Poole Ch.P., Jr. Handbook of Superconductivity

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256 Chapter 7: Cuprates

Fig. 7.5.

k .... ""' "'": '"" " .....

BaO

l:xlu

I~o

.... d

Yttrium Superconductor YBa2Cu~O~

. -,:.. ....

................ ~ .......

~ . ,

, -

(O)Hg

BaO

Mercury Superconductor

HgBa2Ca._ICu.O2.§

]i: - ........... ..... , .~ .,~ . .-. , , .,~, ,., . ,

I OTI

BaO

.... i

,. _.., .......... : ........

Thallium Superconductor TiBa2Ca._xCun02.§

Sequences of MO layers in the binding slabs of aligned compounds, where M stands for

various metal ions. The parentheses around the oxygen atom O in the middle panel indicate

partial occupancy.

slabs of even compounds all of the Cu ions are still one above the other as in Fig.

7.4, but now successive conduction slabs of the even compounds are staggered

with respect to each other, with the copper ions of a particular conduction slab at

sites occupied by oxygens of the adjacent conduction slabs above and below,

as can be seen easily in Fig. 7.2. This staggering or alternation in alignment of

conduction slabs occurs because the even compounds are structurally body-

centered (BC), as we explain in the next section.

C. Aligned and Body-Centered Types 257

Fig. 7.6.

|1 - : : = : ~ .........

LaO

OLa

........ ~J

Lanthanum Superconductor La~CuO 4

- ~,,.-. , . ...... -,-:: ..=~ .... . ~-.. , ,, . , ,~:-.. , _, J,.

........ :~= 1~

Nao U

Neodymium (electron} Superconductor Nc~CuO4

h ' - ....... .... , _ , : ....... ,J , ~., ....... a ,_,r-.:- 9 ....

OBi

BiO

OSr

............ ., , ,, ;_. .......... . .. ..~ ., ...

Bismuth Superconductor Bi2Sr2Ca._zCuRO2a+4

[

i ................ _ ,,,,,, .... , .....

....

BaO

OTI

T10

OBa

........

- _ _:

.....

- .... L.' . . -,. , - ....

Thallium Superconductor TI2Ba2Ca._~Cu.O~.§

Sequences of MO layers in the binding slabs of body-centered compounds, where M stands for

various metal ions indicated on the figure.

Aligned and Body-Centered Types

Each atom in a high-temperature superconductor occupies an edge (E) site on the

edge (0, 0, z), a face (F) site on the midline of a face (0, 89 z) or (89 0, z), or a

centered (C) site at the center vertical axis (89 89 z) of the unit cell. The atoms in a

particular horizontal layer can be designated by the notation [E F C], where, for

example, a copper oxide layer with copper at edge sites and the oxygens at face

258

Chapter 7: Cuprates

Fig. 7.7.

I ZX e,, e~,e~s~,r

Laylr i, iot~o, lie r Cl

BASIC CELL SITES

CuO Layer OCu Layer

[C.O,- ] [- O,C.]

B|O Layer OBa Layer

[B=- O] [O- aa]

c't& ~7 ...... ~,,.,

[- - C=l

Lsyers

Imllge Layers

Types of atom positions in the layers of a high-temperature superconductor structure, using the

edge, face, center notation [E F C]. Typical occupancies are given in the upper right. [Poole

al.

1995, p. 181.]

Fig. 7.8.

1-Z

lj2+ Z

1/2

REFLECTED

PLANE

[CuO 2- ]

BODY

CENTERED

PLANE

[- o2cu]

REFLECTED

AND BODY

CENTERED

1- O2Cul

INITIAL

PLANE

[CuO 2-1

Body-centered tetragonal unit cell containing four puckered CuO 2 groups showing how the

initial group (bottom) is replicated by reflecting in the horizontal reflection plane a h at z = ~,

by the body centering operation, and by both. [Poole

et al.

1995, p. 188.]

C. Aligned and Body-Centered Types

259

sites is designated [Cu

0 2 --].

The complementary layer [--0

2 Cu]

has

copper in the centered sites. Figure 7.7 illustrates the notation for several

commonly occurring layers.

All of the cuprates under discussion have a horizontal reflection plane, ah at

the center of the unit cell, and a h planes at the top and bottom of the cell. This

means that each atom in the lower half of the unit cell (z < 89 at the position x, y, z

has a counterpart in the upper half of the cell (z > 89 at the position

x =:~ x, y =~ y, z =:~ 1- z

(1)

Atoms exactly on the

symmetry planes only occur once since they cannot be

reflected. Figure 7.8 shows a layer at a height z reflected to the height 1 - z. This

symmetry operation preserves the structure of the layer, i.e., a [Ba O] layer

reflects to [Ba O] under a h.

The even-type cuprates have, in addition to the ah plane, the body centering

operation, whereby every atom at a position x, y, z generates another atom at the

following position:

1 89 1

x =C, x • , y =:> y zk. , z =~ z zk ~ .

(2)

Thus, a layer at the height z forms an image layer at the height z 4- 89 in which the

edge atoms become centered, the centered ones become edge types, and each face

atom moves to another face site. The signs in these operations are selected so that

the generated points and layers remain within the unit cell. Thus, if z is less than

I the plus sign must be selected, viz. z =r z + 89 etc. The body centering

operation converts [Cu O2 --] and [--O2 Cu] conduction layers into each

other. Figure 7.8 illustrates these symmetry features, whereby for both aligned

and body-centered compounds an initial [Cu O2 --] layer at a vertical position

z < 89 has a reflection layer [Cu O 2 --] at the height 1- z. Body-centered

compounds generate two additional layers, namely, a [-- O 2 Cu] layer at the

height 89 + z and another [-- O2 Cu] layer at the height 89 z, in which the Cu

ions are out of alignment because of the interchange of edge and center positions,

Fig. 7.9.

4----- a --------~ ,t~----- a '----------~

Rectangular (top) and rhombal (bottom) type distortions of a tetragonal unit cell of width a to

an orthorhombic cell of dimensions a', b'. [Poole et al. 1995, p. 177.]

260

Chapter

Cuprates

TABLE 7.2

Superconducting transition temperatures of the cuprates containing n = 1, 2 and 3 copper oxide layers

in their conduction slabs. Some compounds have aligned (alig) and others have body-centered (BC)

crystallographic structures

Compound Type Formula n = 1 n = 2 n = 3

Bismuth BC Bi2 Sr2Can_ 1Cu n O2n+4 9 92 110

Thallium Alig T1Ba2 Can-1Cun O2n+3 9 80 120

Thallium BC T12Ba2Can-lCunO2n+4 90 110 125

Mercury Alig HgBa2 Can_ 1CunO2n+2+6 95 114 133

as shown. The aligned compounds have one formula unit per unit cell, and the

body-centered ones have two formula units per unit cell. Table 7.2 identifies the

cuprates of each type and gives their transition temperatures. We see from this

table that increasing the number of n of CuO2 layers in the conduction slabs raises

T c, but unfortunately T c begins to decrease for further increases in this number

beyond 3. Some cuprates are tetragonal and others are orthorhombic because of

either rectangular or rhombic distortion, as illustrated in Fig. 7.9. Rhombic

distortion increases the a, b lattice parameters by ~/2 and doubles the number of

formula units per unit cell.

Consider an aligned cuprate with n atoms per formula unit, which also

means n atoms per unit cell. If its structure is tetragonal it is probably in space

group

P4/mmm

(#123,

Dlh)

with the Pearson code of tPn, and if it has undergone

a rectangular distortion to orthorhombic it is in space group

Pmmm

(#47,

Dlh)

with the Pearson code oPn. A rhombic distortion could produce the orthorhom-

bic space group

Cmmm

(#65, D 19) with the Pearson code oS2n. A body-centered

cuprate with n atoms per formula unit has 2n atoms in the unit cell. If it is

tetragonal it is in space group

I4/mmm

(#139, D~ 7) with the Pearson code

tI2n. A rhombic distortion could bring it to the orthorhombic space group Azaa

TABLE 7.3

Ionic radii for some selected elements. See Table VI-2 of our earlier work

(1988) for a more extensive list

Small Cu 2+ 0.72/k Bi 5+ 0.74/k

Small-medium Cu + 0.96 ]k y3+ 0.89

Bi 3+ 0.96/~ T13+ 0.95/~

Ca 2+ 0.99 ~,

Nd 3+ 0.995/k

Medium-large Hg 2+ 1.10 .~ La 3+ 1.06

Sr 2+ 1.12/k

Pb 2+ 1.20 ,~ Ag + 1.26 ,~

Large K + 1.33 ,~ 02- 1.32/k

Na 2+ 1.34 A F- 1.33/~

C. Aligned and Body-Centered Types

Fig. 7.10.

261

[CuO- 17 [- O=Cu]

[o. Ba]/ [La- O]

I~l

[ [O- Lal

/[O-Ba]F [La- O]

L[CuO - ]~ [ " O=Cu]

Ba=YC%O 7 La=CuO,

[- %Cul

[Ba - O]

[o- "n]

['T~

[o - ca]

[o. ea]

F~-

[o -

[Ba- O]

[- O2Cu]

TI 2 Ba 2CUO6

[Ca-- ]

[- o=cu]

[sa. Ol

[o - "hi

['n - o]

[o- Ba]

[CuO=- ]

[--

Ca]

[CuO2- ]

- Ba]

[n - Ol

[o. "n]

[Ba- O]

[- O2Cu]

[ca--]

TI2ea2CaCuzO e

[- o=cul

[c= - - ]

[- O2Cu]

[ea- o]

[o - TI]

[O- ea]

[CuO2- ]

[ - - Ca]

[CuO=- ]

[-- Ca]

[CuO2- ]

[O- Ba]

l'TI - O]

[O- TI]

[ ea - o]

[. O=Cu]

[Ca -. ]

O=Cu]

TI2 Ba2Ca 2Cu3010

Unit cells of various high-temperature superconductors showing the layering schemes.

Conduction slabs are enclosed in small, inner boxes, and the groupings of slabs that make

up a formula unit are enclosed in larger boxes. The Bi-Sr compounds

BizSrzCan_lCunOzn+4

have the same layering schemes as their T1-Ba counterparts shown in this figure. [Poole

et al.,

1995, p. 195.]

(#37, C~v 3) with the Pearson Code oS4n. Chapter 8 describes these various

structures for the cuprates, and the Pearson code notation is explained in Sections

5,C and 6,A,d.

The atoms are distributed in the slabs in a manner that permits efficient

stacking of layers one above the other. The size of an ion determines how it can

substitute in a crystal structure, and Table 7.3 lists the ionic sizes of some

elements that appear commonly in the cuprates. Steric effects prevent large

atoms such as Ba (1.34 A) and O (1.32 .A) from overcrowding a slab, and from

aligning directly on top of each other in adjacent layers. Stacking occurs in

accordance with two empirical rules:

1. Metal ions can occupy either edge or centered sites, and in adjacent layers they

alternate between E and C sites.

2. Oxygens can be found on any type of site, but can occupy only one type in a

particular layer, and in adjacent layers they must be on different types of sites.

Figure 7.10 illustrates these rules for several cuprates using the [E C F]

notation explained in Fig. 7.7. Puckering or symmetry lowering from tetragonal

to orthorhombic can provide more room for the atoms. The side-centered

YBazCu408 and intergrowth YBazCu7015 compounds do not follow these

rules, as will be explained later.

262

Chapter 7: Cuprates

Role of the Binding Slab

These binding slabs sketched in Figs. 7.2, 7.5, and 7.6 are sometimes called

charge reservoir slabs because they contain the source of charge that brings about

the hole (h +) doping of the conduction layers through the interaction

Cu 2+ ~ Cu 3+ + e-

(3)

which can also be written in hole notation as

h + + Cu 2+

~ Cu 3+.

(4)

In normal-state cuprates, holes carry the electric current, and hence in the

superconducting state the Cooper pairs are positively charged. This is in contrast

to classical superconductors, in which the electrical transport is via negative

electrons.

Holes can arise from an oxygen deficiency, as in the compound

YBa2Cu3OT_6, where the subscript 7- 6 designates the oxygen content, and

in a typical superconducting compound we have YBa2Cu306. 9 with ~i--0.1.

Another way to achieve the hole doping is to replace some of the positively

charged ions of the binding slab with other positive ions of lower charge. For

example, the compound (Lal_xSrx)2CuO 4 has the fraction x of La 3+ replaced by

Sr 2+, and a comparison of the reactions

La :=~ La 3+ + 3e- (5)

Sr =~ Sr 2+ + 2e- (6)

shows that this leads to hole doping.

Particular Cuprate Superconductors

We see from Table 7.1 that the 123 compound YBa2Cu307_ a and the mercury

family compounds

HgBa2Can_lCUnO2n+2+a

with n = 1 to 6, often referred to as

Hg-1201 to Hg-1256, respectively, are aligned types. There is also a set of

aligned thallium compounds with the formula

T1Ba2Can_lCUnO2n+3

designated

by 1201 to 1245, but they are less often studied. The 123 yttrium compound

differs from the other cuprates by having Y instead of Ca in its conduction slab,

and in having -Cu-O-Cu-O- chains along its b axis as a structural component of

its binding slab. These chains may contribute to carrying some current. We

notice from the figures that the copper atoms are all stacked one above the other

on edge (E) sites, as expected for an aligned-type superconductor. The families

E. Particular Cuprate Superconductors 263

of isostmctural bismuth and thallium compounds,

Bi2Sr2Can_lCUnO2n+4

and

TlzBazCan_lCUnOzn+4 ,

as well as (Lal_xSrx)zCuO 4 and (Ndo.9Ceo.1)zCuO4, are

body-centered. The superconducting BC, compounds are designated by Bi-2212,

Bi-2223, and T1-2201 to T1-2234, as indicated in the table. The general stacking

rules mentioned in Section C are satisfied by these compounds, namely, that the

metal ions in adjacent layers alternate between edge (E) and centered (C) sites,

Fig. 7.11.

[ ..... OSr

Binding slab of Srn+ICUnO2n+1+6

I .......... .... i .... !u+: ............. ....

.......... ~ .--_.'.7 .7. _. ~~. .-_, ........ "_, ".2 .... ~ .--'Y".

Conduction slab (layer) of Sr2Cu03~ ~

Conduction slab of Sr3Cu205§

Cu02

CuO 2

Conduction slab of Sr4CuaO.7, ~

Binding slab (top) followed by, in succession, conduction slabs of the first three infinite layer

phase compounds, namely SrzCuO3+~3 , Sr3Cu205+6, and Sr4Cu307+ 6. The figures are drawn

assuming 6 = 0. [Owens and Poole, 1996, p. 117.]

264 Chapter 7: Cuprates

and adjacent layers never have oxygens on the same types of sites. The aligned

and body-centered compounds all have about the same a and b lattice parameters.

In addition to the aligned and body-centered varieties, there exist some

other types of cuprate superconductors. The YBazCu408 compound, sometimes

referred to as a 124 type, is side-centered since for each atom at the position (x, y,

z) there is another identical atom at the position (x, y + 89 z + 1), and hence the

stacking rules of Section B do not apply. The compound

YzBa4Cu7015

may be

considered as an intergrowth of the 123 and 124 compounds YBa 2Cu 307 and

YBazCu408. The body-centered compound M2CuO 4 has three structural varia-

tions. The two common types called the T-phase (M = La) and the T' phase

(M = Nd) correspond to the superconductors (Lal_xSrx)zCuO 4 and

(Nd0.9Ceo.1)zCuO4, and the third variety, called the T* phase, is a hybrid structure

adopted by the compound

(Ndl_x_ySrxCey)4Cu208_ 6.

The

upper half of its unit

cell is T type and lower half is T' type. The structures of these compounds are

described in the next chapter. In Chapter 8 the T, T' and T* phases are designated

by the codes 0201, 0021 and 0222, respectively.

Fig. 7.12.

COPPER STRONTIUM OXYGEN

\ 9

~ O q--,.. -~ -o

O- O o .... ]0,...

-'0

0 CL 0 C~ 0

-0 ~ -0

0.353_ 0

-0

Crystal structure of the infinite layer phase SreuO 2. [Owens and Poole, 1996, p. 118.]

References 265

infinite-Layer and Related Phases

In 1993 superconductivity was discovered in the body centered series of

compounds with the general formula

Srn+lCUnO2n+l+6.

These are among the

simplest of the copper oxide superconductors since they contain only two metallic

elements strontium and copper. Like the cuprates they are layered compounds

with the simple scheme presented in Fig. 7-11. The binding slabs resemble those

of La2CuO 4 but with Sr in place of La. The conduction slabs are the same as the

cuprate ones sketched in Fig. 7-4, but with strontium atoms between the CuO 2

layers, instead of calcium or yttrium. The n = 1, 2, 3 compounds

Sr2CuO3.1

[0201],

Sr3Cu2Os+ 6

[0212] and Sr4Cu30 8 [0223] have T c values of 70 K, 100 K

and 100 K, respectively. There is also a 0234 compound with T c = 70 K which

contains some Ca in place of Sr. If the binding layers of

Srn+lCUnO2n+l+6 are

replaced by Sr layers then one obtains SrCuO 2 which is called an infinite layer

compound with the structure presented in Fig. 7-12. Structurally all of its atoms

form a macroscopic conduction layer. This material, denoted by the code 0011,

can be made an electron doped superconductor by replacing some of the divalent

Sr 2+ with trivalent La 3+, which has the effect of putting electron carriers in the

copper oxide layers, and Sr0.9La0.1CuO 2 has a transition temperature of 42 K.

These various structures are described in the next chapter.

References

E J. Owens and C. E Poole, Jr., The New Superconductors, Plenum, New York, 1996.

C. P. Poole, Jr., T. Datta and H. A. Farach, Copper Oxide Superconductors, Wiley, New York, 1988.

C. P. Poole,, Jr., H. A. Farach and R. J. Cheswick, Superconductivity, Wiley, New York, 1995.

C. C. Torardi, M. A. Subramanian, J.C. Calabrese, J. Gopalakrishnan, M. K. Morrisey, T. R. Askew,

R.B. Flippen, U. Chowdhry and A. W. Sleight, Science 240, 631 (1988).