3 Lns-Mössbauer and Lattice Parameter Data of DF Oxides
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4 LANTHANIDES (151EU AND 155GD) MOSSBAUER
SPECTROSCOPIC STUDY OF DEFECT-FLUORITE OXIDES COUPLED
80
This gives a reference point to fix the BL(Eu3ỵO)IS(Eu3ỵ) correlation. In mostly diphasic y > 0.50 range,
we found a C-type line phase at y $ 0.86 plausibly corresponding to an Eu analogue of d [U6ỵ]A[Y3ỵ6]BO12 at
y ẳ6/7 ẳ 0.857 [29]. But its C-type structure implies the possibility that a partially oxidized C-type
U5ỵ,6ỵEu3ỵ6O12z (z > 0) is formed there.
(2) DF-Type CeEu and Th–Eu. These two have very similar smoothly increasing near-linear IS(Eu3ỵ)y curves, that
is, very similar smoothly decreasing near-linear BL(Eu3ỵO)y curves, as expected for the stable M4ỵ-bearing
DF oxides wherein the CN(random) ¼ 8 À 2y in Eq. (4.7) decreases linearly from 8 to 6 for y ¼ 0–1.0 [4]. This is
a notable IS(Eu3ỵ) feature in view of the largely a0(ThEu) ) a0(Ce–Eu) behavior over the entire y range in
Fig. 4.4a. Moreover, both IS(Eu3ỵ)s at y ! 0 extrapolate not to $0.49 for the Eu3ỵ(VIII) in the above UEu in
ossbauer evidence that both
Eq. (4.10) but to the obviously higher $0.64. This IS(Eu3ỵ) feature is a clear 151 Eu-M€
the systems are near-equally significantly case (1) Eu3ỵVO associative so that both the BL(Eu3ỵO)s are
definitely shorter than that of U–Eu. Their strong case (1) nonrandom nature was clarified in Ref. 1 with the
DCC model analysis of each one representative a0 data set reported in Refs. 4 and 40, respectively. We will
make the more complete a0 analysis of both systems in Section 4.4 using all the available a0 data.
(3) P-Type Stabilized Zr–Eu and Hf–Eu. These two again exhibit very similar characteristic V-shaped IS(Eu3ỵ) minima
at the ideal P composition of y $ 0.50 in sharp contrast with the above two. These data highlight this 151 Eu
M€
ossbauer study, giving a convincing evidence for the intermediate P-based local structure of the apparently
disordered cubic-stabilized DF phase of SZ(SH)s. Both IS(Eu3ỵ)s (and therefore both BL(Eu3ỵO)s) appear to
decrease (increase) initially rather slowly in the $0.20 y $0.33 range and then sharply for y > $0.33 toward
each deep minimum (sharp maximum) at y $ 0.50. As argued in Ref. 4, the former $0.20 y < $0.33 and the
latter $0.33 y < $0.45 range are judged to represent the less distortion-dilated mutually isolated P-like Eu
(VIII)À
À8O cluster state and the increasingly more distortion-dilated P-type short-range ordered axialanisotropic Eu(VIII)ÀÀ8O microdomain state in Fig. 4.1c, respectively. The sudden upturn of both a0–y curves
at y $ 0.33 in Fig. 4.4a, that is, the beginning of a0 hump, is a macroscopic signal for such abrupt coupled
microscopic–macroscopic structure change of the system accompanying “distortion–dilation.” 155 Gd
M€
ossbauer data of Zr–Gd described in Section 4.3.2 further reinforce this conclusion. Such P-type order
seems to be quickly lost with a slight y ¼ 0.50–0.55 increase, and hence a narrow single phase found at y $ 0.70
for both systems would probably be non-P type.
Figure 4.5 shows 89 Y MAS-NMR CN(Y3ỵ, Zr4ỵ) data of YSZ [15a] and some other CN(Ln3ỵ, Zr(Hf)4ỵ) data.
The former data clearly show that even this macroscopic d-type YSZ is P-type strongly case (2) Zr4ỵVO associative, the
CN(Y3ỵ) lying close to the highest CN $ 8 till y $ 0.25 and then deceasing gradually to $7.24 at y $ 0.50. This was so
above mentioned in the sense that YSZ has more nonrandom CN((Y3ỵ, Zr4ỵ) curves than those of the d-type Zr3Y4O7
at y ¼ 4/7 given by Eq. (4.2b) and drawn here in pink symbol. Macroscopic P-type Eu-SH, Eu-SZ, and Gd-SZ are therefore
expected to have the respective CN(Eu3ỵ)s and CN(Gd3ỵ) lying even closer to the highest CN $ 8 up to the higher y
range till y $ 0.50, as drawn there in each (red, black, and green) color line.
V-shaped deep minima in both IS(Eu3ỵ)s at y $ 0.50 in Fig. 4.4b, that is, inverse V-shaped sharp maxima in both BL
3ỵ
(Eu O)s at y $ 0.50, means that with increasing y both BL(Eu3ỵO)s are increasingly more distortion dilated with the
growth of P-type short-range order until the most anisotropic and the most distortion-dilated ideally P-type macroscopic
phase with the longest average BL(Eu3ỵ(VIII)O) is realized at y ẳ 0.50, while keeping the near-highest CN(Eu3ỵ) $ 8 state
throughout in Fig. 4.5. Eu-SH has clearly a deeper IS(Eu3ỵ) minimum than Eu-SZ in Fig. 4.4b, that is, the longer and in fact the
longest BL(Eu3ỵ(VIII)O) near equal to that of UEu in the y 0.50 range, albeit the former has certainly the shorter a0
than the latter in Fig. 4.4a. Yet, their a0 difference seems to get smaller with increasing y ¼ 0.20–0.50. These facts suggest that
the smaller M4ỵ (Hf) system is locally more severely distortion dilated than the larger M4ỵ (Zr) system, also giving rise to a
larger macroscopic a0 dilation. One can thus conclude that a clear slope change at y $ 0.33 both of a0 À y in Fig. 4.4a and of IS
(Eu3ỵ)y in Fig. 4.4b to the steeper one observed for either system is a decisive signal of the isolated P-like ! collective Ptype-coupled microscopic–macroscopic distortion–dilational structure change of the system. In Section 4.4, we will derive a
O)IS(Eu3ỵ) correlation for all these M-Eus to extract their quantitative BL(Eu3ỵO) data.
quantitative BL(Eu3ỵ
4.3.2
155
ssbauer and Lattice Parameter Data of Zr1ÀyGdyO2Ày/2
Gd-Mo
Zr–Gd has many unique properties, such as the second s(ion)(max) in the ideal P Gd2Zr2O7 at y ¼ 0.50 [32] that
diminishes by a factor of $1/5 by the P ! DF disordering treatment above Ttr ¼ 1530 C [41] and the high radiation
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4.3 Lns-MOSSBAUER
AND LATTICE PARAMETER DATA OF DF OXIDES
81
FIGURE 4.5
89
Y MAS-NMR CN(Y3ỵ, Zr4ỵ) data
plotted as a function of composition (y) of YSZ, Zr1ÀyYyO2Ày/2
[15a]. Also the calculated
CN(Ln3ỵ, Zr4ỵ) data for d-type
Zr(Hf)3Ln4O12 at y ẳ 0.5714
(in Eq. (4.2b)) are plotted for
comparison. Those of Hf–Eu,
Zr–Eu, and Zr–Gd are also drawn
(see text for details).
tolerance as a prominent Pu immobilizer that has caused a hot debate on the origin and mechanism of radiation tolerance
of DF oxides [42]. Together with the growing nuclear value of SZs as minor—An transmutation, inert-matrix fuels, and
radioactive nuclear-waste form, this system is today one of the two most intensively investigated SZs with YSZ. Many of
its unique properties most plausibly stem from the marginal structural character locating just at the P/DF stability border
of IRR $ 1.463 in Eq. (4.2a); this is the last system in the early (i.e., larger) Ln3ỵs (La-Gd) that forms macroscopic P at
y ¼ 0.50. This is no longer the case for the next Ln3ỵ ẳ Tb (IRR ẳ 1.444), although a metastable P-type Tb2Zr2O7
microdomain is reported to form here in the microscopic scale [7a].
To gain further insight into its unique P–DF phase and structure features, we have performed a detailed 155 Gd
ossbauer property, we could
M€
ossbauer and powder XRD study over the entire y range [19]. Due to the unique 155 Gd M€
ossbauer data than the above151 Eu M€
ossbauer case measured at 12 K using the highobtain its more colorful 155 Gd M€
energy (86.53 keV) g-ray of a ($231 MBq) 155 Eu/154 SmPd3 source [19e], such as IS, QS, peak-height (e), linewidth (2G),
and RAA (¼e Á 2G). As they were already discussed in detail in Refs 4,19, referring to the a0 data in Fig. 4.6a, we focus here
on the minimum necessary: the IS(Gd3ỵ) and QS data in Fig. 4.6b and c and the recoil-free fraction (f) and Debye
temperature (QD) data derived from the RAA in Fig. 4.7a and b.
Figure 4.6a includes all the reported reliable a0 data of Zr–Gd and shows that this has simpler phase diagram than EuSZ (Fig. 4.4a), the central P being sandwiched with the “apparently disordered” stabilized DF phases on either side
($0.18 y < $0.45 and $0.55 < y $0.62) and the latter coexisting with pure C GdO1.5 at 1500 C. A sigmoid a0–y
curve with a clear kink at y $ 0.33 and $0.50 is more evidently seen than in Eu-SZ(SH) in Fig. 4.4a. The a0 kink at y $ 0.50
just coincides with a IS(Gd3ỵ) ẳ 0.55 – 0.57 shift for y ¼ 0.50 – 0.60 in Fig. 4.6b, but obviously the latter occurs in the
opposite direction to those ($0.50–0.51) for the two doublets of 8b- and 24d-Gd3ỵ for pure C GdO1.5. In view of the
constant IS(Gd3ỵ) $ 0.55 behavior over the whole lower half $0.18 y 0.50 range for the near-constant CN
(Gd3ỵ) $ 8 throughout in Fig. 4.5, this clear IS(Gd3ỵ) upward-shift in the narrow Gd-excess P–DF 0.50 y 0.62
range coincident with the a0 kink is striking. This is supposed to reflect a sort of reordering of the system as observed for
YSZ in Fig. 4.5 as a clear CN(Y3ỵ) uprise with y ẳ 0.50 0.60. These results show that the IS(Gd3ỵ) is also sensitively
detecting the Gd–O local structure change of the system, though in a different fashion from the above IS(Eu3ỵ) case.
When the QS (e2qQ) data in Fig. 4.6c and the f and QD data in Fig. 4.7a and b are compared by turns, they further
reveal many intriguing coupled local versus average-structure evolutions with y. First, mention those of the limiting ref. C
GdO1.5 at y ẳ 1.0: as above noted for the IS (Gd3ỵ) data, this has well-resolved apparent two QS doublets in Fig. 4.6c, the
inner- and outer one in 3:1 ratio in the RAA (see Fig. 3 of Ref. 19c) consistent with the presence of 24d- and 8b-Gd3ỵ sites
in 3:1 ratio in Fig. 4.1b. As the Gd3ỵ has spherical 4f7 electron configuration (8S7/2 ground state), these QS data directly
reflect the anisotropic ionic-charge distribution about the 155 Gd [4,19b], that is, the lattice contribution to the electricfield gradient (q), the major part coming from the first NN distorted oxygen octahedron (CN ¼ 6) in Fig. 4.1b. Then, in
Fig. 4.6c, the minor 8b-Gd3ỵ with body-diagonal 2VOs (the outer-doublet) is known to have much more (in fact most)
distorted oxygen (ỵ cation) environment than the major 24d-Gd3ỵ with face-diagonal 2VOs (the inner doublet);
82
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4 LANTHANIDES (151EU AND 155GD) MOSSBAUER
SPECTROSCOPIC STUDY OF DEFECT-FLUORITE OXIDES COUPLED
FIGURE 4.6
(a) Reported phase-diagram (a0) data of Zr1yGdyO2y/2. (b) IS(Gd3ỵ) data of Zr1yGdyO2y/2. (c) QS (e2qQ) data of
Zr1yGdyO2y/2.
QS(24d-Gd3ỵ) $ 5.6 < QS(8b-Gd3ỵ) $ 10.9. Such well-separated two-site QS behavior of C GdO1.5 was reproduced
with the point-charge model (PCM) QS calculation in Refs. 46 and 19b.
This means that the minor 8b-Gd3ỵ has much more distorted Gd3ỵ(VI)6O2 octahedron than the major
ossbauer and distortionaldilation viewpoint [14]. However,
24d-Gd3ỵ in Fig. 4.1b both from the present 155 Gd M€
À6O) too, that is, BL(Gd3ỵ(8b)O) >
whether the more distorted former has indeed more dilated BL(Gd3ỵ
3ỵ
O), needs more careful examination of XRD structure data of various C LnO1.5s [18c,47–49], for, as
BL(Gd (24d)À
listed in Table 4.1, in both C GdO1.5 and EuO1.5 the reverse possibility of BL(Ln3ỵ(24d)O) > BL(Ln3ỵ(8b)O) cannot
be excluded. However, it appears much more certain in Table 4.1 that the overall average XRD BL(Ln3ỵO)s for the
total 24dỵ8b Ln3ỵs are longer than those calculated as the Shannons rC(Ln3ỵ(VI)) ỵ ra(O2) for the three systems also
including YO1.5. This fact implies that different from the above VO-free cubic F-type U–Eu (CN ¼ 8) in Eq. (4.10), the
macroscopic a0 distortional–dilation of defective C-type LnO1.5 (fC > fF in Fig. 4.2a) has indeed its coupled microscopic
BL(Ln3ỵO) and rC(Ln3ỵ) distortionaldilation, that is, rC(Ln3ỵ(VI))(XRD) > rC(Ln3ỵ(VI))(Shannon). This has also much
4.3 Lns-MOSSBAUER
AND LATTICE PARAMETER DATA OF DF OXIDES
83
FIGURE 4.7
Recoil-free fraction (f) (a) and
Debye temperature QD(Gd) data
(b) of Zr1ÀyGdyO2Ày/2.
to do with the present DCC model a0 formalism in Ref. 1 using Shannon’s rC(Ln3ỵ(VI)) data shown in Fig. 4.2a. This point
will be discussed later. Note that in Fig. 4.7b, its QD $ 420 K agrees well with those reported for some other C LnO1.5s
[4].
Unlike C GdO1.5, all the DF solid solutions over the entire $0.18 y $0.62 range have very broad single QS
doublet in Fig. 4.6c. This means that all these solid solutions, whether P-type ordered or disordered, have basically the
single strongly axial-anisotropic P-type or P-like Gd3ỵ(VIII) site yet with a nontrivial QS distribution. The origin of such
QS distribution is manifold, for example (i) the oxygen disorder [6,10,14c,17a,32,42];
O148f ị ỵ VO 8aị $ VO 48f ị ỵ Oi 8aị;
(4.11a)
TABLE 4.1 BL(Ln3ỵO) (nm) Data of Three C-Type LnO1.5s (Ln3ỵ ẳ Eu, Gd, and Y)
3ỵ
Ln
(Ref.)
Eu [18c]
Eu [48]
Gd [47]
Y [49]
Ln(24d)O
Ln(8b)O
6
Average
2
2
0.23703
0.23040
0.22972
0.2282
0.23174
0.23514
0.23352
0.2282
0.21426
0.22870
0.23143
0.2270
0.23432
0.23419
0.23226
0.2333
2
Ln(total)O
(rC(Ln3ỵ) (XRD)a)
Ln(VI)Oa
(rC(Ln3ỵ) (Shannon))
0.24664
0.24254
0.23688
0.2243
0.23306 (0.09576, $0.09506)
0.23396 (0.09666, $0.09596)
0.23257 (0.09627, $0.09557)
0.2282 (0.0909, 0.0902)
0.23203, $0.2327 (0.0947)
BL(Ln(8b)
O) ẳ rC(Ln3ỵ)(Shannon) ỵ r(O2) assuming r(O2À) ¼ 0.1373–0.138 nm.
a
0.23113, $0.2318 (0.0938)
0.22733, $0.228 (0.090)
84
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4 LANTHANIDES (151EU AND 155GD) MOSSBAUER
SPECTROSCOPIC STUDY OF DEFECT-FLUORITE OXIDES COUPLED
(ii) the cation antisite disorder [50,51] to the lesser extent;
4ỵ
4ỵ
3ỵ
Ln3ỵ
A ỵ ZrHf ịB $ ZrHf ịA ỵ LnB ;
(4.11b)
and (iii) the antiphase (AP)-domain-type interfacial disorder of P microdomains [4,6,7,10,17,32]. These three are
supposed to produce a nontrivial amount of differently distorted oxygen CN ẳ 86 Ln3ỵ sites, broadening the
Gd3ỵ(VIII)-based quasisingle QS doublet of these solid solutions.
The QS data in Fig. 4.6c over the whole lower y side “disordered” cubic-stabilized DF phase in the
$0.18 y < $0.45 range exhibit a rapid continuous increase with y from the lowest QS $ 5.0 at y $ 0.18 straight
to a broad maximum at the central P, yet, the QS(max) $8.2 is much lower than $10.9 of the most distorted 8bGd3ỵ in C GdO1.5. This QS trend with y has also been confirmed semiquantitatively by our PCM QS calculation
assuming the P-type local structure [19b]. These results indicate that as in Eu-SZ(SH) this “apparently disordered”
stabilized DF phase in Gd-SZ has in fact a growing initially P-like (for y < $0.33) and then P-type (for y > $0.33)
axial-anisotropic Gd3ỵ8O coordination (Fig. 4.1c). According to Moriga et al. [17a] the P microdomain structure
as evidenced by the presence of diffuse XRD superstructure peaks indeed extends down to y $ 0.33, and hence the
“really disordered” cubic-stabilized DF phase only exists in the lowest $0.18 y $0.33 range. In view of the
additional fact that once the macroscopic P is realized at y $ 0.45, the QS exhibit only a minor change thereafter
within the 0.45 y 0.55 range, these QS data in the “disordered” solid solutions are judged to be most faithfully
detecting the local Gd3ỵ8O anisotropy change, that is, the near-continuous growth of isolated P-like Gd(VIII)À
8O clusters in the $0.18 y $0.33 range and collectively P-type Gd(VIII)ÀÀ8O microdomains in the $0.33
y $0.45 range in Fig. 4.1c.
The f and QD data in Fig. 4.7a and b representing the same “semilocal more extended-scale” rigidity of the crystal
lattice around the 155 Gd exhibit a clear discontinuity first for y ¼ 0.30 – 0.33 (at y $ 0.315) and then for y ¼ 0.45 – 0.50
(at y $ 0.46), in sharp contrast to the above QS data. Much lower near-constant QD $ 200–210 K for the initial
$0.18 y $0.30 range than the bulk QD $ 500–600 K of pure ZrO2 [4] indicates that this initially stabilized DF phase
has indeed mutually isolated P-like weakly anisotropic fragile Gd3ỵ(VIII)8O clusters not firmly rooted in the host ZrO2
lattice. It appears that first after y increases to $0.300.33 level at which the CN(Zr4ỵ) $ 7 is arrived in Fig. 4.5 they can
start moving collectively to the next-stage short-range P-type microdomain formation in the $0.33 y $0.45 range
toward the macroscopic-P realization at y ¼ 0.50 with CN(Zr4ỵ) $ 6 [14c], thereby drastically improving the systems
structural integrity first at y $ 0.315 and then at y $ 0.46.
Disordering of P at y ¼ 0.50 at 1600 C causes no IS, QS, f, and QD. changes, because also in line with [17a] the shortrange P-type order persists up to over 2000 C far above the apparent Ttr ¼ 1530 C. This is a similar situation to the
above mentioned in that first in the lowest y side $0.18 y $0.30 range far apart from the central P, a truly disordered
cubic-DF phase with no P-type order is realized. It is in this sense that we call this “P-like” cluster phase. This y $ 0.315 at
which P-type short-range order and its associated AP domain start appearing in the XRD and ED patterns [4,7a,17a] just
coincides with the turning point of s(ion) from down to up trend toward the second s(ion)(max) at y ¼ 0.50. The latter is
thus just the reverse DF ! P phenomenon of the drastic second s(ion)(max) decrease at y ¼ 0.50 upon P ! DF
ossbauer results clearly
disordering above Ttr ¼ 1530 C noted in this section. All these XRD and Lns (151 Eu and 155 Gd) M€
evidence that in Zr–Eu, Hf–Eu, and Zr–Gd the collective P-like ! P-type local structure ordering initiates at y $ 0.315,
causing various basic-property (a0 and s(ion)) changes of the system.
€
4.4 DCC MODEL LATTICE PARAMETER AND Lns-MOSSBAUER
DATA ANALYSIS
The combination of the DCC a0 model in Section 4.2 with the Lns M€
ossbauer structure and XRD a0 data of these DF
oxides in Section 4.3 enables us to undertake some crucial preparation works for our near-future model extension to Ptype SZ(SH)s. Although these two types of DF oxides, that is, parent F-type M4ỵ ẳ Ce, Th, and Ans, and P-type SZs and
SHs, have superficially quite different non-Vegardian a0-nonrandomness behavior as seen above, we still think that both
can be described with some unified a0 model to which the current F–C binary one for the former and its extended/or
modified version for the latter can be further sublated. One strong ground for us to believe this is the fact that the linear
BL(Eu3ỵO)IS(Eu3ỵ) correlation [39] works very well in interpreting apparently so-much different coupled a0M
ossbauerIS(Eu3ỵ)BL(Eu3ỵO) behavior of the five M-Eus including both types in a unified manner in Section 4.3.1,
also consistently with that of P-type Zr–Gd in Section 4.3.2.
€
4.4 DCC MODEL LATTICE PARAMETER AND Lns-MOSSBAUER
DATA ANALYSIS
85
Since the accurate macroscopic a0 data of P-type Zr–Eu and Hf–Eu are known in Fig. 4.4a, to construct such extended
DCC a0 model for SZs and SHs, we have to know their accurate microscopic BL(Eu3ỵO) data over the entire y range. So,
our first task here is to derive them by refining the above qualitative near-linear BL(Eu3ỵ
O)IS(Eu3ỵ) correlation to the
more rigorous quantitative one. This was not possible to carry out in Ref. 4 with the random CN a0 model [3] available at that
time dealing only with the limiting “random” case of the system. Below we do this by a two-step process, first by performing a
more complete DCC model a0 analysis of the two parent F-type Ce–Eu and Th–Eu than that in Ref. 1 and then by extending
the obtained results to the two P-type Zr–Eu and Hf–Eu. This process simultaneously involves some further modifications
and/or improvements of the current F–C binary DCC model itself.
4.4.1 DCC Model Lattice Parameter Data Analysis of CeEu and ThEu
Derivation of Quantitative BL(Eu3ỵO)IS(Eu3ỵ) Correlation in M-Eus For the sake of clarity, let us introduce
beforehand Fig. 4.8a and b showing in pair the derived quantitative BL(Eu3ỵO)IS(Eu3ỵ) correlation (a) and quantitative
BL(Eu3ỵO)y relationship (b) for the five M-Eus and explain how both are derived using these figures. In Section 4.3, we had
O)IS(Eu3ỵ)
already obtained the two reference points at (i) CN ¼ 8 and (ii) CN ¼ 6 plotted in Fig. 4.8a to fix the BL(Eu3ỵ
correlation
iịBLEu3ỵ VIIIịOị ẳ 0:2439 0:2446 nm
iiịBLEu3ỵ VIịOị ẳ 0:232 0:234 nm
at ISEu3ỵ VIIIịị ẳ 0:49 mm s1 ;
at ISEu3ỵ VIịị ¼ 1:024 mm sÀ1 :
(4.12a)
(4.12b)
These two reference points at both ends almost completely fix the allowable existence range of such quantitative BL
(Eu3ỵ
O)IS(Eu3ỵ) correlation within the two limiting (steepest and most gradual) straight (dotted and dashed black) lines
FIGURE 4.8
(a) BL(Eu3ỵO2) versus IS(Eu3ỵ)
plot of the five M1yEuyO2y/2
(M4ỵ ẳ Hf, Zr, Ce, U, and Th).
(b) BL(Eu3ỵO2) versus composition (y) plot of the five
M1yEuyO2y/2 (M4ỵ ẳ Hf, Zr, Ce,
U, and Th).
86
4 LANTHANIDES (151EU AND 155GD) MOSSBAUER
SPECTROSCOPIC STUDY OF DEFECT-FLUORITE OXIDES COUPLED
drawn there. These are given by the following respective expressions, assuming their linearity
the steepestịBLEu3ỵ O2 ịsị ẳ f11:18 ISEu3ỵ ịg=43:75;
(4.13a)
the most gradualịBLEu3ỵ O2 ịgị ẳ f13:46 ISEu3ỵ ịg=53:15:
(4.13b)
Since the reference (i) in the upper left corner is far more accurately known within Æ3.5 Â 10À4 nm, their major uncertainty
comes from that of the reference (ii) for C EuO1.5 at y ¼ 1.0 in the lower right corner having afore-noted large uncertainty
arising from the choice of BL(Eu3ỵ(VI)O) ẳ 0.232 or 0.234 nm for the Shannons or XRD rC(Eu3ỵ)(VI)) ẳ 0.0947 or
0.0967 nm, respectively (Table 4.1). The lower right corner of Fig. 4.8b shows this discrepant situation in C EuO1.5 at y ! 1.0
in a more direct manner. As alluded to there, the microscopic distortion-dilated rC(Eu3ỵ)(VI))(XRD) ẳ 0.0967 nm that
corresponds to the macroscopic distortion-dilated a0(C)(¼2fC) of C EuO1.5 is judged to be the more reasonable choice. The
problem here is, however, that this choice is superficially not compatible with the present DCC a0 model formalism in which
the much more accurately known former rC(Ln3ỵ)(VI)(Shannon) data in Fig. 4.2a are used to derive the fC curve in Eq. (4.5b)
[1]. As to this problem we only mention here that such Shannons ! XRD rC(Ln3ỵ)(VI) data-source change at the other
y ! 1.0limitafterallcauseslittle changeofthea0 analysisresultsintheprime-importantlowerhalfDF-type y $0.50rangeof
the system. This point will be again discussed later.
Figures 4.9a and b and 4.10a and b summarize the Da0 analysis results for Ce–Eu and Th–Eu, respectively, with the
current F–C binary DCC model. As in [1], the analysis was made not for the raw a0 data but for the extracted Da0
(=a0 À a0(VL)) data to attain the higher precision. The main point of the present analysis is that this is the more complete
one using all the available each three sets of a0 data for either system, [4,52a–b] for Ce–Eu or [4,40,53] for Th–Eu, than
the previous one in Ref. 1 using only each representative single a0 data set of Refs 4 or 40, respectively. In Figs. 4.9a
and 4.10a, we have drawn the respective several DCC Da0 model curves derived by employing several different
nonrandom CN(M4+, Ln3+) pairs in Figs. 4.9b and 4.10b. As more clearly seen in Fig. 4.10a for the much more nonVegardian Th–Eu, the present F–C binary DCC model can reproduce any of these three mutually largely different a0 data
sets very well with no difficulty by employing the respective most relevant (mutually largely different) non-random CN
(Th4+, Eu3+) pairs in Fig. 4.10b. This in turn means that one can hardly decide which is the most reasonable model based
on this kind of Da0 analysis alone, unless one had some additional information of “which is the most reliable and accurate
a0 data set.” Almost the same can be said for Ce–Eu too in Fig. 4.9a and b.
For the later discussion, we shortly note that in the F–C binary a0 model, the following simple proportional
relationship holds between the random ! non-random a0, rC, and CN(Ln3ỵ) changes of the system [1]
da0 $ A Á dr C $ A Á y Á DaLn-M dCNLn3ỵ ị;
where DaLn-M ẳ aLn -aM ;
(4.14)
where A is a proportional constant and aLn and aM are the linear slope of rC(Ln3ỵ) and rC(M4ỵ) versus CN plot in
6 CN 8 range in Fig. 4.3, respectively. Equation (4.14) means that the random ! non-random CN(Ln3ỵ) change, for
example, dCN(Eu3ỵ) in Fig. 4.9b, produces first the proportional drC in Fig. 4.2a and then the da0 in Fig. 4.9a. This forms
FIGURE 4.9
(a and b) DCC model Da0 analysis
results of Ce1ÀyEuyO2Ày/2. (See
the color version of this figure in
Color Plates section.)
€
4.4 DCC MODEL LATTICE PARAMETER AND Lns-MOSSBAUER
DATA ANALYSIS
87
FIGURE 4.10
(a and b) DCC model Da0 analysis
results of Th1yEuyO2y/2.
the basis of why the nonrandom CN(Ln3ỵ) of the system can be extracted with the DCC model a0 data analysis,” as seen
in these figures. Add here also that from the second near equality in Eq. (4.14), the condition that DaLn-M 6¼ 0, that is,
aLn 6¼ aM is essential for dCN(Ln3ỵ) to be able to produce drC and da0: as seen in Fig. 4.3, rC(Ln3ỵ) has generally the
steeper CN slope than rC(M4ỵ); aLn > aM, that is, DaLn-M > 0. Since the latter slope gets steadily steeper with decreasing
rC(M4ỵ) (Th ! U ! Ce ! Zr ! Hf), the sensitivity of the system to dCN(Ln3ỵ) steadily decreases in this order, as
pointed out in Appendix B of [1]. The smaller M4ỵ (Zr and Hf) having aLn$aM (DaLn-M $ 0) are thus guessed to be much
more insensitive to dCN(Ln3ỵ) than the larger M4ỵ ẳ Ce and Th. In other words, this means that the strongly sigmoid
non-Vegardian a0 behavior of these SZ(SH)s in Figs. 4.4a and 4.6a is not describable by this simplistic F–C binary DCC a0
model.
We propose here the model IV (in red) as the most reasonable instead of the model I (in green) in Ref. 1 for both the
systems in the light of their known local structure property:
(i) Ce–Eu. It was found in Ref. 1 that the model-I CN(Eu3ỵ) is near-identical with those of CeY and CeGd; CN
(Y3ỵ) $ CN(Gd3ỵ) $ CN(Eu3ỵ). Since more likely is the case that 7.25 $ CN(Y3ỵ) < CN(Gd3ỵ) < N(Eu3ỵ)
< CN(Sm3ỵ) $ 7.55 at y ! 0 in view of the well-known increasing s(ion)(max) trend with increasing rC(Ln3ỵ)
in these Ce-Lns [1,2], only the model IV fulfilling this requirement in Fig. 4.9b remains reasonable. Then in
Fig. 4.9a its Da0 curve is only a little more positively non-Vegardian than that of the model I. Namely, a small Da0
difference requires here a relatively large CN(Eu3ỵ) change, necessitating other related local structure data to
correctly identify its Da0 behavior, as demonstrated here.
(ii) ThEu. From its closely linear IS(Eu3ỵ)y curve near-identical with (but slightly higher (at y ! 0) than) that of the
above Ce–Eu in Fig. 4.4b, it is judged that this should also have a near-linear and near-identical CN(Eu3ỵ) and BL
(Eu3ỵO) curves with (but slightly smaller (at y ! 0) than) those of Ce–Eu. Comparing Figs. 4.9b and 4.10b,
the model-IV CN(Eu3ỵ) fulfills this requirement best. Then in Fig. 4.10a its Da0 curve is found to be much more
non-Vegardian and closer to our data [4] than that of the model I.
The here selected best model-IV rC(M4ỵ, Eu3ỵ) (M4ỵ ẳ Ce and Th) curves are calculated in Eqs. (4.6a) and (4.6b) by
inserting the respective CN(M4ỵ, Eu3ỵ) curves in Figs. 4.9b and 4.10b, and are converted to the respective BL(Eu3ỵO)
(rC(Eu3ỵ) ỵ ra(O)) curves using the ra(O) expression derived in Ref. 1
r a Oị ẳ 0:1373 ỵ 1:7654 frC 0:0992g2 nmị:
(4.15)
Thus obtained both BL(Eu3ỵO)y curves are drawn in Fig. 4.8b in filled orange and open blue symbol for Ce–Eu and
Th–Eu, respectively. Qualitatively speaking, the derived BL(Eu3ỵO)y curve of each system has similar y dependence to
each CN(Eu3ỵ)y curve in Fig. 4.9b or 4.10b, because the BL(Eu3ỵO) is nearly proportional to CN(Eu3ỵ) as a good first
approximation [1].
88
€
4 LANTHANIDES (151EU AND 155GD) MOSSBAUER
SPECTROSCOPIC STUDY OF DEFECT-FLUORITE OXIDES COUPLED
By combining the BL(Eu3ỵO)y curves in Fig. 4.8b with the respective 151 Eu-M
ossbauer IS(Eu3ỵ)y curves in
3ỵ
3ỵ
Fig. 4.4b, we can further derive the direct BL(Eu ÀÀO)–IS(Eu ) curves as drawn in Fig. 4.8a using the same filled orange
and open blue symbol, respectively. Thus obtained direct BL(Eu3ỵO2)IS(Eu3ỵ) data curves of these two systems in
Fig. 4.8a closely overlap with each other and are found to follow well the steepest BL(Eu3ỵO) line in Eq. (4.13a). The
slight deviation of this BL(Eu3ỵO2)IS(Eu3ỵ) data curve of Ce–Eu from the latter in the larger BL > $0.90 nm range
does not matter much, for the real Da0-nonrandomness behavior of Ce–Eu as well as of Th–Eu in such EuO1.5-rich
narrow C-type solid solution phase is not known well from the beginning, as seen in Figs. 4.9a and 4.10a. Since we already
know that the upper side reference (ii) point of BL(Eu3ỵO2)(XRD) ẳ 0.234 nm at IS(Eu3ỵ) ẳ 1.025 nm sÀ1 in
Eq. (4.12b) is the more proper choice for C EuO1.5 in Fig. 4.8a and b, this agreement of these derived data curves
with the steepest BL(Eu3ỵO) line at the y ! 1.0 limit in Fig. 4.8a should be regarded as an artifact resulting from the
deficiency of the current F–C binary a0 model in which the rC(Ln3ỵ)(VI)(Shannon) data in Fig. 4.2a are used to derive the
fC curve in Eq. (4.6b).
We can eliminate such contradictory situation in the higher y range of these two systems in the following manner.
Inserting the IS(Eu3ỵ)y curves of Ce–Eu and Th–Eu in Fig. 4.4b into the right-hand side of these two limiting BL
(Eu3ỵO2)IS(Eu3ỵ) lines in Eqs. (4.13a) and (4.13b), we can obtain their simulated model BL(Eu3ỵO2)y curves.
These are drawn in Fig. 4.8b in the same dotted and dashed lines as in Fig. 4.8a and are compared with their above BL
(Eu3ỵO2)y data curves. As expected, the BL(Eu3ỵO2)y data curves and the Eq. (4.13a)-based (dotted) curves of
both the systems show good mutual agreement over the entire y range, both heading straight to the lowest BL(Eu3ỵO2)
(Shannon) ẳ 0.232 nm point at the y ! 1.0 limit. However, the Eq. (4.13b)-based (dashed) curves, although they certainly
ÀO)(XRD) ¼ 0.234 nm at the y ! 1.0 limit, show nontrivial positive deviation from
have the more proper highest BL(Eu3ỵ
O2)y data curves down to the y ! 0 limit for both systems. Since their enough reasonable a0the respective BL(Eu3ỵ
nonrandomness picture is obtained in the lower half 0 y $0.50 range in Figs. 4.9a, b and 4.10a, b, the most appropriate BL
(Eu3ỵO)IS(Eu3ỵ) correlation in Fig. 4.8a and BL(Eu3ỵO2)y relationship in Fig. 4.8b for these two systems are judged
to be the ones that agree with Eq. (4.13a) in the higher BL and lower y range and with Eq. (4.13b) in the lower BL and higher y
range. We therefore propose the following Eq. (4.13c) with the additional higher order term that fulfills this requirement as
the most appropriate BL(Eu3ỵO2)IS(Eu3ỵ) correlation for these two parent F-type systems
2
the bestịBLEu3ỵ O2 ị ẳ f11:175 ISEu3ỵ ịg=43:75 ỵ 0:025 f0:6 ISEu3ỵ ịg :
(4.13c)
This best BL(Eu3ỵO2)IS(Eu3ỵ) correlation curve in Eq. (4.13c) is drawn as a thick red line in Fig. 4.8a and the
corresponding BL(Eu3ỵO2)y curves of both CeEu and ThEu are drawn in Fig. 4.8b as each (orange or blue) thick
solid line; both systems indeed exhibit a well-behaved transit from Eq. (4.13a) to Eq. (4.13b) with increasing y.
From the all foregoing discussion in Section 4.3.2, we can naturally expect that Eq. (4.13c) will also apply to P-type
Eu-SZ(SH). So, this is proposed as a possible unified quantitative BL(Eu3ỵO)IS(Eu3ỵ) correlation valid for both parent
F- and P-type M-Eus.
4.4.2 Quantitative BL(Eu3ỵO)-Composition (y) Curves in ZrEu and HfEu
Inserting the IS((Eu3ỵ)y curves of P-type ZrEu and HfEu in Fig. 4.4b into the right-hand side of Eq. (4.13c), their most
reasonable quantitative BL(Eu3ỵO)y curves are obtained and drawn in Fig. 4.8b in each (black or red) colored thick
solid line. For comparison, we have also drawn their Eqs. (4.13a) and (4.13b)-based BL(Eu3ỵO)y curves in dotted and
dashed line, respectively, to estimate their maximum uncertainty range. Above all, Fig. 4.8b indeed reveals a strikingly
strong sigmoid BL((Eu3ỵO) variation with y both in P-type Eu-SZ and in Eu-SH in a quantitative manner. From the
comparison of each three sets of BL(Eu3ỵO2)y curves based on Eqs. (4.13a, b and c), it is clear that the uncertainty of
these best BL(Eu3ỵO) curves is maximum at the minimum BL composition of y $ 0.20, ranging from the best 0.2385 nm
to the higher 0.2392 or to the lower 0.2382 nm. Obviously, this level of uncertainty hardly alters their enough strong basic
sigmoid feature.
ÀO) minima at y $ 0.20 in both systems might be an artifact, for the actual BL
Of course, the onset of BL(Eu3ỵ
3ỵ
O) behavior in the M/DF diphasic y < $0.20 range is not known; as represented in thin solid red line, it is equally
(Eu
possible to postulate the BL(Eu3ỵO) curve that is constant independent of y or steadily decreasing down to y ! 0.
Although it would be meaningful to ponder which is the case if some single-phase DF-type Eu-SZ(SH) be prepared down
to such lower y $ 0.10–0.05 range, for the consistency of the present supposition that P-type Eu-SZ(SH) approaches to
the cubic Zr(Hf)O2 with CN(Zr(Hf)4ỵ) ẳ 8 at the y ! 0 limit, we postulate here that the BL(Eu3ỵO) approaches to
the BL(Eu3ỵ(VIII)O) at y ! 0 as well, as naturally expected from the almost constantly highest CN(Eu3ỵ) $ 8 state
4.4 DCC MODEL LATTICE PARAMETER AND Lns-MOSSBAUER
DATA ANALYSIS
89
realized for the y < 0.30 range in both systems in Fig. 4.5. That is, the closely overlapping thick solid (black and red) curves
rising steeply to the limiting BL(Eu3ỵ(VIII)O) $ 0.2443 nm at y ! 0 are adopted here for both systems.
Anyway it is certain that both Eu-SZ and Eu-SH have a near-common BL(Eu3ỵ(VIII)
O) $ 0.2385 nm at y $ 0.20 in close
vicinity of the lower y side M/DF phase boundary, which is much shorter than the supposed BL(Eu3ỵ(VIII)O) $
0.24390.2446 nm in UEu in the y $0.50 range in Eq. (4.10). This BL(Eu3ỵ(VIII)O) $ 0.2385 nm at y $ 0.20 is even
closer to the BL (Eu3ỵ(VI)O)(XRD) ẳ 0.234 nm for C EuO1.5 at y ẳ 1.0 than to the BL (Eu3ỵ(VIII)O) ẳ 0.2442 nm for the
ideal-P Hf2Eu2O7 at y ¼ 0.50. Eventually this just coincides with the Shannons BL(Eu3ỵ(VII)O) ẳ 0.101 ỵ
0.1373 $ 0.138 ẳ 0.2383 $ 0.239 nm for the Eu3ỵ(VII) at CN ẳ 7. This is a surprising result in the light of the fact in
Fig. 4.5 that their CN(Eu3ỵ)s indeed remain very close to 8 almost over the entire lower half 0 y $0.50 range. It was
clarified in Section 4.3 that the initially cubic-stabilized $0.20 y $0.315 range of Eu-SZ(SH) as well as that of Gd-SZ is a
weakly anisotropic least distortion dilated mutually isolated fragile P-like Ln3ỵ(VIII)8O cluster state. To emphasize this
special situation, we inserted there a legend, P-based BL(Eu3ỵ(VIII)O) reduction, with a downward-arrow line, for it is
our basic recognition that this “P-like” cluster state is also a part of P-type structural entity that is decomposed into the
mutually isolated molecular-cluster unit. Why such an extraordinarily short average BL(Eu3ỵ(VIII)O) $ 0.2385 nm could be
realized for the dopant Eu3ỵ cation at this special composition of y $ 0.20 at which the cubic-DF phase is just first stabilized
seems to be an intriguing question/problem of lattice-dynamics as well as defect physics/chemistry.
On the other hand, the onset of sharp BL(Eu3ỵO) maxima at y ẳ 0.50 in Fig. 4.8b is undoubtedly the physical reality
of these P-type Eu-SZ and Eu-SH originating from the formation of the microscopic most distortion-dilated axialanisotropic unique Eu(VIII)À
À8O cube in the macroscopic most-highly ordered and most distortion-dilated ideal P at this
stoichiometric y ¼ 0.50 in Fig. 4.1c. Including Gd-SZ discussed in Section 4.3.2, these ideal P Zr(Hf)2Ln2O7s at y ¼ 0.50 are
indeed the most rigid and most stable intermediate compound with the highest QD $ 650–700 K formed in these Zr(Hf)
O2–LnO1.5 binary systems, as seen in Fig. 4.7a and b. Namely, it appears certain that in the $0.20 y $0.50 range the
growth of collective P-type short- and long-range order in the $0.315 y $0.50 ranges from a mutually isolated initial
P-like cluster in the $0.20 y 0.315 range is drastically enhancing the distortion–dilational chemical and structural
stability of the system both in the microscopic BL(Ln3ỵO) and in the macroscopic average crystal-structure level. The
sharp drop of the BL(Eu3ỵO)s for y > 0.50 is again most plausibly related to the rapid loss of such P-type order and
structural integrity. Then, one possible qualitative answer to the above question/problem is that “distortional–dilation” is
associated with the short- or long-range ordered “network” structure of the system, but not with its isolated each cluster
state. In any event, the way and mode of this strongly nonlinear sigmoid average BL(Eu3ỵO) and a0 variation with y is
definitely judged to originate from the P-type intermediate-ordered structure of these SZ(SH)s absent in the naively
parent F-type DF oxides.
4.4.3 Model Extension Attempt from Macroscopic Lattice Parameter Side
We have suggested in 4.2 that the current F–C binary a0 model might be further refined to an applicable form to SZ(SH)s
by properly incorporating the P- and d-based extra a0 distortional–dilation of fP at y ¼ 0.50 in Eq. (4.5c) drawn in Fig. 4.2a
and b. In order to validate the F–C binary a0 model and its such possible extended version, we have conducted the Da0
analysis of three P-type Zr–Eu, Hf–Eu, and Zr–Gd, first with the former, as was done in Section 4.4.1 for Ce–Eu and
Th–Eu in Figs. 4.9a, b and 4.10a, b, and then with the latter. The results are summarized in Fig. 4.11a and b for Zr–Gd and
in Fig. 4.12a and b for Zr–Eu and Hf–Eu. Figures 4.11a and 4.12a show the individual cations’ rC(M4+, Ln3+) in Eqs. (4.6a)
and (4.6b) calculated by inserting the respective nonrandom CN(M4+, Ln3+) curves shown in Fig. 4.5 and their overall
average cation radius of rC in Eq. (4.3b). Figures 4.11b and 4.12b show the extracted Da0(exp) data and their model curves
for the respective systems.
Zr–Gd was first picked up here, for this has much more ample a0(exp) data as seen in Fig. 4.6a, and the extract
Da0(exp) data in Fig. 4.11b indeed exhibit much clearer y dependence than those more sparse and scattered in Fig. 4.12b
of Zr–Eu and Hf–Eu. However, the overall trend of their strongly sigmoid Da0 variation with y is very similar to one
another, so that we have drawn their single (thick solid pink) master curve in these figures. Though somewhat lengthy,
this has the following functional form
Da0 ¼ 2:25 104 1 yị5 ỵ 1:5104 expfy 0:15ị2 =0:004g 0:0016 expy 0:31ị2 =0:05ị
ỵ 9 104 expfy 0:515ị2 =0:005g ỵ 6 Â 10À4 Á expfÀðy À 0:61Þ2 =0:02gðnmÞ:
(4.16)
The more global Da0 trend of more various Ln-SZs (Ln3ỵ ẳ La, Nd, Sm, Eu, Gd, Y, Dy, Er, and Yb) (A. Nakamura,
unpublished work) is that such strongly sigmoid Da0 variation with y steadily weakens with decreasing rC(Ln3ỵ), that is,
90
4 LANTHANIDES (151EU AND 155GD) MOSSBAUER
SPECTROSCOPIC STUDY OF DEFECT-FLUORITE OXIDES COUPLED
FIGURE 4.11
(a and b) DCC model Da0 analysis
results of Zr1yGdyO2y/2
obtained by using Shannons rC
(Zr4ỵ, Gd3ỵ) data.
with decreasing systems IRR from Ln3ỵ (La to Yb) in Eq. (4.1). As far as these three systems are concerned, however, all
their Da0 À y curves are well approximated by this single Eq. (4.16) within their reported a0(exp) data scatter. These
figures clearly reveal that their Da0(exp) data indeed have deep minima at y $ 0.315 and a clear kink at y $ 0.50–0.55 in
common, substantiating the former observation in their raw a0–y plot in Figs. 4.4a and 4.6a. The close resemblance of this
ÀO)–y curves of Eu-SZ and Eu-SH in Fig. 4.8b is also evident, although the
master Da0 À y curve with the BL(Eu3ỵ
O) minima, y $ 0.315 and 0.20, respectively, are certainly different from each other.
positions of the Da0 and BL(Eu3ỵ
This is also natural, for the Da0 is also dependent on the hostcations BL(Zr(Hf)4ỵO) behavior.
In contrast to simply largely positively non-Vegardian Da0 (>0) parent F-type M4ỵ (Ce and Th) in Figs. 4.9a and 4.10a,
these SZ(SH)s are all basically negatively non-Vegardian Da0 (<0) over the major cubic-DF $0.20 y $0.46 range with
its much deeper Da0(min)$À1.5 Â 10À3 nm at y $ 0.315 than its much lower peak Da0(max)$ ỵ 0.75 10À3 nm at
y $ 0.55. Their total jDa0j is ${1.5 À (À0.75)} Â 10À3 ¼ 2.25 Â 10À3 nm, which is almost equally as large as that in Ce–Eu
in Fig. 4.9a. In view of the afore-clarified structural fact that this Da0(min) composition of y $ 0.315 is the starting point of
the “isolated P-like ! collective P-type” structural reorganization of all these P-type systems, the appearance of the
macroscopic least distortional dilated most shrunk Da0 state at y $ 0.315 seems to indicate that this is the most unstable
critical point of the system to be destined to move to the collective P-type ordering.
In Figs. 4.11b and 4.12b, the current F–C binary a0 model cannot reproduce such strongly sigmoid Da0 (both <0
and >0) behavior for any of these three systems, only producing a slightly negatively non-Vegardian Da0(<0) À y
curves for either random or nonrandom CN(M4ỵ, Ln3ỵ) pair in Fig. 4.5. This confirms the aforementioned poor
sensitivity of SZ(SH)s to the random ! nonrandom dCN(Ln3ỵ) change of the system as predicted by Eq. (4.14). In
Fig. 4.5, we have derived the most plausible CN(M4ỵ, Ln3ỵ) curves of each system based on the reported XRD and
XAFS result that CN(Gd3ỵ) ẳ 7.6 and CN(Zr4ỵ) ẳ 6.4 at y ¼ 0.50 in Eq. (4.7) for the “supposedly ideal” P Zr2Gd2O7
[14c,17a]. Then, by giving a proper more convexity to the accurately known thick blue CN(Y3ỵ) curve of YSZ [15a] so
as to go through this CN(Gd3ỵ) ẳ 7.6 at y ẳ 0.50, its CN(Gd3ỵ, Zr4ỵ) curves drawn in the respective solid and dashed