4.2. Superconductors - Springer

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Superconduct
o
4.2.Superconductors
Superconductors are characterized by an anoma-
lous temperature dependence of the electrical
resistivity.Below a critical temperature T
c
,their
resistivity drops by more than a factor of 10
10
.
In superconductors the magnetic flux den-
sity B =µ
r
B
a
induced by an externally applied
field H
a
is zero,like in ideal diamagnets with
µ
r
=0 (Meißner–Ochsenfeld effect).If H
a
exceeds
a critical value H
c
the superconductor becomes
normal conducting.But the magnetic induc-
tion B decreases from B
a
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
c
(
T
)
=H
c
(
0
)
[1 −
(
T/T
c
)
2
],where
H
c
(
0
)
=H
c
(
T =0K
)
.According to the isother-
mal field dependence of the magnetization
I
(
H
a
)
=−µ
0
H
a
,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,at H
c
;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
c1
at which the drop of −I sets in and an upper
critical field H
c2
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
a
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
e
,
which carry the superconducting current,to the normal
conductinglamellae where n
e
=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-
der of 1µm 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
c
oxide superconductors (see
Sect.4.2.2.1).
Since superconductivity is caused by electron–
phonon interaction,the upper critical field H
c2
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
µ
0
H
c2
(0) =3.11ργT
c
.
As both ρ and T
c
are affected by impurities and struc-
tural defects,H
c2
depends not only on composition and
structure but also on structural defects accordingly.
Magnetization –I (T ×10
2
)
6
4
2
5 10 15 20
(A/m ×10
4
)
Pb
85Pb – 15In
H
c1
H
c
H
a
H
c2
Fig.4.2-1
−I(H
a
) curves for pure Pb as a Type I and the Pb

In15
alloy as a Type II superconductor [2.1]
Part4
2
696 Part 4
Functional Materials
Type II superconductors in a magnetic field of in-
termediate strength H
c1
< H
a
< H
c2
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,eachcarryinga quantumof 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
c
(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
3
Sn and the solid solution
phase Nb

Ti.Recent developments have also led to
high field oxide high-T
c
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
c
=7.2K),V
(T
c
=5.5K),Nb (T
c
=9.3K),and Tc (T
c
=7.7K).
4.2.1.1 Elements
Table 4.2-1 lists T
c
and H
c
of the superconducting
metallic elements along with their relevant thermo-
dynamic properties,the Debye temperature Θ
D
and
the Sommerfeld constant γ which determines the
electronic specific heat in the superconducting state
C
p,el
=9.17γT
c
exp(−1.5T
c
/T).Table 4.2-2 lists the
pressure dependence of T
c
.
Pb Alloys
Ready availability and easy alloy formation of Pb have
led to extensive studies of superconductivityof 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.
T
C
(K)
C (at.%)
8.4
8.2
8.0
7.8
7.6
7.4
7.2
7.0
6.8
6.6
0 2 4 6 8 10
As
Sb
Bi
Sn
Hg
Cd
Ti
In
Fig.4.2-2
Composition dependence of T
c
in Pb solid so-
lution alloys [2.1]
Part4
2.1
Superconductors
2.1 Metallic Superconductors 697
Table4.2-1
Superconducting properties of metallic elements [2.1]
Element
Purity (%)
Residual resistivity
T
c
µ
0
H
c
Θ
D
γ
ratio ρ
293K

4.2K
(K)
(mT)
(K)
(mJ mol
−1
K
−2
)
Al
2000–4100
1.175
10.49
420
1.35
Am
0.6
Be
99.996
0.026
1390
0.21
Cd
>38000
0.517
2.805
209
0.69
Ga
46500
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
17000
0.916
9.686
460
1.83
Nb
500–16500
9.25
206
276
7.80
Os
0.66
7.0
500
2.35
Pa
1.4
Pb
15000
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
57000
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
Table4.2-2
Pressure dependence of the superconductivity of metals [2.1]
Metal
Pressure range
a
T
c
T
c(max)
/p
a
δT
c
/δp
(10
2
MPa)
(K)
(K10
−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
Part4
2.1
700 Part 4
Functional Materials
Table4.2-4
Critical magnetic field µ
0
H
c2
of binary Pb alloys
Material
a
µ
0
H
c2
Temperature
(mT)
(K)
Pb–1.6–8.6%Na
205–600
4.2
Pb–3–5%Ag
82
0
b
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–30–45nm
c
2200
4.2
200–700nm
c
80–110
4.2
Pb pore diameter 3.2–5.8nm
d
5500–9600
0
Pb–25%Bi,126nm
c
14500
4.2
Pb–40%Bi,2–5 nm
d
12500–11300
4.2
a
At.%
b
Extrapolated to 0K
c
Layer thickness
d
Particle diameter in porous glass
V Alloys
Table 4.2-5 and Fig.4.2-3 contain T
c
data of binary Val-
loys.Even though V
3
Ga with its cubic A15 structure has
a T
c
≤16.8K and was,therefore,studied extensively,it
Table4.2-5
Critical temperature T
c
of superconductivity of V compounds [2.1]
Compound
Crystal
T
c
Compound
Crystal
T
c
structure
(K)
structure
(K)
V
3
Al
a
Cub.A15
b
9.6–11.65
V
2
O
5
Rhomb.
<4.2
V
5
Al
8
a
Cub.D8
2
<1.2
c
V
3
Os
2
a
Cub.B2
<0.37
VAl
3
Tetr.D0
22
<4.2
VOs
a
Cub.A15
5.7–3.0
V
4
Al
23
Hex.
<4.2
V
3
P
Tetr.
0.07
V
7
Al
45
Monocl.
<4.2
VP
a
Hex.B8
1
<1.02
VAl
11
a
Fcc
<4.2
VP
2
Monocl.
<0.035
V
3
As
a
Cub.A15
<1.0
V
3
Pb
a
Cub.A15
a
<4.2
VAs
a
Rhomb.
<1.0
V
3
Pd
a
Cub.A15
0.082
VAs
2
Monocl.
<0.33
VPd
Tetr.

e
V
3
Au
Cub.A15
3.22–0.015
VPd
2
Tetr.

VAu
2
a
Rhomb.
<1.2
VPd
3
Tetr.

VAu
4
Tetr.
<1.2
V
3
Pt
a
Cub.A15
3.62–0.98
V
3
B
2
Tetr.
<0.1
VPt
a
Cub.L1
0

VB
Rhomb.B
f
1.2
VPt
2
a
Tetr.
1.02
has never been considered as a practical superconduct-
ing material seriously because of the cost and difficulties
of handling of Ga.
Part4
2.1
702 Part 4
Functional Materials
Table 4.2-5
Critical temperature T
c
of superconductivity of V compounds [2.1],cont.
Compound
Crystal
T
c
Compound
Crystal
T
c
structure
(K)
structure
(K)
VNi
2
a
Rhomb.
<4.2
V
3
Ti
a
Cub.A15
b
<4.2
VNi
3
Tetr.DO
22
<4.2
V
4
Zn
5
Tetr.
<4.2
V
4
O
a
Tetr.
<4.2
VZn
3
Cub.L1
2
<4.2
V
2
O
a
Hex.
<4.2
VZn
16
d


VO
a
Cub.B1
<0.07
V
2
Zr
d
Cub.C15
8.8–6.5
V
2
O
3
Rhomb.
<1.28
Rhomb.
j
8.5
a
Compound with a range of homogeneity
b
Metastable phase
c
“<” means that no superconductivity was found above the temperature indicated
d
Supposed compound
e
Superconducting properties not investigated
f
Unstable in the absence of carbon
g
Non-stoichiometric composition
h
Low-temperature modification
i
High-temperature modification
j
Formed by martensitic transformation
8
6
2
5 10 15
T
C
(K)
C (at.%)C (at.%)
51015
Ge
Os, Ru
Cu
Sb
Ga
Al Au
Sn
Si
H
O
Pt
N
Sc
Ti
Zr
Nb
Ta
Hf
C
Mo
Cr
Mn
Fe
W
Ir
Ni
V
Fig.4.2-3
Composition dependence of T
c
of superconductivity in
V solid solution alloys [2.1]
Nb Alloys
Based on its highest T
c
among all elements Nb has been
considered the most likely base metal for superconduct-
ing materials from the beginning and its alloys and
intermetallic compounds have been investigated most
extensively.Table 4.2-6 shows T
c
values for binary Nb
compounds,where Nb
3
Al,Nb
3
Ga,Nb
3
Ge,and Nb
3
Sn
with the cubic A15 type crystal structure stand out for
their particularly high T
c
.Of these,Nb
3
Sn has been de-
veloped into a high-field superconducting material (see
Sect.4.2.1.2).Figure 4.2-4 shows the effect of alloying
additions on T
c
in Nb solid solutions.The Nb

Ti alloys
have,finally,been selected to form the most versatile
and widely applied high-field superconducting material
for present applications (see Sect.4.2.1.2).
Part4
2.1
704 Part 4
Functional Materials
Table 4.2-6
Superconductivity of Nb compounds [2.1],cont.
Compound
Crystal
T
c
Compound
Crystal
T
c
structure
(K)
structure
(K)
Nb
2
N(β)
Hex.
9.5–<1.2
NbSn
2
Rhomb.
2.68
Nb
4
N
3
(γ)
Tetr.
12.2–7.8
NbTc
3
Cub.A12
12.9–10.5
NbN(δ

)
Tetr.
7.2
Nb
3
Te
g
Cub.A15
<2.5
NbN(δ)
Cub.B1
16.5–9.7
Nb
5
Te
4

<1.1
NbN(ε)
Hex.
<1.20
Nb
3
Te
4
Hex.
1.49
Nb
5
N
6
Hex.
<1.77
NbTe
2
Hex.C7
0.74–0.5
Nb
4
N
5
Tetr.
8.0–8.5
NbTe
4

<0.025
NbO
Cub.B1
1.61–1.38
Nb
3
Tl
b
Cub.A15
9.0
NbO
2
Tetr.
<1.2
NbZn
3
Cub.L1
2
<1.02
a
“<” means that no superconductivity was found above the temperature indicated
b
Low-temperature modification
c
High-temperature modification
d
Non-stoichiometric composition
e
Metastable phase
f
Extrapolated maximum T
c
g
Under extreme conditions
h
Stabilized by adding interstitial elements
i
Phase is stable at >850

C only
Ge
Cu
Sb
Al
Au
Sn
Si
H
O
Pt
N
Sc
Ti
Zr
Ta
Hf
C
Mo
Cr
Fe,Ni
W
Ir
Co
Ru
Pd
Rh
Os
Tc
Re
MaMa
Ma
V
Fig.4.2-4
Composition dependence of T
c
of superconduc-
tivity in Nb solid solution alloys [2.1]
Tc Alloys
Since Tc is rare and difficult to prepare in the alloy
form,its superconducting properties have been studied
to a limited extent only (see Table 4.2-7 and Fig.4.2-5).
4.2.1.2 Practical Metallic Superconductors
Practical metallic superconductors for DC or AC
applications are invariably composite wires with super-
conducting filaments which are embedded in a normal
conductingmatrix,usuallyCu.Theyhave a highlongitu-
dinal conductivity and may contain further components
such as lowconductivity barriers consisting of a Cu

Ni
alloy,or diffusion barriers of Nb or Ta.Accounts of
combining the aspects of the physics of superconductiv-
ity,materials science and technology,and electrical and
mechanical performance criteria which have to be taken
into account and are mastered in producing supercon-
ducting wires are given in [2.4–8].
Part4
2.1
Superconductors
2.1 Metallic Superconductors 705
Table4.2-7
T
c
of superconductivity of Tc compounds [2.1]
Compound
Crystal
T
c
Compound
Crystal
T
c
structure
(K)
structure
(K)
Tc
3
As
7
Cub.D8
f
<0.3
a
Tc
6
Ti
b
Cub.A12
8.10–7.73
TcBe
Cub.
5.21
TcTi
Cub.B2
<1.7
TcBe
22
Cub.ZrZn
22
5.25
Tc
2
Th
Hex.C14
5.3
c
TcC
Cub.
3.85
Tc
3
V(δ)
Cub.
7.8–4.0
Tc
2
Hf
Hex.C14
5.6
TcV(ε)
Cub.B2
<1.39
Tc
7
Mo
3
Tetr.D8
b
15.8–14.7
Tc
3
W
2
Tetr.D8
b
7.88–8.35
Tc
2
Mo
3
Cub.A15
14–12
Tc
6
Zr
Cub.A12
9.7
Tc
3
Nb
Cub.A12
12.9–10.5
Tc
2
Zr
Hex.C14
7.6
Tc
3
SN
d
Hex.
5.92
a
“<” means that no superconductivity was found above the temperature indicated
b
Formed as an ordered phase by extended annealing of the solid solution phase
c
Non-stoichiometric composition
d
Compound not determinded definitely;T
c
may be related to the solid solution
Only two superconducting metallic phases are used
routinely in superconducting wires for applications:the
Nb

Ti solid solution phase and the Nb
3
Sn intermetallic
phase.Due to the difference of their intrinsic supercon-
ducting properties T
c
and B
c2
,they have different ranges
of application as indicated in Table 4.2-8.
The critical current density J
c
(T,B) obtained by ap-
plying optimal microstructural pinning of the flux lines
in conductors of different composition and at different
temperatures is shown in Fig.4.2-6.Two factors of influ-
ence may be applied to obtain a higher critical current
density J
c
(T,B) through effects of the intrinsic prop-
erties:either a decrease in temperature of application,
e.g.,from4.2 to 1.8K,or an increase of B
c2
by alloying
as shown for (Nb,Ta,Ti)
3
Sn in both Table 4.2-8 and
Fig.4.2-6.It should be noted that the intrinsic properties
are affectedonlymarginallybydifferences inprocessing
of the conductors.
Table4.2-8
Characteristic properties of practical metallic superconductors (After [2.8])
Superconducting phase
Composition
T
c
(K)
B
c2
(T)
Magnetic field in application B(T)
Nb

Ti
46–52wt%Ti,
≈10
≈10.5 (4.2K)
≤9 (4.2 K)
≈47wt%Ti optimal
>9 (1.8 K)
Nb
3
Sn
25 at.%Sn,
≈18
≈23 (4.2K):
≤20T (4.2K)
(Nb,Ta,Ti)
3
Sn
≤7.5wt%Ta,
≈26–29 (4.2K)
several T (<4.2K)
≤0.2wt%Ti
12
10
6
T
C
(K)
C (at.%)C (at.%)
0 1 2 3 4 512345
Nb
Ti
V
Mo
W
Cr
Ni
Pd
Re
Ru,Os,Rh
Co
Fe
Fig.4.2-5
Composition dependence of T
c
of superconductivity in
Tc solid solution alloys [2.1]
Part4
2.1
708 Part 4
Functional Materials
9 111 3 5 7
F
P
(GN/m
–3
)
20
18
16
14
12
10
8
6
4
2
0
B (T)
Fig.4.2-9
Bulk pinning force F
p
versus magnetic field,
corresponding to the J
c
data shown in Fig.4.2-8e.Typical
particle spacings for the optimum J
c
is d ≈20nmand d ≈
3–5nm,respectively [2.9]
Based on systematic variations and optimizations
such as those shown in Fig.4.2-8,commercial Nb

Ti
superconducting composite wires are provided for
a wide range of specifications.Figure 4.2-10 shows
a typical wire cross section and Table 4.2-9 lists some
characteristic data.
Table4.2-9
Characteristic data at 4.2K of commercial Nb

Ti superconductors,round wires
Filaments
A
Cu
/A
NbTi
a
Wire diameter
Filament diameter
Critical current J
c
,(A) at µ
0
H(T)
(mm)
(µm)
3T 5T
7 T
9T
54
1.35
0.3
27
100
70
45

54
1.35
0.6
53
380
265
170

54
1.35
0.85
75

480
310
140
45
1.8
0.4
36
150
105
70

45
1.8
0.7
62
420
295
185

a
Ratio of cross sectional area
b
Data extracted froma commercial brochure of Vacuumschmelze GmbH (9/1990)
Fig.4.2-10
Typical cross section of a Cu-stabilized Nb

Ti
superconducting wire
Nb
3
Sn Superconductors
The production of superconductors based on Nb
3
Sn as
the superconducting phase [2.7,8] is hampered by the
brittle behavior of this intermetallic phase which cannot
be deformed by wire drawing.Consequently the con-
ductors are produced by composing ductile components
first,reducing the cross section of the composite into the
final wire formby extrusion and drawing processes,and
finally forming the Nb
3
Sn phase by a diffusion–reaction
treatment after the specified wire diameter has been
obtained.Five routes of processinghave beendeveloped:
1.Bronze process:The initial rod composite con-
tains Nb rods surrounded by Cu

Sn alloy rods
(13–15wt%Sn) in a suitable arrangement such
that after processing into wire form the diffusion–
reaction treatment leads to the formation of Nb
3
Sn
at the interface of Nb and Cu

Sn.The initial com-
posite,if composed in a suitable configuration,has
excellent deformation properties such that a geo-
Part4
2.1
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