There has also been great progress in understanding the proper-ties of these materials, developing different methods of preparation, and realizingsuperconducting devices which use these
Trang 1ery of high-T c materials, several high-T csuperconductors have been discoveredwhich show superconductivity at temperatures higher than liquid-nitrogen tem-perature (77 K) There has also been great progress in understanding the proper-ties of these materials, developing different methods of preparation, and realizingsuperconducting devices which use these superconductors.
This chapter will give a brief description of the historical developments in
raising the transition temperature (T c) of the superconductors, preparation, and
structure of the material Different properties of the high-T cmaterials such as ical magnetic field, penetration depth, coherence length, critical current density,weak link, and so forth are also discussed
Trang 2crit-1.2 RAISING THE TRANSITION TEMPERATURE
Superconductivity is the phenomenon in which a material loses its resistance on
cooling below the transition temperature (T c) Superconductivity was first ered in mercury by Onnes (2) in 1911 The temperature at which mercury becomessuperconducting was found to be close to the boiling point of liquid helium (4.2K) Subsequently, many metals, alloys, and intermetallic compounds were found
discov-to exhibit superconductivity The highest T c known was limited to 23.2 K (3) in
the Nb3Ge alloy; however, in September 1986, Bednorz and Muller (1) discoveredsuperconductivity at 30 K in La–Ba–Cu–O The phase responsible for supercon-ductivity was identified to have nominal composition of La2xBaxCuO4y (x0.2) The discovery of high-temperature superconductivity in ceramic cuprate ox-ides by Bednorz and Muller led to unprecedented effort to explore new supercon-
ducting oxide material with higher transition temperatures The value of T cin
La2xBaxCuO4was found to increase up to 57 K with the application of pressure(4) This observation in La2xBaxCuO4material raised the hope of attaining evenhigher transition temperatures in cuprate oxides This, indeed, turned out to be truewhen Chu and co-workers (5) reported a remarkably high superconductivity tran-
sition temperature (T c) of 92 K on replacing La by Y in nominal composition
Y1.2Ba0.8CuO4y Later, different groups identified (6–8) that the ing phase responsible for 90 K has the composition YBa2Cu3O7y
superconduct-The discovery of superconductivity above the boiling point of liquid gen led to extensive search for new superconducting materials Superconductivity
nitro-at transition tempernitro-atures of 105 K in the multiphase sample of theBi–Sr–Ca–Cu–O compound was reported by Maeda et al (9) in 1988 The high-
est T cof 110 K was obtained in the Bi–Sr–Ca–Cu–O compound having a sition Bi2Sr2Ca2Cu3O10 (10,11) Sheng and Hermann (12) substituted the non-magnetic trivalent Tl for R in R-123, where R is a rare-earth element By reducingthe reaction time to a few minutes for overcoming the high-volatility problem as-sociated with Tl2O3, they detected superconductivity above 90 K in TlBa2Cu3Ox
compo-samples in November 1987 By partially substituting Ca for Ba, they (13)
discov-ered a T c 120 K in the multiphase sample of Tl–Ba–Ca–Cu–O in February
1988 In September 1992, Putillin et al (14) found that the HgBa2CuOx(Hg-1201)compound with only one CuO2layer showed a T cof up to 94 K It was, therefore,
rather natural to speculate that T ccan increase if more CuO2layers are added inthe per unit formula to the compound In April 1993, Schilling et al (15) reportedthe detection of superconductivity at temperatures up to 133 K in HgBa2
Ca2Cu3Ox The transition temperature of HgBa2Ca2Cu3Oxwas found to increase
to 153 K with the application of pressure (16)
Figure 1.1 depicts the evolution in the transition temperature of ductors starting from the discovery of superconductivity in mercury The slow butsteady progress to search for new superconductors with higher transition temper-
Trang 3supercon-atures continued for decades until superconductivity at 30 K in La–Ba–Cu–O ide was discovered in 1986 Soon after this, other cuprate oxides such asY–Ba–Cu–O, Bi–Sr–Ca–Cu–O, Tl–Ba–Ca–Cu–O with superconductivity abovethe liquid-nitrogen temperature were discovered.
ox-Table 1.1 gives a list of some of high-T csuperconductors with their tive transition temperature, crystal structure, number of Cu–O layers present inunit cell, and lattice constants Transition temperature has been found to increase
respec-as the number of Cu–O layer increrespec-ases to three in Bi–Sr–Ca–Cu–O,Tl–Ba–Ca–Cu–O, and Hg–Ba–Ca–Cu–O compounds In all of the cuprate super-conductors described so far, the superconductivity is due to hole-charge carriers,except for Nd2xCexCuO4(T c 20 K), which is an n-type superconductor (17).
The superconductor Ba0.6K0.4BiO3, which does not include Cu, was reported by
Cava et al (18) in 1988 exhibiting T c 30 K A homologous series of compounds(Cu,Cr)Sr2Can1CunOy [Cr12(n 1)n] has been synthesized under high pressure.
F IGURE 1.1 The evolution of the transition temperature (T c) subsequent to the discovery of superconductivity.
Trang 4In the Cr series, the value of n can be changed from 1 to 9, with a maximum T cof
107 K at n 3 The Pr(Ca)Ba2Cu3Oycompound has also been synthesized underhigh pressure, showing a transition temperature of 97 K (19)
SUPERCONDUCTORS
The structure of a high-T csuperconductor is closely related to perovskite ture The unit cell of perovskite consists of two metal (A, B) atoms and three oxy-gen atoms, with the general formula given as ABO3 The ideal perovskite struc-ture is shown in Fig 1.2a Atom A, sitting at the body-centered site, is coordinated
struc-by 12 oxygen atoms Atom B occupies the corner site and the oxygen atom pies the edge-centered position
occu-T ABLE 1.1 Transition Temperature (T c), Crystal Structure and Lattice Constants of
Some High-T cSuperconductors
c 27.23
Y 2 Ba 4 Cu 7 O 14 247 40 2 Orthorhombic a 3.85, b 3.87,
c 50.2
Bi 2 Sr 2 CuO 6 Bi-2201 20 1 Tetragonal a 5.39, c 24.6
Bi2Sr2CaCu2O8 Bi-2212 85 2 Tetragonal a 5.39, c 30.6
Bi2Sr2Ca2Cu3O10 Bi-2223 110 3 Tetragonal a 5.39, c 37.1
TlBa 2 CuO 5 Tl-1201 25 1 Tetragonal a 3.74, c 9.00
TlBa 2 CaCu 2 O 7 Tl-1212 90 2 Tetragonal a 3.85, c 12.74
HgBa 2 CuO 4 Hg-1201 94 1 Tetragonal a 3.87, c 9.51
HgBa2CaCu2O6 Hg-1212 128 2 Tetragonal a 3.85, c 12.66
HgBa2Ca2Cu3O8 Hg-1223 134 3 Tetragonal a 3.85, c 15.78
(Nd2xCex) CuO 4 T 30 1 Tetragonal a 3.94, c 12.07
(Nd, CeSr) CuO 4 T* 30 1 Tetragonal a 3.85, c 12.48
an represents the number of Cu-O planes in the unit cell.
Trang 5Figure 1.2b shows the unit cell of La2xBaxCuO4, which has a tetragonalsymmetry and consists of perovskite layers separated by rock-salt-like layers made
of La (or Ba) and O atoms This compound is often termed 214 because it has two
La, one Cu, and four O atoms The 214 compound has only one CuO2plane ing at the exact center of Fig 1.2b, the CuO2plane appears as one copper atoms sur-rounded by four oxygen atoms, with one LaO plane above the CuO2plane and onebelow it The entire structure is layered The LaO planes are said to be intercalated.The CuO2plane is termed the conduction plane, which is responsible for supercon-ductivity The intercalated LaO planes are called “charge-reservoir layers.” Whenthe intercalated plane contains mixed valence atoms, electrons are drawn away fromthe copper oxide planes, leaving holes to form pairs needed for superconductivity.The structure of YBa2Cu3O7 is shown in Fig 1.2c The unit cell ofYBa2Cu3O7 consists of three pseudocubic elementary perovskite unit cells (8).Each perovskite unit cell contains a Y or Ba atom at the center: Ba in the bottomunit cell, Y in the middle one, and Ba in the top unit cell Thus, Y and Ba are
Look-stacked in the sequence [Ba–Y–Ba] along the c-axis All corner sites of the unit
cell are occupied by Cu, which has two different coordinations, Cu(1) and Cu(2),with respect to oxygen There are four possible crystallographic sites for oxygen:O(1), O(2), O(3), and O(4) The coordination polyhedra of Y and Ba with respect
to oxygen are different The tripling of the perovskite unit cell (ABO3) leads tonine oxygen atoms, whereas YBa2Cu3O7has seven oxygen atoms accommodat-
F IGURE 1.2 Structure of (a) perovskite ABO3, (b) (La,Ba)2CuO4, and (c) YBa 2 Cu 3 O 7
Trang 6ing the deficiency of two oxygen atoms Thus, the structure of the 90 K phase viates from the ideal perovskite structure and, therefore, is referred to as an oxy-gen-deficient perovskite structure Oxygen atoms are missing from the Y plane
de-(i.e., z 1/2 site); thus, Y is surrounded by 8 oxygen atoms instead of the 12 if ithad been in ideal perovskite structure Oxygen atoms at the top and bottom planes
of the YBa2Cu3O7unit cell are missing in the [100] direction, thus giving (Cu–O)chains in the [010] direction The Ba atom has a coordination number of 10 oxy-
gen atoms instead of 12 because of the absence of oxygen at the (1/2 0 z) site The
structure has a stacking of different layers: (CuO)(BaO)(CuO2)(Y)(CuO2)(BaO)(CuO) One of the key feature of the unit cell of YBa2Cu3O7 (YBCO) is thepresence of two layers of CuO2 The role of the Y plane is to serve as a spacer be-tween two CuO2planes In YBCO, the Cu–O chains are known to play an impor-
tant role for superconductivity T cmaximizes near 92 K when 0.15 and thestructure is orthorhombic Superconductivity disappears at 0.6, where thestructural transformation of YBCO occurs from orthorhombic to tetragonal
The crystal structure of Bi-, Tl-, and Hg-based high-T csuperconductors arevery similar to each other Like YBCO, the perovskite-type feature and the pres-ence of CuO2layers also exist in these superconductors However, unlike YBCO,Cu–O chains are not present in these superconductors The YBCO superconduc-
tor has an orthorhombic structure, whereas the other high-T c superconductorshave a tetragonal structure (see Table 1.1)
The Bi–Sr–Ca–Cu–O system has three superconducting phases forming ahomologous series as Bi2Sr2Can1CunO42ny (n 1, 2, and 3) These threephases are Bi-2201, Bi-2212, and Bi-2223, having transition temperatures of 20,
85, and 110 K, respectively (10,11) The structure of 2201 together with
Bi-2212 and Bi-2223 is shown in Fig 1.3 All three phases have a tetragonal ture which consists of two sheared crystallographic unit cells The unit cell of
struc-these phases has double Bi–O planes which are stacked with a shift of (1/2 1/2 z)
with respect to the origin The stacking is such that the Bi atom of one plane sitsbelow the oxygen atom of the next consecutive plane The Ca atom forms a layerwithin the interior of the CuO2layers in both Bi-2212 and Bi-2223; there is no Calayer in the Bi-2201 phase The three phases differ with each other in the number
of CuO2planes; Bi-2201, Bi-2212, and Bi-2223 phases have one, two, and threeCuO2planes, respectively The c axis of these phases increases with the number
of CuO2planes The lengths of the c axis are 24.6 Å, 30.6 Å, and 37.1 Å
respec-tively for the Bi-2201, Bi-2212, and Bi-2223 phases The coordination of the Cuatom is different in the three phases The Cu atom forms an octahedral coordina-tion with respect to oxygen atoms in the 2201 phase, whereas in 2212, the Cu atom
is surrounded by five oxygen atoms in a pyramidal arrangement In the 2223 ture, Cu has two coordinations with respect to oxygen: one Cu atom is bondedwith four oxygen atoms in square planar configuration and another Cu atom is co-ordinated with five oxygen atoms in a pyramidal arrangement
Trang 7struc-Figure 1.4 shows the unit cells of two series of the Tl–Ba–Ca–Cu–O conductor (20) The first series of the Tl-based superconductor containing oneTl–O layer has the general formula TlBa2Can1CunO2n3, whereas the second se-ries containing two Tl–O layers has a formula of Tl2Ba2Can1CunO2n4with n
super-1, 2, and 3 In the structure of Tl2Ba2CuO6, there is one CuO2layer with the ing sequence (Tl–O) (Tl–O) (Ba–O) (Cu–O) (Ba–O) (Tl–O) (Tl–O) In
stack-Tl2Ba2CaCu2O8, there are two Cu–O layers with a Ca layer in between Similar tothe Tl2Ba2CuO6 structure, Tl–O layers are present outside the Ba–O layers In
Tl2Ba2Ca2Cu3O10, there are three CuO2layers enclosing Ca layers between each
of these In Tl-based superconductors, T cis found to increase with the increase inCuO2 layers However, the value of T c decreases after four CuO2 layers inTlBa2Can1CunO2n3, and in the Tl2Ba2Can1CunO2n4compound, it decreasesafter three CuO2layers
The crystal structure of HgBa2CuO4 (Hg-1201), HgBa2CaCu2O6 1212), and HgBa2Ca2Cu3O8(Hg-1223) is similar to that of Tl-1201, Tl-1212, and
(Hg-Tl-1223 (Fig 1.4) with Hg in place of Tl (21) It is noteworthy that the T cof the
Hg compound (Hg-1201) containing one CuO2layer is much larger as compared
to the one-CuO2-layer compound of thallium (Tl-1201) In the Hg-based
super-conductor, T cis also found to increase as the CuO2layer increases For Hg-1201,
Hg-1212, and Hg-1223, the values of T care 94, 128, and 134 K respectively, asshown in Table 1.1. The observation that the T cof Hg-1223 increases to 153 K un-
der high pressure (16) indicates that the T cof this compound is very sensitive tothe structure of the compound
F IGURE 1.3 Unit cells of the Bi2Sr2Can1CunOx compound with n 1, 2, and
3 (Adapted from Ref 11.)
Trang 81.4 PREPARATION OF HIGH-T cSUPERCONDUCTORS
High-T csuperconductors are prepared in the form of bulk, thick films, thin films,single crystals, wires, and tapes Fabrication in the form of wires and tapes are re-quired for high-current applications On the other hand, thick and thin films areneeded for electronic application Strict control of the stoichiometry of the com-
position is very much required for preparing high-T csuperconductors with able characteristics Even a small change in oxygen content or a small change incation doping level can transform the material from a superconductor to a low-car-rier-density metal or even to an insulator The following paragraphs give a brief
desir-F IGURE 1.4 Unit cells of the Tl1Ba2Can1CunO2n3compound containing one Tl–O layer and the Tl 2 Ba 2 Can1 CunO2n4compound containing two Tl–O lay-
ers for n 1, 2, and 3 (Adapted from Ref 20.)
Trang 9description of high-T csuperconductors in the form of bulk and thick films The
preparation of high-T cthin films is given in more detail in the other chapters ofthis book
The simplest method for preparing high-T csuperconductors is a solid-statethermochemical reaction involving mixing, calcination, and sintering The appro-priate amounts of precursor powders, usually oxides and carbonates, are mixedthoroughly using a ball mill Solution chemistry processes such as coprecipitation,freeze-drying, and sol–gel methods are alternative ways for preparing a homoge-nous mixture These powders are calcined in the temperature range from 800°C to950°C for several hours The powders are cooled, reground, and calcined again.This process is repeated several times to get homogenous material The powdersare subsequently compacted to pellets and sintered The sintering environmentsuch as temperature, annealing time, atmosphere, and cooling rate play a very
important role in getting good high-T c superconducting materials The(La1xBax)2CuO4 high-T csuperconductor is prepared by heating a mixture of
La2O3, BaCO3, and CuO in a reduced oxygen atmosphere at 900°C After grinding and reheating the mixtures, the pellet is prepared and sintered at 925°Cfor 24 h The YBa2Cu3O7 compound is prepared by calcination and sintering of
re-a homogenous mixture of Y2O3, BaCO3, and CuO in the appropriate atomic ratio.Calcination is done at 900–950°C, whereas sintering is done at 950°C in an oxy-gen atmosphere The oxygen stoichiometry in this material is very crucial for ob-taining a superconducting YBa2Cu3O7 compound At the time of sintering, thesemiconducting tetragonal YBa2Cu3O6 compound is formed, which, on slowcooling in oxygen atmosphere, turns into superconducting YBa2Cu3O7 The up-take and loss of oxygen are reversible in YBa2Cu3O7 A fully oxidized or-thorhombic YBa2Cu3O7 sample can be transformed into tetragonal YBa2Cu3O6
by heating in a vacuum at temperature above 700°C
The preparation of Bi-, Tl-, and Hg-based high-T c superconductors isdifficult compared to YBCO Problems in these superconductors arise because
of the existence of three or more phases having a similar layered structure Thus,syntactic intergrowth and defects such as stacking faults occur during synthesisand it becomes difficult to isolate a single superconducting phase For
Bi–Sr–Ca–Cu–O, it is relatively simple to prepare the Bi-2212 (T c 85 K) phase,
whereas it is very difficult to prepare a single phase of Bi-2223 (T c 110 K) TheBi-2212 phase appears only after few hours of sintering at 860–870°C, but thelarger fraction of the Bi-2223 phase is formed after a long reaction time of morethan a week at 870°C (11) Although the substitution of Pb in the Bi–Sr–Ca–Cu–O
compound has been found to promote the growth of the high-T cphase (22), a longsintering time is still required
Toxicity and low vapor pressure of Hg–O and Tl–O make fabrication of
Hg-and Tl-based high-T csuperconductors much more difficult and one has to followspecial precautions and stringent control on the preparation atmosphere The Tl-based superconductor is prepared by thorough mixing of Tl2O3, BaO, CaO, and
Trang 10CuO in appropriate proportions and pressing the powders into a pellet The pellet
is wrapped in a gold foil and fired at 880°C for 3h in a sealed quartz tube taining 1 atm oxygen to reach superconductivity (20)
con-For the preparation of a Hg-based high-T csuperconductor (15), first a cursor material with the nominal composition Ba2CaCu2O5is obtained from a ho-mogenous mixture of the respective metal nitrates by sintering at 900°C in oxy-gen Dry boxes are used for grinding and mixing of the powders After regrindingand mixing with HgO powder, the pressed pellet is sealed in an evacuated quartztube This tube is placed horizontally in a tight steel container and sintered at800°C for a few hours
pre-Several techniques such as screen printing (23–27), spin-coating (28) and
spray pyrolysis (29–33) are used in preparing high-T cthick films For the screenprinting or spin-coating method, the first step is to prepare homogenous powders
of high-T cmaterials; this is accomplished by solid-state reaction or by a chemicalroute involving mixing, calcination, and sintering of appropriate powders in theform of oxides or carbonates After sintering the powders are sieved through ascreen woven from stainless steel or nylon wire The diameter of the screen wireand the size of the opening can vary depending on the process requirement Theopening size is usually given in terms of a standard mesh number that varies from
100 to 400 The fine sieved powders are converted into thick paste by mixing with
an organic solvent such as propylene glycol, octyl alcohol, heptyl alcohol, ethanolamine, or cyclohexagonal In the screen-printing technique, thick paste isused for printing the substrate through the mesh screen and dried at an appropri-ate temperature In the spin-coating method, one drop of the paste is put on thesubstrate and the substrate is spun to get a uniform coating of the material The re-sultant films are fired at a suitable annealing temperature In general, single-crys-tal and polycrystalline substrates of magnesium oxide (MgO), strontium titnate(SrTiO3), lanthanum aluminate (LaAlO3), yattria-stabilized zirconia (YSZ), andaluminum oxide (Al2O3) are used for the high-T cthick-film preparation
tri-For YBCO thick films, the sintering temperature is kept between 940°C and970°C followed by slow cooling in an oxygen atmosphere (23) In order to achieveYBCO films with a larger grain size and higher current density, the firing temper-
ature is increased to 1000°C (24) Bi-2212 high-T cfilms are prepared by firing thefilms at 880–885°C It has been found that partial melting and quenching of the Bi-
2212 films from 885°C to room temperature leads to a T cas high as 96 K (25) For
high-T cfilms with a Bi-2223 phase, the films are fired at 880°C for a few utes and then annealed at 864°C for a duration of 70–80 h (26) The preparation ofTl–Ba–Ca–Cu–O thick films requires a two-step process (27) In the first step, afilm of Ba–Ca–Cu–O is prepared, and in the second step, this precursor film isheated in Tl2O3vapor followed by slow cooling to room temperature
min-Spray pyrolysis is another simple and inexpensive technique for preparing
high-T cfilms (30–33) For YBCO film, an aqueous solution for the spray is
Trang 11pre-pared by dissolving Y(NO3)6H2O, Ba(NO3), and Cu(NO3)3H2O in tilled water in a 1 : 2 : 3 stoichiometric ratio (29) The solution is sprayed on a sin-gle-crystal YSZ or SrTiO3substrate through a glass nozzle using oxygen for fewminutes and then slowly cooled to room temperature The starting solution for de-positing Bi-2212 film is prepared by mixing aqueous solution of Bi2O3, SrCO3,CaCO3, and CuO in dilute nitric acid (30) A two-step process is used for prepar-
triple-dis-ing Tl- and Hg-based high-T cfilms by the spray pyrolysis technique (31–33) Thefirst step involves preparation of Ba–Ca–Cu–O precursor films by spraying anaqueous solution of Ba, Ca, and Cu nitrates on a single-crystal substrate In thesecond step, Tl or Hg is incorporated in the precursor films by annealing the film
in a controlled Tl–O or Hg–O vapor atmosphere
Different techniques such as sputtering, evaporation, molecular beam taxy, laser ablation, chemical vapor deposition, and so forth have been used suc-
epi-cessfully to prepare thin films of high-T csuperconductors A detailed account ofthese techniques is given in Chapter 2 Most of these techniques work in a vacuumenvironment and the oxygen partial pressure near the substrate is controlled to ob-tain a superconducting film This can be done during the film deposition (in situprocess) or by postdeposition oxygen annealing The substrate temperature duringthe deposition is a crucial parameter that determines microstructural details such
as texture and the degree of epitaxy of the film Substrate–film interaction such asinterdiffusion can affect the quality of the films Thus, it is desirable to developprocesses that allow a low substrate temperature
1.5.1 Anisotropy
As described in Section 1.3, the crystal structure of high-T csuperconductors ishighly anisotropic This feature has important implications for both physical and
mechanical properties In high-T csuperconductors, electrical currents are carried
by holes induced in the oxygen sites of the CuO2sheets The electrical conduction
is highly anisotropic, with a much higher conductivity parallel to the CuO2planethan in the perpendicular direction Other superconductivity properties such as co-herence length (), penetration depth (), and energy gap () are also anisotropic
The mechanical properties of high-T cmaterials are also very anisotropic For
Trang 12ex-ample, in YBCO, upon cooling, the lattice contracts far more along a-b planes than along c axis Torque magnetometry measurements have been made for sev- eral high-T csuperconductors for studying anisotropy (34,35) For Tl-2212, ananisotropy of 105
is found for the ratio of the mass along the c axis to that of
a-b plane A similar large ratio is oa-btained for the Bi-2212 compound In Y-123, the
value of this ratio is found to be 25, which is much smaller compared to Bi and
Tl compounds The anisotropy factor of a high-T csuperconductor at the optimallydoped composition is related to the interlayer spacing between CuO2layers in theunit cell It has been also noted that increasing carrier doping or substituting ions
on the blocking layer for certain other ions such as Pb in Bi-2212 reducesanisotropy without changing the interlayer spacing significantly
1.5.2 Critical Magnetic Field
The abrupt transition from the normal to superconducting state occurs at a
bound-ary defined not only by the transition temperature (T c) but also by the magnetic
field strength There is a critical value of magnetic field, H c, above which the perconductivity is destroyed If a paramagnetic material is placed in a magneticfield, then the magnetic lines of force penetrate through the material However,when the same material is made superconducting by cooling to a low temperature
su-below T c, then the magnetic lines of force are completely expelled from the rior of the material This effect is called the Meissner effect Based on the Meiss-ner effect, the superconducting materials are classified as type I and type II su-perconductors If there is a sharp transition from the superconducting state to thenormal state, then this type of material is called a type I superconductor This kind
inte-of behavior is shown, in general, by pure metals In type II superconductors, there
are two values of the critical field: the lower critical field, H c1, and the upper
crit-ical field, H c2 For H H c1, the field is completely expelled from the
supercon-ductor However, for H c1, the magnetic field penetrates the material slowly
and continues up to H c2, beyond which the material transforms completely from
the superconducting state to the normal state The state between H c1 and H c2iscalled the vortex or mixed state Figure 1.5a shows the H–T phase diagram for conventional low-T csuperconductors At low fields, there is Meissner state, and
at high fields, vortices enter the material and form a vortex lattice
Superconduc-tivity is completely destroyed at H c2, for which the density of vortices is such that
the normal cores fill the entire material For low-T csuperconductors, this ior is exhibited, in general, by alloys and compounds On the other hand, all high-
behav-T c superconductors behave as type II superconductors For high-T c
superconduc-tors, the value of H c1(0) is low (100 Oe), whereas the value of H c2(0) is quitehigh (about few hundred tesla) The value of the critical field is anisotropic
for these materials For a YBCO single crystal, values of H c1(0) in the direction
parallel to the c axis and in the a-b plane are estimated as 850 and 250 Oe,
Trang 13respectively (36), whereas the value of H c2(0) is estimated to be 670 T and 120 T
in the a-b plane and along the c axis, respectively (37).
Cuprate high-T c superconductors display a complex H–T phase diagram (Fig 1.5b) due to their high-T c, short coherence length, layered structure and
anisotropy (38) Apart from H c1 and H c2 , there are irreversibility (H i) and melting
(H m) lines The melting line separates a vortex lattice and a vortex liquid state Theirreversibility line occurs in the vicinity of the melting line This line provides aboundary between the reversible and irreversible magnetic behavior of a super-conductor
The structure of the vortex line in high-T csuperconductors is different fromthe conventional type II superconductors The individual two-dimensional “pan-cake” vortices on neighboring layers couple to form three-dimensional vortex
F IGURE 1.5 H–T phase diagram of (a) low-T ctype II superconductors and (b)
high-T csuperconductor.