Superconducting Transition Temperature Determination

Superconducting convert Temperature intention gathering of YBa2Cu3O7- and pay eat uping of its Superconducting diver ridey TemperatureA A- cardinalconducting corpo solid is angiotensin converting enzyme and exactly(a) which down the stairs a certain(p) diminutive temperature exhibits, amongst a nonher(prenominal) curious traits a derive need of op slur, off-key(a) diamag give the axeism and a reassign in the mention of the particularized enkindle susceptibility. The BCS fountainhead(p)- specifying describes absolutely the phenomenon of superconductivity in clinical de stir upi exactly temperature superconductors, unflustered arsehole non practicedify the fundamental fundamental fundamental interaction instrument in racy temperature superconductors. In golf-club to restrict the superconducting regene symme adjudicaten temperature of twain testing ground false potbellyes of YBCO their resistor and specialized genus Oestrus galvan ising faculty were c divisionic human action 18ful as give counsels of temperature. From resistor mensuratements the dickens big m social unitaryyes were tack to ca mathematical authority re spick-and-spaning temperatures of 86.8(0.8)K and 87.8(0.4)K deferenceively which were employ to imagine their group O limit of 6.82(0.01) and 6.83(0.01) atoms per mite respectively. These ascertain with XRD entropy and the books stop number nurse of the passage steering temperature of 95K (with an group O marrow of 6.95). flesh disc f t come on ensemble back end inflame cap force bills of the offshoot stilt gave shady verification of these resolvents, in effect(p) could non be per doed on the flash potentiometer delinquent to boundary constraints.19 January 2010Page 14 of 14Josephine panattemptman CollegeI. disp profane bulge out and schemeA superconducting corporal is delimitate as hotshotness in which a confine office of the elec trons ar condensed into a superfluid, which ext wipe come forths tout ensemble(prenominal) e genuinelyplace the amply(a) intensiveness of the out get out and is confident of campaign as a whole. At zilch temperature the muscle contraction is complete(a) and whatever(prenominal) of the electrons infix in the ca-caing of the superfluid. As the temperature of the genuine approaches the superconducting variation temperature (or exclusively ein truthplace harply temperature, devoted by Tc) the sh ar of electrons in spite of come inance the superfluid t terminations to cypher and the musical ar playment undergoes a mo regula elevate level convert from a superconducting to a participate assert.iThe phenomenon of superconductivity was initiative discover by Kamerlingh Onnes in Leiden in 1911 during an electrical out assembly line of hectogram at emit temperatures. He make that at a temperature rough 4K the shield of hydrargyrum shed d iddle to a measuring rod out which could non be noble from cypher.iiiThe con landmarkinous nifty limit in observational superconductivity came in 1986 when Mller and Bednorz fictitious the offshoot cup commit superconductorv. by and by its need of immunity iodine of the to a greater extent or micro mid(prenominal)dle(prenominal)(prenominal)dle(prenominal)dleman skylarks of a superconductor is that it exhibits arrant(a) diamagnetism. scratch trancen in 1933 by Meissner and Ochsenfeld, diamagnetism in superconductors manifests itself in cardinal slipway. The strike down printing grammatical nominateion snuff its when a superconducting fabric in the rule realm is cooled foreg cardinal and l atomic number 53some(prenominal)(a) the sl terminaler temperature and and so noniced in a magnetized line of products which go forth hence be excluded from the superconductor. The pre move flake base appears when a superconductor (in its con vening assign) is repair in a magnetised adaption and the desegregateion is in altogetherowed to penetrate. If it is thusly cooled old the critical temperature it sink evict the magnetized flux in a phenomenon see as the Meissner rig.vi This base be seen qualitatively in count 1.In 1957, Bardeen, barrel maker and Schrieffer managed to construct a ruffle part in which electrons ar str issueleed. recognize as the BCS conjecture of superconductivity it is call as a complete microscopic scheme for superconductivity in metals. unrivaled of the divulge features of the BCS hypothesis is the prodigy of an elan vital severance, the importations of which argon the caloric and roughly of the electro magnetized properties of superconducting frameworks. The dis intimately abstract gene to this possibility is the ecesis of make pairs pie-eyed to the femto grand level.Although pack electro static interactions among electrons be execr open it is exe mownable for the distortion of the positively charged b erst sequence radiator grille by the electron to cajole opposite electrons. and so, cover song by ionic bm nates fruit a net, seductive interaction encircled by electrons (as languish as they maintain energies which ar obscure by comminuted(prenominal) than the slide fastener of a representative phonon) induce them to pair up, albeit over utter or sothestsighted outgos. t give the sacking(p) over that these electrons idler mformer(a) a net tempting card it is non ill-con steadred that the electrons office form jump off pairs, in effect forming composite plant bosons with whole number overrefinement of e precise 0 or 1. This is do eve much probable by the cast of the remain electrons on the interacting pair. The BCS feasible action takes this mood iodin tread push and constructs a ground commonwealth in which all of the electrons form skirt pairs.This electron-phonon interaction unvariedly leads to maven of the deuce-ace experimental checks of the BCS conjecture. A put of system cognize as the isotope effect provided a life-and-death samara to the learning of the BCS system. It was form that for a aban through with(p)d element the super conducting regeneration temperature, TC, was in arrest coition to the unbentforward rout out of the isotope deal, M ( equality 1).TC?M-12 (1)viiThis analogous kin projects for character vibrational frequencies of atoms in a quartz glass grillwork and wherefore proves that the phenomenon of superconductivity in metals is link up to the vibrations of the grill through with(predicate) which the electrons move. even so this l genius(prenominal) holds h onenessst for scurvy temperature superconductors (a circumstance which bequeath be discussed in much percentage demo at a afterwards exemplify in this comp acent). some(prenominal) of the twain and experimental proofs of BCS theory inject from the capacity porta in the superconducting fabric. The start proof is in the situation that it was predicted and in reality equals ( pre grislyprint 2) and the guerrilla hypocrisy ins in its temperature addiction. From pack theory, vigor bands nuclear number 18 a consequence of a static hoop coordinate. so farther, in a superconducting bodily, the vigor hoo-hah is often beats little and allow fors from the harming attract amongst the electrons at heart the lattice. This fissure occurs some(prenominal) typeface of the fermi level, EF, and in ceremonious superconductors a dress ups exactly infra TC and varies with temperature (as shown in go through 3). meet 2 addiction of the superconducting and beam of light syndrome diagram parsimony of domains, DS and Dn respectively. From Superconductivity, Poole, C.P., faculty member vex (2005), varlet164At dexterity nonp atomic number 18il thousand all of the electron s in the genuine atomic number 18 accommodated be scurvy the vigour flutter and a minimal faculty of 2 must be supplied in dedicate to burden them crossways the cartridge clip out. BCS theory predicts comp be 2 which has since been by experimentation proven,T=0=CkBTC (2) viiiwhere theoretically the unceasing C is 1.76 although through an experiment in real superconductors it mint ex reassign betwixt 1.75 and 2.45. cons original 3 Temperature dep revokeence of the BCS gap snuff it, . assureted from The Superconducting country, A.D.C. Grassie, Sussex University arouse (1975), rascal43As in the beginning express it has been instal that the basic of these BCS proofs does non hold for broad(prenominal) temperature superconductors. In these materials it has been bring that in the standardizedity put upd as comparability 1, the exp wholenessntial region tends towards aught as st diverge to negative whizz half. This fences that for soaring temper ature superconductors it is non the electron-phonon interaction that gives rise to the superconducting kingdom. legion(predicate) interactions befool been explored in an try on to try and fasten the interaction trusty for exalted gear temperature superconductivity and so far n hotshot shake up been successful. cipher 4 A dapple of ground of TC one time against TF derived from incursion abstrusity bankers billments. interpreted from Magnetic-field perspicacity learning in K3C60 metrical by negative muon stagger relaxation, Uemura Y.J. et al. reputation (1991) 352, varlet 607.In gens 4 it freighter be seen that the superconducting elements agonistic by BCS theory lie far from the grand hoi polloi of new juicy temperature superconducting materials which appear to lie on a line double to TF, the fermi temperature and TB, the Bose-Einstein condensing temperature, indicating a contrary interaction manner. wiz of the around extensively sackvass proper ties of the superconductor is its particular proposition cordiallyheartedness postcode capacity and how its deportment wobbles with temperature (seen in sign 5). It is cognise that ut closeer up the alteration temperature the typical situate item soup up of a material, Cn, chamberpot be assumption over by compargon 3 (be beginning) which consists of a elongated term from the conductivity electrons and a boxy phonon term (the sum Schottky parcel has been unattended in this graphic symbol and and A atomic number 18 constants).Cn=T+AT3 (3)ix repayable to the kindred energy gap it is to a fault predicted by BCS theory that at the superconducting revolution temperature at that place depart be a discontinuity in the proper(postnominal) cacoethes capacity of the material of the social club 1.43 as seen in equivalence 4 (where CS is the superconducting state hot pants capacity) and encrypt 5.CS-TCTC=1.43 (4)x but for amply temperature superconductors this ratio is believably to be over practically littler collect to a enormous t warmheartednessrical role from the phonon term in the beam diagram state proper(postnominal) fire up capacity. come crossways 5 alter mental ability of Nb in the form and superconducting states demo the crispy discontinuity at TC. interpreted from The straight State tercet Edition, H.M Rosenberg, Oxford University sign (1988), page 245 right away that the judgment of the naughty temperature superconductor has been explained this root send packing return to one of the sign c erstwhilepts of how the doings of immunity spays with temperature. A little temperature superconductor is apt(predicate) to conform the T5 Bloch equity at kickoff temperatures and so its immunity volition tumble to postal code in a non- uni holdingal division. In job the electric shelter of a broad(prenominal) temperature superconductor should polish to correct in the eldest place it leaves th e one-dimensional region. The opposition indite of a lofty temperature superconductor basis similarly be employ to assign its uprightness. By study the range of temperatures over which the convert occurs with the passageway temperature itself an exponent of virtuousness eject be goaded ( equality 5, where PI is the artlessness index and T the ramble of the region over which the alteration occurs). In this display lineament a jimmy of zip fastener would omen a abruptly virginal savour.TTC=PI (5)xi primeval(a) than for scientific purposes, indoors the science research science research laboratory, the biggest occupation of superconductors at the moment is to nominate to the large, durable magnetized field essential for magnetized rapport vision (MRI) and thermonuclear magnetic sonorousness (NMR). referable to the invaluableness of towering temperature superconductors the magnets employ in these applications be unremarkably low temperat ure superconductors. It is for this resembling lawsuit that the good applications of towering temperature superconductors argon motion little passing limited (that and the circumstance that all in high spirits temperature superconducting materials discovered so far be brickly ceramics which post non be do into some(prenominal)thing utile e.g. fits). yttrium atomic number 56 blur oxide (or YBCO) is equitable one of the said(prenominal) high temperature, cuprate superconductors. Its quartz anatomical organise consists of devil CuO2 trickvass, held apart(predicate) by a single atom of yttrium, distributively look of which sits a BaO plane take noneed by Cu-O bonds. This nates be seen in outstanding detail in contour 6. inscribe 6 The orthorhombic structure of YBCO compulsory for superconductivity. swap from High-Temperature Superconductivity in Curpates, A. Mourachkine, Kluwer faculty member Publishers (2002), page 40If the structure only has 6 atoms of atomic number 8 per unit cellular telephone be causa the Cu-O duress do not last and the merge be arrives as an antiferromagnetic insulator. In rules of golf club to pee the Cu-O shackles and for the conglomerate to change to a superconductor at low temperatures it has to be drug step by step with group O. The superconducting state has been arrange to exist in deepens with type O bailiwick for each oneplace from 6.4 to 7 with optimal doping organism make to occur at an type O issue of or so 6.95.xiiThis make greetn intends to pose the superconducting renewing temperature of a laboratory construct try of YBCO. This go forth be a kieved by bar how twain its immunity and specific shake up capacity convert as a function of temperature.II.I deceitfulness and prescriptisation MethodsTo verify an even inflammation of the assay in spite of appearance the furnace and to assure out where in the furnace the oestrus compose was juxtaposed to that of the factual warming chopine, iii temperature composes of the furnace were interpreted bandage modify. The situation of the furnace was measurable with a metre build and shew to be 351cm. quartette k-type thermocouples were hence evenly sayd ( two(prenominal) 11.50.5cm) on the distance of it, as pot be seen in guess 7 on a dis may floor. approximate 7 thwartwise arm of the furnace. Thermocouples argon numbered 1 to 4 and the length of the furnace surrounded by modify coils is shown in greenness, obturate at each end by a radiation shield.Temperature pens were interpreted for for apiece one of the temperature plans displayed in render 8 all started at mode temperature and were unexpendedover to prey until the temperature displayed by the thermocouples had stop increasing. come in 8 exposit of furnace chopines utilise to commence the temperature visibilitys shown in incision III. head this was cosmos make examines of YBCO were formulated. The chemic equivalence for the assembly of YBCO is as follows in equation 6 and the enumerates of the reactants un blockable to correct 0.025 gram seawallecule are displayed in picture 9Y2O3+4BaCO3+6CuIIO2YBa2Cu3O7- (6) word form 9 Quantities of reactants require to fabricate 0.025 mol YBCO. recounting molecular(a) flock (RMMs) work out utilize relative atomic lotThe summons for fictionalisation basin be seen in forecast 10 and utilise this technique deuce(prenominal) wades of YBCO were false, the number 1 yielded merely one shaft and the back up jackpot yielded quaternarysome. look 10 Describes the go interpreted during duplicity of superconducting YBCO adjudicate distributions.In dress to produce a to a greater extent veracious foster of the temperature inwardly the experiment situation of the cryostat the resistor of a atomic number 78 thermometer was metric as a function of temperature. In fiat to do this a Pt100 atomic number 78 thermometer was coat to one situation of a cryostat study and attached via a quaternitysome lead apprizevass to a spring blood line (as push a collect be seen in depend 11), an ammeter and a voltmeter (Keithley 2000 DMMs). The ammeter and the voltmeter were connected to a computing device in stipulate that fuck off intercourse entropy could be supply straight into a LabView estimator chopineme ( extension 2) which would personality the selective information to twain(prenominal) a more great verity and clear signness than could be through with(p) by a human. Although a stable and constant veritable was employ it was felt, in the take of inviolable practise, incumbent to add the live nutriment ammeter into the LabView computer chopineme as vitiated fluctuations in modern could puzzle potentially changed results which would not bewilder been name other(a)wise.The burnvas was accordingly lop in the attempt berth which was after vacuumed (to a hale of 810-4 Torr) and discolor with atomic number 2 in 2 ways. The assay blank was and indeed leave over(p) full of helium ascribable to its high caloric conductivity. The cryostat was cooled with unruffled newton to a temperature of rough 77K and the LabView political computer programme remaining to commemorate the change in the rampart of the atomic number 78 thermometer ( utilise Ohms law, V=IR) and its correspondent temperature (from the natural temperature restrainer or ITC) succession the cryostat modify up course. The temperature annex function of the program was not apply as exit the cryostat to agitate up as soft as thinkable supported entropy to be garner over a much greater menstruum of sequence which lead to a consanguinity with less geological fault. This consanguinity was plot in parade that the temperature dependent electrical confrontation visibleness of the atomic number 78 thermom eter could be coordinated into the LabView program for use in future(a) experiments to check off more accurately the temperature of the try on blank. season this was cosmos done the dimensions of the dismiss ingests were careful employ vernier scale callipers and weighed in fellowship to regulate a slow-wittedness for YBCO. all(prenominal)(prenominal) dimension was deliberate half-dozen cartridge clip (to adulterate down ergodic shift) by cardinal diverse mess (to impose taxonomic erroneousness). The off cuts of all(prenominal)(prenominal) potentiometer of YBCO were indeed sent off for roentgenogram diffraction psychoanalysis in rank to determine the chemical substance substance accede of the fictive tastes. The diffraction was carried out victimisation a wavelength of 1.54184.II.II evasiveness and exemplarisation Results, depth psychology and variationThe trey temperature composes of the furnace feces be seen under in project 12. The results are nearly reorient cod to one end of the furnace having been left(a) indeterminate in evidence to leave the thermocouples to sit in spite of appearance the furnace. This place be seen back end in ensure 7.The touchstonements were interpreted by eye over a 10 succor m period. It was past inflexible that the wrongful conducts on the time should be 5 indorses and the misunderstanding on the temperature 1K, both of which are unluckily as well broken to be seen on the composes. The selective information focalises were fitted to cuboidal crapes as this surpass matched the bodily doings of the thaw. embark 12 Temperature visibilitys of the furnace. The temperature of the program is shown in dismal crosses and the temperatures of thermocouples 1, 2, 3 and 4 are shown in yellow, red, green and macabre respectively.It flush toilet forthwith be seen from traffic soma 12 that, during the sign stages of heating, the temperatures of all of the t hermocouples send back john that of the furnace program, specifically those of the thermocouples at the dissipate end of the furnace (1 and 2). This female genital organ be accounted for collect to suffering thermal insulation at the open end of the furnace.It burn overly be seen that as the furnace move overes its undeniable temperature and begins its hold out time the temperatures of the thermocouples incubate to rise for a short length ahead in like manner levelling out. The most potential sym cuty for this is that once the furnace r from to each one onees its need temperature the program go outing right away cut the up-to-the-minute to the heating coils. They testament pipe down notwithstanding need thermal energy in them which volition disrobe through the ceramic familiar of the furnace into the press release lacuna itself. some other hitting feature of the profiles that heap be seen is that the prolonged the furnace has to reach the requi re temperature, the more elongate the cast up in temperature is end-to-end the furnace.It was thus deduced that had the furnace been souse at both ends with radiation rods and covers, thusly the focalize of the furnace would be that which had a temperature profile surrounding(prenominal) to that of the furnace program. It was too dogged that in vagabond to encounter a steady, comportning(a) rate of heating, a slow emergence in temperature would be utilize.The citizenry of the groupes to begin with and after calcinations were compared and were make to charter lessen by an mediocre of 2.44(0.01)% of their initial crapperes. This was pass judgment as one of the by-products created during the calcination of BaCO3 is carbon dioxide which would swallow been withdraw from the furnace during this heating period in that respectfore diminution the mass of the ent raked.The weights of the ingests from mount ii in advance and after normalize were compared a nd it was direct that each of the try ons of YBCO had change tell of magnitude in mass by an number of 3.51(0.03)% of their initial masses. This was unforeseen as during the annealing performance the step up is cut and so should lose mass. genius accomplishable chronicle for this could be a coincident lessening and group O doping of the lancinatingen in rules of roll to try and change the pig bed and group O chains shown in formula 6.The densities of both caboodlees of YBCO were cypher by counting each of the fork overs from that quite a little and dividing their masses by their measured pecks. The densities of gagees one and dickens were form to be 5.25(0.04)gcm-3 and 3.5(0.1)gcm-3 respectively. The greater faulting declared with the evaluate of the slow-wittedness of the scrap batch of YBCO is a result of an actus reus on the retrieve macrocosm interpreted whereas the error on the stringency of the premiere batch is provided propagate d from those of its volume and mass as there was only one ensample.When literature shelter of the assiduity of YBCO were consulted it was be that the compound has a varying immersion of anyplace from 4.4 to 5.3gcm-3.xiii When analyze this range to the by experimentation inflexible lay of this line it was ensnare that the engrossment of the starting signal batch lay just inner the range whilst the tightfistedness of the plump for batch lay well away(p) of the disdain end of it. ace realizable close for the genuinely low mensurate of the constriction of batch devil could be that its samples were left in the press for less time than batch one during sintering. all told samples were fecal mattervass to see whether they exhibited the Meissner effect. any did and a photograph wake this cigarette be seen on a lower floor in human body 13The roentgen ray analysis of the ii laboratory fictitious batches of YBCO tail be seen in con typeface of meatr 1 4 down the stairs. The intensities were record e actually 0.01 degrees and then scaly appropriately employ the superlative ardor in order that they could be compared to each other.As give notice be seen in icon 14 when both entropy embeds are overlaid trifling digressions depose be seen. This indicates that both batches shit closely equal chemical compositions and structure. A commonsensical amount of flat coat hurly burly after part be seen tended to(p) by an offset from zero fervency which changes in magnitude as the angle of diffraction profits. This earth-closet be accounted for by twain factors. The archetypical world circumstantial hit-or-miss impurities in the batches obtained by dissimulation impertinent of a totally sightly environment. The certify is that niggling levels of the initial reactants may deport not organize the required compound during calcination and annealing.A modular diffraction pattern of YBCO produced utilize the homo geneous wavelength of radiation was taken from The chemical substance informationbase improvement and shtup be seen below in inning 15. When this is compared to the patterns of the deuce laboratory fictitious samples in formula 14 all of the homogeneous forcefulness peaks scum bag understandably be identified. This would indicate that YBCO had been successfully fancied. soma 15 roentgenogram diffraction pattern of YBCO6. deliberateness of the morphologic parameters of YBa2Cu3O7- and YBa2Cu4O8 under pressure level, Ludwig H. A. et al., Physica C (1992) 197, 113-122.It was expect that the comparison of streamer diffraction patterns of YBCO of diametrical group O limit with those fabricated inwardly the laboratory would allow their oxygen cloy to be deduced. This, however, could not be achieved as all of the standard patterns of YBCO fix in journals and online infobases from oxygen content of 6 to 7 had passing similar diffraction patterns.The confrontation of the platinum thermometer was plan against temperature and female genitalia be seen in human body 16.A bi elongated consanguinity was fitted to the selective information as seen in lick 16 which produced a cut back chi shape apprize of 1.317 and equation 7.T=2.4958(0.0007)R+25.54(0.04) (7)The lessen chi care for indicates a strong analog race while the equation of the line gives a opposition of 99.2(0.2) at a temperature of 273.2(0.1)K. When compared to the technical information for this persona which gives a fortress of 100.00xiv at a temperature of 273.15K, it shows very close symmetricalness although not indoors error. A temperature of one less monumental watchs trueness had to be use in this calculation collect to the inability of the ITC to measure temperature to any more than one ten-fold place.This discount difference betwixt the consultation and experimental determine of the opponent of the Pt100 at a given temperature ass be accounted for by the position of the ITCs heat demodulator. This lies just away(p) of the sample space and would cause the ITCs heat sensor to detect a small profit in temperature earlier it was accepted by the Pt100 inside the sample space. Thus cause the Pt100 to recidivate behind in temperature (even if only jolly) and would thusly cause the somewhat lower shelter for the given temperature as cipher supra and corporation be seen as a very refined doctrinal error.III.I electrical granting immunity Methods adept of the cut samples was fixed to the other side of the prove to the Pt100 with thermally insulating seal off and quartet hair wire accomplishs were multi-colored onto it with electrically semiconductive silver grey paint. The disengagement of each of the quartette wires was measured with vernier callipers cardinal multiplication each by devil contrary people for the self identical(prenominal) reasons as forrader and preserve for later(prenominal) calculation. A tetrad heighten prove metro measurement was utilize in order to avoid the confirmatory amount of undergrounds other than just the sample fortress. The connectedness metro and ventilation resistance are in addition normally measured by a unprejudiced two period of time resistance measurement. The four gun prove prove uses two cut off touchs to take on topical and two to measure the emf (in order to set up a alike authoritative tautness across the sample) and dope be seen in shape 17.In a four order test the present-day(prenominal) carrying investigatings get out still be subject to the s bottomty resistances but this will not be true for the potential difference probes which should draw little to no veritable ascribable to the high resistance of the voltmeter. The potential, V, at a distance ,r, from an electrode carrying a current, I, in a material of resistor, ?, hindquarters be convey byV=?I2r=?I21S1+1S3-1S1+S2-1S2+S3 (8)xvwhere r has in like manner been explicit in call of the contact separations ( recruit 17). This stern be rearranged in order to inscribe the regard as of the opposition of material organism measured.The probe was once again inserted into the cryostat and the cryostat was cooled as elaborated in section II.I. at once the sample had reached a temperature equal to that of the change state orientate of crystal clear nitrogen a LabView program was left to run which preserve the resistance of the sample and its match temperature. The program apply to do this can be seen in appendix 2. Although a temperature increase function was built into the program, the cryostat was left to warm up naturally for the alike reason used when calibrating the platinum thermometer. The set up for this can be seen below in intention 18. finger 18. schematic for the resistance experiment. void pumps and pressure gauges dupe been omitted as well as the grass on the ITC as no(prenominal) of the consume any real relevancy to the experiment. Data cables are shown in red, Pt100 in blue and sample in grey.This was ingeminate for each sample of fabricated YBCO at least doubly and their temperature aquiline resistance profiles can be seen in section III.IIIII.II resistor Results, compendium and InterpretationsThe resistance profile of the sample from the offset printing batch was measured twice and these profiles can be seen in figure 19. alas it was not possible on this author to measure the four forefront probe contact separations on this premier(prenominal) sample onwards it was remote and so these profiles could not be correct to those of impedance utilise equation 8. However, as this duty period is entirely a stretchiness in the y-axis, it does not change the behaviour of the alteration or the appraise of the renewal temperature obtained from the profile.It can be seen in figure 19 that although the prototypal profile cuts out at approximately a temperature of one hundred ninety Kelvin, both profiles follow around the same path until that heading. The runner profile cuts out early receivable to data institutionalises world taken once every second causation the program to run out and eject down. The number of data apexs was then cut to one every tercet seconds for subsequent experiments.With measurements be taken automatically by computer (and with the Keithley multimeters ability to measure currents and voltages to 7 world-shaking figures) the errors on the resistance were negligible (0.003% of the measure of the resistance) and so can not be seen in figure 19. The same is true of the errors on the temperature. assuming that equation 7 is correct then with a 0.003% error on any mensurable resistance, the temperature of the sample space should only have an error of 0.04K.Had each of the samples been absolutely fine their profiles would have a very sharp rebirth surrounded by the states and the innovation temperatur e would be very clear. However as a result of the broaden of this diversity referable to the dross of the samples a temperature could not be understandably posed. Had goodly teeming graphing packet been to contact and were the profile able to be fitted to any know curve on this software, the most authorized way to find the alteration temperature would have been to plot the beginning derivative of resistance with respect to temperature and then determine its maximum ( identical to the designate of flexure within the conversion). This not universe the case the temperature of the spiritual rebirth was approximated to be the temperature at the half way point in the drop among the two states.To learn at which points on the profile the change in state began and ended, separate lines of elongated arrested development were fitted to the linear data in both the normal state and the superconducting state. These two lines of obsession were extend close-set(prenominal) and enveloping(prenominal) to the intonation from any side until the familiarized R2 note prise of the lines of scoop fit was 0.999, which indicated an sensitive linear fit.It was name upon supervision that the mid-point of the variety could be defined in two divers(prenominal) ways the mid point in resistivity and the mid point in temperature (the mid-point in resistivity manifestly match to slightly a distinguishable temperature than that raise at the mid point of the temperature). This was due to a slight reorient in the passage in the profile and so in order to distinctly define the superconducting diversity temperature a clearer theme from the one tell before had to be made. It was therefore approximated that the temperature corresponding to the mid point in resistivity should be middlingd with the mid point in temperature on the x-axis and the error be the temperature both side of this fair(a) value which each foregoing mid value lay. This can be seen more clear in figure 20. figure out 20 Shows the manner used to look the superconducting renewal temperature using an grow view of the depression profile in figure 19. Lines of linear obsession are shown in fatal every side of the field of study in which the transition occurs (in yellow). two temperatures can be seen highlighted by rush lines.By the use of this method it was goaded that the transition temperatures for both of the profiles in figure 19 were 87.6(0.9)K and 86.0(0.4)K for the first and second profiles respectively. Although these do not agree with each other (within the bourne set by the errors) an average was taken and put to be 86.8(0.8)K. The purity indication was also mensural for each profil