Transition Temperatures in Yttrium Barium Copper Oxide (YBCO)

Department of Physics: PH 2651,Worcester Polytechnic Institute,

Worcester, MA 01609(Dated: February 24, 2015)

In 1911 it was observed that mercury, when cooled below a critical temperature (TC) would exhibitno electrical resistance. This effect, called superconductivity, occurs in many materials at varyingTC ’s. This paper attempts to measure by direct observation the critical temperature of YttriumBarium Copper Oxide (YCBO) as well as the dependence of resistance on temperature in classicalresistors and semiconductors. The results were found to agree well with previous experiments andwith theory. A measurement of the dependence of TC on the magnetic field was attempted. However,experimental limitations prevented significant results from being derived.

INTRODUCTION

Superconductivity was first observed in 1911 by Dutchscientist Heike Kamerlingh Onnes in the metal mercury.He found that when the material was cooled below 4.4Kit would have no electrical resistance. The temperaturebelow which this effect was observed was called the criti-cal temperature and is denoted by the symbol TC . Manyother materials were found to exhibit superconductivityincluding many metals and alloys.

In 1933, Walther Meissner and R. Ochsenfeld observedthat superconductors are more than just good conduc-tors. They found that superconductors do not allowmagnetic fields to penetrate their interior. This effect,called the Meissner effect, causes permanent magnets tobe repelled by and ”levitate” above superconducting ma-terials.

Theoretical Background

Classically, resistance increases nearly linearly withtemperature. This is because greater temperature cor-responds to greater thermal interactions which in turndecreases the electron mobility and increases resistance.Superconductivity flies in the face of this classical result.According to BCS theory there is an effective pairing ofelectrons which are then called Cooper pairs. An elec-tron attracts and deforms the lattice of ions, resulting inan effective pairing of electrons that travel through thelattice together. These pairs allow electrons to movethrough the atomic lattice more efficiently than theywould if traveling alone making a material with effec-tively no resistance.

Figure 1 details electrons moving in Cooper pairsthrough a lattice. This theory is a simplification ofthe quantum mechanical effects behind superconduc-tors, but provides a good idea into why the resistancedrops suddenly at the superconducting transition tem-perature. The general plot of resistance versus temper-ature is shown in figure 2.

FIG. 1: Cooper Pairs Moving Through an Ion LatticeObtained from:

http://webs.mn.catholic.edu.au/physics/emery/hsc ideas implementation.htm

Type I and Type II Superconductors

Superconductors may be divided into two categories,Type I and Type II superconductors. Type I supercon-ductors are mainly metals and metalloids and are rela-tively insensitive to material impurities. These materialshave some conductivity at room temperature, but theyrequire extremely low temperatures (< 10K) to transi-tion to superconductivity. Additionally, type I supercon-ductors are disabled by relatively low applied magneticcurrents. They completely exhibit the Meissner effectand conduct only on their surface.

Type II superconductors are similar to type I super-conductors in many ways. Type II superconductors canbe metal compounds or even ceramics and generallytransition to superconductivity at temperatures around100K. Compared to type I superconductors, type II su-perconductors are much more sensitive to impurities.Even minuscule impurities can remove superconductingability from type II superconductors. They also aremuch less sensitive to magnetic fields, although mag-netic fields do lower their transition temperature. Infact, there are actually a range of magnetic field magni-tude that will create a mixed state (between supercon-

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FIG. 2: General Resistance vs Temperature for YBCOObtained From:

http://www.superconductors.org/Y258.htm

FIG. 3: Differences in Magnetic Field Effect for Type Iand Type II Superconductors

Obtained From:http://www.gitam.edu/eresource/Engg Phys/

semester 2/supercon/type 1 2.htm

ducting and normal). The differences in magnetic fieldsensitivity between type I and type II superconductors isshown in figure 3. Finally, type II superconductors onlypartially exhibit the Meissner effect, with most magneticfield being repelled but some becoming trapped withinthe material.

The YBCO sample we tested in this experiment is atype II superconductor, and we hope to compare its be-havior to many of the expected behaviors stated above.

Applications

Resistance in electrical circuits causes energy dissipa-tion which reduces efficiency and results in an overallwaste of energy. Superconductors, due to their lack ofresistance, greatly increase the efficiency of power sys-tems. Significantly less energy is lost and less stray heatis developed, leading to the effectiveness of superconduc-

FIG. 4: Internal Transition in a SuperconductorLeading to the Meissner Effect

Obtained From:http://hyperphysics.phy-astr.gsu.edu/

hbase/solids/meis.html

tors in numerous settings including delicate electronics,magnetic field detection, and acceleration of small par-ticles.

The Meissner Effect

One interesting effect of superconductivity is the re-pulsion of magnetic fields, known as the Meissner effect.Surface currents produce magnetic fields which cancelapplied magnetic fields, and the magnetic fields are re-pelled from the inside of the superconductor. This ef-fect is shown in figure 4. The Meissner effect is key inmany applications of superconductivity that involve levi-tation of bodies. Specifically, Maglev transportation usessuperconductors and magnets to levitate trains abovetracks to greatly minimize the friction of transportationsystems. A diagram of a Maglev train is shown in figure5.

Converting Voltages to Resistivities

The raw data taken through MATLAB in this experi-ment comes in the form of three variables: time, voltage,and temperature. By ohm’s law (equation 1), the voltageis linearly related to the resistance by the current.

V = IR (1)

However, resistance is not the best quantity to measurebecause it depends on the geometry of the sample. Resis-

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FIG. 5: Diagram of a Maglev TrainObtained From:

http://www.wou.edu/∼rmiller09/superconductivity/

TABLE I: Measured Parameters to CalculateResistivity

A 5.613x10−5m2

` 0.0147m

tivity is a better quantity because it is a material prop-erty and not dependent on geometry. The formula forresistivity of a bar is

ρ =RA

`(2)

where A is the cross sectional area of the sample and ` isthe length between the two voltage leads on the sample.The parameters needed to calculate resistivity for thisexperiment are shown in table I. Combining equations1 and 2 gives the resistivity in terms of the measuredvoltage and the known current (equation 3.

ρ =V A

I`(3)

The data represented in the plots will all be kept involtage because equation 3 proves that voltage trans-forms linearly to resistivity. When resistivity drops tozero, so will the voltage. The superconducting transi-tion can still be calculated (and viewed) from a plot ofvoltage versus temperature.

Hysteresis

The experimental setup of the YBCO has it mountedon a piece of aluminum. The temperature of the alu-minum is the actually reported temperature during thedata recording process. Because the aluminum coolsand warms at a different rate than the YBCO, a slighthysteresis effect should be observed. Hysteresis means

FIG. 6: Setup of Sample on Circuit Board

that the output of a process depends not only on in-put but also previous states. What this means is thatthe measured superconducting transition temperature ofthe YBCO will depend on whether it is warming uppast Tc or cooling down below Tc. Specifically, themeasured transition temperature should be slightly highwhen putting in the YBCO (cooling it down) and slightlyhigh when taking it out (warming it up).

PROCEDURE

In order to record the voltages and temperatures ofthe YBCO, the lab setup included Styrofoam containersto hold the liquid nitrogen and the YBCO sample andaluminum temperature sensor mounted on a printed cir-cuit board. The general configuration of the sample’ssetup is shown in figure 6. When dunked into liquid ni-trogen, the YBCO was also covered in a plastic coverso that condensed water would not continuously freezeand refreeze on the YCBO (which would cause it to de-grade and crumble). Additionally, figure 7 shows threepieces of equipment that measured various parameters.From top to bottom, there is a current supply, a multi-meter used to measure voltage, and the temperature con-troller. The temperature and voltage data were trans-mitted to MATLAB, which recorded them continuously(taking approximately one data point per second).

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FIG. 7: Various Equipment Used in Data Collection

Data Acquisition Without Magnetic Field

In order to get multiple trials of the YBCO transition,the YBCO was dipped down into the liquid nitrogen withthe MATLAB logger running. After the temperaturehad settled out around 75K, the sample was removedfrom the liquid nitrogen. The sample heated up muchmore slowly than it cooled down, so once the tempera-ture was above 150K, the sample was put back into theliquid nitrogen. The MATLAB logger gave a continu-ous plot of voltage versus temperature, so heating andcooling progress of the YBCO could be observed. Aftertwo cycles on each current, the current was turned up.Currents used were 0.1A, 0.3A,0.5A,0.9A,1.5A, and (atthe end) 0.05A. It was evident on the voltage versustemperature plot each time the YBCO crossed throughthe superconducting temperature range.

Magnetic Field Addition & Measurement

In order to measure the magnetic field between thepoles of the permanent magnets, a transverse hall probewas used. This hall probe is able to measure magneticfields that arrive perpendicular to the probe. A photo ofthe hall probe used in the experiment is shown in figure8.

This setup was used to determine the most sensitiveorientation of the hall probe. The hall probe was rotatedabout its long axis 180o in increments of 10o. The hallprobe is a long rod with a cross section that is a rectan-gle with a longer and shorter side (as shown in figure 9.It was determined that the hall probe measures perpen-

FIG. 8: Hall Probe Testing Setup

FIG. 9: Geometry of Hall Transverse Hall ProbeObtained From:

http://www.lakeshore.com/products/hall-probes/transverse-probes/Pages/Overview.aspx

dicular to the longer side of the cross section, as shown.A plot of the relative magnetic field ( B

Bmax) versus θ of

rotation is shown in figure 10. The plot of relative mag-netic field versus cos θ, meanwhile, produces a linear plotand is shown in figure 11. The results for the sensitivityof the hall probe were used in accurately measuring themagnetic field that the YBCO is placed in.

Magnetic Field Application to YBCO To add a mag-netic field to the area where the YBCO was placed, twomagnets were taped onto the outside of the Styrofoamcontainer with liquid nitrogen in it. Great care was takento measure the magnetic field in the precise spot wherethe YBCO would be placed. The YBCO went into theliquid nitrogen and cooled as with the sample not in a

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−100 −50 0 50 1000

0.2

0.4

0.6

0.8

1

θ (degrees)

B/B

max

Magnetic Field Measured by Hall Probe vs θ of Rotation

FIG. 10: Graph of Relative Magnetic Field vs θ

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Cos(θ)

B\B

max

Magnetic Field Magnitude vs Cos(θ) of Rotation of Hall Probe

FIG. 11: Graph of Relative Magnetic Field vs cos θ

magnetic field. Next, when the YBCO needed to be re-moved, it was removed and heated. After it warmedthrough its transition temperature, the magnetic fieldat the location where the YBCO was left to warm upwas taken. Because this was not directly in between themagnets, the magnetic field that it warmed up in wassignificantly less than the magnetic field it was cooleddown in. The transition temperature in a magnetic fieldwere measured to compare to YBCO transition withouta magnetic field.

Meissner Effect

The final part of the experiment was meant to observethe Meissner effect. In order to observe the repulsion ofmagnetic flux of a superconductor, YBCO sat in a smallStyrofoam cup with a foam like material surroundingit. This setup is shown in figure 13. Liquid nitrogenwas poured into the container and placed a rare earthmagnet on top of the YBCO. Once the YBCO cooledinto its superconducting region, the magnet began tofloat above the YBCO. The magnet was be spun abovethe YBCO in order to show that the magnet is effectivelyheld in place above the YBCO due to the Meissner effect.

TABLE II: Data Points for a ParticularSuperconducting Transition

Temperature (K) Voltage (mV )106.1 0.5764105.3 0.5724104.6 0.5683103.8 0.5590102.8 0.5495101.7 0.5364100.4 0.408999.08 0.215697.56 0.030696.18 0.009094.85 0.008293.60 0.007392.41 0.006891.31 0.006090.31 0.0060

MEASUREMENTS, OBSERVATIONS ANDDISCUSSION

Many trials were run to test the transition temper-ature of the YBCO. Each trial gave pretty consistentresults, with the transition temperature ranging fromjust under 90K to just over 100K. Tables III and IVshow the results for cooling down and heating up theYBCO respectively. They are separated because of theexpected hysteresis effect mentioned in the methodol-ogy. In both tables, there is a Tupper value and a Tlower

value. Those two values were measured at both ends ofthe transition to superconductivity. Because the transi-tion is pretty rapid but not instantaneous, the one tem-perature was measured when the voltage first began torapidly drop and the other temperature was measured atthe first voltage that seemed to be nonzero. The aver-age of these two values is shown in the Tavg column andis the value taken to be the actual transition tempera-ture. Additionally, an example of data points (taken atconstant time intervals) approaching and departing thesuperconducting transition are shown in table II. No-tice that as the YBCO begins to become superconduc-tive, it begins to temporarily cool more quickly. Thisis due to I2R heating vanishing when the material be-comes superconductive, which is discussed later on. Forthe particular transition shown in the table, the uppertemperature where the transition begins would be readas 101.7K and the lower temperature would be read as97.56K.

Meissner Effect

Because YBCO is a type II superconductor, it doesnot exhibit the complete Meissner effect. Some of themagnetic flux becomes trapped within its fibers, whichcreates an interesting levitation effect. A rare earth mag-

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TABLE III: Superconducting Transition Temperaturewhen Cooling Down YBCO

B(G) I(A) Tupper(K) Tlower(K) Tavg(K)31.5 0.1 100 95.49 97.75

0 0.1 101.7 97.56 99.630 0.1 104.8 98.7 101.750 0.3 101.3 96.05 98.680 0.3 102.9 97.37 100.140 0.5 97.68 93.74 95.710 0.5 97.15 94.55 95.850 0.9 97.76 92.08 94.920 0.9 104.1 97.83 100.970 1.5 99.44 94.56 97.000 0.05 94.28 93.69 93.990 0.05 98.69 96.16 97.43

TABLE IV: Superconducting Transition Temperaturewhen Up YBCO

B(G) I(A) Tupper(K) Tlower(K) Tavg(K)0.36 0.1 93.09 90.89 91.99

0 0.1 94.52 91.14 92.830 0.1 94.11 92.2 93.160 0.3 93.82 90.87 92.350 0.3 93.75 91.32 92.540 0.5 93.48 90.32 91.900 0.5 93.54 90.28 91.910 0.9 92.35 89.38 90.870 0.9 92.93 88.93 90.930 1.5 91.95 87.03 89.490 0.05 93.41 92.23 92.820 0.05 93.53 92.14 92.84

net will still levitate above the superconductive YBCO,but it will actually be held in place by the trapped mag-netic field. Therefore, the magnet will actually be ableto spin freely and will not be knocked out of levitationby small disturbances. In the experiment, the magnetbuilt up ice soon after being placed above the YBCO,so it oscillated instead of rotating freely. Diagrams ofthe Meissner effect the actual observation are shown infigures 12 and 13, respectively.

Superconducting Transition Temperature WithoutMagnetic Field

As seen in table V, the result observed and calcu-lated for the superconducting transition temperature is94.89K±3.57K. The lab manual mentions that the tran-sition temperature should be around 95K, which 94.89Kclearly is. All of the data included in the calculation ofthis value showed consistency, and no values were sig-nificantly outlying from the calculated value. The tablealso shows the effect of hysteresis as described in themethodology. The average difference in transition tem-perature when heating up and cooling down was 5.85K,which is a around 7% of the measured transition tem-perature. This shows that hysteresis in this experiment

FIG. 12: Diagram of Rare Earth Magnet ExhibitingMeissner EffectObtained From:

http://www.imagesco.com/articles/superconductors/superconductor-meissner-effect.html

FIG. 13: Experimental Setup With the Meisser EffectShown

is significant.

In addition to the hysteresis effect from the differencein heating and cooling rate, there is an extra elementof heating on the YBCO. This heat source, known asI2R heating, comes from power generated from currentrunning through the YBCO. The concept of I2R heat-ing comes, not surprisingly, from the equation for powerP = I2R. Because of this heating effect, the coolingeffect from the liquid nitrogen is slightly counteracted.Similarly, the heating effect from the room is slightlyboosted. In order to counteract this I2R heating, thelast two trials were run with a very low current, whichled to a very low resistance. Smaller values of resistancedo give rise to slightly higher relative uncertainties, butthere were not extensive calculations done that would

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TABLE V: Compiled Results of All Trials

Magnetic Field Trials Cooling 97.75K ± 2.23KMagnetic Field Trials Warming 92.00K ± 1.10KAll Trials With Magnetic Field 94.87K ± 4.07K

Trials w/o Magnetic Field Cooling 97.82K ± 2.59KTrials w/o Magnetic Field Warming 91.97K ± 1.12K

Average Hysteresis Effect 5.85KAll Trials w/o Magnetic Field 94.89K ± 3.57K

propagate these uncertainties. The hysteresis effect isstill present in the low current trials, but the effect ofthe extra heating is nearly eliminated at minimal cur-rents.

TABLE VI: Resistivity Values for Various Currents andVoltages (in Ω ·m)

0.1A 0.5A 0.9A 1.5A0.1V 0.00382 0.00076 0.00042 0.000250.3V 0.01146 0.00229 0.00127 0.000760.5V 0.01909 0.00382 0.00212 0.001271.0V 0.03818 0.00764 0.00424 0.002551.5V 0.05728 0.01146 0.00636 0.003822.0V 0.07637 0.01527 0.00849 0.005092.5V 0.09546 0.01909 0.01061 0.00636

Revisiting Resistivity vs Voltage

In the methodology, it was mentioned that the read-ings taken in voltage were left in voltage in all plots be-cause voltage transforms linearly to resistivity. To givean idea of values of resistivity, table VI shows the resis-tivity of the YBCO at given current and voltage reading,based on equation 3. Note that not all current-voltagecombinations shown in the table are obtained in this ex-periment. The table is mainly meant to show how resis-tivity varies as current and voltage vary. As current goesup and voltage goes down, resistivity drops. Conversely,as current goes down and voltage goes up, resistivity in-creases. Resistivity, as previously mentioned, is more ofa material property than resistance, because resistancedepends on geometry. If this experiment were to dealwith more materials than just YBCO, it would be idealto report the resistances in terms of resistivity insteadof reporting voltages.

Voltage Versus Temperature Plots

The curve of temperature plotted versus voltage for asuperconducting transition should produce a shape sim-ilar to that in figure 2. Figure 14 shows voltage plottedversus temperature for many of the transitions observed.There is a convincing similarity between the two figures,

which shows that the physical transition observed in theYBCO is likely very similar to the expected transition.

YBCO Transition in Presence of Magnetic Field

The theory of superconductors suggests that when theYBCO is cooled down in the presence of a magnetic field,the transition temperature will be lower than the tran-sition temperature in zero magnetic field. In order toobserve this, the YCBO was cooled down in a 31.5Gmagnetic field. Unfortunately, it was discovered that amagnetic field of this magnitude did not noticeably af-fect the transition temperature. When taken out of theliquid nitrogen, the YBCO was subjected to about oneone-hundredth of that magnetic field, which, not surpris-ingly, did not affect the transition temperature either.The lab manual suggests that a magnetic field of severalhundred Gauss would affect the transition temperature,which was not attainable with the setup and the magnetsused.

Resistivity vs Temperature Properties forNon-Superconducting Materials

After performing all tests with the superconductingYBCO, the temperature dependence of resistivity onother materials was tested. Results from a typical metaland a semiconductor were compared to their respectivetheories.

Metal (Copper) In order to investigate the resistanceversus temperature properties of a metal, copper wasstudied. The setup of the copper mounted on the cir-cuit board can be viewed in figure 15. Theory suggeststhat as temperature drops, resistance drops somewhatlinearly. Figure 19 shows the general difference in resis-tance versus temperature for superconductive materialsand non-superconductive metals.

This decrease of resistance with temperature is notwhat was observed, likely due to copper’s very low resis-tivity. The graph obtained, shown in figure 16 shows arise in resistance with a decrease in temperature, whichis likely due to noise of the power supply and the sensorrecording the voltage. If copper had a higher resistiv-ity to begin with, it would have dominated the graphinstead of the noise.

Semiconductor (MOSFET) The second non-superconducting material tested was a metal-oxide-semiconductor field-effect-transistor (or MOSFET). Thesetup for the MOSFET on the circuit board is shownin figure 17. For a MOSFET, the theory and actualexperimental observations matched together quite well.Semiconductors conduct electricity when their valenceelectrons jump to the conduction band across a smallband gap. The band gap for semiconductors is muchsmaller than that of insulators, which gives them their

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1.5A

0.9A

0.3A

0.5A

0.1A

0.05A

FIG. 14: Voltage versus Temperature for Many Transitions to Superconductivity

FIG. 15: Copper Test Setup

FIG. 16: Voltage vs Temperature Curve for Copper

FIG. 17: Setup of the Mosfet Semiconductor

limited conductivity. The conductivity versus tem-perature curve theoretically will follow that of metalsat higher temperatures (by increasing as temperaturedrops) and decrease exponentially once temperaturegets low enough. These expectations come from theprobability of electrons being in the conduction band(predicted by statistical mechanics).

Figure 18 shows the voltage versus temperature curvemeasured for the Mosfet. As was mentioned, this curveis linearly related to the resistivity versus temperatruecurve. Because resistivity is the inverse of conductivity,the general shape of the curve observed matches theory

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FIG. 18: Voltage versus Temperature Curve for theSemiconducting Mosfet

FIG. 19: Resistance versus Temperature forSuperconductors and Ordinary Metals

Obtained From:http://www.superconductors.org/type1.htm

pretty well. As temperature drops, the resistivity drops,and once the temperature gets down to about 125K, theresistivity exponentially increases.

CONCLUSION

Superconducting Transition Temperature in YBCOAs part of experimental focus, the properties of super-conductors when the materials temperature dropped be-low its critical temperature were observed. The recordedresults were what the theory accurately predicted, de-spite the significant (although expected and explain-able) influence from the hysteresis effect. As the YBCOdipped into the liquid nitrogen, it began to quickly de-crease its temperature while its voltage decreased as well.The data graph containing measurements for tempera-ture vs voltage display the kind of plot curve similar tothe theoretical result for the transition. However, theeffect of an external magnetic field from two permanentmagnets was not strong enough to significantly affect thetransition temperature, probably due to the positioningversus strength of the magnets.

Resistance versus Temperature for Other MaterialsIn addition to testing the YBCO, observations of thecharacteristics of a metal and a semi-conductor weretaken. The metal did not give results that matched the-ory due to already low resistance and noise from the cur-rent supply. However, the semi-conductor gave a curvethat matched theory extremely well. Neither of these de-vice produced superconductive behavior, though, whichis expected.

The Meissner Effect The Meissner Effect was clearlyobserved when liquid nitrogen cooled the YBCO, causingthe rare earth magnet to levitate above the superconduc-tor, held in place by the expelled and trapped magneticfield. The levitating is an excellent qualitative observa-tion that strongly supports the superconductive prop-erties of the YBCO. The magnet did not levitate untilthe liquid nitrogen had significantly cooled the YBCO,and the transition is clearly noticed when the magnetseemingly comes to life above the YBCO sample.