Poole Ch.P., Jr. Handbook of Superconductivity

Подождите немного. Документ загружается.

146 Chapter 6: Crystal Structures of Classical Superconductors

structure. The atoms from the other Mn site form columns of face-linked

octahedra, susceptible to host interstitial atoms. The Si atoms center trigonal

prisms formed by Mn atoms. A structure where all octahedral voids are filled is

defined on the intermetallic compound l-IfsCuSn 3 with CuHf 6 octahedra. In

carbides and related compounds, the octahedral site is only partly occupied. In

superconducting M04.8Si3C0. 6 the Mo-Mo distances within the chains are

2.52A. An isotypic O-stabilized phase, identified in a sample of nominal

composition Nbo.s1Itro.3000.19 , was found to become superconducting at 11.0 K.

Certain superconducting compounds crystallizing with a Ti2Ni-type struc-

ture are also stabilized by oxygen. Also for this structure type, many alloys

originally reported as binary were later shown to contain small amounts of a

nonmetal. The cubic face-centered cell of Ti2Ni contains 96 atoms and the Ti

atoms occupy two crystallographically independent sites. The atoms from the

site of lowest multiplicity form tetrahedra. This site may in some cases be

occupied by atoms of the other element, resulting in a different ordered

substitution derivative, defined on NiCd. The atoms from the other Ti site

form relatively large empty octahedra. The structure type was in fact first

identified on its filled-up form, on the so-called q-carbide, W3Fe3C , with C

atoms inside W 6 octahedra. Superconductivity is reported for several O-stabi-

lized Ti2Ni-type alloys formed by Zr or Ti and a group VIII transition metal. A

maximum value of 11.8 K is observed for a sample of nominal composition

Zro.61Rho.28500.105. The full occupation of the octahedral site in Zr3V30 was

confirmed by neutron diffraction experiments.

Unlike the superconducting Pd hydride, which crystallizes with the NaC1-

type structure, Th4H15 (T c = 7.6 K) is stable at room temperature. The structure

type was first identified on its antitype version, the silicide CUlsSi 4. The Th

atoms in ThaH15 are located on infinite nonintersecting lines parallel to the body

diagonals. Four atoms, one from each of four neighboring chains, together form

a tetrahedron. The metal atom substructure is identical to the one formed by the

metal atoms in Pu2C 3 and

5c4C3,

the latter crystallizing with a Th4P3-antitype

structure. One-fifth of the H atoms center the Th 4 tetrahedra just mentioned,

whereas the atoms from the other H site form triangles (d(D-D)= 2.25 A). Each

Th atom is surrounded by 12 H atoms.

Borides, Carbides, and Borocarbides with Nonmetal Polymers

a. Layered Carbohalides

The compound GdCBr crystallizes with two structural modifications of layered

character, ls-GdCBr and 3s-GdCBr, shown in Fig. 6.18. Both structures

contain C 2 dumbbells, octahedrally surrounded by Gd atoms. The C-C distance

E. Borides, Carbides, and Borocarbides with Nonmetal Polymers 147

Fig.

6.18.

Structures ofYCI (ls-GdCBr type) (a) and 3s-GdCBr (b) in projections along [0 1 0]. Large

spheres: I, Br; medium spheres: Y, Gd; small spheres: C. Dark shading: y -- 89 light shading:

y -- 1. Solid lines connect atoms forming octahedra around the C 2 dumbbells.

(1.3 A) approximately corresponds to a double bond. The (C2)Gd 6 octahedra

share edges to form infinite sheets, which are separated by double layers of

bromine ions. The Gd and Br atoms form approximately close-packed layers,

which are arranged in simple hexagonal stacking in the variant called l s. In the

variant 3s a stacking sequence with a three times larger translation unit,

corresponding to the stacking code

h2c2,

found. The structures where each

metal atom octahedron is centered by a single atom can be described in space

groups

P~3m

1 and

R~3m,

respectively, and are known for two structural modifica-

tions of TazCS 2. The replacement of the atoms centering the octahedra by atom

dumbbells, all parallel and oriented along 4-fold axes of the octahedra, lowers the

symmetry to monoclinic. The structures of the two modifications of GdCBr are

isopointal (same space group and Wyckoff sequence), but the unit cells can be

distinguished from the value of the monoclinic angle. The infinite stacking of

condensed

RCzR

layers corresponds to the tetragonal structure of CaC2,

described later.

At first sight, the chemical bonding can be approximated by the formula

(R3+)2(Cz)4-(X-)2,

but the compounds are conducting in two dimensions

because of a mixing of C 2 antibonding and

R-d

states. Band structure

calculations have revealed a very flat band (localization) with a significant

C2 ~* contribution at the Fermi level, corresponding to a maximum density of

states. The Fermi level also crosses bands with a large slope (delocalization).

Such a situation is considered to be favorable for superconductivity (Simon,

1997). Superconducting properties are observed for compounds with nonmag-

netic rare-earth elements such as Y and La. Substitution of one halogen by

148 Chapter 6: Crystal Structures of Classical Superconductors

another modifies the cell dimensions and alters the degree of covalence of the

R-C

bonds. T c increases from 2.3 K for YCC1 to 5.1 K for YCBr, reaches a

maximum of 11.1 K for YCBr0.2510.75, and then decreases to 9.7 K for YCI. The

structure changes from ls to 3s, and back to ls, during the progressive

substitution. The variation of T c appears to be independent of the actual stacking

of the slabs, which seems to indicate that superconductivity takes its origin in the

YC2Y slabs. The incorporation of Na atoms into YCBr increases the translation

unit along the stacking direction and produces a transition from the 3s- to the Is-

modification. As expected, the interstitial atoms were found to occupy the

octahedral sites between the two bromine layers (partial occupation of Wyckoff

position 2(d) 0 1 89 in space group

C2/m).

Superconductivity at 6 K is reported for the compound La9B3C6Br 5. The

orthorhombic crystal structure, defined on Ce9B3C6Brs, contains C-B-C units

with an angle of 148 ~ at the central atom. As in the carbohalides discussed

earlier, nonmetal atom layers are sandwiched between two R atom layers to form

slabs, separated by halogen atom layers. However, the R atom layers differ

significantly from the close-packed layers found in the carbohalides. The B

atoms center R 6 trigonal prisms and the C atoms R 5 square pyramids, which are

fused to the trigonal prisms via common rectangular faces and share edges with

each other. The resulting R3(CBC)zR3 slabs are corrugated and separated by

single Br layers.

CeCo4B 4

Type and Stacking Variants

Superconductivity is observed at the composition RT4B 4 in several temary rare-

earth-transition metal boride systems. A series of different structure types have

been identified for this general composition, all characterized by the presence of

boron dimers, empty transition metal atom tetrahedra, and single rare-earth metal

atoms. In the structure types defined on CeCo4B4, LuRu4B 4 and LuRh4B4,

shown in Fig. 6.19, T 4 tetrahedra and R atoms are arranged as the Na and C1

atoms in the simple NaC1 type (compare Fig. 6.17). The main difference between

the three structures concems the relative orientation of the T 4 tetrahedra. A

structural slab may be considered where tetrahedra and R atoms altemately

occupy the points of a 2D square-mesh lattice. Neighboring tetrahedra within the

slab are rotated by 90 ~ with respect to each other. When two slabs are stacked

upon each other, an R atom is always placed over a tetrahedron and vice

versa. For convenience we will label the comers of the square mesh A (0 0),

(1 0), B (1 1), and fl (0 1). The translation unit of the square-mesh lattice itself,

a(mesh), is identical to the thickness of the slab. In the starting layer, points A

and B are occupied by tetrahedra, points ~ and fl by R atoms. The tetrahedra at A

and B are rotated by 90 ~ with respect to each other. A tetrahedron in the same

orientation as the one placed at A in the starting layer, may in the second layer be

found either in position ~ or in position ft. In the third layer a similarly oriented

E. Borides, Carbides, and Borocarbides with Nonmetal Polymers 149

Fig. 639.

Structures of ErRh4B 4 (CeCo4B 4 type) (a), LuRu4B 4 (b), and LuRh4B 4 (c) in projections

along [0 0 1], [1 0 0], and [1 0 0], respectively, emphasizing the arrangement of R atoms, T 4

tetrahedra, and B 2 dumbbells. Note that R atoms are sometimes hidden by overlying T 4

tetrahedra.

tetrahedron may occupy position A, as in the first layer, or be placed in position

B. The stacking mode Aa is observed in CeCo4B4 . The resulting structure is

tetragonal primitive with a-~ ~/2a(mesh) and c ~ 2a(mesh). The boron dumb-

bells are located across the slab interface. When the slabs are stacked together,

distances of the same magnitude as those observed within the tetrahedra appear

between tetrahedra in the same orientation, so that infinite 2D frameworks result.

The slabs in LuRu4B 4 are stacked according to the sequence

AczBfl.

The

structure is tetragonal body-centered with the arrangement of the mutually rotated

tetrahedra along [0 0 1] described by a 4-fold screw axis (space group

I41/acd ).

The cell parameters are related to the translation units of the square-

mesh lattice according to a-~ 2a(mesh), c ~ 4a(mesh). The general character-

istics of the structure are otherwise similar to those described for CeCo4B 4, with

the difference that the interconnections of the T 4 tetrahedra lead to the formation

of two independent interpenetrating 3D frameworks.

The stacking mode observed in LuRh4B 4,

AaAflBfl

is a combination of

the former two. This structure is orthorhombic and the cell parameters of the

conventional C-centered cell may be derived from the translation unit of

the square-mesh lattice by the following relations: a~ c~ 2a(mesh),

150

Chapter 6: Crystal Structures of Classical Superconductors

b--~ 6a(mesh). The CeCo4B 4 type is formed by RT4B 4 compounds with Co or

Rh, less often Ir. Superconducting transition temperatures above 10K are

observed for isotypic YRh4B 4 and LuRhaB 4. A few Rh-based compounds,

such as LuRhaB4, form the three stacking variants under different condi-

tions. The three modifications become superconducting at 11.8, 9.2 (stabilized

by Ru), and 6.2 K, respectively.

c. Other Structures with Nonmetal Atom Dumbbells

The structure of CaCz may be considered as a substitution derivative of the NaC1

type with single anions replaced by C2 dumbbells. The dumbbells are all parallel

to [0 0 1] of the tetragonal body-centered cell. The structure is isopointal (same

space group and Wyckoff sequence) with the MoSi 2 type, discussed in the section

on intermetallic compounds. However, the presence of atom dumbbells in one

structure, but not the other, excludes isotypism. The structure type is formed by

most rare-earth elements; however, superconductivity is observed only for

nonmagnetic ions. The C-C distance within the acetylene ion increases with

increasing valence of the cation, e.g., from 1.19 for CaC 2 to 1.29 for YC 2 and

1.32A for UC2. Of these three compounds, only YC2 is a superconductor

(T c = 3.9 K).

Of the many R2C 3 compounds crystallizing with the Pu2C 3 type, three

truly binary compounds show superconducting transition temperatures above

10 K. The carbon atoms are arranged in dimers, with C-C distances ranging

from 1.2 to 1.4 A which can be assimilated to a multiple bond. The cubic body-

centered unit cell contains 16 metal atoms and 12 carbon dumb-bells. As shown

in Fig. 6.20, the dumbbells are parallel to the cell axes. The lanthanide atoms

Fig. 6.20.

Structure ofLu2C 3 (Pu2C 3 type), content of one unit cell (a) and Lu 8 dodecahedron around a

C 2 dumbbell (b). Large spheres: Lu; small spheres: C.

E. Borides, Carbides, and Borocarbides with Nonmetal Polymers ISI

were found to be in the trivalent state, except cerium, for which an average value

of 3.4+ was determined. Each carbon atom has short distances to six surround-

ing rare-earth metal atoms forming a distorted octahedron. The other carbon

atom of the dumbbell centers an octahedron edge that is significantly longer than

the other edges. This crystallographically equivalent carbon atom is surrounded

by an identical distorted octahedron, perpendicular to the preceding one. The two

octahedra interpenetrate each other and the C 2 dumbbell is surrounded by a total

of eight R atoms.

In most binary systems the PuzC3-type phase presents a certain homo-

geneity range that presumably corresponds to the substitution of a certain

proportion of C2 dumbbells by single C atoms. If all dumbbells are replaced

by single atoms, the composition becomes R4C 3 and the structure that of the

Th3P 4 antitype. This structure has been reported for nonsuperconducting Sc4C 3,

whereas a superconducting transition temperature of 8.5 K is observed at the

approximate composition Sc13C10 . The structure of the superconducting phase

may correspond to a small replacement of single atoms by dumbbells, but

additional lines in the diffraction pattern could not be indexed. The super-

conducting properties of the PuzC3-type phases are very sensitive to variations

in the carbon content, the highest values being recorded at the C-rich boundary.

They can be further enhanced by alloying and the highest critical temperature,

17.0 K, is known for the nominal composition Y1.4Th0.6C3.1. In this case the

cubic structure is formed by synthesis at high pressure and high temperature,

whereas the product obtained by arc melting contains a tetragonal phase that is

not superconducting.

The LuRuB2 type is also characterized by nonmetal dimers. In contrast to

the RT4B 4 borides, where the boron dimers are well separated from each other,

they are here arranged in infinite zigzag chains where B-B distances of 1.74/~

alternate with distances of 1.92)~. The angles are close to 120 ~ and the chains

may be considered as cut from the hexagon-mesh boron nets found, for example,

in A1B 2 and CeCo 3 B 2. Each boron atom centers a trigonal prism formed by three

Lu and three Ru atoms. The B-B dimer distances occur when the prisms share

rectangular faces. Relatively short distances are observed between the metal

atoms, in particular between the Lu atoms (3.10 A). Ruthenium may be replaced

by osmium, and lutetium by other trivalent rare-earth elements. Superconductiv-

ity is observed for compounds with nonmagnetic lanthanide elements, the highest

critical temperature, 10.0 K, being reached by the type-defining compound itself.

A superconducting transition temperature near 7 K was measured for the

carbon-rich phase LasB2C 6, with 52 atoms in the tetragonal unit cell. The

orthorhombic structure is virtually isotypic with that of nonsuperconducting

CesBzC 6. Double square-mesh NaCl-type

slabs may be considered in the

structure, however, every fifth C atom is replaced by a C2 dumbbell, changing the

composition of the slab to R5C 6. The dimers are approximately perpendicular to

the NaCl-type slabs, but slightly tilted away from the 4-fold axes with a certain

degree of disorder. Four partly occupied carbon sites were refined for CesB2C6,

152

Chapter 6: Crystal Structures of Classical Superconductors

eight for LasB2C 6. The "single" carbon atoms of neighboring slabs are

interconnected via the boron atoms and form approximately linear CBC units

(d(C-B) ~ 2.0A). A limited homogeneity range with respect to the carbon

content probably corresponds to different proportions of single C atoms and C2

dumbbells. The superconducting transition temperature was found to decrease

smoothly on both sides of the composition Las(CBC)2C 2.

d. LuNi2B2C Type and Members of the Same Structure Series

A short time aiter the discovery of the high-T c superconducting oxides, the more

than 30-year-old record held by Nb3Ge thin films was reached also by classical

superconductors. A few temary borocarbides (e.g., Mo2BC) were known to be

superconducting below 10 K. However, the discovery that by doping "YNizB3"

with small amounts of carbon, Tc could be increased to 13.5 K, and the almost

simultaneous report on superconducting samples in the Y-Pd-B-C system with

critical temperatures above 20 K, stimulated an intensive search for superconduct-

ing borocarbides in 1994. The identification of La3Ni2BzN3 with a closely

related structure and a superconducting transition temperature of 12 K extended

the interest to boronitrides. The crystal structures of this family of superconduc-

tors are strongly reminiscent of those of the high-Tr superconducting oxides.

The structure type defined on LuNi2B2C, shown on the left side of Fig.

6.21, is a filled-up derivative of the tetragonal CeA12Ga 2 type. More than 400

intermetallic compounds, among which several temary borides, crystallize with

this well-known type, discussed in the section on intermetallic compounds. The

insertion of carbon into the rare-earth metal atom layers is accompanied by an

increase of the translation unit along the 4-fold axis. Like the structures of the

high-T c superconductors, the tetragonal structure of LuNi2B2C can be decom-

posed into atom layers with square mesh. The stacking along the c-axis

corresponds to the sequence-B-Ni2-B-LuC-. The distances between the Ni

atoms within the square mesh (2.45 A) are slightly shorter than in metallic

nickel. There is a considerable amount of covalent bonding extending in three

dimensions, in particular between nickel and boron and between boron and

carbon atoms. The short interatomic distances between the latter elements

(1.47 A) suggest double bonds. The Ni atoms center B 4 tetrahedra that share

edges to form slabs, which may be considered as characteristic of the PbO

antitype or of the CaF 2 (fluorite) type. These Ni2B 2 slabs are held together by

linear BCB units to form a relatively rigid, porous 3D framework that can accept

rare-earth metal atoms of different sizes. Band calculations have shown that the

Fermi level coincides with a sharp peak in the density of states, with contributions

mainly from the d orbitals of nickel, but also from the BCB units.

The LuNi2B2C type is formed by all lanthanide nickel borocarbides. The

variation of the cell parameters with the radius of the rare-earth metal atom shows

Fig. 6.21.

Schematic drawings of members of the structure series

RnT2B2C n

(n = 1,2, 3, and 4) formed by borocarbides and boronitrides, with Pearson codes. Shading

indicates relative heights. Thick lines connect nonmetal atoms, thin lines Ni and B atoms.

154 Chapter 6: Crystal Structures of Classical Superconductors

an approximately linear increase of a but a decrease of c, corresponding to an

overall increase of the cell volume. The apparently contradictory behavior

observed for the c-parameter is explained by the relative rigidity of the Ni-B-C

skeleton. When a larger rare-earth metal atom is inserted into the framework, the

R-C distances become longer and the translation parameter of the square-mesh

RC layer, i.e., the a-parameter, is increased. Structural refinements have revealed

that the C-B, as well as the Ni-B, distances remain approximately constant for

the whole series of lanthanides and that, in order to keep the latter unchanged

when the a-parameter is increased, the tetrahedral angle in the NiB 4 unit is

progressively decreased. The tetrahedra are distorted so that the thickness of the

Ni2B 2 slab is reduced, and consequently also the c-parameter.

Superconductivity is observed for lanthanide nickel borocarbides where the

R atoms are not too large. A critical temperature of 16.6K is reached by

LuNi2B2C, the structure of which contains less distorted NiB 4 tetrahedra than

the isotypic compounds. As observed for the RT4B 4 borides and the Chevrel

phases, some magnetic elements also form superconductors. HoNi2B2C, for

instance, orders antiferromagnetically at 8 K and becomes superconducting at a

slightly lower temperature. The pair-breaking effect is believed to be diminished

by the fact that the magnetic system is electronically well isolated from the

superconducting system. GdNi2B2C, on the contrary, orders magnetically at

19 K, and shows no superconductivity. When Ni is doped by small amounts of

Co or Cu, the superconductivity is rapidly destroyed.

Superconducting transition temperatures above 20K are observed for

multiphase samples in the system Y-Pd-B-C. The samples are readily repro-

duced, but there is controversy over the exact composition and structure of the

contributing phase. It is most commonly believed to be an off-stoichiometric,

possibly boron-deficient variant of the LuNizBzC-type structure. By progres-

sively replacing platinum by gold, nearly single-phase samples could be obtained

for nominal compositions with a slight excess of transition metal

(R(Pt,Au)z.IB2C), for which the diffraction patterns indicated a LuNizBzC type

structure. Transition temperatures above 20K have also been reported for

multiphase samples in the Th-Pd-B-C system, where two superconducting

phases were found to coexist.

The square-mesh atom layers found in the structure of LuNizBzC can be

combined in different proportions. LuNi2BzC may be considered as the first

member of a homologous structure series of the general formula

RnTzBzCn,

which several members with higher values of n have been reported since the

discovery of LuNizBzC (n = 1). Consecutive RC layers are stacked upon each

other like in the NaC1 type, revealing another analogy with high-T~ super-

conducting cuprates. The first four members of this structure series are shown in

Fig. 6.21. Thicker NaCl-type slabs are expected to accentuate the 2D character of

the superconductor. For odd values of n the unit cell is tetragonal body-centered

(space group of highest symmetry

I4/mmm);

for even values it is tetragonal

E. Borides, Carbides, and Borocarbides with Nonmetal Polymers 155

primitive

(P4/nmm).

In contrast to the high-To superconductors, few planar

defects or intergrowths are observed on HREM images.

The structure of the second member of the

RnTzBzC n

series was identified

on LuNiBC (n -- 2), i.e., in the same system as LuNizBzC. The structure type

was later found also for the quaternary boronitride LaNiBN. The nonmetal atoms

form BC (or BN) dimers, but the insertion of an additional LuC layer destroyed

the strong connection between the slabs of edge-linked NiB 4 tetrahedra. The

structure is a substitution variant of a structure type known for ternary carbides,

the ScCoC2 type. It may also be considered as a filled-up derivative of the

universal type PbC1E of which several branches are known. None of the isotypic

compounds is superconducting, and band calculations performed on LuNiBC

have shown that the Fermi level is located in a well-defined valley.

A structure with three NaCl-type layers has been reported for another

boronitride, La3Ni2B2N 3 (n = 3), which becomes superconducting at 13 K. The

structure contains BN units and single nitrogen atoms inside La 6 octahedra.

Vacancies on the latter nitrogen site, situated in the central NaCl-type layer,

are probably responsible for minor variations in T~.

A member of the same structure series with n = 4 was deduced from

HREM images for nonsuperconducting Y2NiBC2 (Li

et aL,

1995). The authors

claim that a larger cell must be used for the indexation of the electron diffraction

pattern. A different structure, where the two central RC layers are replaced by

two R layers separated by a layer containing carbon atoms, was proposed for the

same composition but another rare-earth element, LuzNiBC 2 (Zandbergen

et al.,

1994a). The true symmetry of this phase was stated to be monoclinic. An

intergrowth structure with B-Niz-B slabs separated by alternately one and two

YC layers was reported for Y3Ni4B4C3.

e. Structures with Nonmetal Polymers

Only a few binary borides are known to be superconducting, among these YB 6

(T c --7.1 K), which crystallizes with the cubic CaB 6 type. The primitive unit

cell contains seven atoms. The B atoms form octahedra, centered at 1 1 89 which

are interconnected via interatomic distances of the same length as those within the

octahedra to form a 3D framework with large voids. Each B atom is bonded to

five others, which form a surrounding square pyramid. The coordination poly-

hedron around the cation is made from 24 boron atoms, all located at the same

distance from the central atom.

The cubic face-centered UB12 type contains empty B12 cuboctahedra in a

cubic close-packed arrangement. The cations are situated between the cubocta-

hedra so that polyhedra and cations form a NaCl-type arrangement. The

B12

cuboctahedra are interconnected via exo bonds to form a 3D framework with BB 5

square pyramids, similar to those found in CaB 6. This structure type is also