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692 Part 4 Functional Materials

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Part 4 1

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Part 4 1

695

Superconduct

4.2. Superconductors

Superconductors are characterized by an anoma-

lous temperature dependence of the electrical

resistivity. Below a critical temperature T

,their

resistivity drops by more than a factor of 10

In superconductors the magnetic ﬂux den-

sity B = µ

induced by an externally applied

ﬁeld H

is zero, like in ideal diamagnets with

= 0 (Meißner–Ochsenfeld effect). If H

exceeds

a critical value H

the superconductor becomes

normal conducting. But the magnetic induc-

tion B decreases from B

at the free surface to

B = 0 in the interior through a layer of ﬁnite

thickness characterized by the Landau pene-

tration depth λ. The critical ﬁeld varies with

temperature as H

(T ) = H

(0)[1−(T/T

)

],where

(0) = H

(T = 0K). According to the isother-

mal ﬁeld dependence of the magnetization

) =−µ

, two types of superconductors may

be differentiated, as shown in Fig. 4.2-1:

•

Type I superconductors such as Pb with

a sudden drop of −I,atH

; all pure metallic

elements and their dilute solid solutions

belong to this group;

•

Type II superconductors such as Pb

−

In15 which

are characterized by a lower critical ﬁeld H

at which the drop of −I sets in and an upper

critical ﬁeld H

at which −I reaches 0.

In Type I superconductors, the transition from the fully

superconducting to the fully normal conducting state

as a function of the applied magnetic ﬁeld H

passes

through an intermediate, mixed state in which the total

volume decomposes into lamellae in the superconduct-

ing and the normal conducting state. At their interface,

the transition from the superconducting lamellae of the

maximum density of electron pairs (Cooper pairs) n

which carry the superconducting current, to the normal

conducting lamellae where n

=0 occurs through a tran-

sition layer characterized by the coherence length ξ.In

terms of the microscopic theory of superconductivity,

ξ is the size of the Cooper pairs which is of the or-

derof1µm in pure metals. The coherence length ξ as

4.2.1 Metallic Superconductors .................... 696

4.2.1.1 Elements................................ 696

4.2.1.2 Practical Metallic

Superconductors ..................... 704

4.2.2 Non-Metallic Superconductors ............. 711

4.2.2.1 Oxide Superconductors ............ 711

4.2.2.2 Superconductors Based

on the Y–Ba–Cu–O System ....... 720

4.2.2.3 Superconductors Based

on the Bi–Sr–Ca–Cu–O System.. 736

4.2.2.4 Carbides, Borides, Nitrides ....... 744

References .................................................. 749

well as the penetration depth λ can be highly anisotropic

in compounds with crystal structures of low symmetry,

which is the case in low-T

oxide superconductors (see

Sect. 4.2.2.1).

Since superconductivity is caused by electron–

phonon interaction, the upper critical ﬁeld H

depends

on the mean free path of the electrons, and thus on the

electrical resistivity ρ in the normal conducting state,

and on the electronic speciﬁc heat γ as

(0) = 3.11ργT

As both ρ and T

are affected by impurities and struc-

tural defects, H

depends not only on composition and

structure but also on structural defects accordingly.

Magnetization –I (T ×10

)

5 101520

(A/m ×10

)

85Pb – 15In

Fig. 4.2-1 −I(H

) curves for pure Pb as a Type I and the Pb

−

In15

alloy as a Type II superconductor [2.1]

Part 4 2

696 Part 4 Functional Materials

Type II superconductors in a magnetic ﬁeld of in-

termediate strength H

< H

are in a mixed

state (Shubnikow phase) consisting of a superconduct-

ing matrix through which magnetic ﬂux “lines” of ﬁnite

thickness, also termed ﬂuxoids or vortices are penetrat-

ing, each carrying a quantum of magnetic ﬂuxΦ =h/2e.

The movement of these ﬂux lines may be pinned by

point defects, dislocations, and interfaces due to var-

ious modes of interaction. Deliberate introduction of

pinning defects is the basis of increasing the critical

magnetic ﬁeld such that the materials – termed non-ideal

Type II, Type III or hard superconductors – can bear an

increased critical external ﬁeld and/or critical current

at a given temperature. High-ﬁeld superconducting ma-

terials are developed on this basis of microstructural

design.

Practical superconductors are mainly applied to

generate high magnetic ﬁelds in wound magnet coils.

Accordingly they are produced as wires or cables. The

materials used are based on non-ideal Type II super-

conductors with a specially optimized microstructure

such that strong ﬂux line pinning persists up to a high

critical current density J

(T ). A second ﬁeld of ap-

plication are superconducting electronic devices, most

frequently based on the Josephson effect. The present

practical superconductors for high ﬁeld applications

are highly complex composite materials, based essen-

tially on two groups of superconducting alloy phases,

the intermetallic phase Nb

Sn and the solid solution

phase Nb

−

Ti. Recent developments have also led to

high ﬁeld oxide high-T

superconductors for practical

applications in wire, electronic device, and massive

form, the latter serving as high ﬁeld permanent mag-

nets.

Superconducting substances of fundamental as well

as practical interest may be divided into 3 main groups

which are dealt with in the subsequent sections:

•

Metallic superconductors

•

Superconducting oxides

•

Superconducting carbides, nitrides and borides

An extensive listing of individual publications

containing data of both metallic and non-metallic super-

conductors is given in [2.2]. An encyclopaedic survey of

all essential aspects of superconductivity may be found

in [2.3].

4.2.1 Metallic Superconductors

The basic superconducting properties of metals and al-

loys have been compiled comprehensively in [2.1, 2].

While the superconducting properties of all pure met-

als have been determined, the studies of alloys have

been concentrated on those of the elements with the

highest critical temperatures, i. e., Pb (T

= 7.2K),V

= 5.5K),Nb(T

= 9.3K), and Tc (T

= 7.7K).

4.2.1.1 Elements

Table 4.2-1 lists T

and H

of the superconducting

metallic elements along with their relevant thermo-

dynamic properties, the Debye temperature Θ

and

the Sommerfeld constant γ which determines the

electronic speciﬁc heat in the superconducting state

p,el

= 9.17 γT

exp(−1.5T

/T ). Table 4.2-2 lists the

pressure dependence of T

Pb Alloys

Ready availability and easy alloy formation of Pb have

led to extensive studies of superconductivity of Pb alloys

results of which are given in Tables 4.2-3 and 4.2-4, and

Figs. 4.2-1 and 4.2-2.

(K)

C (at.%)

8.4

8.2

8.0

7.8

7.6

7.4

7.2

7.0

6.8

6.6

0246810

Fig. 4.2-2 Composition dependence of T

in Pb solid so-

lution alloys [2.1]

Part 4 2.1

Superconductors 2.1 Metallic Superconductors 697

Table 4.2-1 Superconducting properties of metallic elements [2.1]

Element Purity (%) Residual resistivity T

ratio ρ

293 K

/ρ

4.2K

(K) (mT) (K) (mJ mol

−1

−2

)

Al 2000–4100 1.175 10.49 420 1.35

Am 0.6

Be 99.996 0.026 1390 0.21

Cd >38 000 0.517 2.805 209 0.69

Ga 46 500 1.0833 5.93 325 0.60

Hf 80 0.128 1.27 256 2.21

Hg 99.9999 4.154 41.1 87 1.81

In 9000 3.4087 28.15 109 1.672

Ir >2000 0.1125 1.6 425 3.19

La >99.9 4.87 9.8 151 9.8

Lu 15 0.1 35.0 210 10.2

Mo 17 000 0.916 9.686 460 1.83

Nb 500–16 500 9.25 206 276 7.80

Os 0.66 7.0 500 2.35

Pa 1.4

Pb 15 000 7.196 80.34 105 3.36

Re 1700 1.697 20.1 415 2.35

Ru 0.493 6.9 580 2.8

Sn 3.722 30.55 195 1.78

Ta 29–120 4.47 82.9 258 6.15

Tc 80–100 7.77 141 411 6.28

Th 1200 1.374 16.0 165 4.32

Ti >99.9 0.40 5.6 415 3.3

Tl 53 2.38 17.65 87.5 1.47

V 24–430 5.46 140 383 9.82

U 0.68 10.0 206 10.60

W 57 000 0.0154 0.115 383 0.90

Zn 99.9999 0.857 5.41 310 0.66

Zr 99.9 0.63 4.7 290 2.77

Table 4.2-2 Pressure dependence of the superconductivity of metals [2.1]

Metal Pressure range

c(max)

δT

/δ p

(10

MPa) (K) (K 10

−2

MPa

−1

) (10

−4

KMPa

−1

)

Al 0–62 2.1–1.7 2.1/0 −4.5

As I <100 <0.1

As II 100–140 0.2–0.25 0.25/100 >0

As III 140–220 0.31–0.5 0.5/140 <0

Ba I 0–55 <1

Ba II 55–85 1–1.8 1.8/83 100

Ba III 85–144 1.8–5 5.0/100 −15

Ba IV 144–192 4.5–5.4 5.4/175 1.3

Bi II 25–27 3.9 3.9/25 <0

Part 4 2.1

698 Part 4 Functional Materials

Table 4.2-2 Pressure dependence of the superconductivity of metals [2.1], cont.

Metal Pressure range

c(max)

δT

/δ p

(10

MPa) (K) (K 10

−2

MPa

−1

) (10

−4

KMPa

−1

)

Bi II



25–30 8.2 8.2/30 −3.2

Bi III 27–37 6.55–7.25 7.25/27 −4.0

Bi VI 80–200 8.55 8.55/90 −2.3

Cd 0–28 0.52 0.52/0 <0

Ce (α) 20–35 0.020–0.045 0.045/35 >0

Ce (α)



45–125 1.9–1.3 1.9/45 <0

Cs V 125–150 1.5–1.6 1.6/125 <0

Ga II 30–38 6.24–6.38 6.38/35 −3

Ga II



35 7.5

Ge 115–120 5.35 5.35/115 <0

Hf 0–160 0–0.25 0.25/160 0.06

α-Hg >10 4.2–3.9 4.156/0 −3.47

β-Hg >10 4.0–3.9 4.017/0 −4.48

α-La 0–23 4.9–8.2 8.2/23 14.1

0–225 4.8–11.5 11.5/225

β-La 23–250 5.5–12.9 12–12.9/140–200 11.3

Lu 45–190 0.024–1 1.0/180 1.2

Nb 0–24 7–9.2 9.214/0 −0.25

25–250 9.7 9.7/250 2.6

P 0–260 5.8–3.6 5.8/170 <0

Pb I 0–110 ≈7.2–4.2 7.2/0 −4.9

Pb II 135–200 3.55–2.9 3.55/160 −2.2

Re 0–20 1.7 1.7/0 Minimum at

Re II 2.3 700 MPa

Sb 0–120 2.6–2.7

Sb III 85–150 3.40–3.55 3.55/85 <0

Sb II 0–130 6.75–6.95 6.95/130 <0

Si 120–130 6.7–7.1 7.1/120 <0

Sn I 0–113 3.7 3.7/0 0

Sn II 125–160 5.2–4.85 5.2/125 −5.04

Sn III 113–270 5.3 5.3/113 −4.95

Ta 0–250 4.3 4.3/0 −0.26

Tc 0–15 8.0–7.8 8.0/15

Te II 39–70 2.5–3.9 3.9/70 7.7–8.5

Te III 68–80 4.28–4.15 4.3/70 −0.3–1.7

Bi IV 43–62 6–8.7 8.7/43 −4.6

Bi V 68–81 6.7–8.3 6.7/81 −3.0

Te IV 80–260 4.3–2.8 4.3/80 −4.2

Th 0–170 1.4–0.64 1.4/0 Minimum at

700 MPa

Ti 0–25 − − 0.06

TI II 0–35 2.395/2 −1.0

TI III 35–50 1.45/35 (bcc) −4.95

Part 4 2.1

Superconductors 2.1 Metallic Superconductors 699

Table 4.2-2 Pressure dependence of the superconductivity of metals [2.1], cont.

Metal Pressure range

c(max)

δT

/δ p

(10

MPa) (K) (K 10

−2

MPa

−1

) (10

−4

KMPa

−1

)

TI IV 40–60 2.32/40 (fcc) −2.0

α-U 10–85 2.4–0.4 2.4/10

β-U 0–12 1.15/95 >0

U 90–160 <0.35

V 0–250 5.5–7.15 0.7

Y 110–170 2.7–1.7 2.7/160 3.7

Zn 0–26 0.87 0.87/0 <0

α-Zr 0–45 0.69/45 0.35–0.8

ω-Zr 60–130 1.7 1.17/130 0.77

0 = ambient pressure

Table 4.2-3 Critical temperature of superconductivity of binary Pb compounds [2.1]

Compound Crystal T

structure (K) structure (K)

PbLi

Cub. B2 7.2 Pb

Th Cub. 5.5

Cub. 5.62 PbZr

Cub. A15 0.76

PbMg

C1 5.6 PbZr

Hex. D8

4.6

Ca Cub. L1

0.84 PbV

Cub. A15 <4.2

Sr Tetr. L1

1.85 PbNb

Cub. A15 9.6

Y Cub. L1

4.72 PbTa

Cub. A15 17

<4.2

PbRh

<0.32

<4.2 Pb

Tetr. C16 2.66–1.32

<4.2 PbPd

Cub. L1

<0.10

<4.2 Pb

Pd Tetr. C16 3.01–2.95

<4.2 Pb

Pt Tetr. C16 2.80

La <4.2 PbAu

C15 1.18

La Cub. L1

4.10–4.05 Pb

Au Tetr. C16 3.15

PbSm

<4.2 Pb

Au 4.4

<4.2 PbIn

(α) Hex. 6.05–5.65

<4.2 Pb

Bi()

8.2–8.5

<4.2 PbO

<1.02

Sm 6.7 PbS B1 <1.0

Sm Cub. L1

<4.2 PbSe B1 <1.26

Yb Cub. L1

0.23 PbP 7.8

Compound has a range of homogeneity

No superconductivity is observed above 4.2 K

Compound is formed under high pressure and high temperature

Part 4 2.1

700 Part 4 Functional Materials

Table 4.2-4 Critical magnetic ﬁeld µ

of binary Pb alloys

Material

Temperature

(mT) (K)

Pb–1.6–8.6% Na 205–600 4.2

Pb–3–5% Ag 82 0

Pb–∼ 25% Cd 135 0

Pb–5–15% Hg 230–> 900 4.2

Pb–2–30% In 98–390 4.2

Pb–14% Sn 100

Pb–12.9–64% Sn 110–204 1.3

Pb–30% Tl 280 4.2

Pb–0.8–40% Tl 70–290 4.2

Pb–2–50% Bi 73–190 4.2

Pb–30% Bi(ε) 3500 0

Pb–30–45 nm

2200 4.2

200–700 nm

80–110 4.2

Pb pore diameter 3.2–5.8nm

5500–9600 0

Pb–25% Bi, 126 nm

14 500 4.2

Pb–40% Bi, 2–5 nm

12 500–11 300 4.2

At.%

Extrapolated to 0 K

Layer thickness

Particle diameter in porous glass

V Alloys

Table 4.2-5 and Fig. 4.2-3 contain T

data of binary V al-

loys. Even though V

Ga with its cubic A15 structure has

a T

≤ 16.8 K and was, therefore, studied extensively, it

Table 4.2-5 Critical temperature T

of superconductivity of V compounds [2.1]

Compound Crystal T

structure (K) structure (K)

Cub. A15

9.6–11.65 V

Rhomb. <4.2

Cub. D8

<1.2

Cub. B2 <0.37

VAl

Tetr. D0

<4.2 VOs

Cub. A15 5.7–3.0

Hex. <4.2 V

P Tetr. 0.07

Monocl. <4.2 VP

Hex. B8

<1.02

VAl

Fcc <4.2 VP

Monocl. <0.035

Cub. A15 <1.0 V

Cub. A15

<4.2

VAs

Rhomb. <1.0 V

Cub. A15 0.082

VAs

Monocl. <0.33 VPd Tetr. −

Au Cub. A15 3.22–0.015 VPd

Tetr. −

VAu

Rhomb. <1.2 VPd

Tetr. −

VAu

Tetr. <1.2 V

Cub. A15 3.62–0.98

Tetr. <0.1 VPt

Cub. L1

−

VB Rhomb. B

1.2 VPt

Tetr. 1.02

has never been considered as a practical superconduct-

ing material seriously because of the cost and difﬁculties

of handling of Ga.

Part 4 2.1

Superconductors 2.1 Metallic Superconductors 701

Table 4.2-5 Critical temperature T

of superconductivity of V compounds [2.1], cont.

Compound Crystal T

structure (K) structure (K)

B Rhomb. <4.2 VPt

Tetr.

0.07

Hex. C32 <1.2 Cub. L1

0.07

Hex. −

Cub. A15 8.4–7.6

VBe

Hex. C14 <4.2 VRe

Tetr. D8

6.26–4.52

VBe

Tetr. − V

Cub. A15 1.075

– < 0.015

Bi Cub. A15

<4.2

Hex. <1.2 VRh

(α

) − −

Fcc − VRh

(α

) Tetr. L1

−

Cub. B1 <0.03 VRh

(α

) Rhomb. −

Cub. A15

<4.2 V

Rhomb. −

Cub. A15 0.015 VRh

Cub. L1

1.2

VCo Tetr. D8

<4.2 VRu Cub. B2 5

– < 0.14

VCo

Hex. <4.2 V

S Tetr. <1.15

VFe

Tetr. D8

<0.3 V

Tetr. <4.2

VFe Cub. B2

<4.2 VS

Hex. B8

<4.2

Cub. A15 16.8–14.2 V

Hex. <4.2

Hex. D8

<4.2 V

Sb Cub. A15 0.80

Hex. <4.2 V

Tetr. <4.2

Cub. D8

4.2 VSb Hex. B8

<4.2

Tetr. 2.1–4.07 VSb

Tetr. C16 <0.06

VGa

Tetr. <4.2 V

Tetr. −

Cub. A15 6.3–5.88 (7.5–11.2)

VSe

Hex. B8

−

Tetr. T1 <4.2 V

Low −

Hex. D8

<1.02 Sym.

Cub. A15 17.2–17

Rhomb. <1.2 V

Tetr. T1 <0.30

Tetr. <1.2 V

Hex. D8

<0.30

Tetr. L

<1.02 V

Tetr. <1.2

VH Cub. <4.2 VSi

Hex. C40 <1.2

Cub. C15 9.4–9.0 V

Cub. A15 7.0–3.8

Cub. A15

13.9 (12.3–17.9)

Cub. A15 1.71

– < 0.015 V

Rhomb. <1.15

Hex. C14

10.0

VIr(α)

Rhomb. <1.6 VTc

Cub. C15

3.6

β−V

1−x

1+x

Tetr. L1

<1.36 Cub. B2 <1.39

VIr

Cub. L1

<4.2 V

− −

VMn

Tetr. D8

<4.2 VTc

Cub. 7.8–4.0

Hex. <1.2 V

− −

VN Cub. B1 8.5–7.5 VTe

Hex. B8

−

Cub. A15 <0.35 VTe

Monocl. <1.13

Tetr. D8

<4.2 VTe

Monocl. <0.05

Part 4 2.1