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742 Part 4 Functional Materials

Critical current density (A/cm

)

Frequency

Average wire length: 200 m

Total wire length: 17000 m

77K, self-field

12000 13000 14000 15000 16 000

Fig. 4.2-52 Distribution of the engineering critical current

density J

at 77 K in self-ﬁeld for 200-m long BiPb2223/Ag

tapes produced in one 17 000-m manufacturing run [2.109]

Critical current density (kA/cm

)

1991 1992 1993 1994 1995 1996 1997 1998 1999

Year

Fig. 4.2-53 Critical current density J

for short length

multiﬁlamentary BiP2223/Ag tapes versus year of produc-

tion [2.110]

The development of Bi2212 conductors has also

reached a level in recent years which allows the man-

ufacture of long-length wires and tapes. For instance,

70-m long wires with an average critical current den-

sity, J

, of 200 kA cm

−2

at 4.2 K in self-ﬁeld were

produced [2.112]. On tapes of 0.1 to 0.3 mm thickness,

values of up to 35 kA cm

−2

at 77 K and 0 T were

measured.

The ﬁeld dependence of J

at 77 K is strongly

anisotropic for both BiP2222 and Bi2212 conductors. In

Fig. 4.2-54a, the J

(B, T ) correlations are demonstrated

for BiPb2223 tapes in magnetic ﬁelds, H

c

, aligned

perpendicularly to the wide plane of the tape, that is

parallel to the crystallographic c axis. At temperatures

near 77 K, J

already drops at B ≈ 0.1 T to very small

values. This tendency, which is also observed in Bi2212

(Fig. 4.2-46) and Bi2223 thin ﬁlms (Fig. 4.2-47), respec-

tively, is attributed to the thermally activated motion of

the pancake vortices near the temperature of liquid ni-

trogen (see Sect. 4.2.2.1). At 4.2 K, the activation energy

of vortex motion is large compared to the thermal en-

ergy, k

T , and therefore a much weaker dependence

of J

on B is observed. Figure 4.2-54b represents the

(B, T ) dependence of BiPb2223 tapes in ﬁelds, H

⊥c

aligned parallel to the plane of the tape (parallel to

the crystal ab-plane). A comparison of Fig. 4.2-54b

with Fig. 4.2-54a shows that J

is less dependent on B

for H

⊥c

than for H

c

(also at 77 K). This can be at-

tributed to the strong intrinsic pinning of Josephson

vortices.

Even the highest J

values observed for the Ag-

sheathed tapes are about one order of magnitude lower

than those of monocrystalline thin ﬁlms. These results

pose the question of which microstructural features are

responsible for this discrepancy. One cause might be

different densities of the ﬂux pinning centers. The ﬂux–

pinning interactions in BSCCO superconductors are not

well known. In particular, due to the small coherence

length of the high-T

superconductors, it is generally

expected that even atomic-sized point defects can pin

vortices. It could be shown experimentally that single-

atomic impurities of Zn and Ni in Bi2212 [2.113] or

line defects such as edge [2.114] and screw dislo-

cations [2.115] in YBa

7−x

can effectively pin

pancake vortices.

The essential reason for the much lower J

of the

BSCCO tapes compared to monocrystalline ﬁlms stems

from the existence of grain boundaries, which act as

barriers to current ﬂow as discussed above. Consider-

ing the importance of grain boundaries in a frame of

mechanism of the supercurrent ﬂow in BiPb2223 tapes,

two models were proposed, the “brick-wall” [2.116] and

“railway-switch” [2.117] models, which were combined

afterwards within the “freeway” model [2.118].

The models were based on microstructural investi-

gations. Figure 4.2-55 shows the cross-sectional detail

of a BiPb2223/Ag tape and reveals a platelet-like mi-

crostructure of the superconducting phase. Each platelet

called “colony”, with a typical diameter of 10–20 µm

and a thickness of about 1 µm, consists of a group of

single crystal grains sharing a common c axis. The

grains inside the colony have random ab-orientations,

with planar twist basal grain boundaries (BGB‘s) lying

along the ab-planes (Fig. 4.2-56a). Using transmission

electron microscopy, the dominant colony-boundaries

schematically depicted in Fig. 4.2-56b–c were observed.

Considering these microstructural details, the main fea-

Part 4 2.2

Superconductors 2.2 Non-Metallic Superconductors 743

⏐⏐c

⊥c

Critical current density (A/cm

)

810120246

a) b)

Critical current density (A/cm

)

810120246

Magnetic field (T) Magnetic field (T)

20K

25K

30K

35K

40K

50K

60 K77K

20K

30K

35K

40K

50K

60 K

77K

Fig. 4.2-54a,b Critical current density J

of BiP2223/Ag-alloy tapes as a function of the temperature and magnetic ﬁeld

aligned parallel

(a) and perpendicular to the to the c axis (b) [2.119]

5µm

Fig. 4.2-55 REM micrograph of the cross-sectional detail

of a BiP2223/Ag tape [2.119]

tures of the “freeway” model can be summarized as

follows:

•

The “freeway” represents current ﬂow along

ab-planes.

•

The current ﬂows primarily across edge colony

boundaries (ECB) rather than small-angle colony

boundaries (SCB).

•

The relative twist orientation of the ab axes across

the ECB of adjacent colonies is considered as the

a) b)

One colony Two colonies

SCB

BGB

single-crystaline grain

Two colonies

BGB ECB EGB

a/b

Fig. 4.2-56a–c Scheme of colony and single-crystal

grain boundaries proposed for the “railway-switch mod-

el” [2.117] and in a modiﬁed picture for the “freeway

model” [2.118]

dominant factor in the current ﬂow limiting the

critical current density.

•

Misorientation angles of the ab-axes that are less

than 10

◦

are required to achieve strong super-

conducting links across the edge crystal grain

Part 4 2.2

744 Part 4 Functional Materials

boundaries (EGB) within an edge colony boundary

(ECB) of adjacent colonies.

•

The probability of overlap of the ab-axes at the

boundary of adjacent colonies within the 10

◦

crite-

rion is about 1/9 for any one grain inside the colony.

Thus the colony structure can carry a current ﬂow (I )

at a fraction f

ECB

≈ 1/9 of what a single crystal

with the ab-plane parallel to the current direction

(I ) could carry. The ECB current is expected to be

on the scale of the ab-current ﬂow.

•

An important assumption required for this mecha-

nism is the possibility that high current can shift

along the c axis between different ab-planes, oth-

erwise the strongly coupled ab-planes cannot be

accessed. This possibility is controversial, since the

current must cross many c axes boundaries (BGB)

inside the colony and the dependence of J

on the

twist angle is not clear yet, as discussed above.

From the model one can derive opportunities to in-

crease J

of Bi2223 tapes, e.g., through biaxial texturing

of the colony grains and increasing the critical current

density of the grains. Furthermore, the model provides

Table 4.2-29 Structure and T

of carbides

(K) Structure type Ref.

28 BiF

[2.120]

BEDT-TTF-based salt 12.8 (HP) organic [2.120]

MoC

1−x

14.3 NaCl [2.121]

NbC 12 NaCl [2.121]

TaC 10 NaCl [2.121]

C 12.2 orthorh. [2.120]

LaBrC 7.1 Gd

[2.120]

YIC 10 Gd

[2.120]

Y(Br, I)C 7.1 Gd

[2.120]

C 10 β-Mn [2.120]

MgNi

C 8.5 SrTiO

[2.122]

SC 5 Tm

SC [2.123]

C 7.6 Tm

C [2.124]

LaC

1.6 CaC

[2.121]

LuC

3.3 CaC

[2.121]

4.0 CaC

[2.120]

(La, Th)NiC

7.9 CeNiC

[2.120]

PtC

1.5 U

IrC

[2.121]

11 Pu

[2.120]

8.2 Pu

[2.121]

4.1 Pu

[2.121]

(Y, Th)

17 Pu

[2.120]

a coherent explanation of a variety of data observed on

Bi2223 tapes such as the J

(B, T ) dependence discussed

above.

4.2.2.4 Carbides, Borides, Nitrides

Superconductivity is found in many carbides, nitrides,

and borides. Several of these compounds contain tran-

sition metals T , forming a close-packed lattice with the

small atoms, X = C, N, or B, in the interstices of the

lattice. The simplest compound of the form TX has a cu-

bic lattice of the NaCl-type. Compounds of TX with

T = Nb, V, Mo, etc., are generally very hard, corrosion-

resistant, and of high thermal stability. These desirable

properties are understood to arise from strong covalent

bonding. According to the BCS theory, superconduc-

tivity in these and related compounds can be explained

by high-frequency phonon modes of the light X atoms

combined with a high density of states of the conduction

electrons at the Fermi level. A further precondition for

high superconducting transition temperatures (which is

not included in the BCS theory) is a strong coupling of

the phonon modes to the electrons. Recently, a supercon-

Part 4 2.2

Superconductors 2.2 Non-Metallic Superconductors 745

Table 4.2-30 Structure and T

of boron and borides [2.120]

(K) Structure type

B 11.2 (at 250 GPa)

NbB 8.3 CrB

TaB 4.0 CrB

B 5.1 CuAl

B 4.7 Re

MgB

39 AlB

ReB

6.3 AlB

7.1 CaB

LaB

5.7 CaB

4.7 UB

ZrB

5.8 UB

YRUB

7.8 LuRuB

LuRuB

10.0 LuRuB

YOs

6.0 CeCo

LuOs

4.7 CeCo

ErRh

8–9 CeCo

YRh

10–11 CeCo

LuRh

8–12 CeCo

ducting transition temperature T

= 39 K was found in

MgB

[2.125], essentially metallic boron bonded by co-

valent B

−

B and ionic B

−

Mg bonds. This is the highest

of binary compounds and close to or above the theo-

retical value predicted by the BCS theory. The material

MgB

has been known since the early 1950s, but its

transport and magnetic properties have not been investi-

gated until recently despite an intensivesearch for higher

values of T

in the family of binary compounds. The T

of 23 K obtained for the intermetallic A15 compound

Ge in the early seventies could not be exceeded

until the discovery of the high-T

superconductors in

1986. Since 1994, there has been a renewed interest in

intermetallic superconductors which incorporate light

elements such as boron due to the discovery of the

new class of quaternary rare-earth transition metal boro-

carbides RT

C(R =Y, Lu, or rare-earth metals;

T = Ni, Pt, or Pd) [2.126, 127]. These compounds are

interesting with regard to the strong interplay between

magnetism and superconductivity, including magnetic

pair-breaking and the coexistence of superconductivity

and magnetism.

Carbides

Several carbon-containing superconductors are listed in

Table 4.2-29. Superconductivity in the fullerenes can

be achieved by alkali metal intercalation, resulting in

electronically-doped bulk material. This was at ﬁrst

demonstrated by Rosseinsky et al. [2.128] who found

superconductivity in Rb

at 28 K. Among the super-

conductors in Table 4.2-29 that have not been mentioned

so far are: a) organic compounds, e.g., in BEDT-TTF

in which superconductivity is induced by high pres-

sure (HP), b) the layered rare-earth carbide halides

with Gd

structure, c) the niobium carbosulﬁdes

with Tm

SC and Tm

C structure, d) the lanthanoid

dicarbides which crystallize in the body-centered tetrag-

onal CaC

structure, e) the lanthanoid (and actinide)

sesquicarbides with Pu

structure, and f) the in-

termetallic compound MgNi

C with cubic perovskite

structure in which superconductivity was found very

recently [2.122]. Not included in Table 4.2-29 are the

rare-earth transition metal borocarbides RT2B2C, which

will be described in more detail later.

Borides

The superconducting transition temperatures of boron

and selected borides are listed in Table 4.2-30. Boron

itself, which is an isolator at ambient pressure, was re-

cently found to become superconducting under high

pressure [2.129]. The boron atoms in transition metal

borides can form chains, nets, and three-dimensional

networks. In this respect the borides differ markedly

from other interstitial compounds such as carbides

Part 4 2.2

746 Part 4 Functional Materials

Table 4.2-31 Superconducting parameters (ranges of experimental and derived data) of MgB

[2.130]

Parameter Values reported

Superconducting transition temperature T

39–40 K

Lattic parameters a =0.3086 nm, b = 0.3524 nm

Theoretical density 2.55gcm

−3

Resistivity near T

ρ(40 K) 0.4–360 µΩ cm

“Residual” resistance ratio RRR = ρ(300 K)/ρ(40 K) 1–27

Coherence lengths ξ

4–12 nm

1.6–3.6nm

Penetration depths λ(0) 85–180 nm

Upper critical ﬁelds H

c2(ab)

(0) 14–40 T

c2(c)

(0) 2–24T

Anisotropy parameter H

c2(ab)

(0)/H

c2(c)

(0) 2–13

Lower critical ﬁelds H

(0) 27–48 mT

Irreversibility ﬁelds H

irr

(0) 6–35T

and nitrides. Among the transition metal orthorhom-

bic monoborides, NbN and TaN which crystallize in the

CrB structure are superconductors. Some properties of

MgB

, which has the highest T

among the borides, are

presented in the next section.

MgB

The boride MgB

crystallizes in the simple hexagonal

AlB

-type structure and contains graphite-type boron

layers which are separated by hexagonal close-packed

layers of magnesium (see Fig. 4.2-57). MgB

has not

only an attractively high transition temperature, but, in

contrast to high-T

superconductors, the advantage of

strongly-linked grains.

Therefore, high currents can ﬂow across the grain

boundaries of bulk polycrystalline MgB

. This is due

to the relatively large coherence length ξ of this super-

conductor (Table 4.2-31). On the other hand, this large

coherence length is responsible for the relatively low

values of the upper critical ﬁeld H

∝ ξ

−2

observed,

especially for clean MgB

single crystals in a magnetic

ﬁeld parallel to the c axis. Studies of the electronic

structure of MgB

revealed two relevant bands which

have to be taken into account in order to explain the

magnitude and temperature dependence of the upper

critical ﬁeld H

(T ). Considerably higher upper critical

ﬁelds than for bulk and single-crystalline MgB

can be

achieved in thin ﬁlms by the introduction of impurities

to decrease the mean free path. In such ﬁlms, enhanced

resistivity, reduced values of T

, and upper critical ﬁelds

up to 40 T have been reported. One of the open ques-

tions concerns the anisotropy of H

. Reported values

of H

(ab) and H

Borocarbides

Table 4.2-32 gives an overview of superconducting

borocarbides. Most of them belong to the family of qua-

ternary rare-earth transition metal borocarbides RT

(R = Y, Lu, or other rare-earth metals; T = Ni, Pt, or

Pd). In this table the superconducting transition tem-

perature T

and the magnetic ordering temperature T

are listed. The LuNi

C-type structure of these com-

pounds can be considered as the ThCr

-type (space

group I4/mmm) interstitially modiﬁed by carbon. They

consist of alternating sheets of T

tetrahedra and

RC layers as shown in Fig. 4.2-58 for RNi

C. The

Fig. 4.2-57 Structure of MgB

Part 4 2.2

Superconductors 2.2 Non-Metallic Superconductors 747

Table 4.2-32 Borocarbide superconductors [2.120]

(K) T

(K) Structure type

LuB

2.4 − LaB

3.6 − LaB

BC 7.5 − Mo

LuNi

C 16 − LuNi

YNi

C 15.5 − LuNi

ScNi

C 15.5 − LuNi

ThNi

C 15 − LuNi

CeNi

C 0.1 − LuNi

TmNi

11 1.5 LuNi

ErNi

C 10.5 6.8 LuNi

HoNi

C 7.5–8 5.8 LuNi

DyNi

C 6.2–6.4 11 LuNi

YRu

C 9.7 − LuNi

YPd

C 23 − LuNi

ThPd

C 14.5 − LuNi

LaPd

C 1.8 − LuNi

YPt

C 10–11 − LuNi

LaPd

C 10–11 − LuNi

ThPt

C 6.5 − LuNi

PrPt

C 6 − LuNi

structure of RNi

C is highly anisotropic with a c/a ra-

tio of about 3. Nevertheless, these compounds have

a three-dimensional globally isotropic structure, but due

to the complicated shape of the Fermi surface there is

a pronounced dispersion in the Fermi velocity. This pe-

Fig. 4.2-58 Structure of the rare-earth nickel borocarbides

culiarity of the electronic structure is important for the

upper critical ﬁeld H

(T ) because these superconduc-

tors are in the clean limit, i. e., their coherence length is

smaller than the mean free path. The magnitude of H

at low temperatures and an unusual positive curvature

of H

(T ) observed near T

, especially for the non-

magnetic RNi

C(R = Y, Lu) compounds, can be

understood by taking their two-band electronic structure

into account.

The superconducting transition temperature of non-

magnetic RNi

C compounds (R = Sc, Lu, Y, Th,

La) strongly depends on the lattice parameter a,as

shown in Fig. 4.2-59. The highest T

is obtained for

LuNi

C, which has an optimum lattice parame-

ter corresponding to a maximum density of states at

the Fermi level. In Fig. 4.2-59, magnetic R elements

(Tm, Er, Ho, Dy, Yb, Tb, Gd, Eu, Nd, Pr) are also

included. The T

of the superconducting compounds

among the magnetic RNi

C compounds (R = Tm,

Er, Ho, and Dy) scales roughly with the de Gennes

factor dG = (g −1)

J(J +1) of the R

Hund’s-rule

ground state, where g is the Landé factor and J the

total angular momentum. Such so-called de Gennes

scaling is observed for both T

and the magnetic or-

Part 4 2.2

748 Part 4 Functional Materials

RNi

Transition temperature T

(K)

Lattice parameter a (nm)

0.33 0.34 0.35 0.36 0.37 0.38

LaPrNdEuGdTbYb

Fig. 4.2-59 Transition temperature T

and lattice param-

eter a for RNi

C compounds for non-magnetic (circles)

and magnetic (triangles) R elements [2.131]

dering temperature T

as shown in Fig. 4.2-60. The

reason is that both effects, i. e., antiferromagnetism and

the suppression of superconductivity, are governed by

the exchange interaction of conduction electrons with R

4f electrons.

A striking feature distinguishing the supercon-

ducting RNi

C compounds from other magnetic

superconductors is their high magnetic ordering tem-

perature T

being comparable with T

. Therefore, the

interplay between superconductivity and magnetism in

these compounds is particularly pronounced. In partic-

ular, DyNi

C is the unique member of the RNi

series which becomes superconducting in the antiferro-

magnetically ordered state.

Nitrides

The refractory transition metal nitrides with NaCl-type

crystal structure have been widely studied in the past.

The basic features of superconductivity in these com-

pounds indicate a standard BCS mechanism. The highest

among these compounds was found for NbN (see

Table 4.2-32). Niobium nitride which can easily pre-

pared as a thin ﬁlm is a promising material for the

application in various cryogenic devices such as high

resolution X-ray detectors or superconducting quantum

mixers. For NbN thin ﬁlms, very high upper crit-

ical ﬁelds up to 30 T and high critical currents, e.g.,

0 5 10 15

Temperature (K)

de Gennes factor

afm + sc

afm

R Ni

YTm Er Ho Dy Tb Gd

Fig. 4.2-60 Superconducting transition temperature T

and antiferromagnetic ordering temperature T

for

RNi

C compounds, with R = Lu, Tm, Er, Dy, Tb, and

Gd as functions of the de Gennes factor (see text). (afm

= antiferromagnetic, sc = superconducting, afm +sc =

coexistence of superconductivity and antiferromagnetism)

Acm

−2

at 4.2 K in ﬁelds of 19 T [2.132] were re-

ported. For MoN with the NaCl structure, T

= 29 K

was predicted [2.133], although this structure does

not appear in the equilibrium phase diagram of the

−

N system. Attempts have been made to prepare

it by techniques leading to non-equilibrium states. In

single-phase ﬁlms with the NaCl structure, T

= 12.5K

was found [2.134]. This unexpectedly low T

was ex-

plained by the presence of nitrogen vacancies and

interstitial defects. The transition metal nitrides crys-

tallize in several other structures, too. Some of these

compounds are superconducting and have similar T

values as the corresponding NaCl-type compounds (see

Table 4.2-33). Recently, a new route of preparation was

developed for lithium intercalated metal nitride chlo-

ride. Superconductivity with T

= 14 K and even 25 K

was reported for Li

0.16

ZrNCl and Li

0.48

(THF)

HfNCl,

respectively [2.135,136], where THF =tetrahydrofuran.

Part 4 2.2

Superconductors References 749

Table 4.2-33 Nitrides superconductors

(K) Structure type Reference

TiN 6.5 NaCl 2.121

ZrN 10.6 NaCl 2.121

HfN 8.3 NaCl 2.121

Vn 8.8 NaCl 2.121

NbN 17.3 NaCl 2.121

NbN 9 W 2.132

NbN 15 Fcc 2.121

TaN 10.4 NaCl 2.121

TaN 10.8 Fcc 2.137

MoN 12.5 NaCl 2.121

MoN 13.2 Hexagonal 2.134

ReN 5 NaCl 2.121

N 8.6 Hexagonal 2.132

N 10.6 Hexagonal 2.137

N 6–7 Fcc 2.134

0.16

ZrNCL 14 2.135

0.48

(THF)HFNCl 25.5 2.136

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