Electron Transfer in Biology and the Solid State - American Chemical

17 Geometrical Control of Superconductivity in Copper Downloaded by UNIV LAVAL on September 19, 2015 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0226.ch017

Oxide Based Superconductors Jeremy K . Burdett and Gururaj V. Kulkarni Department of Chemistry and The James Franck Institute, University of Chicago, Chicago, IL 60637

The geometrical control of the electronic structure of some of the recently synthesized copper oxide based high-critical-temperature (T ) superconductors is presented. Although current thinking concerning these fascinating materials is in a state of flux and unconventional theories abound, it is shown how many of the properties of these systems may be understood by using rather conventional orbital ideas that have been used for a long time by the chemical community. c

THE SERIES OF HIGHT -EMPERATURE COPPER OXIDE CONTAINING conductors that has b e e n synthesized o v e r the past 3 years (1-7) has attracted considerable speculation c o n c e r n i n g the nature of the m e c h a n i s m b e h i n d t h e i r n o v e l electrical properties. A question of parallel i m p o r t a n c e is h o w the electronic structure of these materials leads to a situation that is favorable for the operation of a s u p e r c o n d u c t i n g m e c h a n i s m . W e have l o n g k n o w n that geometrical structure i n t i m a t e l y controls the e l e c t r o n i c structure of b o t h molecules a n d solids. I n this chapter w e want to s h o w that some of the f u n d a m e n t a l observations c o n c e r n i n g the structure of these electronically n o v e l systems are r e a d i l y i n t e r p r e t e d i n terms of c o n v e n t i o n a l o r b i t a l ideas (although at the present t i m e some w o u l d regard t h e m as a little speculative). W e shall c o m m e n t too o n some of the salient features of the e l e c t r o n i c state of affairs i n these systems that w e feel are i m p o r t a n t .

0065-2393/90/0226-0323$07.25/0 © 1990 American Chemical Society

In Electron Transfer in Biology and the Solid State; Johnson, M., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1989.

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E L E C T R O N TRANSFER IN BIOLOGY A N D T H E SOLID STATE

Electronic Structure of Copper Oxides T h e structures o f the k n o w n c o p p e r oxide c o n t a i n i n g superconductors have b e e n r e v i e w e d elsewhere (8). T h e y all have a c o m m o n feature, a C u 0 plane that is not always flat, o f four-coordinate, approximately square-planar, c o p p e r atoms a n d two-coordinate oxygen atoms, l i n k e d i n t h e w a y s h o w n i n F i g u r e l a . Sheets of this t y p e , i f they w e r e l i n k e d v i a t w o apical oxygen atoms as i n F i g u r e l b , w o u l d l e a d to t h e s i m p l e R e 0 structure t y p e . I n sertion of a large cation (A) i n the cavity of this structure leads to t h e structure of perovskite, of A B 0 stoichiometry. T h u s , the r e t e n t i o n o f the C u 0 p l a n e leads to a c o m m o n l y u s e d d e s c r i p t i o n o f these systems as o n e d e r i v e d f r o m the perovskite arrangement. 2

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F i g u r e s 2 a - 2 c show different e n v i r o n m e n t s f o u n d i n k n o w n structures.

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Figure 1. a, The Cu0 sheet, a fundamental constituent of all high-temperature copper oxide superconductors; b, the relationship of the Cu0 sheet to the perovskite structure. 2

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Copper Oxide Based Superconductors

Figure 2. Geometrical arrangements found in copper oxide superconductors. F i g u r e s 2a a n d 2b show the e n v i r o n m e n t f o u n d i n the tetragonal a n d o r t h o r h o m b i c forms, respectively, of the 2 - 1 - 4 c o m p o u n d ( L a _ S r C u 0 ) . H e r e the c o p p e r atom is six-coordinate. T h e C u 0 planes contain an extra two oxygen atoms attached to c o p p e r at somewhat l o n g e r distances t h a n those i n the p l a n e . T h e sheets are flat i n the tetragonal f o r m a n d r u m p l e d i n the o r t h o r h o m b i c f o r m . I n this chapter w e shall present the first e l e c t r o n i c explanation of this i n t e r e s t i n g transformation. F i g u r e 2c shows the structure of the p u c k e r e d C u O sheet (ζ > 90°) w i t h a five-coordinate c o p p e r atom f o u n d i n the 1 - 2 - 3 c o m p o u n d ( Y B a C u 0 _ ) . A s i n the 2 - 1 - 4 c o m p o u n d , the apical C u - O distance is longer than that i n the plane. T h i s apical oxygen is c o n n e c t e d to another part of the structure i n a way w e w i l l d e s c r i b e later. F i g u r e l a shows the bare G u 0 plane itself, f o u n d i n ( T l O ) B a C a C u 0 , for example. 2

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C o o r d i n a t i o n Shell Plasticity. T h e structural c h e m i s t r y o f C u is one of the most c o m p l e x a n d fascinating of the d-block e l e m e n t s . P a r t i c u l a r l y i n t e r e s t i n g is the plasticity of the c o o r d i n a t i o n s h e l l . I n S c h e m e I, a d i a g r a m adapted from a w e l l - k n o w n r e v i e w article (9), w e show some pathways c o n n e c t i n g the variety of geometries f o u n d for species w i t h o x y g e n - c o n t a i n i n g ligands. T r a d i t i o n a l l y such distortions have b e e n d e s c r i b e d as r e s u l t i n g f r o m the J a h n - T e l l e r instability o f octahedral d C u , b u t t h e r e are c l e a r l y o t h e r factors at w o r k (10) i n v o l v i n g the 4s a n d 4p h i g h e r - e n e r g y orbitals o n copper. In these systems it is difficult to u n d e r s t a n d , a n d thus p r e d i c t , the size of the d i s t o r t i o n away f r o m octahedral for a g i v e n system. T h e r e is a s p e c t r u m of C u - O distances i n systems that are closely r e l a t e d c h e m i c a l l y , a n d q u i t e different distances are often f o u n d i n p o l y m o r p h s of the same m a t e r i a l . F o r n

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Scheme I

example (9), i n the α f o r m of C u ( N H ) B r t h e C u - N distances are (a p a i r at) 1.93 A , a n d the C u - B r distances (a p a i r at) 2.45 Â a n d (a p a i r at) 3.08 Â. I n the β f o r m t h e y are (a p a i r at) 2.03 Â a n d (a set o f four at) 2.87 Â , respectively. 2

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W h a t is clear is that the d i s t o r t i o n coordinates are i n v a r i a b l y soft, p r o b ably q u i t e a n h a r m o n i c , a n d apparently i n f l u e n c e d b y the l i g a n d e n v i r o n m e n t v i a the u b i q u i t o u s " c r y s t a l - p a c k i n g forces". F o r the e x t e n d e d arrays u n d e r discussion, this means that the geometrical p i c t u r e is c o n t r o l l e d not o n l y b y d i r e c t C u - O interactions b u t b y the nuances o f O - O interactions a n d b y the effect of the cations of different sizes a n d charges. E q u i l i b r i u m C u - l i g a n d distances are, as a result, e x t r e m e l y difficult to p r e d i c t . T h e s e interactions have b e e n m o d e l e d (22) for the present series of c o m p o u n d s w i t h s o m e success. T h i s chapter concentrates o n o r b i t a l interactions. T h e s t r u c t u r a l c h e m i s t r y of d systems, (for e x a m p l e , C u ) is v e r y different. L o w - s p i n d complexes (those o f P t a n d P d ° are the best known) are n e v e r o c t a h e d r a l , b u t always square-planar. T h i s m a y be i n t e r p r e t e d (22) i n terms of a larger J a h n - T e l l e r d r i v i n g force (twice as large b y u s i n g the angular-overlap m o d e l ) away from octahedral for the d configuration, c o m p a r e d to that for d . 8

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Local Coordination Geometries. F r o m a c h e m i c a l p o i n t of v i e w , the electronic structure of these materials may b e b u i l t u p b y consideration of the energy levels associated w i t h local c o o r d i n a t i o n geometries. W e w i l l see that this p r o v i d e s a v e r y useful a i d i n u n d e r s t a n d i n g the l e v e l shifts of the bands themselves as the structure is changed. T h r o u g h - b o n d c o u p l i n g i n oxides is generally considerably smaller t h a n i n sulfides, a n d because t h e angles of the structure are close to e i t h e r 90° o r 180°, σ/ττ separability is a reasonable a p p r o x i m a t i o n for m a n y purposes. F i g u r e 3 shows the energies of the d orbitals b y u s i n g the a n g u l a r overlap m o d e l (22) for a set of relevant geometries. R e c a l l that the e n e r g y



Figure 3. Angular-overlap energy-level diagrams for some coordination environments important in these materials.


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p a r a m e t e r e depends u p o n the b o n d l e n g t h . It increases i n m a g n i t u d e as the i n t e r n u c l e a r separation decreases. Because of the geometry at c o p p e r , the i m p o r t a n t part of the electronic structure (that associated w i t h the highest o c c u p i e d m o l e c u l a r o r b i t a l of a n isolated fragment, the x - y orbital) is v e r y s i m i l a r i n a l l of the geometrical e n v i r o n m e n t s f o u n d . W e can u n d e r s t a n d this b y reference to F i g u r e 3. T h e energy o f the x - y o r b i t a l is c o n t r o l l e d solely b y the β values of the i n - p l a n e ligands, of w h i c h t h e r e are always four. T h e energy of the filled, d e e p e r - l y i n g z is m u c h m o r e sensitive to geometry. T h e energy of z drops to l o w e r energy, e i t h e r as the apical distances are increased, or as one or b o t h apical ligands are r e m o v e d . I n a l l of the structure types f o u n d (Figures 1 a n d 2), e i t h e r t h e r e are no apical ligands attached to the C u 0 planes or the ones that are present are b o u n d at large i n t e r n u c l e a r separations. T y p i c a l values for the 2 - 1 - 4 c o m p o u n d are 1.90 Â (in-plane) a n d 2.45 Â (apical); t y p i c a l values for the 1 - 2 - 3 c o m p o u n d are 1.93 Â (in-plane) a n d 2.30 Â (apical). a

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T h e b a n d structure associated w i t h the c o p p e r atoms i n the C u 0 planes is thus s i m p l y d e r i v e d as s h o w n i n F i g u r e 4. It is clear that a m a n y - b o d y p i c t u r e of these materials w i l l have to b e e m p l o y e d to u n d e r s t a n d these systems i n d e p t h , b u t h e r e w e w i l l use a traditional c h e m i c a l m o d e l , w h e r e m a n y - b o d y terms i n the energy are a d d e d to a basically o n e - e l e c t r o n a p p r o a c h to h i g h l i g h t some aspects of t h e i r structure. T h e s i m p l e o r b i t a l ideas w e have d e s c r i b e d l e a d to the result that the highest-energy electrons l i e i n an o r b i t a l of x - y s y m m e t r y , h e a v i l y m i x e d w i t h oxygen σ orbitals a n d a n t i b o n d i n g b e t w e e n c o p p e r a n d oxygen. T h i s v i e w is not u n i v e r s a l l y h e l d . A r g u m e n t s have b e e n p u t forward (13) for holes i n an oxygen 2 p i r d e r i v e d b a n d . I n L a _ S r C u 0 (with χ = 0) the c o p p e r atoms are clearly w e l l 2

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Figure 4. Diagram showing construction of the energy hands of the infinite Cu0 sheet from the orbitals of a fragment. 2


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d e s c r i b e d as C u

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, a n d this x - y b a n d is exactly h a l f f u l l o f electrons. S u c h 2

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electronic situations, invariably unstable, are usually a l l e v i a t e d (14,15) e i t h e r b y a P e i e r l s - t y p e d i s t o r t i o n or b y the generation o f a n antiferromagnetic i n s u l a t i n g state. A n example of a P e i e r l s - t y p e d i s t o r t i o n is f o u n d (16) i n the m i x e d - v a l e n c e platinum chain compounds, P t L n

an a m i n e (Scheme II). H e r e P t

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atoms disproportionate to a l t e r n a t i n g oc-

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. . . . X - P t - X P t

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/ I

I, X - P t - X

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Scheme II tahedral Pt™ a n d square-planar P t centers. T h e energetics d r i v i n g the distortion are a c o m b i n a t i o n o f one-electron terms (leading to a stabilization of the full z b a n d o n P t " ) a n d m a n y - b o d y terms (leading to a c o u l o m b i c r e p u l s i o n b e t w e e n the two electrons i n the same orbital). P e i e r l s - t y p e d i s tortions m a y sometimes p r o c e e d w i t h o u t any obvious c o u l o m b i c p e n a l t y . C o n s i d e r the ( J a h n - T e l l e r ) instability associated w i t h singlet c y c l o b u t a d i e n e , or the analogous (Peierls) structural instability associated w i t h a n infinite c h a i n o f equidistant h y d r o g e n atoms (15). T h e o p e n i n g o f a H u b b a r d gap, a feature of the antiferromagnetic insulating state, involves no g e o m e t r i c a l change (in first o r d e r , at least) a n d is c o n t r o l l e d b y m a n y - b o d y effects. A n example is f o u n d i n the u n d o p e d m a t e r i a l L a C u 0 . I n fact, i n a l l o f the superconductors m a d e to date there is some m e c h a n i s m , e i t h e r b y d o p i n g (making χ Φ 0 i n L a ^ S r ^ C u O ^ or b y overlap w i t h orbitals associated w i t h other structural features (as i n Y B a C u 0 _ ) , w h i c h r e m o v e s some of the x — y density. T h i s feature is i m p o r t a n t because it reduces the p o s s i b i l i t y o f these half-filled b a n d effects. A s the charge transfer increases, the t e n d e n c y for the o p e n i n g of a H u b b a r d gap, a n d the t e n d e n c y for a P e i e r l s d i s t o r t i o n , or other instability is r e d u c e d . T h u s , a diamagnetic m e t a l l i c state m a y result. T h e properties of this state, f r o m w h i c h (on this model) s u p e r c o n d u c t i v i t y occurs, are i m p o r t a n t h e r e . T h e electron o c c u p a n c y o f this x - y b a n d is c r u c i a l to the electronic properties of the m a t e r i a l a n d , as w e shall see, is i m p o r t a n t i n the geometrical c o n t r o l o f the structure. 1 1

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The 2-1-4 Compound I n the 2 - 1 - 4 c o m p o u n d , L a _ S r C u 0 , the o c c u r r e n c e o f s u p e r c o n d u c t i v i t y is associated w i t h the value of x. A s n o t e d e a r l i e r , for χ = 0, the m a t e r i a l is an antiferromagnetic insulator. It becomes a s u p e r c o n d u c t o r o n l y for χ > 0.05, p r e s u m a b l y w h e n e n o u g h electron d e n s i t y is r e m o v e d from the x y b a n d to a l l o w the existence o f a stable m e t a l l i c state. T h i s c o m p o u n d exists i n (at least) two forms, one of tetragonal a n d the o t h e r of o r t h o r h o m b i c 2

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s y m m e t r y . T h e relative stability o f the t w o is strongly c o n t r o l l e d b y χ (17). A s the a m o u n t of s t r o n t i u m d o p i n g (x) increases (i.e., as the average c o p p e r d count decreases), the tetragonal structure gradually b e c o m e s m o r e stable than the o r t h o r h o m b i c structure. T h i s manifests i t s e l f i n a d r o p i n the t r a n sition t e m p e r a t u r e for the transformation as χ increases (17,18). F o r e x a m p l e , w i t h χ = 0 the orthorhombic-to-tetragonal t r a n s i t i o n occurs at 533 ° C ; w i t h χ = 0.15 it appears at 190 °C; a n d w i t h χ = 0.2 it is the o n l y a r r a n g e m e n t k n o w n . I n c r e a s i n g χ leads to a d e p l e t i o n o f the highest e n e r g y b a n d of the system, x - y . F i g u r e 5 shows a n energy difference c u r v e b e t w e e n the two forms, from t i g h t - b i n d i n g calculations o n the two solids (19) as a f u n c t i o n of e l e c t r o n count, d e s i g n e d to explore this transformation. Downloaded by UNIV LAVAL on September 19, 2015 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0226.ch017

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d-count Figure 5. Calculated energy difference between the tetragonal and orthor hombic forms of the 1-2-3 compound from a tight-binding calculation. I n g o o d agreement w i t h e x p e r i m e n t s (17), the tetragonal s t r u c t u r e is p r e d i c t e d to b e increasingly favored w i t h decreasing d count. T h e energet ically i m p o r t a n t part o f the plot (around d ) , w h e r e the slope is largest, occurs i n that r e g i o n w h e r e the x - y b a n d is b e i n g p o p u l a t e d . O n e o f the p u z z l i n g things about this d i s t o r t i o n is that no gap is o p e n e d u p at the F e r m i l e v e l , as i n the P e i e r l s - t y p e d i s t o r t i o n n o t e d i n the p r e v i o u s section. (Par enthetically, w e note that the shape of this d - c o u n t - d e p e n d e n t c u r v e f r o m m o m e n t s considerations (20) also tells us that the d i s t o r t i o n is not of the Peierls type.) W h a t is the d r i v i n g force for the d i s t o r t i o n , a n d w h y does i t appear to b e so d e p e n d e n t o n d count? 9

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P u c k e r i n g D i s t o r t i o n . A n i m p o r t a n t c l u e comes from studies o f the p u c k e r i n g d i s t o r t i o n of the five-coordinate arrangement s h o w n i n F i g u r e 2c.


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A s i m i l a r c u r v e is f o u n d for this d i s t o r t i o n . F o r d d

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systems ζ = 90°, b u t for

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systems ζ > 90°. T h e r e is not a good c o l l e c t i o n o f e x p e r i m e n t a l data to

c o m p a r e w i t h theory for these c o p p e r - b a s e d systems, b u t the c a l c u l a t e d p l o t is exactly w h a t w o u l d b e e x p e c t e d f r o m the w e l l - e s t a b l i s h e d v a r i a t i o n i n m o l e c u l a r g e o m e t r y w i t h d e l e c t r o n c o u n t for Bve-coordinate t r a n s i t i o n m e t a l systems. A m o l e c u l a r o r b i t a l diagram for the p u c k e r i n g d i s t o r t i o n (shown i n F i g u r e 6b) comes from the w o r k o f R o s s i a n d H o f f m a n n (21). T h e stabilization associated w i t h the x - y o r b i t a l d u r i n g the d i s t o r t i o n , d r i v e n b y the r e l i e f 2

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of strong m e t a l - l i g a n d a n t i b o n d i n g interactions ( F i g u r e 6), shifts the e n e r g y m i n i m u m o f the structure away from those geometries w i t h 90° a n d 180°


O - C u - O angles. D e s t a b i l i z a t i o n o f the o c c u p i e d levels favors the ζ =

90°

structure. I n F i g u r e 6a the m i x i n g of σ interactions into these yz a n d xz orbitals as the angle ζ increases leads to t h e i r d e s t a b i l i z a t i o n . A s the p o p u l a t i o n o f the x - y o r b i t a l (band) decreases, the d r i v i n g force for i n c r e a s i n g 2

2

ζ is r e d u c e d . ι ι I

Figure 6. Energy-level diagrams during puckering distortion. T h e r e are other solid-state examples of the same t y p e . O n e that involves a iT-type interaction (rather t h a n the σ - t y p e i n t e r a c t i o n d e s c r i b e d here) is the q u e s t i o n o f planar or p y r a m i d a l g e o m e t r y at oxygen i n the M O

a

structures

of r u t i l e ( T i O 2 ) (planar) a n d C a C l (pyramidal). T h e planar s t r u c t u r e is f o u n d 2

for l o w electron counts w h e r e a n t i b o n d i n g orbitals are not o c c u p i e d .

How

ever, b y the t i m e the I T * levels are f u l l (at d ) , the p y r a m i d a l s t r u c t u r e (the 6


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analog o f the p u c k e r e d structure i n the c o p p e r oxides) is favored (22). S u c h o r b i t a l ideas are useful i n m a n y areas o f c h e m i s t r y ; see ref. 23, for example.

Orthorhombic Distortion.

A v e r y similar m e c h a n i s m applies to the

distortion i n t h e 2 - 1 - 4 c o m p o u n d . H e r e t h e g e o m e t r i c a l change is m o r e complex, b u t the p r i n c i p l e is the same. T h e d i s t o r t i o n changes the O - C u - 0 angles ( F i g u r e 6c) such that m e t a l - l i g a n d o v e r l a p is r e d u c e d a n d the desta b i l i z a t i o n associated w i t h t h e a n t i b o n d i n g x - y b a n d is l o w e r e d . A s χ increases from zero i n the 2 - 1 - 4 c o m p o u n d , the e l e c t r o n o c c u p a t i o n o f the x - y b a n d is r e d u c e d , t h e stabilization e n e r g y associated w i t h t h e o r t h o r h o m b i c structure decreases, a n d e v e n t u a l l y the tetragonal structure is f o u n d as t h e lowest energy alternative. D e p l e t i o n o f the x - y b a n d o n increasing χ is associated w i t h a decrease i n m e t a l - l i g a n d a n t i b o n d i n g i n teractions o n this m o d e l . C o r r e l a t i o n w i t h e x p e r i m e n t a l l y d e t e r m i n e d C u - O distances provides s u p p o r t i n g e v i d e n c e for this v i e w p o i n t . T h e y are (17, 24) 1.9035(1) Â for χ = 0 a n d 1.8896(1) Â for χ = 0 . 1 5 . 2


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2

2

T h u s , the p u c k e r i n g d i s t o r t i o n o f the 1 - 2 - 3 c o m p o u n d a n d the o r t h o r h o m b i c d i s t o r t i o n o f the 2 - 1 - 4 c o m p o u n d are manifestations o f the same electronic p h e n o m e n o n . T h e difference b e t w e e n the t w o lies c l e a r l y i n the c o o r d i n a t i o n n u m b e r at copper. A p u c k e r i n g d i s t o r t i o n is less l i k e l y for sixcoordinate systems t h a n for five-coordinate ones, s i m p l y because i n t h e f o r m e r there are oxygen atoms o n b o t h sides o f the C u O p l a n e . A m o r e c o m p l e x d i s t o r t i o n , at first sight difficult to u n d e r s t a n d , appears to b e t h e energetically favored alternative h e r e . It is i n t e r e s t i n g to see that these structural variations are w e l l d e s c r i b e d b y a s i m p l e c o n v e n t i o n a l c h e m i c a l m e c h a n i s m . C e n t r a l to the a r g u m e n t is that these h i g h e s t - e n e r g y electrons are located i n a n x - y o r b i t a l , c e r t a i n l y h e a v i l y m i x e d w i t h oxygen, b u t w i t h a strong C u - O a n t i b o n d i n g i n t e r a c t i o n that is a n g l e - d e p e n d e n t . T h e r e is no i n d i c a t i o n from this analysis of the structural p r o b l e m , that the electrons are located o n a n o r b i t a l w h i c h is largely oxygen ττ i n character, as suggested b y other models. £

2

2

Sleight (e.g., ref. 8) has l o n g i d e n t i f i e d t h e local c o p p e r g e o m e t r y as p l a y i n g a c r u c i a l role i n these systems a n d has made some correlations b e t w e e n T (critical temperature) a n d C u - O distances a n d angles. H e has e m p h a s i z e d , h o w e v e r , t h e i m p o r t a n c e o f the i r - t y p e m e t a l - o x y g e n i n t e r actions i n c o n t r o l l i n g geometry. Sleight's m o d e l calls for r e l i e f o f I T * i n t e r actions associated w i t h yz a n d xz orbitals o n b e n d i n g , i n a w a y exactly analogous to the r e l i e f o f σ interactions (via the x - y orbital) h e r e . It is not possible o n such a m o d e l to d i r e c t l y b u i l d i n the effect o f e l e c t r o n c o u n t changes. F o r the m o d e l d e s c r i b e d h e r e , the C u - O distance is sensitive to the p o p u l a t i o n o f the x - y b a n d . T h i s sensitivity leads us to ask the q u e s t i o n w h e t h e r the S l e i g h t correlation of C u - O distance w i t h T is r e a l l y one w h i c h is m e a s u r i n g x - y density. O n c e w e have e x p l o r e d the results o f an o r b i t a l m o d e l , i t is i m p o r t a n t c

2

2

2

2

c

2

2


17.

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333


to p u t the results i n perspective. T h e c o m p u t e d result of F i g u r e 5 is actually q u i t e sensitive to the geometries chosen for the calculation. E x p e r i e n c e tells us that i f this is the case, there are usually energetic c o n t r i b u t i o n s not p r o p e r l y m o d e l e d b y u s i n g such a o n e - e l e c t r o n theory. I n the p r e s e n t case, n o n b o n d e d interactions b e t w e e n the oxygen atoms are a n obvious source of the p r o b l e m . O u r study (25) o f the details of the g e o m e t r y of r u t i l e ( T i O 2 ) f o u n d an i n t e r p l a y b e t w e e n the d i r e c t T i - O interactions a n d the m a t r i x O - O interactions of the approximately close-packed solid. S h o r t C u - O distances i n the present series of systems signal an i m p o r t a n t c o n t r i b u t i o n f r o m this source. T h e s e results a n d the " m o l e c u l a r m e c h a n i c s " results o f ref. 11 t h e r e Downloaded by UNIV LAVAL on September 19, 2015 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0226.ch017

fore present a c o m p l e m e n t a r y p i c t u r e o f this structural p r o b l e m .

The 1-2-3 Compound YBa Cu 0 _$ 2

3

7

T h e basic geometrical arrangement of Y B a C u 0 _ , the first a b o v e - l i q u i d 2

3

7

8

n i t r o g e n - t e m p e r a t u r e superconductor, is s i m p l y d e r i v e d f r o m the p e r o v s k i t e structure (it w o u l d have the f o r m u l a Y B a C u 0 ) b y the o m i s s i o n of some 2

3

9

of the oxygen atoms. T h e structure is s h o w n for the δ = 0 system i n F i g u r e 7 (δ varies from 0 to 1.) D e f e c t perovskites are w e l l k n o w n . C a M n 0 3

3

7 5

Ba

0(2)

Y Cu

Figure 7. The 1-2-3

structure, YBa Cu 0 ^, 2

3

7

with δ = 0.

(i.e., C a M n 0 ) , w h i c h m a y be generated b y h e a t i n g the parent p e r o v s k i t e C a M n 0 , contains s q u a r e - p y r a m i d a l m e t a l atoms. I n the 1 - 2 - 3 c o m p o u n d there are square planes a n d square p y r a m i d s for δ = 0. T h e vacancy o r d e r i n g i n C a M n 0 5 m a y be r e a d i l y u n d e r s t o o d (26) u s i n g c h e m i c a l ideas. W e shall see that they are also useful for the vacancy p r o b l e m i n the 1 - 2 - 3 c o m p o u n d . T varies (27) w i t h oxygen stoichiometry i n a most i n t e r e s t i n g w a y ( F i g u r e 8). F o r l o w δ it appears to be almost flat, b u t at a r o u n d δ = 0.3 there is a r a p i d d r o p . T h i s d r o p is f o l l o w e d b y another plateau region before T sharply drops to 0 at a r o u n d δ = 0.6. 2 5

3

2

c

c


334



100K

δ-0.6 OK YBa Cu 0 2

3

7

\ YBa Cu 0

δ —*

2

3

6

Figure 8. Variation of T with oxygen stoichiometry in the 1-2-3 compound. c

T h i s m a t e r i a l clearly has a different structural c h e m i s t r y from the 2 - 1 - 4 c o m p o u n d , a n d one c o m p l i c a t e d b y a variable oxygen stoichiometry. T h e r e are m a n y questions w e have to ask. I n p a r t i c u l a r , w h y are t h e vacancies o r d e r e d i n the w a y s h o w n for 8 = 0, a n d w h a t controls the o r d e r i n g for δ Φ 0? I n Y B a C u 0 _ for δ = 0, diffraction studies (see t h e c o l l e c t i o n o f references i n ref. 28) have s h o w n that t h e site l a b e l e d w i t h a n asterisk i n F i g u r e 7 [0(5)] is e m p t y , a n d thus the structure is c o m p o s e d o f five c o o r dinate planes a n d four coordinate chains o f c o p p e r atoms. A p i c t u r e emerges for the structure consistent w i t h the geometrical e n v i r o n m e n t s w e expect to see for the various oxidation states o f copper. T h e structure consists o f C u ( 2 ) 0 sheets l i n k e d b y rather l o n g C u ( 2 ) - 0 ( 4 ) linkages t o C u ( l ) 0 chains. T h e sheets thus contain r o u g h l y s q u a r e - p y r a m i d a l C u atoms. T h e chains c o n t a i n C u atoms i n approximately square-planar c o o r d i n a t i o n , l e a d i n g o v e r a l l to an o r t h o r h o m b i c structure ( Y B a ( C u 0 ) ( C u 0 ) ) . F o r δ = 1, a l l o f the sites l a b e l e d as 0 ( 1 , 5 ) are u n o c c u p i e d , the square planes have b e e n r e p l a c e d b y l i n e a r O - C u ' - O d u m b b e l l s , a n d n o w t h e structure is tetragonal ( Y B a ^ C u ^ ^ C u ^ ) . 2

n

3

7

8

m

2

3

1 1

m

n

2

Computed Band Structure.

2

m

2

3

T h i s v i e w p o i n t also comes from t h e

c o m p u t e d b a n d structure. F i g u r e 9 shows h o w t h e o r b i t a l diagrams asso ciated w i t h the local (square a n d square-pyramidal) units get b r o a d e n e d i n t o bands i n t h e e x t e n d e d solid. Because t h e electronic area o f interest lies b e t w e e n d a n d d , w e o n l y show t h e x - y a n d z - y bands. T h e u n c o n v e n t i o n a l l a b e l i n g of the latter comes about s i m p l y f r o m the axis choice for the s o l i d . I t is r e a l l y o n l y an x - y o r b i t a l t u r n e d o n its side. T h e r e are twice as m a n y x - y levels as there are z - y levels, reflecting t h e 8

2

1 0

2

2

2

2

2

2

2

2

2



17.

BURDETT & KULKARNI

d

9


Cu"

Is d C u 8

I M

335

(short Cu-O)

Figure 9. Broadening of the levels of local fragments into energy bands in the extended solid for the 1-2-3 structure. Only the two highest levels are shown. stoichiometry of the m a t e r i a l . T h e p i c t u r e that results shows t w o r o u g h l y half-full bands c o r r e s p o n d i n g to x - y orbitals o n the two C u atoms, a n d an almost e m p t y z - y b a n d o n the C u atom. W e s h o u l d ask w h y the z 2

2

1 1

2

1 1 1

2

2

- y b a n d associated w i t h the c h a i n atoms lies to h i g h e r energy t h a n the x - y b a n d associated w i t h the plane atoms. T h i s is a natural c o n s e q u e n c e of the shorter average C u - O distance i n the chains (1.86 a n d 1.94 Â) c o m p a r e d to the planes (1.93 a n d 1.96 Â), w h i c h gives rise to a larger value of e„ for the former. If the C u ( l ) - 0 distances w e r e the same as the C u ( 2 ) - 0 distances, the two bands w o u l d o c c u p y v e r y s i m i l a r energetic positions a n d each c o p p e r w o u l d have approximately the same oxidation state. 2

2

2

T h i s s m a l l a m o u n t o f overlap that w e show is v i t a l l y i m p o r t a n t because this is the m e c h a n i s m b y w h i c h the x - y bands of the planes a v o i d the half-filled e l e c t r o n configuration, w i t h a l l of the drawbacks d e s c r i b e d e a r l i e r . T h e c o n n e c t i v i t y of the atoms i n this structure allows an i n t e r e s t i n g f l e x i b i l i t y for the c h a i n atom c o o r d i n a t i o n , w h i c h t h e n feeds back i n t o the s t r u c t u r a l p r o b l e m . Because the C u ( l ) - 0 ( 4 ) distance is not fixed b y the c o o r d i n a t i o n demands of other atoms, i t is able to adjust to such a l e n g t h that the z y b a n d lies to h i g h e r energy than the x - y bands, a n d , i n so d o i n g , preserves the approximate C u " a n d C u labels. T h e exact details o f the plane-to-chain charge transfer are difficult to c o m p u t e , as t h e y w i l l b e s e n sitive to s m a l l variations i n the structure. H o w e v e r , the i m p o r t a n t p o i n t is that w h i l e i n the 2 - 1 - 4 c o m p o u n d ( L a _ . S r C u 0 ) , the e l e c t r o n d e n s i t y i n the x - y bands is b r o a d l y c o n t r o l l e d b y the a m o u n t of s t r o n t i u m d o p i n g ; 2

2

2

2

2

2

m

2

2

I

I

4

2


336


the c o r r e s p o n d i n g feature i n t h e 1 - 2 - 3

c o m p o u n d is d e t e r m i n e d b y t h e

g e o m e t r i c a l effects w e have j u s t d e s c r i b e d . T h e result o f d o p i n g o f this m a t e r i a l w i t h z i n c is i n t e r e s t i n g . Z n " is a d system, a n d substitution of Cu(2) b y z i n c w i l l t e n d to increase the e l e c t r o n density i n the x - y b a n d . E v e n t u a l l y , w h e n the b a n d is close e n o u g h to half-full, s u p e r c o n d u c t i v i t y w i l l b e s w i t c h e d off. (This s w i t c h i n g off occurs 1 0

2

2


(29) for close to 1 4 % zinc.) W i t h the a s s u m p t i o n o f a p p r o x i m a t e l y e q u a l densities o f states for the t h r e e bands at the F e r m i l e v e l , this corresponds to the a d d i t i o n o f about 0.043 e l e c t r o n p e r Cu(2). W e s h o u l d r e c a l l a s i m i l a r figure (around 0.05 electron p e r copper) for the c r i t i c a l r e m o v a l o f e l e c t r o n d e n s i t y f r o m the half-filled c o p p e r b a n d i n the 2 - 1 - 4 c o m p o u n d .

Oxygen Stoichiometry.

O f particular interest i n this system is the

variation i n g e o m e t r i c a l a n d electronic structure w i t h oxygen s t o i c h i o m e t r y . A l t h o u g h t h e r e have b e e n m a n y structural studies, the fine details are u n fortunately not as w e l l established as w e w o u l d l i k e . T h e v a r i a t i o n i n c e l l parameters w i t h δ is w e l l k n o w n , b u t the i d e n t i t y o f the sites from w h i c h oxygen is lost is still not c o m p l e t e l y d e t e r m i n e d , because diffraction e x p e r iments are n o t sensitive to local o r d e r i n g features. F o r δ = 0 t h e r e a r e o r d e r e d square planes o f c o p p e r atoms i n the chains, a n d for δ = 1 t h e r e are o r d e r e d d u m b b e l l s , b u t the details o f the structure for arbitrary δ are somewhat elusive. M o s t studies show loss o f oxygen from the planes p e r p e n d i c u l a r t o ζ that c o n t a i n the C u ( l ) atoms, b u t b o t h O ( l ) a n d 0(5) sites s e e m to b e o c c u p i e d for δ > 0. F o r some values of δ the crystal s y m m e t r y appears to b e tetragonal rather t h a n o r t h o r h o m b i c . T h e r e are p r o b a b l y locally o r d e r e d regions o f the structure so that such a result m a y b e u n d e r s t o o d i n t e r m s o f chains o f square-planar c o p p e r atoms o f v a r y i n g lengths r u n n i n g i n b o t h the a a n d b directions. O n e w a y o f r e g a r d i n g the tetragonal structure is thus as a n e q u a l m i x t u r e o f the two. E x p e r i m e n t a l e v i d e n c e supports this v i e w (30, 31). A schematic p i c t u r e o f this situation is s h o w n i n F i g u r e 10, i n w h i c h the t w o coordinate C u atoms are r e p r e s e n t e d b y e m p t y space a n d the C u atoms b y lines t o indicate chains. 1

m

O n e i m p o r t a n t q u e s t i o n c o n c e r n i n g the changes i n p r o p e r t i e s w i t h ox y g e n s t o i c h i o m e t r y is h o w this s h o u l d b e treated t h e o r e t i c a l l y (32). Is i t , f o r e x a m p l e , realistic to a d d 2 δ electrons to the F e r m i l e v e l o f a c a l c u l a t i o n , w i t h δ = 0 reflecting the loss of δ oxygen atoms? (This is the so-called r i g i d b a n d m o d e l . ) C o n s i d e r first a m o d e l w h e r e a single oxygen atom is lost from one o f the O ( l ) sites o f the material. S c h e m e I I I shows h o w t w o o r i g i n a l l y square-planar c o p p e r atoms n o w l i e i n a T - s h a p e d e n v i r o n m e n t . F i g u r e 3 shows that the e n e r g y levels associated w i t h s u c h a g e o m e t r y l i e d e e p e r t h a n the x - y b a n d o f the square p l a n e , a result that leads to a loss o f electrons from the F e r m i l e v e l rather t h a n the gain o f the r i g i d b a n d approach. T h i s comes about s i m p l y because t h e r e are t w o T - s h a p e d c o p p e r atoms, w h o s e 2

2


17.

BURDETT & KULKARNI


planes


chains

planas

337

chains

T-shape and

5 = 0

^-y

δ>ο

2

planas planas chains

mI dumbells T-shapa and

δ=

after c axis anomaly

1

Figure 10. Schematic variation of the band structure of the 1-2-3 compound with oxygen stoichiometry. At the bottom of each figure is a schematic picture showing the arrangement of regions of chain (Cu ) atoms (lines) and dumbbell (Cu ) atoms (space). m

1


338

E L E C T R O N TRANSFER IN BIOLOGY A N D T H E S O L I D STATE


V

Scheme HI

levels r e q u i r e four extra electrons to b e filled, b u t t h e r e are o n l y t w o e l e c trons m a d e available b y the loss o f a single oxygen a t o m . If, h o w e v e r , t h e oxygen vacancies o r d e r so that chains o f c o p p e r d u m b b e l l s are f o r m e d , as i n S c h e m e I V , o n l y one c o p p e r l e v e l p e r oxygen a t o m drops to l o w e n e r g y a n d needs to b e filled. T h e r e f o r e , there is n o change i n t h e n u m b e r o f electrons at the F e r m i l e v e l . T h e w a y the vacancies o r d e r i n the s t r u c t u r e thus c r u c i a l l y controls the e l e c t r o n i c d e s c r i p t i o n at the F e r m i l e v e l . ( E l s e w h e r e (19) w e suggest that an o r d e r i n g process is r e s p o n s i b l e for the first d i p at δ = 0.3 i n T , as s h o w n i n F i g u r e 8). c

F i g u r e 10 shows i n a schematic w a y h o w the b a n d s t r u c t u r e o f the m a t e r i a l changes w i t h i n c r e a s i n g δ. T h e n u m b e r o f levels (represented b y

mm Scheme IV


17.

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339


the b r e a d t h o f the box i n the picture) associated w i t h the x - y bands of the p l a n a r c o p p e r ( C u ) atoms remains constant, b u t loss o f oxygen atoms from the chains generates C u atoms at the expense o f C u atoms. A t δ = 1 t h e r e are of course n o C u z - y l e v e l s , a n d the x - y bands o f the planar c o p p e r atoms are exactly h a l f f u l l . R a v e a u et a l . (33) c a l l e d the T shape geometry a r o u n d c o p p e r an a b n o r m a l one. (In m o l e c u l a r c h e m i s t r y it is f o u n d for a single l o w - s p i n d m o l e c u l e (34).) O n e w a y of e n v i s a g i n g the o r d e r i n g process is thus one w h i c h m i n i m i z e s the n u m b e r of s u c h l o c a l structures. 2

2

11

1

m

m

2

2

2

2


8

S o m e other evidence suggests o r d e r i n g i n the structure as the oxygen is r e m o v e d . F i g u r e 11 shows the e x p e r i m e n t a l l y d e t e r m i n e d v a r i a t i o n (28) i n atomic o a x i s parameters w i t h δ. T h e absence of l i n e a r v a r i a t i o n w i t h δ i n these values suggests that a cooperative effect is c o n t r o l l i n g the s t r u c t u r e . O n this m o d e l , t h e n , for l o w δ the d i m e n s i o n s are c o n t r o l l e d b y C u and for h i g h δ b y C u . T h e r e is another feature of these plots w h i c h is also i n t e r e s t i n g , a n d leads to f u r t h e r correlation w i t h e x p e r i m e n t . I n F i g u r e 11 a smooth c u r v e has b e e n d r a w n t h r o u g h the e x p e r i m e n t a l points. E q u a l l y w e l l at a r o u n d δ = 0.6 the data c o u l d b e i n t e r p r e t e d as suffering a sharp change. T h i s has b e e n c a l l e d (35) " t h e c-axis a n o m a l y " . I n t e r e s t i n g l y , this is the p o i n t w h e r e T r a p i d l y drops to zero ( F i g u r e 8). O f p a r t i c u l a r i m p o r tance to us a n d o u r m o d e l is that at this p o i n t , the C u ( l ) - 0 ( 2 ) distance a b r u p t l y shortens from 1.85 to 1.80 Â. A s a result, w e calculate that the ζ - y b a n d is p u s h e d to h i g h e r energy, a n d e l e c t r o n transfer to the chains is s u d d e n l y cut off. N o w the p l a n a r c o p p e r atoms have exactly h a l f - f i l l e d x y bands, a n d w e have a s i m p l e explanation for the disappearance of s u p e r c o n d u c t i v i t y . F i g u r e 10 puts these ideas together. 1 1 1

1

c

2

2

2

2

Charge Movement on Distortion T h e distortions d e s c r i b e d i n the section o n the 2 - 1 - 4 c o m p o u n d left a l l of the c o p p e r atoms e q u i v a l e n t i n the structure. T h e change i n e l e c t r o n d e n s i t y associated w i t h each atom d u r i n g the d i s t o r t i o n is p r o b a b l y small. S u c h a c o m m e n t does not a p p l y to the distortion of the p l a t i n u m h a l i d e c h a i n s h o w n i n S c h e m e I I . I n this disproportionation process, considerable f o r m a l charge transfer has taken place. T h e distortion of the C u 0 planes, s h o w n i n S c h e m e V a n d d e s c r i b e d as a " b r e a t h i n g " m o t i o n , has s i m i l a r features. A d y n a m i c m o t i o n of this type is favored b y m a n y i n the c h e m i c a l c o m m u n i t y as a m e c h a n i s m for s u p e r c o n d u c t i v i t y , w h i c h is associated w i t h v e r y strong e l e c t r o n - p h o n o n c o u p l i n g . (See, for example, ref. 36 a n d the series of articles i n ref. 6.) F i g u r e 12 shows h o w the densities of states associated w i t h the x - y bands change d u r i n g such a m o t i o n from a calculation o n the 1 - 2 - 3 compound. 2

2

2

As the distances a r o u n d one c o p p e r atom contract, the b a n d (A) is p u s h e d to h i g h e r energy (recall o u r earlier discussion of the v a r i a t i o n of e w i t h b o n d a


340


5.9V 53-

·-·*.—t

Y (=c/2)

*

ο: 0(3)

4.5·-^


8

4.20 »

2.3*ί.«^

Cu(2)

2.2Ba

1.85..

·. 0(4) (=Cu(1)-0(4))

• -· ·

-4-

1.75

2Λ0\

2.30|δ = 1.0 YBs^Ci^Og

• ν

f

δ = ο.5

Cu(2)-0(1) δ-ο YBî^CugC^

Figure 11. Changes in geometry as a function of oxygen stoichiometry for the 1-2-3 compound. Shown are the changes in ζ coordinate for the rele vant atoms.

length) a n d becomes largely associated w i t h this c o p p e r a t o m . A s t h e d i s tances a r o u n d t h e o t h e r c o p p e r atom e x p a n d , t h e b a n d (B) moves to l o w e r e n e r g y a n d becomes largely associated w i t h this second type of c o p p e r atom. O v e r a l l , the effect is to transfer electrons from A to B . A s a result, t h e c o p p e r atom w i t h t h e shorter C u - O distances b e c o m e s m o r e C u - l i k e a n d t h e c o p p e r atom w i t h the longer C u - O distances becomes m o r e C u ' - l i k e . I n creasing a n d decreasing t h e C u - O distances b y a n a m o u n t e q u a l to t h e m



17.

BURDETT & KULKARNI


341

Scheme V

2.y2

2.y2

x

x

Contracted

Equilibrium

Expanded

-ID

Β

A >

-11

)

LU

-12

ι

-13 Figure 12. Changes in the x - y densities of states on breathing (Scheme V). 2

2

m a g n i t u d e o f t h e t h e r m a l v i b r a t i o n parameters associated w i t h t h e C u - O distances d e t e r m i n e d e x p e r i m e n t a l l y f r o m n e u t r o n diffraction studies (37) of the 1 - 2 - 3 c o m p o u n d leads to a calculated charge transfer o f 0.22 e l e c t r o n . O u r one-electron calculations ( F i g u r e 13) show too a stabilization o f t h e distortion for a m e t a l d-count appropriate to t h e half-filled b a n d o n t h e C u 0 planes. S u c h global pictures are v e r y useful i n u n d e r s t a n d i n g t h e o r i g i n o f such distortions. I n t h e language o f the m o m e n t s m e t h o d (20), t h e shape o f 2


342



0.1

-0.4 I 0

•

ι 2

•

ι 4

•

ι • ι 6 8 d-Count

1

ι I 10

Figure 13. Computed stabilization energy of the breathing mode (Scheme V) in the 1-2-3 compound as a function of the average number of d electrons per copper. the c u r v e associated w i t h d o r b i t a l configurations c o r r e s p o n d i n g to occupancy of x - y a n d z orbitals is a f o u r t h - m o m e n t one, t y p i c a l of J a h n - T e l l e r a n d P e i e r l s distortions. N o static distortion of this type is actually o b s e r v e d , w h i c h i m p l i e s that an i m p o r t a n t i n g r e d i e n t has b e e n left out of the p r o b l e m . 2

2

2

W e m e n t i o n e d the i m p o r t a n c e of b o t h o n e - a n d t w o - e l e c t r o n t e r m s i n the energy, i n c o n t r o l l i n g distortions o f molecules a n d solids. T h u s , for e x a m p l e , the e n e r g y difference b e t w e e n h i g h - a n d l o w - s p i n octahedral N i complexes is (crudely) d e t e r m i n e d b y the t w o - e l e c t r o n t e r m s i n the e n e r g y , whereas the d i s t o r t i o n of the octahedral structure to the square comes about v i a one-electron terms. W h e t h e r a g i v e n N i c o m p l e x is octahedral a n d h i g h - s p i n or square-planar a n d l o w - s p i n is thus a balance b e t w e e n the two types of forces. 1 1

1 1

I n the distortion of the C u 0 planes t h e r e is a s i m i l a r balance. H e r e it involves the cost of p l a c i n g two electrons o n the same c o p p e r a t o m . T h e effect is largest w h e n the x - y b a n d is close to half-full. I n this case, o n d i s t o r t i o n , electrons w i l l have to b e p a i r e d i n some o f t h e orbitals o n a t o m Β as a consequence of the P a u l i p r i n c i p l e . T h e s e on-site repulsions associated w i t h the two electrons i n the x - y b a n d of the C u M i k e atoms w i l l desta b i l i z e such a d i s t o r t i o n . F i g u r e 13 indicates that as the e l e c t r o n count moves away from the h a l f - f i l l e d b a n d , the d r i v i n g force associated w i t h the o n e e l e c t r o n part of the energy also decreases. T h u s , the d-count d e p e n d e n c e of these two terms works i n opposite directions. S i m i l a r c o m m e n t s a p p l y to analogous distortions i n the 2 - 1 - 4 a n d other c o m p o u n d s c o n t a i n i n g sheets of square-planar c o p p e r atoms. 2

2

2

2

2


17.

B u R D E T T & KULKARNI

343


T h e size o f these m a n y - b o d y terms is difficult to evaluate. F r o m values of a t o m i c i o n i z a t i o n energies (38), the d i s p r o p o r t i o n a t i o n reaction 2 C u Cu

1

+ C u

m

n

—•

costs 16.54 eV. C l e a r l y , the actual charge transfer i n the s o l i d

is considerably less, a n d the m e t a l orbitals are c o n s i d e r a b l y d e l o c a l i z e d v i a extensive m e t a l - o x y g e n interactions. (A s i m i l a r explanation can b e offered for the nephelauxetic effect i n transition m e t a l complexes.) D i s p r o p o r t i o n ation is o b s e r v e d b o t h i n s o l i d B a B i 0

3

a n d i n C s A u C l . T h e atomic values 3

for the energetics o f these two cases c a u t i o n against g e n e r a l use o f s u c h n u m b e r s i n solids. F o r b i s m u t h , the d i s p r o p o r t i o n a t i o n ZBi

w

B i

m

+ Bi

v

costs m u c h less t h a n a similar d i s p r o p o r t i o n a t i o n i n c o p p e r (4.7 e V ) . H o w Downloaded by UNIV LAVAL on September 19, 2015 | http://pubs.acs.org Publication Date: May 5, 1989 | doi: 10.1021/ba-1990-0226.ch017

ever, for g o l d , 2 A u

n

—> A u

1

+

Au

1 1 1

, the

figure

is not v e r y different

(13.5 e V ) . O n e variant o f the b r e a t h i n g m o t i o n is s h o w n i n structure 1 a n d S c h e m e V I for the C u 0

2

sheet of the 1 - 2 - 3 c o m p o u n d . H e r e the oxygen atoms

Cu

Scheme VI r e m a i n fixed a n d the C u - O s t r e t c h i n g is r e a l l y associated w i t h a n increase i n the p u c k e r i n g o f the sheet. (The a s y m m e t r i c m o t i o n w e show occurs o n l y at the edge of the B r i l l o u i n zone, as s h o w n i n structures 2 a n d 3. A t the c e n t e r o f the zone, the t w o c o p p e r atoms m o v e in-phase a n d c h e m i c a l l y r e m a i n equivalent.) F o r this d i s t o r t i o n , b o t h an increase i n p u c k e r i n g a n d an increase i n C u - O distance l e a d to a d r o p i n the e n e r g y o f the x - y b a n d associated w i t h that c o p p e r a t o m , a n d so the p i c t u r e is s i m i l a r to that s h o w n i n F i g u r e 10. A s before, the unfavorable e l e c t r o n - e l e c t r o n c o u l o m b i c 2


2


344


r e p u l s i o n b e t w e e n two electrons forced to l i e o n the same c o p p e r atom resists the d i s t o r t i o n . T h e p a r t i c u l a r m o t i o n s h o w n i n structure 1 a n d S c h e m e V I is i n t e r e s t i n g i n that the p u c k e r e d structures show no m o t i o n of the oxygen atoms. A l t h o u g h w e have yet to establish the connection b e t w e e n s u c h a m o t i o n a n d s u p e r c o n d u c t i v i t y , w e do p o i n t out the observation (6, 7) of a zero or near-zero oxygen isotope d e p e n d e n c e of T i n the 1 - 2 - 3 compound. c

H o w does the m a g n i t u d e o f the e l e c t r o n transfer o n p u c k e r i n g v a r y w i t h the geometry? It is easy to see that i f the sheets are flat t h e n the d y n a m i c e l e c t r o n transfer is zero i f the oxygen lattice remains fixed. T h i s is s h o w n i n structure 4. I f the a m p l i t u d e of the p u c k e r i n g is the same at the two

Cu ο-

X

Cu

„o

centers, t h e n no a s y m m e t r y i n b a n d p o s i t i o n can o c c u r o n v i b r a t i o n . T h u s , a m e c h a n i s m o f this t y p e suggests that e l e c t r o n transfer w i l l increase w i t h puckering.

The 2-2-1-3 System, Fb Sr (Ln _ 2

2

l

y

M )Cu 0 lI

y

3

8+x

Pb Sr (Ln . M j , ) C u 0 (where L n is a lanthanide or early t r a n s i t i o n e l e m e n t s u c h as y t t r i u m a n d M is a two-valent i o n s u c h as S r o r Ca) has r e c e n t l y b e e n characterized (39). It has several features of the 1-2-3 and 2 - 1 - 4 compounds. I n the s t o i c h i o m e t r i c compound P b S r L n ( C u 0 ) C u 0 (x = y = 0), w e can envisage ( F i g u r e 14) 2

2

1

n

y

3

8 + I

1 1

2

n

2

I I

m

I I

3

2

I

2



17.


BURDETT & KULKARNI

Figure

14.

The observed structure of PhzS^Ln^y

M, )Cu 0 n

3

8+i

the 2-2-1-3

345

compound

c.

C u 0 d u m b b e l l s a n d C u 0 square p y r a m i d s , j u s t as i n t h e 1 - 2 - 3 c o m p o u n d Y B a ( C u 0 ) ( C u 0 3 ) w i t h δ = 1. F i g u r e 15 shows a schematic b a n d p i c t u r e h i g h l i g h t i n g this. T h e role o f the M species h e r e is s i m i l a r to that i n t h e 2 - 1 - 4 c o m p o u n d . E l e c t r o n s are r e m o v e d f r o m t h e x - y bands o f C u " w h e n y Φ 0 b u t χ = 0 a n d t h e electron o c c u p a n c y moves away from half-full. T h e analogy w i t h t h e 1 - 2 - 3 c o m p o u n d m a y b e p u s h e d f u r t h e r to !

n

2

2

I I

2

2

3

I

1 1

2

2

ask w h e t h e r , w h e n χ > 0, b e h a v i o r similar to that d e s c r i b e d e a r l i e r w i l l b e

x -y2 2

dumbells Cu

1

Figure 15. Schematic band picture showing the arrangement ofCu 0 dumbells and Cu 0 square pyramids. l

u

3


2

346

E L E C T R O N T R A N S F E R IN B I O L O G Y A N D T H E S O L I D STATE

f o u n d . A d d i t i o n of oxygen to the d u m b b e l l r e g i o n c o u l d result i n chains of square-planar c o p p e r atoms i f χ = 1. F o r χ close to 0, T - s h a p e d C u 0 u n i t s w i l l b e f o r m e d . T h u s , geometrically (and perhaps e l e c t r o n i c a l l y , too), this process is s i m p l y the reverse of that for the 1 - 2 - 3 c o m p o u n d s h o w n i n Schemes I I I a n d IV. T h e situation i n P b S r ( L n _ M ) C u 0 is v e r y interesting. T h e m a t e r i a l m e r i t s future d e t a i l e d study o f its p r o p e r t i e s as χ a n d y are v a r i e d . 3

2

2

1

y

y

n

3

8 + I


Conclusions W e have s h o w n h o w m a n y o f the e l e c t r o n i c aspects of these fascinating systems are c o n t r o l l e d b y geometrical features of t h e s t r u c t u r e . T h e focus of attention has b e e n o n o r b i t a l ideas, b u t it is clear that o t h e r types o f interactions are i m p o r t a n t h e r e too. (See ref. 11, for example.) O u r c o m putations o f the a p i c a l - b a s a l angle at the square p y r a m i d i n t h e 1 - 2 - 3 c o m p o u n d show a sensitivity of 2° o r so, d e p e n d i n g o n w h e t h e r the Y atoms are i n c l u d e d i n the calculation (19). T h i s sensitivity suggests a c o m p l e x t r a d e off b e t w e e n different types of interactions. W e look f o r w a r d to the synthesis o f m o r e c o m p o u n d s o f this t y p e to test the p r e d i c t i o n s of the m o d e l d e s c r i b e d here.

Acknowledgments T h i s research was s u p p o r t e d b y T h e N a t i o n a l Science F o u n d a t i o n a n d b y the U n i v e r s i t y o f C h i c a g o . W e thank K a t h r y n L e v i n for m a n y useful d i s cussions. F i g u r e s 2, 5 - 8 , 1 0 - 1 2 , a n d 14 have b e e n a d a p t e d from ref. 19. T h i s chapter has b e e n e d i t e d for style b y m e m b e r s o f the A C S B o o k s D e partment.

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for review May

f2fâî^Oftîët^^ ^ S€

>tïC ir U USt

Library

1155and 16th In Electron Transfer in Biology the St, Solid N.W. State; Johnson, M., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1989. Washington, D.C. 20036

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