1992.

7 200 V vs T V, mv V vs T V (nor) vs T T, K F=36KHz

8 V/I 2 V/I V/I(second) V/I, Ω T, K F=36KHz