Fig. 80. Specific heat Cp/T as a function of temperature for an oxygen-rich sample with two distinct peaks (ACp/T = 3 K). This splitting was found also in the resistive and magnetic transitions. The figure was schematically reconsmacted, not considering all measured data. After Ishikawa et al.
(1988a).
Loram et al. (1991) investigated the specific heat of oxygen-rich samples as a function of nonstoichiometry. Using a high-precision differential technique, with as reference a YBa2(Cu0.93Zn0.7)3Ox sample to suppress the large phonon term, they found that their highly oxygenated 123-Ox (x ~ 7) samples showed a double transition in the range of x ~> 6.95. The splitting changed systematically with x and was present in all samples. At x ~ 7 two peaks were observed at Tel ~ 88 K and Tc2 ~ 92.5 K in 4 samples from three different laboratories. Resistivity measurements showed similar effects. These authors also considered the specific-heat anomaly to be a bulk effect and to be definitive evidence for a multicomponent order parameter. Several arguments support a bulk effect (Loram et al.
1991):
- The comparable magnitudes of the anomalies at Tel and Tc2 show that each o f them is connected with approximately half the sample volume. The authors explicitly reject the existence of minority (impurity) phases with a different Tc than the bulk, or nucleation of superconductivity on grain or twin boundaries.
- The sharp anomalies are not consistent with a spread of T~ due to inhomogeneities in the oxygen distribution and with the sequence in which the measurements were performed (first x ~ 7.0, then 6.50, then 6.75).
- As the resistivity onset of the diamagnetic transition coincides with To2 it is clear that the long-range order of superconductivity starts at this temperature. As the resistive transition is finished at T > T~ the authors conclude that the long-range order is fully established at this temperature.
As a possible explanation of this phenomenon the authors consider, in the case of non s-wave pairing, the coupling between the superconducting order parameter with an environment of different symmetry and propose that it may lead to two different T~'s dependent on the crystallographic direction. Thus, Td, which changes with the chain oxygen, may be the transition temperature for c-axis superconductivity while To2, which seems rather independent of oxygen, may be the transition temperature for the superconductivity o f the planes.
The crystallographic phase separation (chemical phase separation) (YouHoydoo et al.
1988) reappeared in the work of Claus et al. (1992b). They found that single crystals with x > 6.92 had split c-axis with slightly different c-parameters. The corresponding resistive and (dc) diamagnetic transitions show the two-step behavior o f Loram et al.
(1991), but their specific heat did not show the two peaks. For the structural investigation they used a two-axis goniometer and recorded 0 - 2 0 XRD spectra in the Bragg-Brentano focusing geometry. Only c-axis reflections (00l) could be measured for l = 2 - 1 4 . The absolute accuracy of the c-axis parameter was estimated to be rather low, -0.01 A.
A narrow rocking curve (-0.025 FWHM) was measured for one crystal; other crystals had much broader rocking curves corresponding to misorientations of 0.5 °, and some showed several peaks indicating that they consisted of several grains with similar misorientations. However, each of these grains (-6) could be measured individually. The crystals were thermally treated under known conditions to reach oxygen contents near 6.92 and then 6.94 reversibly and were measured in the two states. Figures 81a,b show the lattice constants and the relative intensities of the crystal parts, with larger c-parameter
OXYGEN NONSTOICHIOMETRY AND LATTICE EFFECTS IN YBa2Cu30 x 133
_~ 11,71!
11,70- E 11,69-
~, 11,68- U 11,67-
t~ 11,66-
1 1 , 7 2 . . . . , .... I .... I I ,1 I I ] ....
i n g [ e p h a s e " i 2 p h a s e s ( a )
2 i
a5 ', ',
1 2 3 - O ~ ~ 4 C1
g ' 3
1992 i I
,.54i
1 D = 1 4
, ~ C 2 11,65 . . . . , . . . . ! . . L , . . . .
6,75 6,89 6,85 6,90 6,95 7,00
O x y g e n c o n t e n t x
. . . . r . . . . r . . . . i . . . . i . . . .
12- (b)
C1
l O . . . . . ' 5 . 3
21
1230~ =4
XRD
Claus et aL 1992
0 . . . ~'/
6,75 6,so 6,85 6,90 6,95 7,oo
O x y g e n c o n t e n t x
" " 8-
+ ~ 6 .
J
z"
Fig. 81. (a) Splitting of the XRD c-lattice parameters for crystals reversibly oxygenated and deoxygenated between x ~ 6.92 and 6.94.
At x < 6.92 the lattice constants follow the normal x dependence (C1). At x>6.92 the splitting starts (C2). (b) Relative intensities of the (0013) diffraction line of the part of the crystals with the larger c-parameter (C 0.
Above oxygen content 6.94 (C1) the intensity disappears reversibly with the oxygen con- tent. The numbers show measurements on the same crystal. After Claus et al. (1992b).
Cj at x~<6.92 and smaller C2 at x~>6.92. F r o m fig. 81a we see a miscibility gap, two phases coexisting in the 6 . 9 2 - 6 . 9 5 range. F r o m fig. 81b we see that the intensity o f the larger (C1) disappears - as expected - with increasing x, after we cross the m i s c i b i l i t y gap. This is the classical picture o f phase rule thermodynamics. In view o f the estimated o x y g e n contents they used, it is possible that these figures illustrate the c - p a r a m e t e r anomaly (fig. 28a) and the displacive phase transformation found at the onset o f the overdoped region at x = 6 . 9 5 (Rusiecki et al. 1990, Conder et al. 1994a, Kaldis 1997, Kaldis et al. 1997b, R6hler et al. 1998), which also lead to phase separation.
Possibly due to hysteresis, the grains o f the various crystallites measured above could be frozen at different stages o f the transition and the m i n i m u m o f the c-parameter could show, therefore, different dimplings and c-parameters. Figures 81a,b also r e m i n d o f the m i s c i b i l i t y gaps tentatively p r o p o s e d for the a - p a r a m e t e r o f the BAO samples (fig. 29c).
7.2. The shell model
Soon after the work o f L o r a m et al. (1991) and before the work o f Claus et al. (1992a,b) N a k a z a w a finished his Ph.D. thesis (Nakazawa 1991) at Tokyo University. This thesis
summarized and discussed the numerous investigations performed since 1987 by the Ishikawa group, with particular care for the quality of the material (e.g., Ishikawa et al.
1988a,b). The highlights of this thesis were published later (Nakazawa et al. 1994). These authors were, therefore, the first to show that improvement of the sample preparation by avoiding quenching and by the use of low-temperature annealing allows the development o f the two specific-heat peaks at Tc (fig. 80), and were also among the few teams at that time which measured directly the oxygen content o f each of their samples by iodometry (Nakazawa 1991, Nakazawa et al. 1994). They also developed the shell model we will discuss below (Nakazawa 1991, Nakazawa and Ishikawa 1991).
An extensive investigation o f the specific heat and the a.c. susceptibility as a function of the annealing temperature ofpolycrystalline samples was presented by Janod et al. (1993).
They found for all investigated samples the double peaks for annealing temperatures 350-550°C, except for 460°C. It is unfortunate that their expertise in specific-heat and ac-susceptibility measurements could not be supported by accurate determination of the oxygen content of each sample. They did not measure the oxygen of the samples they used for specific-heat and susceptibility measurements, but that of another series of samples which showed a smaller splitting. Thus, all the figures of this work have only the annealing temperatures as parameters, and only the Tc vs. x shows estimated oxygen contents based on the work of Claus et al. (1992a), which in turn also used thermodynamically estimated oxygen contents. Further, no investigation o f the change of the lattice constants with oxygen was presented, which would trace the trends of structural changes. Nevertheless, the work of Janod et al. (1993) is an important contribution to the splitting of the diamagnetic transition because it supports and extends the experimental findings of Ishikawa et al. (1988a,b), Nakazawa (1991) and Loram et al. (1991):
(a) that careful straightforward synthesis with low-temperature annealings leads to two very well-developed peaks at To, and
(b) that both peaks correspond to superconducting transitions and to substantial super- conducting volumes of the sample, reversible with oxygen change.
The two peaks of the specific heat of 5 samples annealed at 300°C for 240 h appear at two critical temperatures Tel = 87 K and To2 = 92 K, corresponding to 40% and 60% of the sample volume. With increasing annealing temperature a cross-over of Tel and To2 takes place in the samples of Janod et al., as shown in fig. 82, but unfortunately we do not know exactly the corresponding change of the oxygen or carrier concentration.
The authors claim that they have reached an oxygen content of x =7.0 under 100 bar of oxygen and refer to a Russian team who have reached x = 7.2. It is questionable whether such samples are homogeneous at mesoscopic scale, due to the T - x phase diagram shown in fig. 55 (Karpinski et al. 1991) and discussed in sect. 5.4. Also one would like to know more about the accuracy of the indirect methods used for such oxygen determinations.
Janod et al. (1993) propose the same model as Nakazawa (1991), namely that the grains of the sample consist of a surface layer (shell) with higher oxygen content and lower Tc, and a core with lower oxygen content and higher Tc. Nakazawa's model is based on the lattice-constant anomalies reported earlier (Rusiecki et al. 1990) for x=6.92, which he could reproduce in carefully synthesized low-temperature-annealed samples: a minimum
OXYGEN NONSTOICHIOMETRY AND LATTICE EFFECTS IN YBa2Cu30 , 135 94
92-
~
90-I-- 8s-
86- 300
core (O-poorer) ~ 6 . 9 1 2)
,o00) / , \
(6.8 / / / ~ surface (O-richer) ~
(720) ~
123-0×
Janod et al. 1993 3;0 400 4;0
6()0 annealing temperature [°C]
94 92 '90 88 86 550
Fig. 82. Evolution o f Tel and T.2 with annealing temperature. After data of Janod et al. (1993). The authors propose that T¢1 corresponds to an oxygen-rich shell on the surface of the grains and To2 to an oxygen-poor core o f the grains.
of the c-parameter and a maximum of the orthorhombicity (Nakazawa et al. 1994). Based on these structural changes Nakazawa proposes that in the surface layer of the grains with x > 6.90, 05 sites are occupied, which decreases To. In fact, the same argument has been used later by Krfiger et al. (1997) to explain the changes of the lattice constants in the overdoped regime, but this could not be proven experimentally up to now (sect. 5.4.2).
However, in order that the Nakazawa/Ishikawa/Janod et al. shell model is valid, the surface layer has to strongly reduce the diffusion of the oxygen through the surface to the core of the grains. As we will discuss in the next section, this is not the case (Conder et al.
1994a,b).
7.2.1. Oxygen diffusion in the grains: no surface barrier
In order to test the above "shell" model, the diffusion rate of oxygen in 123-Ox grains at 320°C was calculated for various grain sizes, using measured diffusion coefficients (Conder et al. 1994b). Self-diffusion coefficients were measured in thermogravimetric studies o f the oxygen isotope exchange (Conder et al. 1993). The chemical diffusion coefficient D was calculated from the self-diffusion coefficient D* using the equation
D = D*Fh, (12)
with an estimated thermodynamic factor F and the Haven factor h which has a value near unity (Salomons and de Fontaine 1990).
Due to the strong anisotropy of the oxygen diffusion coefficient in 123-Ox a one- dimensional bilateral diffusion model (Schmalzried 1981) was used for the calculation of D (Conder et al. 1993). From the solution of Fick's second law the total concentration of the diffusing oxygen was obtained. This is equivalent to the diffusion progress a, which is 0 at the beginning and 1 at the end of the diffusion process. This parameter has been determined directly from thermogravimetric weight-change measurements (Conder et al. 1993, Kr/iger et al. 1993) of the oxygen isotope exchange 180 ~ 160 at very low temperatures (225-290°C, thermobalance resolution 1 ~tg). The experimental results
8 0 0 7 5 0 7 0 0 6 5 0 6 0 0 5 5 0 5 0 0 [K]
1 E - 1 0 • . I " I " ! • I " ' " ! " I
1E-11
E==1.23 -'0.15 eV
"~" E.=O.97Z0.05 eV " ' . "... ~
1 E - 1 2 a
1 E - 1 3 r, single crystal= (RothmanetaL 1 9 9 1 / ~ t = ~ , , x polyc.,,~tals (Rothman et al. 1989) ,, " ~
• P°wderlS-501am'%(Conderetal. 1994b) a powder not sieved"
1 E - 1 4 , , , , ...
1.3 1;4 l'.s 1.6 13 1;8 1.9 i.o
1000/-r [K 4]
Fig. 83. Arrhenius plot of the oxygen tracer self-diffusion coefficient D*. Comparison of the data of Conder et al. (1994b) with those of Rothman et al. (1989, 1991). After Conder et al. (1994b).
showed that at these temperatures only the 0 4 sites of the chains are exchanged, justifying the use of a one-dimensional model (Conder et al. 1993). As in these experiments the oxygen content remains constant, the tracer-diffusion (self-diffusion) coefficients can be calculated from isothermal runs. To receive as high an oxygen content as possible, the synthesis method of sect. 3.2.1 (table 2, CAR method) was extended by an additional annealing at 320°C for 300 h in 1 bar of oxygen or in other samples by slow cooling down to 500°C with 5°C/h and then by 4"C/h down to room temperature.
The oxygen tracer coefficient D* was calculated for many values of a obtained from the isotope-exchange experiments at different temperatures. Satisfactory constant values near 10 13 cm2/s were obtained in the vicinity of 250°C. Arrhenius plots are shown in fig. 83 including the data of Rothman et al. (1989, 1991). We note that their data have been based on secondary ion mass spectroscopy (SIMS), taking depth profiles of the tracer in the sample. Conder et al. (1994b) from their high-resolution thermogravimetric measurements obtained the value E a = 1.23-4-0.15eV at low temperatures for powder samples with grain size 15--50 ~m. To calculate the chemical diffusion coefficient from eq. (12), the thermodynamic factor F must be known.
F is given by (Murch 1980, Salomons and de Fontaine 1990)
d ln(po/p° )
F = 0 . 5 (13)
d ln(7 - x) '
with Po2 the oxygen pressure and 7 - x the oxygen content of the sample. Therefore, F can be calculated from the slope of the 123 equilibrium isotherms in the ln(po2)- l n ( 7 - x ) coordinates measured earlier (Conder et al. 1992). Using the value F = 2 0
OXYGEN NONSTOICHIOMETRY AND LATTICE EFFECTS IN YBa2C%O x 137
o 0.0
-0.2
-0.4
o d < 15urn
• d > 50urn
x unfiltered
, • ..., o e O ~ "
oOxo @ o°xe Ox@
X O O X •
×0 ° X ° °
-0.6
-0.8 , , ,
8 5 8 7 8 9 91 9 3
T ( K )
Fig. 84. Magnetization curves vs. T for three samples, two of them resulting from sieved fractions of the first, after grinding. Solid lines are Shoenberg fits (cf. sect. 7.3). (a) Equilibrium sample (crosses), T~,o,~o t = 92.2 K.
(b) Sieved fraction with grains <15 btm (open circles). (c) Sieved fraction with grains >50 p,m (solid circles).
No changes of T~] = To, onset =92.2 K and Tc2 = 90.2 K with grinding or grain size were found (see text). After Conder et al. (1994a,b).
(corresponding to x = 6.93) the chemical diffusion coefficient for 320°C was found to be D = 8 × 10 -11 cm2/s.
With these values, grains up to 100 ~ m should be completely oxidized after annealing at 320°C for 300h. Using the data of Rothman et al. (1989, 1991) with F = 2 0 one calculates a chemical diffusion coefficient D = 1.4 × 10 - j l cmZ/s. With this smaller value which does not correspond to equilibrium samples the grains remain homogeneous up to 50 ~tm.
100 g m grains would show only a difference A x = 0.02 between surface and center.
To confirm these calculations directly with magnetization experiments an oxygen- rich sample (To, onset = Tel = 92.2 K) was measured and then fractionated with ultra-sound sieving equipment to three fractions o f different grain sizes. The magnetization o f the two extreme fractions with grain size d < 15 ~tm and d > 50 btm was measured again and is shown in fig. 84. From the fit in the temperature regime T < 8 8 K (see sect. 7.3) it is found that the broadening o f the transition at T > 88 K - leading to two Tc's - is observed for both fractions in the same temperature range, both fractions having an identical Tc2=90.2K. The second fit parameter R/Xo (eq. 15, sect. 7.3) for the fraction d > 50 ~ m is ~3 times larger than that for d < 15 ~m, in agreement with the grain sizes.
This shows that both fractions have grains with identical magnetic properties. The small difference in the shape o f the magnetization curves is, therefore, due only to the different grain sizes and not to different superconducting properties o f the grains. The Shoenberg equation (Shoenberg 1940) (eq. 14, sect. 7.3) fits the magnetization curves o f both grain sizes (fig. 84) very well, but only in the T < 89.9 K regime. This means that the anomalous magnetization behavior near Tc is not due to an inhomogeneous oxygen distribution in the grains, because this would have been different for different grain sizes also for T < 89.9 K (Conder et al. 1994b). The above magnetic and thermodynamic investigations show that the "shell" model cannot be used to explain the splitting o f the diamagnetic transition.
7.3. The splitting of the diamagnetic transition as a function of ttle exact oxygen content." indication for phase separation
The magnetic and structural investigations started by Rusiecki et al. (1990) were continued in the following years and as mentioned in sect. 6 led to the discovery o f the displacive martensitic transformation at the onset o f the overdoped range (Conder et al. 1994a, Kaldis 1997, Kaldis et al. 1997b, R6hler et al. 1998). The magnetization o f more than 150 samples analyzed with high-resolution volumetric analysis, Ax = 0.001 (Conder et al.
1989), has been measured, and some Tc values are shown in fig. 2 and were reported in several occasions (Schwer et al. 1993a, Conder et al. 1994a, Kaldis 1997). At this point we concentrate on the overdoped regime. As fig. 85 shows, the splitting o f the diamagnetic transition starts for equilibrium samples precisely at x = 6 . 9 5 0 , i.e., at the onset o f the overdoped regime coinciding with the martensitic transformation (sect. 6). This
110
100-
~ ' 90-
80"
70
' i ' i , i , ' , i . • '
optimally doped overdoped
. . . • m . . . J m • • m , , , T c 2 , ° " s e t
'1 m m u m
IE ~ n
123-0×, I ~ Tel
Conder et al. 1994 I Zech et a1.1995 I I.~
i_~ Q . i.~_ " 1 o
• I , ' i . ' ,
6,94 6,96 6,98
o x y g e n c o n t e n t x
i •
6,92
es
e~
7,00 7,02
Fig. 85. Splitting of the diamagnetic transition of 123-O~ at x >~ 6.950, indicating the phase separation of the overdoped phase. Tol = T c , optim, doped remains practically unchanged with x, whereas To2 decreases with x. The onset of the splitting coincides with the displacive martensitic transformation (sect. 6.4) at the onset of the
overdoped phase. After data of Conder et al. (1994a) and Zech et al. (1995a,b).
OXYGEN NONSTOICHIOMETRY AND LATTICE EFFECTS 1N YBa2Cu3Q 139 splitting has been found for all investigated samples' with x ~> 6.950. DC magnetization measurements have been performed with a SQUID magnetometer on cold-pressed powder samples (to avoid recrystallization of surface grains when sintering ceramic pellets) sealed under vacuum between two quartz rods in quartz ampoules (internal diameter 3 mm) (Zech et al. 1995a).
High-precision field-cooled (FC) measurements were performed while cooling down from T > Tc with an external field H = 10 Oe. Measurements at very small temperature intervals (down to every 0.5 K) were taken in order to clearly expose changes o f slopes.
We recall that FC magnetization measures the field repulsion of the single grains, in contrast to zero-field cooling (ZFC) which measures the screening of the applied field and therefore, the superconducting properties of the entire sample surface. Figure 8 shows typical magnetization measurements for an optimally doped sample (x = 6.912) and an overdoped sample with x = 6.974. A two-parameter fit with the Shoenberg model is shown by the solid line. This simple model describes the flux expulsion of small grains with diameter comparable to the penetration depth (Shoenberg 1940) according to the equation
M(T)~o~m = 1 - 3 ~(RT)-coth ( ~ T ) ) - 3 ( ~ ) 2 (14) with Mnorm the normalized magnetization, R the radius of the grains, and )~(T) the London penetration depth. For the fitting the two-fluid approximation was used:
a ( r ) 2 _ z ( T ) o 2
(1 - T/T~) 4' ( 1 5 )
with X0 =)~(T=0K). The only fitting parameters are Tc and R/)~o (Zech et al. 1995b).
Figure 8 (curve a, x--6.912) shows an excellent fit up to To, with eq. (14), for the optimally doped samples. It also shows that for overdoped samples (curve b) an excellent fit is possible, but only up to a lower temperature where a broadening of the transition takes place due to change of curvature. For the overdoped sample with x = 6.974, eq. (14) describes the magnetization for T < 89 K. An extrapolation of the fit up to M(T) = 0 gives a Tcl = 89 K clearly different from the onset of the diamagnetic signal at Tc2 = 92.2 K. We recall that these are very near to the values found by the specific-heat measurements of Ishikawa et al. (1988a,b), Loram et al. (1991), and the crystallographic splitting (Claus et al. 1990; sect. 7.1).
This effect shows the existence of two systems with different critical temperatures.
In the underdoped and optimally doped phases only one transition temperature (To) is found. As fig. 85 indicates, the Tc2 values fit without discontinuity to the optimally doped To values. The lower T~ values in the overdoped range decrease with x so that, e.g., AT~ ~ 3.5 K at x = 6.976. More details about the splitting can be seen in fig. 86, showing the susceptibility curve of a x=6.990 sample synthesized with 180. Also drawn is the susceptibility curve of the same sample after a site-selective isotope exchange with 160
~I0-~
I
0
-I
-2
-3
-4
-5
-6
o o o o ÷
÷ + ÷
i
g i
°~
Yo÷
o • °+
o ÷
o +
2'o "~.'o go i• 1~o 12o
TEMPI~RATOP.I~ [K]
Fig. 86. Morphology o f the magnetization curve o f an equilibrium sample due to the splitting o f the diamagnetic transition. The arrow shows the change o f curvature. Open circles, YBa2Cu~806.990. Crosses, the same sample after site-selective isotope exchange with 160 which slightly increased the O content to 6.991. After data o f
Z e c h et al. (1995a) and Conder et al. (1994a).
X10"4 2
e~
r~
0
-2
-4
-6
-8
-10
-12 r,,,
87 ; 8 ;0 ;0 ¢ , - ~ 93 ;4 ;5
TEMI~RATURE [K]
Fig. 87. Magnification of the curves o f fig. 86 to show the extreme reproducibility o f the equilibrium samples even after the series o f manipulations necessary for the isotope exchange. The arrow shows the temperature o f
the change o f curvature. After data o f Zech et al. (1995a).
and a slight increase o f oxygen content to x = 6.991. The change o f slope leading to To2 is clearly shown (arrow). Figure 87 shows a magnification o f the two curves o f fig. 83 in the higher temperature range. As can be seen, the reproducibility of the sample in spite of the manipulations for the isotope exchange is extremely high, the small change