Fragmentary crystal structures of high-Tc superconductors

I

[

Physica C 185-189 (1991) 693-694 North-Holland

FRAGMENTARY CRYSTAL STRUCTURES OF HIGH-T c SUPERCONDUCTORS Eugene G. ROMANOFF P.N. Lebedev Physics Moscow, USSR.

inst.,

Acad.

Sci.

USSR,

53, Leninsky prospect,

117924.

A description of high-Tc structures in the form of different fragment packets allows us to identlfy theoretically the structures of the same type. It is shown that supercoductivity in such substances is connected with the pecullarities of thelr fragmentary structure. I. INTRODUCTION The structures of La-Sr and Y-Ba high-T c SC were shown to be different sequences of the same fragments I Structures of Bi and T1 high-T c SC series, revealed later, happened te be in accordance with those regularities. Progress in understanding the general case was made on the basis of the fragmentary approach to the analysis of crystal structures. 2. METHODS The analytical aspect of the fragmentary approach is based on the use of meaningful symbols, the graphic elements of which can be attributed to some fragment features. So, in order to represent centre-symmetrical fragments, symbols like N are suitable, and for fragments with symmetry planes, the symbols like A. For the representation of the copperoxygen pyramidal layers we have used a polar symbol > (or < ). Dzspiacement of the fragments with respect to each other reflects the symbol position displaced at the the same ( >< ) or different level ( > < ). The independent building fragments for the high-T c SC structures are: square lattices of cation (÷) a) without o

atoms (~), and w i t h o (marked by o) cent e r i n g b) s q u a r e s ( x ) . c) two p a r a l l e l sides

(:

, d) a l l

n

sides

(÷). ,::

C

C

'

C

0

a

I

b

I

I

~:.

"

-

+-

!

I

-~

I ~--I-,

Z'

S'

I

I

I

-I-: I ~:.--I-,

c

~--: I o - + -

Z

C

C

d

FIGURE i The independent building fragments for the high-T c SC structures. Note that each of these fragments contains a cation net o, hence differences in the notation are chosen i.. a way that expresses the distribution of oxygen vacancies. It is the distribution and related distort ion which are so substantlai in determinin~ the pecuiiacities in the structure and properties of high-T c SC. By combining the fragment symbols one should be able to describe any existent structure. As for the method of derlving a new structure, it consists of the selection from arbitrary fragment combinations ef

0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.

K G. Romano~ / FragmentulycOJslats~nucture.s of hi~-T c superconducmn

6'~4

only such structures, which satisfies homogeneity condition 2. This condition requires the identity of fragment surrounding of a given fragment for all fragments of the same sort. Highlighting of pyramidal fragments > as association of + and x was the first step on the way to determine a subset of structures which predominantly deals with high-T c SC. Examples of homogeneous structures with a fragment of > (or e, to be discussed below) required are summarized in Table 1. Some of them are members of accretive series where associations of elementary fragments are regarded as united fragments N I, M 1 = x2< ; + N2' M2 = :: and s = o o.

phase 1021

TABLE I symbol notation <>x<>x <>:<>:

1122

×}

123

:

t223

x<~>x

::

Tc

e~eB

90

e+ge+9

110

j

2122

N1<°>M, 1

124

N2<°>M2J

2223

N*M,I N2~]

~

E9

80 120

E+9 E+9

SC structure fragment is formed as an interface between the fragments of two different structures. Moreover, in all high-T c SC structures an almost identical volume fragment. denoted as e can be identified. It is the sequence o< ° , in which the filling of oxygen positions leads to two possible fragments :
_

3. ANALYSIS OF HIGH-T c SC STRUCTURES If one divides the fragment > into + and x ~. . . . . . . . O~,. it, then in high-T c ou structures, on one side of the line of division, there will be a sequence H = +o''" and on the other, x = ×(×':)"" Note that none of these sequences contain the perovskite-like fragments >, or octahedrons. Thus, a typical high-T c

ACKNOWLEDGEMENTS I would like to thank prof. B.B. Zvyagin and prof. A.I. Golovashkinfor collaboration. REFERENCES 1) E.G. Romanoff, A . I . G o l o v a s h k i n , e t a l . C r y s t a l l o g r a p h y 34. 6 (1989) 1408 ( i n Russian/. 2) B. 8. Zvyagin, E.G. Romanoff, C r y s t a l l o g r a p h y 36, 1 (19911 133 ( i n R u s s i a n ) .