Oxygen concentration on basal plane
AEI 2 AEI 2
5 ~ ~ ~ °oo~_ . , ~ _ ~ , x=6.63
n I n
6 0 70
45
30
:1.5
0 1.2
0 8
b) a,b a x e s ( u n t w i n n e d )
~ = x=6.93
b axis
L
80 g0 100
AE146 = ~ x=6.73
. . ~ " 1 a a x i s
A444~ A~A-- ~4~44~uh4 AA~J. 4
I I I I ,
50 70 go 110
AE187 x=6.59
nuouamnu~ ua b a x i s
i l l I I I I ~ i I I I N I I kA&A AAAAA4 &AA~" "AA AA AA
a s x i s
e l i
50 60 70
T(K) T(K)
Fig. 60. Anomalies of the thermal expansivities at T c (a) along the c-axis and (b) along the b- and a-axes of single crystals of 123-O., after subtracting the background. Note the sign changes of the a-axis at x ~ 6.75 and of the c-axis near optimal doping. The scales of the vertical axes are not the same and some data are shifted
vertically for clarity. After Kraut et al. (1993).
5.4.2. The structural, optical and magnetic anomalies at x ~ 6. 75
After all these investigations the question arises again what is the nature o f the effect at x = 6 . 7 5 (Bucher et al. 1991). Fietz et al. (1996) exclude a diffusional process because oxygen motion effects have time constants which increase strongly at T ~< 240 K. This is supported by findings in the literature (sect. 3.2.1.5). Thus, Veal et al. (1990b) found for an x ~ 6.45 sample an increase o f the time constant from 0.25 to 229 days already by decreasing the annealing temperature from 25°C to 0°C, and Lavrov (1992) with conductivity found an abrupt onset o f oxygen ordering above 250 K. However, latent structural and/or electronic phase transitions or cross-overs can induce structural and electronic anomalies even at very low temperatures. This explanation was proposed by
OXYGEN NONSTOICHIOMETRY AND LATTICE EFFECTS IN YBa2Cu3Q 109 Bucher et al. (1990-1992, 1996) and (Rusiecki et al. 1990); ideas in the same vein were presented by Metzger et al. (1993) and Fietz et al. (1996). They consider atomic displacements or tilting of structural elements with a low activation energy as the possible reason for this effect. Pressure-dependent reorganization o f the charge distribution due to ordering of chain fragments was proposed by Kraut et al. (1993).
We summarize here the anomalies of the structural and physical properties accompa- nying the giant dTc/dP change at x=6.75:
(a) Lattice parameters. From figs. 25a,b (sect. 3.2.2.1) we see that the deviation from linearity takes place in both cases near x = 6.75, leading to a relative decrease of the b-parameter and a relative increase of the a-parameter. These changes culminate in the increase of tetragonality at x = 6.95, where the displacive phase transformation takes place (sect. 6) and the b-axis decreases. The corresponding decrease of the orthorhombicity indicates that, possibly, already at x ~ 6.75 the negative interactions start, leading to the decrease of To in the overdoped phase (see also point c).
The suggestion that the results of fig. 25 could be due to an increase of the 0 5 occupancy (Krfiger et al. 1997) does not seem to be supported by EXAFS. Also, von Zimmermann et al. (1999) did not find 0 5 occupation.
(b) Magnetization measurements/Superstructures. It is well known that the Tc vs. x curve shows a strong change of slope from the so-called 60 K to the 90 K plateau at x = 6.75.
The abrupt change of the onset temperature (fig. 2) illustrates this even more clearly.
As discussed in sect. 5.1.1 this is the locus of a miscibility gap or of several phase boundaries (cf. fig. 109), supporting the above-mentioned idea of a specific feature of the structural phase diagram. A hard X-ray phase diagram (fig. 44b) shows, in this oxygen content range, the 3a0-a0 phase boundary. These superstructures have different a-axis lengths.
(c) Raman measurements. An important change takes place at x ~ 6.75 in the apex frequency, sect. 5.5.1 (fig. 61). In the range 7. 0 ~ x ~ 6. 75 the apex phonon frequency becomes independent o f the oxygen content, in contrast to the underdoped region.
Liarokapis (1997, 2000) measured the Fano asymmetry of the in-phase Blg phonon as a function of the oxygen doping. This asymmetry results from a coherent interference of light scattered by the continuous free carrier spectra and the discrete phonon spectra. The coupling to the carriers (fig. 35c) peaks at x ~ 6.7. Both results support the above-mentioned beginning of overdoping at this composition. Liarokapis et al.
(2000) measured also the anharmonicity of the oxygen phonons in the whole range 6.03 < x < 7.0, and found that particularly for apex the maximum appears at x ~ 6.7.
This will, possibly, activate the discussion about polaron formation.
(d) Pressure-dependent charge redistribution. Pressure-induced ordering in the basal plane cannot be concluded from the results of Kraut et al. (1993) since they have not been obtained by application of pressure. They adopt an alternative explanation for the anomalies of their thermal expansivity measurements and their calculated uniaxial pressure changes of dTc/dP along the three crystallographic axes. Short chain segments have energy levels above the Fermi level and, therefore, they cannot contribute to the charge transfer (Burdett 1992). For chains with a critical size
(x ~ 6.73), the energy bands may shift strongly with pressure, leading to a large pressure-induced charge redistribution, which takes place mainly along the a- and b-axes, being thus different to the commonly known charge transfer along the c-direction. The above-mentioned presence of the superstructure phase boundaries may enhance this redistribution.
The pressure-dependent charge redistribution is also supported from theoretical calculations of the effect of uniaxial pressure on the band structure of stoichiometric YBa2Cu307 (Pickett 1997). The results do not show any charge transfer from the chains to the planes under pressure, which is in agreement with the very small pressure effect on Tc for this stoichiometry. There is, however, a charge redistribution inside the superconducting planes due to relative changes in the potentials of the Cu2, 0 2 and 03 ions. It is generally accepted that at low doping levels the holes go to the Cu2 ions and their four O NN (Zhang-Rice singlets). With increasing doping there is a shift of positive charge towards the oxygens, increasing T¢. This trend is consistent with the increasing charge on 02, 0 3 with uniaxial pressure along the b-axis.
In conclusion, the x ~ 6.75 composition is an important point of the phase diagram where structural, magnetic and optical properties show appreciable changes.
5.5. Raman scattering as a function o f nonstoichiometry - I 5.5.1. The apex Raman phonon and phase separation
Very interesting in this context are the results of micro-Raman scattering on individual single crystallites of equilibrium samples (Liarokapis 1997, Kaldis et al. 1997b) as a function of nonstoichiometry. Some aspects have already been discussed briefly in sect. 3.3.1. A major advantage of Raman scattering is its great sensitivity to the appearance of new phases as it takes only a f e w atoms to form a new phonon. The reason is that the frequency o f the Raman mode of the vibrations of mainly one type of atoms is much stronger influenced by interactions of these atoms with their nearest neighbors than with their next-nearest neighbors (e.g., Iliev et al. 1993). Thus, an effect appearing in approximately 20 atoms (micro domains < 40 A) can still be detected. This should be compared with the 500-1000 A length scale of the X-ray diffraction methods.
Of course this ideal resolution of the Raman scattering may be decreased from case to case due to experimental limitations like, e.g., the laser beam cross-section.
Several results of Raman investigations on equilibrium samples have been reported recently (Poulakis et al. 1996, Liarokapis 1997, 1999, Liarokapis et al. 2000, Palles et al. 2000a). The measurements were performed on individual microcrystallites (platelets) using a T64000 triple Jobin-Yvon spectrometer with a microscope, in the scattering configurations yy(zz)~ and y(xx)~. In these directions the z-axis coincides with the crystallographic c-axis perpendicular to the platelets. Looking at individual platelets with polarized light it is possible to select properly oriented crystallites for micro-Raman measurements. For 29 compositions in the range 6.020 ~<x~< 6.984 several (up to 10) crystallites have been studied from each composition.
OXYGEN NON STOICHIOMETRY AND LATTICE EFFECTS IN YBazCu 30~. 111 An advantage of the micro-Raman method is that probing very small crystallites (>5 ~tm) or several parts of larger crystallites can give a good statistic of the various phases appearing in a certain composition range. Owing to the very cautious cooling of the samples used to reach equilibrium and their very good reproducibility, variations of the Raman signal could be attributed largely to phase changes. An appreciable statistic, the investigation of a large composition range, and the high-resolution determination of the oxygen content allowed to differentiate changes of the signal due to reproducibility and due to phase changes. Thus, it is more instructive not to take the average signal of all crystallites having the same composition, but to plot the value of each individual measured. This shows possibly existing centers of weight inside the normal scattering of the data, indicating the existence of other phases. Thus, in addition to being very useful for the characterization of the phase purity of the samples, inspection of the individual data allows scouting for possible phase separation or phase transitions occurring at certain compositions. We will illustrate this point later, especially with figs. 62 and 64. In the following figures all measured data are shown. This enables the reader to have a realistic impression of the degree of homogeneity that even good samples have. The samples used in these investigations were CAR equilibrium samples (sect. 3.1.2) which show extremely small scattering in their lattice parameters (sect. 3.2.2.3).
An important message emanating from these investigations is that the Raman phonons of equilibrium samples show appreciable deviations from the linear dependence on oxygen doping found in the past (for reviews, see Thomsen 1991 and Thomsen and Cardona 1994). Figure 61 shows the Raman frequency shifts of the apex phonon as a function of the nonstoichiometry (Poulakis et al. 1996, Liarokapis 1997, Liarokapis et al. 2000, Palles et al. 2000a). Contrary to earlier investigations (MacFarlane et al.
1988, Thomsen and Cardona 1994) which found a linear dependence using a rather small number of compositions, a nearly linear increase with oxygen in the insulating range exists only up to the RT N6el transition ( 6 . 0 < x < 6 . 2 , cf. sect. 3.3.1) and then in the superconducting range only for 6.4 < x < 6.75. The hardening of the apex phonon is due to the decrease of the apical bond with oxygen doping (cf. figs. 14, 66). Above the phase boundaries at x = 6.75 the apex frequency becomes independent of the oxygen doping. In this range the charge transfer nears saturation and the frequency remains constant, although the Cu2-O1 bond length is still decreasing (fig. 14). The structural changes starting at x > 6.75 were discussed in sect. 5.4.2. A relative decrease of the orthorhombicity starts at this doping level which is actually leading to a saturation in the optimally doped region and to an absolute decrease in the overdoped range, mimicking Tc (fig. 25c). Also, the width of the out-of-phase-phonon
Big
shows a decrease of the coupling with the superconducting carriers starting at x = 6.7 (fig. 35c), indicating the onset of negative interactions. Figure 61 shows that the apex phonon frequency clearly reflects the transformations and changes at x ~ 6.22, 6.28, 6.40 and 6.75. The first three are correlated with the onset of superconductivity, as discussed in sect. 3.3.1.Figure 62 shows the width of the apex phonon vs oxygen doping after Poulakis et al.
(1996), and Liarokapis et al. (2000). The lines are a guide to the eye and are joining the extreme values. The statistical average for each composition is shown in fig. 35b.
5,9 6,0 6,1 6,2 6,3 6,4 6,5 6,6 6,7 506 .... , ' " , u ' " ' ~ = .. . . I , , , ' , ' " ' u ,
• ~ m
504 - - AF
l a /
480 •
4 7 8 •
T = 3 0 0 K 476 M i c r o - R a m a n 5 0 2 -
E •
o s00-
~ . 4 9 8 - O
~ . 4 9 6 - 4 9 4 -
~
4 9 2 -4 9 0 - E 4 8 8 -
8 O 4 8 6 -
~ " 484 ;
~
(11 ' 4 8 2 -o
II
0 - ~ !
I-"
4 k A
C
• b
"o o ¢J Q_
u) o~
o
. . . . I ' ' ' ' f ' ' ' ' l ' ' ' I . . . I ' ' ' ' 1 ' ' ' ' 1 '
5,9 6,0 6,1 6,2 6,3 6,4 6,5 6,6 6,7
6,8 6,9 7 0 7,1
• , i . . . 506 - 504
~ ) " 5 0 2 I I = Z ' • - 500
• 1 -' 498
- - - 496
o •
" ~ - 494
~ - 4 9 0 -~-- 488 X
< - 486
II
n - 484
p- - 482
- 4 8 0 - 4 7 8
- 476
6 , 8 6 , 9 7,0 7,1 oxygen content x
Fig. 61. Dependence of the apex phonon (Cu2- O1, Ag) fi'equency on oxygen stoichiometry. Five regions appear to exist (cf. fig. 35a); the slope changes take place at the characteristic oxygen contents x=6.22, 6.30, and 6.75. After data of Poulakis et al. (1996), Palles et al. (2000a) and Liarokapis et al. (2000).
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40 c~ >
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" ~ iN ' • " .• •
35 ~ ' i !1 ~ i l m • k I .' "-m ~
: :m • mm : :
:n qmm • m"l m,: unl
: .
" i ' o .~ = " m ,
3o ~:" ~ ' i . . . • F-.mm U