Influence of Synthesis Conditions on the Crystal, Local Atomic, Electronic Structure, and Catalytic Properties of (Pr1-xYbx)2Zr2O7 (0 < x < 1) Powders

Abstract

The influence of Yb3+ cations substitution for Pr3+ on the structure and catalytic activity of (Pr1-xYbx)2Zr2O7 powders synthesized via coprecipitation followed by calcination is studied using a combination of long- (s-XRD), medium- (Raman, FT-IR, and SEM-EDS) and short-range (XAFS) sensitive methods, as well as adsorption and catalytic techniques. It is established that chemical composition and calcination temperature are the two major factors that govern the phase composition, crystallographic, and local-structure parameters of these polycrystalline materials. The crystallographic and local-structure parameters of (Pr1-xYbx)2Zr2O7 samples prepared at 1400oC/3 h demonstrate a tight correlation with their catalytic activity towards propane cracking. The progressive replacement of Pr3+ with Yb3+ cations gives rise to an increase in the catalytic activity. A mechanism of the catalytic cracking of propane is proposed, which considers the geometrical match between the metal–oxygen (Pr–O, Yb–O, and Zr–O) bond lengths within the active sites and the size of adsorbed propane molecule to be the decisive factor governing the reaction route.

Full text

Citation: Popov, V.V.; Markova, E.B.;
Zubavichus, Y.V.; Menushenkov, A.P.;
Yastrebtsev, A.A.; Gaynanov, B.R.;
Chernysheva, O.V.; Ivanov, A.A.;
Rudakov, S.G.; Berdnikova, M.M.;
et al. Influence of Synthesis
Conditions on the Crystal, Local
Atomic, Electronic Structure, and
Catalytic Properties of
(Pr1−xYbx)2Zr2O7(0 ≤x≤1)
Powders. Crystals 2023,13, 1405.
https://doi.org/10.3390/
cryst13091405
Academic Editors: Maria Milanova
and Martin Tsvetkov
Received: 1 September 2023
Revised: 18 September 2023
Accepted: 19 September 2023
Published: 21 September 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
crystals
Article
Influence of Synthesis Conditions on the Crystal, Local Atomic,
Electronic Structure, and Catalytic Properties of
(Pr1−xYbx)2Zr2O7(0 ≤x≤1) Powders
Victor V. Popov 1,2,* , Ekaterina B. Markova 3, YanV. Zubavichus 4,* , AlexeyP. Menushenkov 1,
Alexey A. Yastrebtsev 1, Bulat R. Gaynanov 1, OlgaV. Chernysheva 1, AndreiA. Ivanov 1,
Sergey G. Rudakov 1, Maria M. Berdnikova 1, Alexander A. Pisarev 1, Elizaveta S. Kulikova 2,
Nickolay A. Kolyshkin 2, Evgeny V. Khramov 2, Victor N. Khrustalev 3, Igor V. Shchetinin 5,
Nadezhda A. Tsarenko 6, Natalia V. Ognevskaya 6and Olga N. Seregina 6
1Department of Solid State Physics and Nanosystems, National Research Nuclear University MEPhI
(Moscow Engineering Physics Institute), Moscow 115409, Russia; apmenushenkov@mephi.ru (A.P.M.);
alexyastrebtsev@mail.ru (A.A.Y.); brgaynanov@gmail.com (B.R.G.); ovchernysheva@mephi.ru (O.V.C.);
andrej.ivanov@gmail.com (A.A.I.); sgrudakov@mephi.ru (S.G.R.); mmberdnikova@mephi.ru (M.M.B.);
aapisarev@mephi.ru (A.A.P.)
2Kurchatov Synchrotron Radiation Source, National Research Center Kurchatov Institute,
Moscow 123182, Russia; lizchkakul@mail.ru (E.S.K.); nickelprog@mail.ru (N.A.K.);
evxramov@gmail.com (E.V.K.)
3
Department of Physical and Colloid Chemistry, Faculty of Science, RUDN University, Moscow 117198, Russia;
ebmarkova@gmail.com (E.B.M.); vnkhrustalev@gmail.com (V.N.K.)
4Synchrotron Radiation Facility SKIF, Boreskov Institute of Catalysis SB RAS, Koltsovo 630559, Russia
5
Material Science Department, National University of Science and Technology MISiS, Moscow 119049, Russia;
ingvvar@gmail.com
6JSC Design & Survey and Research & Development Institute of Industrial Technology,
Moscow 115409, Russia; nadatsar@gmail.com (N.A.T.); ognevskayanv@mail.ru (N.V.O.);
marioll1961@mail.ru (O.N.S.)
*Correspondence: vvpopov@mephi.ru (V.V.P.); yvz@catalysis.ru (Y.V.Z.)
Abstract:
The influence of Yb
3+
cations substitution for Pr
3+
on the structure and catalytic activity
of (Pr
1−x
Yb
x
)
2
Zr
2
O
7
powders synthesized via coprecipitation followed by calcination is studied
using a combination of long- (s-XRD), medium- (Raman, FT-IR, and SEM-EDS) and short-range
(XAFS) sensitive methods, as well as adsorption and catalytic techniques. It is established that
chemical composition and calcination temperature are the two major factors that govern the phase
composition, crystallographic, and local-structure parameters of these polycrystalline materials. The
crystallographic and local-structure parameters of (Pr
1−x
Yb
x
)
2
Zr
2
O
7
samples prepared at 1400
◦
C/3 h
demonstrate a tight correlation with their catalytic activity towards propane cracking. The progressive
replacement of Pr
3+
with Yb
3+
cations gives rise to an increase in the catalytic activity. A mechanism
of the catalytic cracking of propane is proposed, which considers the geometrical match between the
metal–oxygen (Pr–O, Yb–O, and Zr–O) bond lengths within the active sites and the size of adsorbed
propane molecule to be the decisive factor governing the reaction route.
Keywords:
praseodymium/ytterbium zirconates; crystal and local structures; catalytic cracking of
propane; synchrotron XRD; X-ray absorption fine structure (XAFS); Raman spectroscopy;
FT-IR spectroscopy
1. Introduction
In the last few decades, complex oxides A
2
B
2
O
7
(where A is typically a rare-earth
cation in the oxidation state 3+, whereas B is a transition d-metal in the oxidation state
4+) with cubic pyrochlore, fluorite, or an intermediate structure derived from the former
two have attracted vivid interest from researchers [
1
–
6
]. Primarily, they feature a rich
Crystals 2023,13, 1405. https://doi.org/10.3390/cryst13091405 https://www.mdpi.com/journal/crystals

Crystals 2023,13, 1405 2 of 23
polymorphism representing a rather rare example of simultaneous disorder in both cation
and anion sublattices upon a phase transition from fully ordered pyrochlore to a disordered
defect fluorite structure [
1
–
9
]. Cubic pyrochlore complex oxides A
2
B
2
O
7
have also attracted
much attention due to their ability to exhibit various types of geometrically frustrated
magnetism [
10
,
11
]. Furthermore, complex oxide compounds and solid solutions from this
family are prospective thermal barrier coatings [
12
–
14
], ion conductors [
15
,
16
], matrices
for the immobilization of nuclear wastes [17,18], neutron-absorbing materials [19,20], and
catalysts [21,22].
Nowadays, propane dehydrogenation is one of the main technologies for production
of light olefins [
23
,
24
]. It has been shown that metal oxide-based materials can be used
as promising catalysts for the conversion of propane to olefins [
23
–
25
]. More specifically,
compounds with a common stoichiometry (Pr
1−x
Yb
x
)
2
Zr
2
O
7
, synthesized at 1000
◦
C, have
been recently successfully tested for the catalytic cracking of propane [
26
]. Unfortunately,
this article does not provide details on the atomic structure of the polycrystalline materials
used. Based on our previous studies [
27
,
28
], we consider all samples reported in [
26
] to
have the same disordered defect–fluorite structure.
It is the cation radii ratio
γ
= r
A3+
/r
B4+
that largely determines the crystal structure of
A
2
B
2
O
7
-type complex oxides. The r
A3+
/r
B4+
radius–ratio threshold values are as follows:
disordered fluorite
<
1.21
<δ
-phase
<
1.42–1.44
<
pyrochlore
<
1.78–1.83
<
monoclinic
pyrochlore
<
1.92 [
29
]. It was shown that Pr
2
Zr
2
O
7
(
γ=
1.564) has a pyrochlore structure
(cubic, sp. gr. Fd
¯
3
m(227)) [
1
,
2
,
30
]. In the case of preparing Pr
2
Zr
2
O
7
by the calcination
of amorphous precursors, the pyrochlore phase is obtained through the formation of
an intermediate fluorite phase (cubic, sp. gr. Fm
¯
3
m(225)) [
27
]. The possibility of the
formation of Pr
4+
cations in Pr
2±x
Zr
2±x
O
7±y
depending on the processing atmosphere
and stoichiometry was shown in [
31
]. Pr
2
Zr
2
O
7
with a pyrochlore structure is a promising
candidate for the quantum spin ices [
10
,
32
]. Yb
2
Zr
2
O
7
(
γ=
1.368) can have both a defect
fluorite structure [
33
] and a
δ
-phase (rhombohedral, sp. gr. R
¯
3
(148)) [
28
,
30
]. In the
scientific literature on rare-earth zirconates, there are numerous reports on the use of
chemical substitution either in the A [
7
,
34
,
35
] or B sites [
36
–
38
] or even in both the A and B
sites simultaneously [
39
,
40
] to deliberately shift or control these phase transitions in other
specific terms.
In this respect, it seems to be important to obtain deeper insights into the phase transi-
tions occurring in praseodymium/ytterbium zirconates (Pr
1−x
Yb
x
)
2
Zr
2
O
7
(0
≤x≤
1) with
exact stoichiometry as control parameter since functional crystalline starting and ending
members of the series Pr
2
Zr
2
O
7
and Yb
4
Zr
3
O
12
are characterized by different syngonies. To
the best of our knowledge, the (Pr
1−x
Yb
x
)
2
Zr
2
O
7
series has not been described in the litera-
ture so far. Herewith, the crystal, local atomic, and electronic structures of the synthesized
samples were studied in detail using multiscale structural analysis, including a combination
of diffraction, spectroscopy, and electron microscopy techniques [
41
,
42
]. In addition, the
adsorption and catalysis-relevant properties of (Pr
1−x
Yb
x
)
2
Zr
2
O
7
polycrystalline materials
synthesized at 1400
◦
C were elucidated, which helped us to establish mutual correlations
between structural features of complex oxides (Pr
1−x
Yb
x
)
2
Zr
2
O
7
(0
≤x≤
1) and their
catalytic characteristics.
2. Materials and Methods
2.1. Catalyst Synthesis
The complex oxides (Pr
1−x
Yb
x
)
2
Zr
2
O
7
(0
≤x≤
1) were prepared by a coprecipitation
method [
43
]. The starting chemicals Pr(NO
3
)
3·
6H
2
O, Yb(NO
3
)
3·
4H
2
O (with purity not lower
than 99.95%), zirconium oxychloride octahydrate ZrOCl
2·
8H
2
O (99+%), and ammonium
hydrate NH
3·
H
2
O (analytical grade) were purchased from CHIMMED (Moscow, Russia)
and used without additional purification. The starting salt solutions were prepared by
mixing the initial reagents in the atomic ratios [
(
1
−x)
Pr +
x
Yb]:Zr = 1:1 (
x
= 0, 0.25, 0.5, 0.75,
and 1) followed by dissolution of the mixtures in distilled water. The mixed salt solutions
were dropwise added into an NH
3·
H
2
O aqueous solution under vigorous stirring. The as-

Crystals 2023,13, 1405 3 of 23
prepared suspensions (pH = 9.5–10.0) were aged for an hour at room temperature to ensure
that the reaction is complete. The precipitates formed were filtered off, washed several
times with distilled water, and then dried at 80
◦
C for 6 h. The dried precursors were then
finely ground in an agate mortar and loaded into a muffle furnace LHT 02/16 (Nabertherm
GmbH, Lilienthal, Germany). The powders were heated to a required temperature in the
range of 600–1400
◦
C in air at a rate of 10
◦
C/min and then calcined isothermally for 3 h.
The calcined samples were then cooled in a furnace to room temperature.
2.2. Characterization
The inductively coupled plasma atomic emission spectroscopy (ICP-AES) was used
to quantify of the mass percentage of the metals in the synthesized precursors. ICP-AES
measurements were carried out with a Vista-PRO spectrometer (Varian Inc., Palo Alto,
CA, USA).
The operating conditions were as follows: auxiliary Ar flow rate 1.5 L/min; plasma
Ar flow rate 13.5 L/min. All of the analyzed solutions were prepared by acid digestion.
Samples (
∼
100 mg, weighed with a precision of
±
0.1 mg) were dissolved in a mixture of
analytical grade concentrated nitric acid (65% m/m; 3 mL), hydrochloric acid (37% m/m;
3 mL), and distilled water (15 mL) by boiling for 30 min. Cooled digested samples were
further diluted with distilled water so that the concentration of the measured cations was
0.1–50 mg/L. The emission wavelengths were 422.293 and 410.072 nm for Pr; 218.572 and
222.447 nm for Yb; and 343.823 nm for Zr.
The simultaneous thermal analysis (STA) of the as-synthesized precursors involving
thermogravimetry (TG) and differential scanning calorimetry (DSC) was carried out using
a SDT Q600 analyzer (TA Instruments, New Castle, DE, USA) in a temperature range of
30–1400 ◦C at a heating rate of 10 ◦C/min in an air flow of 100 mL/min.
The X-ray diffraction (XRD) analysis of all of the synthesized samples was carried out
on a laboratory MiniFlex 600 diffractometer (Rigaku, Tokyo, Japan) with monochromatized
Cu K
α
-radiation (
λ
= 1.5405 Å). All of the measurements were made at room temperature
in the Bragg–Brentano geometry. The diffraction angle (2
θ
) range was 10–100
◦
, with a
step size 0.025
◦
and a dwell time of 3 s for each step. The operation X-ray source voltage
and current were 40 kV and 30 mA, respectively. More detailed structural information
was obtained from synchrotron X-ray powder diffraction (s-XRD) performed at the X-ray
structural analysis beamline (Belok/XSA) of the Kurchatov Synchrotron Radiation Source
(NRC Kurchatov Institute, Moscow, Russia) at the following parameters: the 2.5 GeV
storage ring with an average current of 100 mA and the monochromatic radiation with
a wavelength of 0.8 Å(the photon energy 15,498 eV) achieved using a Si(111) double-
crystal monochromator. All of the measurements were made at room temperature in the
Debye-Scherrer (transmission) geometry with an X-ray beam spot size of 400
µ
m [
44
]. The
exposure time was 5 min. The tilt angle of the 2D Rayonix SX165 detector was 29.5
◦
, with a
sample-to-detector distance of 150 mm. The polycrystalline reference LaB
6
NIST SRM 660a
sample was used for the calibration. Rietveld refinement of the XRD data was performed
with Jana2006 software [45].
X-ray absorption spectra (XAFS) were measured at the BM25A-SpLine beamline [
46
] of
the European Synchrotron Radiation Facility (ESRF) (Grenoble, France) and the Structural
Materials Science beamline [
47
] of the Kurchatov Synchrotron Radiation Source (Moscow,
Russia). EXAFS and XANES spectra were collected at the K-Zr (17,998 eV), L
3
-Pr (5964 eV),
and L
3
-Yb (8944 eV) edges in the transmission mode at room temperature. The EXAFS
spectra were analyzed using the VIPER [
48
] and IFEFFIT [
49
] program packages. The
FEFF-9 [50]
package was used to calculate the photoelectron backscattering amplitudes
and phases. Initial structural models to be fit were constructed based on crystallographic
results. The XANES spectra were fit using the XANDA program [48].
Raman spectra were collected using an inVia Qontor confocal Raman microscope (Ren-
ishaw plc, Wotton-Under-Edge, UK) (
λ
= 532 nm) in a wavenumber range of
50–2700 cm−1
with a spectral resolution of 1 cm−1.

Crystals 2023,13, 1405 4 of 23
The Fourier transform infrared (FT-IR) spectra were recorded with a Nicolet iS50
FT-IR spectrometer (Thermo Fisher Scientific Inc., Waltham, MA, USA) (
λ
= 1064 nm) in a
wavenumber range of 400–4000 cm−1with a spectral resolution of 4 cm−1.
Scanning electron microscopy (SEM) images were obtained on a Vega 3 scanning elec-
tron microscope (Tescan, Brno, Czech Republic). The electron beam energy was 30 keV, the
working distance was 15 mm, and the spot size was approx. 50 nm. Energy dispersive X-ray
spectroscopy (EDS) and elemental mapping images were obtained using an X-Act energy
dispersive detector (Oxford Instruments, Oxford, UK) with a spectral resolution of 125 eV
mounted on the SEM microscope. The characteristic X-ray radiation was automatically
processed with the AZtec program.
The porosity parameters of the samples were determined from nitrogen vapor adsorp-
tion isotherms at 77 K measured with an ASAP 2020-MP (Micromeritics, Norcross, GA,
USA) automatic high-vacuum setup in the relative pressure range from 0.001 to 0.98. The
samples were preliminarily evacuated to a residual vacuum of below 7–10 Torr at 400
◦
C
with a degassing time of 300 min.
A comparative quantification of the number of primary adsorption centers within the
samples was attained. Water adsorption isotherms were measured at 293 K with a vacuum
weighting unit with the McBain quartz spring balances (laboratory bench, Moscow, Russia)
with a sensitivity of 10 µg for a weight of up to 100 mg.
The determination of acid sites was controlled by the UV absorption spectra of the
catalytic systems exposed to pyridine. The concentrations were determined using a single-
beam scanning spectrophotometer Agilent Cary 60 UV-Vis (Agilent Technologies, Santa
Clara, CA, USA).
Catalytic tests for the cracking of propane were carried out over a temperature range
of 100–900
◦
C with a step of 50
◦
C on a bench-top unit with a flow reactor. The catalysis
was carried out at atmospheric pressure in a specially designed flow-through catalytic unit
with a U-shaped quartz reactor under stationary conditions with a feed rate of 55.8 mmol/s.
High purity propane (99.98 wt.%) was used as a feedstock. The reactor load was 0.05 g for
all catalysts. The reaction was monitored at each temperature point using a Kristall 5000 M
chromatograph equipped with a flame ionization detector and a thermal conductivity
detector (Chromatek, Yoshkar-Ola, Russia).
3. Results and Discussion
3.1. Characterization of Catalytic Materials
The ICP-AES results showed that the experimental values of the chemical composition
of the as-prepared precursors are close to the nominal stoichiometric ones (Table 1), which
indicates that the intended complete incorporation of lanthanide and zirconium cations
into the final solid samples has been successfully achieved.
Table 1.
Chemical composition of synthetic precursors (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-prec as determined by
alternative techniques.
Sample Stoichiometry ICP-AES EDS nH2O
x(TG at 200 ◦C)
0 Pr/Zr = 1/1 Pr/Zr = 1/1.11 Pr/Zr = 1/1.05 1.50
0.25 Pr/Yb = 3/1 Pr/Yb = 2.78/1 1.76
(Pr + Yb)/Zr = 1/1 (Pr + Yb)/Zr = 1/0.95
0.5 Pr/Yb = 1/1 Pr/Yb = 1.10/1 Pr/Yb = 0.98/1 2.29
(Pr + Yb)/Zr = 1/1 (Pr + Yb)/Zr = 1/0.95 (Pr + Yb)/Zr = 1/1.12
0.75 Pr/Yb = 1/3 Pr/Yb = 1/3.11 2.47
(Pr + Yb)/Zr = 1/1 (Pr + Yb)/Zr = 1/0.96
1 Yb/Zr = 1/1 Yb/Zr = 1.06/1 Yb/Zr = 1.16/1 1.85
SEM-EDS analysis was used to determine the particle morphology and draw element
distribution maps related to the precursor particles. SEM images of the precursor samples

Crystals 2023,13, 1405 5 of 23
have shown that precursor particles are irregularly shaped aggregates with sizes span-
ning from a few to 10
µ
m and are composed of smaller primary particles (see
Figure 1
and Figure S1 in Supplementary Materials). The Pr, Yb, Zr, and O element maps for
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
-prec samples demonstrate essentially homogeneous distribution for
each element (Figure 1). These results suggest that Pr, Yb, Zr, and O atoms are evenly
distributed and well dispersed on the surface of the as-prepared precursors. SEM-EDS tests
were also performed with the purpose of obtaining a semiquantitative analysis of Pr, Yb,
Zr, and O atomic concentrations. The calculated Pr/Yb and (Pr+Yb)/Zr atomic ratios are
also listed in Table 1. These atomic ratios are close to the ICP-AES results and expected
nominal stoichiometry. This solidly justifies the validity of the coprecipitation method for
the reliable preparation of complex oxides with well controlled chemical composition.
Pr
a
Yb
b
Zr
c
O
d
Overlap
e
Figure 1.
EDS map of Pr-L
α1
(
a
), Yb-L
α1
(
b
), Zr-L
α1
(
c
), O–K
α1
(
d
), and summary EDS/SEM image (
e
)
for the Pr0.5Yb0.5ZrOH-prec sample.
All of the precursors were found to be X-ray amorphous irrespective of exact chemical
composition. We used IR spectroscopy to probe the nature of functional groups present in
the as synthesized precursors (Figure 2a).
500 1000 1500 2800 3800
Pr
0.25
Yb
0.75
ZrOH-prec
Pr
0.5
Yb
0.5
ZrOH-prec
Pr
0.75
Yb
0.25
ZrOH-prec
YbZrOH-prec
Transmission (a.u.)
n
(cm
-1
)
d
(H-O-H)
n
3
(CO
2-
3
)
n
(H-OH)
PrZrOH-prec
a
500 1000 1500
n
(Zr-O)
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
(Pr
0.25
Yb
0.75
)
2
Zr
2
O
7
Pr
2
Zr
2
O
7
Transmission (a.u.)
n
(cm
-1
)
Yb
2
Zr
2
O
7
n
(
Ln
-O)
b
Figure 2.
FT–IR spectra of the precursors (
a
) and the (Pr
1−x
Yb
x
)
2
Zr
2
O
7
powders synthesized at
1400 ◦C (b).

Crystals 2023,13, 1405 6 of 23
As can be seen from Figure 2a, the FT-IR spectra of precursors reveal several distinct
absorption bands at about 465 (vs), 840 (s), 1045 (w), 1075 (w), 1395 (vs), 1472 (vs), 1626
(s), and 3370 cm
−1
(vs) (where vs—very strong, s—strong, and w—weak). Although it
is difficult to assign each band to a specific compound, the very strong band at 465 cm
−1
may be associated with the O–Ln–O bending modes [
14
] or Ln–O vibration bands [
51
]. The
band at about 840 cm
−1
is identified as the out-of-plane bending vibration of carbonate
species. The band with components at about 1045 and 1075 cm
−1
corresponds to the
ν2
symmetric stretching vibration of carbonate anions. The very strong doublet at 1395 and
1472 cm
−1
corresponds to the
ν3
symmetric and asymmetric stretching vibrations, respec-
tively. The observed peak-to-peak separation
∆ν3
(
νas −νs
) is estimated to be about 80 cm
−1
,
which indicates the presence of metal-coordinated unidentate carbonate species [
52
]. The
absorption band observed near 1626 cm
−1
and a broad strong band at ca.
∼
3325 cm
−1
correspond to the bending mode (
ν2
) of H–O–H vibrations and longitudinal stretching
vibrations of the O–H groups (ν1and ν3) of the surface-adsorbed water molecules, respec-
tively [
51
,
53
]. Moreover, a few weak bands at
∼
1045–1075 cm
−1
may be also assigned
to the bending vibrations of the M–O–H dringing hydroxyl group [
53
,
54
]. Therefore, the
as-prepared precursors can be described as X-ray amorphous mixed lanthanide–zirconium
hydrated hydroxycarbonates (Pr
1−x
Yb
x
)Zr(OH)
7−2y
(CO
3
)
y·n
H
2
O. According to previous
reports [54]
, the mean content of carbonate species in precursors of Gd titanates prepared
by both sol-gel and coprecipitation methods was
∼
12–15 wt.%. Based on the close chemical
relation of these precursors and similar synthesis conditions, we formulate synthesized
lanthanide–zirconium hydrated hydroxycarbonates as (Pr1−xYbx)Zr(OH)5(CO3)·nH2O.
A self-consistent combined analysis of STA (Figure S2) and FT-IR (Figure S3) data
enabled us to identify a few characteristic stages of transformations occurring with the
precursors upon annealing. These include the removal of crystallization water (
n
H
2
O)
(up to 200–250
◦
C-see region I in Figure S2 and Table 1); the removal of hydroxyls; the
partial decomposition of carbonate anions; crystallization (up to 600–800
◦
C-see regions
II and III in Figure S2); the complete removal of residual carbonates; and the onset of
structural phase transitions (
≥
800
◦
C-see region IV in Figure S2). It is of note that the
general sequence of these thermally activated transformation stages corresponds well to
recently published experimental results on the synthesis of other types of complex oxides
via coprecipitation [43,51,55,56].
Figure 3a depicts X-ray diffraction patterns of polycrystalline powders calcined at
1400
◦
C for 3 h. The phase composition and essential crystallographic parameters of the
samples are compiled in Table 2.
Figure 3.
XRD patterns (
a
) and Raman spectra (
b
) of the (Pr
1−x
Yb
x
)
2
Zr
2
O
7
powders prepared by the
calcination of precursors at 1400
◦
C/3 h: (1)
x=
0; (2)
x=
0.25; (3)
x=
0.5; (4)
x=
0.75; and
(5) x=1
.
The bars in (a) correspond to the reflexes of the pyrochlore (bottom) and δ-phase (top) structures.

Crystals 2023,13, 1405 7 of 23
Table 2. The results of XRD Rietveld refinement for (Pr1−xYbx)2Zr2O7-1400 powders.
Sample Structure Phase Lattice Unit Cell x48fL, nm e, % RpRwp SG oF
x(sp. gr.) % Parameters, Å Vol., Å3%
0 Cubic 100 a=10.7145(3) 1230.03(5) 0.3315 300(15) 0.02(1) 9.70 12.92 3.85
(Fd ¯
3m)
0.25 Cubic 100 a=10.6338(3) 1202.45(5) 0.3381 245(12) 0.28(3) 4.89 6.54 2.21
(Fd ¯
3m)
0.5 Cubic 73 a=10.6006(3) 1191.22(5) 0.3379 >1000 1.24(5) 6.70 8.49 1.15
(Fd ¯
3m)
Cubic 27 a=5.2431(3) 114.13(5) 325(30) 0.60(4)
(Fm ¯
3m)
0.75 Cubic 100 a=5.2088(3) 141.32(5) 235(12) 0.12(3) 7.52 10.18 1.47
(Fm ¯
3m)
1 Rhomb. 100 a=9.6641(9) 724.18(12) 104(5) 0.27(7) 6.03 8.92 5.30
(R¯
3) c=8.9528(9)
x48f
—48
f
oxygen positional parameter (only for pyrochlore structure); L—the crystallite size;
e
—the
microstrain value; and SGoF —the goodness-of-fit.
As can be seen from Figure 3a and Tables 2and S1, the type of the resultant crystal
structure of (Pr
1−x
Yb
x
)
2
Zr
2
O
7
zirconates strongly depends on the composition as regards
the lanthanide cations (Ln
3+
= Pr
3+
+ Yb
3+
). This ratio defines the effective rare-earth
cation radius
rLn3+
and further the cation radii ratio
γ=rLn3+/rZr4+
. In the cases of
Pr
2
Zr
2
O
7
(
γ
= 1.564) (JCPDS 20-1362, sp. gr. Fd
¯
3
m) and (Pr
0.75
Yb
0.25
)
2
Zr
2
O
7
(
γ
= 1.515),
the samples were characterized by the fcc pyrochlore-type structure. The intermediate
sample (Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
(
γ
= 1.467) was a mixture of the pyrochlore and fluorite phases,
whereas (Pr
0.25
Yb
0.75
)
2
Zr
2
O
7
(
γ
= 1.417) remains the fluorite structure up to 1400
◦
C. In
the case of Yb
2
Zr
2
O
7
(
γ
= 1.368), the rhombohedral
δ
-phase (JCPDS 77-0739, sp. gr. R
¯
3
) is
formed (Figure 3and Tables 2and S1). These results correspond well to reported literature
data [
27
–
29
]. As is clearly shown in Tables 2and S1, an increase in the content of Yb
3+
(0.985 Å) at the expenses of Pr
3+
(1.126 Å) gives rise to a decrease in the lattice parameters
and unit cell volumes of the (Pr1−xYbx)2Zr2O7complex oxides according to Vegard’s law.
Fractional atomic coordinates, isotropic displacement parameters, and fractions of
Ln
Zr
+ Zr
Ln
antisite pairs for the (Pr
1−x
Yb
x
)
2
Zr
2
O
7
samples calcined at 1400
◦
C are given
in Table S2. For the samples (Pr
1−x
Yb
x
)
2
Zr
2
O
7
(
x
= 0.25 and 0.5) containing Pr
3+
and
Yb
3+
cations simultaneously and dominated by the pyrochlore phase, it is Zr
4+
cations
that substitute Pr
3+
ions in the 16d site. Meanwhile, the Zr
4+
cations in the 16c site are
substituted only by Yb
3+
cations that have a smaller ion radius than Pr
3+
. Note that the
total concentration of oxygen vacancies in (Pr
1−x
Yb
x
)
2
Zr
2
O
7
is almost the same for both
pyrochlore and fluorite structures. This parameter is equal to approximately one vacancy
per seven filled oxygen positions. The change in the crystal structure changes only the
spatial distribution of oxygen vacancies: from the precisely specified position of the oxygen
vacancy 8a (1/8, 1/8, 1/8) in pyrochlore (56 occupied oxygen positions out of 64 possible
in the unit cell) to equally probable occupation of oxygen position 8c (1/4, 1/4, 1/4) with
coefficient 7/8 in fluorite.
Vibrational spectroscopy was used to study the oxygen-anion sublattices in the syn-
thesized samples. Figure 3b shows Raman spectra of the (Pr
1−x
Yb
x
)
2
Zr
2
O
7
polycrystalline
powders calcined at 1400 ◦C.
According to Figure 3b, the Raman spectrum of Pr
2
Zr
2
O
7
-1400 reveals the following
set of modes: 295 cm
−1
(F
2g
), 310 cm
−1
(E
g
), 370 cm
−1
(F
2g
), 490 cm
−1
(A
1g
), 500 cm
−1
(F
2g
), and 755 cm
−1
(F
2g
), evidencing the pyrochlore structure. These results correspond
well to recently published literature data [
28
,
57
,
58
], which state that Ln zirconates with the
pyrochlore structure (sp. gr Fd
¯
3
m) should demonstrate six active modes in Raman spectra.
More specifically, five active modes (A
1g
, E
g
, and 3F
2g
) are due to vibrations of the oxygen
O(1) atom located in the crystallographic site 48
f
, and the remaining sixth active mode F
2g
is due to vibrations of the oxygen O(2) atom located in the crystallographic position 8b. The

Crystals 2023,13, 1405 8 of 23
Raman spectrum of (Pr
0.75
Yb
0.25
)
2
Zr
2
O
7
-1400 is characterized by broadened pyrochlore
phase-related modes as well as by an increased intensity of a mode peaked at 605 cm
−1
(F
2g
attributed to the fluorite-type structure). This indicates the onset of pyrochlore phase
disordering, giving rise to the fluorite phase emergence. A further Yb
3+
cation substitution
for Pr
3+
results in a complete disappearance of the disordered pyrochlore phase with the
formation of somewhat defect fluorite-type structure in (Pr
0.25
Yb
0.75
)
2
Zr
2
O
7
-1400. The
Raman spectrum of Yb
2
Zr
2
O
7
-1400 is consistent with the dominant presence of the
δ
-phase
that has been descried by us earlier [
28
]. The Raman trends are in full accord with the
aforementioned XRD conclusions (Table 2).
As it has been mentioned earlier (see Figure S3), an increase in the calcination tem-
perature to 1400
◦
C strongly modifies the FT-IR spectra of (Pr
1−x
Yb
x
)
2
Zr
2
O
7
due to a
variety of effects related to the occurrence of dehydration, the thermal decomposition of
carbonate anions, crystallization, and phase transition processes. Figure 2b demonstrates
FT-IR spectra of (Pr1−xYbx)2Zr2O7powders prepared at 1400 ◦C.
In the FT-IR spectra of (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 (
x=
0; 0.25) samples with the py-
rochlore structure (see Figure 2b and Table 2), the vibration band at 450–460 cm
−1
is dis-
tinctly split into two components: at 420–430 cm
−1
(Ln–O stretching vibration in the Ln–O
8
polyhedron [
59
] or the O–Ln–O bending mode [
14
,
60
]) and at 520–530 cm
−1
(Zr–O stretch-
ing vibrations in the Zr–O
6
unit [
14
,
59
,
60
]). For the similar spectrum of (Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
-
1400 encompassing both the pyrochlore (73%) and fluorite (27%) phases, this splitting is less
pronounced. The respective components arise at 448 cm
−1
and 507 cm
−1
. Meanwhile, the
analogous vibration band shows up completely unsplit at 450–460 cm
−1
in the spectrum of
(Pr0.25Yb0.75)2Zr2O7-1400, which is strictly single-phase defect fluorite (Figure 2b).
More detailed information on the local atomic structure around Zr
4+
, Yb
3+
, and Pr
3+
cations was retrieved using locally sensitive XANES (X-ray absorption near-edge structure)
and EXAFS (extended X-ray absorption fine structure) X-ray absorption spectroscopy.
XANES is especially suitable to probe changes in the electronic configuration of the central
atom and symmetry of its nearest atomic surrounding.
Figure 4shows XANES spectra measured at K-Zr, L
3
-Yb, and L
3
-Pr edges for the series
of materials under study (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400. The Zr K-edge XANES spectra reveal two
well-resolved near-edge peaks for all samples annealed at 1400
◦
C (see Figure 4a). However,
at a closer inspection it becomes apparent that the specific values of the peak intensity
ratio and peak splitting vary somewhat from one sample to another. The maximum
peak intensity ratio (I
B
/I
A∼
1.16) and peak splitting (
∆
E
∼
8.5 eV) are observed for the
two samples (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 (
x=
0; 0.25) that are dominated by the pyrochlore
structure (see Figure 4b and Table 2). This strongly implies that the peak intensity ratio
(I
B
/I
A
) and peak splitting (
∆
E) decrease gradually with an increase in the Yb
3+
content, i.e.,
upon a structural transition from pyrochlore (
x=
0; 0.25) to defect fluorite (
x=
0.5; 0.75) or
δ–phase (x=1.0). Similar results were reported by other authors [61,62].
The exact position and shape of the main X-ray absorption peak, also referred to as the
white line, in the Pr and Yb L
3
-XANES spectra of (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 samples, along
with the small width of the white line (FWHM
∼
6–7 eV), allow us to draw a conclusion
regarding the occurrence of only trivalent Ln
3+
cations in these powders (
Figure 4c,d
) [
63
].
A closer inspection of the post-white line regions in the Pr and Yb L
3
-XANES spectra reveals
a characteristic X-ray absorption minimum with a split two-component structure, which
can be regarded as a fingerprint of the pyrochlore structure [
64
]. This spectral feature is
most pronounced in the Pr L
3
-XANES spectra (see Figure 4c,d). The splitting becomes more
smeared upon a structural phase transition “pyrochlore
→
fluorite” accompanying Yb
3+
substitution for Pr3+.
The pseudo-radial distribution curves represented by Fourier transform (FT) moduli
of EXAFS spectra measured at K-Zr, L
3
-Yb, and L
3
-Pr edges for the (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400
complex oxides are given in Figure 5. In the case of Zr K-edge spectra, all FT moduli of
EXAFS spectra reveal an intense peak
∼
1.7 Å (which is an interatomic distance uncorrected
for the photoelectron backscattering phase shift) attributed to the first Zr–O coordination

Crystals 2023,13, 1405 9 of 23
sphere. At longer distances, somewhat weaker peaks are observed at
∼
3.0–3.5 Å, corre-
sponding to coordination shells encompassing metal cations. Real interatomic distances,
coordination numbers, and Debye–Waller factors (DWF) extracted from EXAFS data quan-
titative analysis are listed in Table 3. One can see from Table 3that the obtained interatomic
distances are in good agreement with the results of XRD refinement.
17,960 17,980 18,000 18,020 18,040 18,060 18,080 18,100
0.2
0.4
0.6
0.8
1.0
1.2
1.4
m
, a.u.
E, eV
Yb
2
Zr
2
O
7
(Pr
0.25
Yb
0.75
)
2
Zr
2
O
7
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7
Pr
2
Zr
2
O
7
K
-Zr
a
18020 18030
B
A
0.0 0.2 0.4 0.6 0.8 1.0
1.04
1.06
1.08
1.10
1.12
1.14
1.16
1.18
D
E, eV
I(B)/I(A)
x
7.0
7.5
8.0
8.5
b
Peak intensity ratio (I(B)/I(A))
The interpeak split (
D
E)
T=1400
o
C
8920 8940 8960 8980
0.0
0.5
1.0
1.5
2.0
2.5
3.0
m
, a.u.
E, eV
Yb
2
Zr
2
O
7
(Pr
0.25
Yb
0.75
)
2
Zr
2
O
7
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7
L
3
-Yb
c
8960 8970 8980
5950 5960 5970 5980 5990 6000
0.0
0.5
1.0
1.5
2.0
2.5
Pr
2
Zr
2
O
7
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
m
, a.u.
E, eV
L
3
-Pr
d
5980 5990
Figure 4.
XANES spectra measured at K-Zr (
a
), L
3
-Yb (
c
), and L
3
-Pr (
d
) edges for the series of
(Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 complex oxides; (
b
) the interpeak split (
∆
E) and peak intensity ratio (I
B
/I
A
)
in Zr K-edge XANES spectra as a function of Yb3+content (x).
The long-distance FT peak of the Zr-Ln coordination shell grows weaker with an
increase in the Yb
3+
content. This correlates with gradually increasing local disorder in the
atomic environment of the Zr
4+
cations in the (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 structure induced by
the “pyrochlore →defect fluorite →δ-phase” structural transitions.
One can see that the Ln L
3
-edge EXAFS spectra are also sensitive to the appearance
and further evolution of the pyrochlore phase enabled by an ongoing replacement of the
lanthanide cations from Pr to Yb (Figure 5b,c). The FT moduli of Pr L
3
-edge EXAFS spectra
demonstrate an evident splitting of the first Pr–O coordination shell into two components
corresponding to 2 shorter Pr–O(2) and 6 longer Pr–O(1) bonds for those (Pr
1−x
Yb
x
)
2
Zr
2
O
7
materials that possess the pyrochlore structure (
x
= 0, 0.25 and 0.5). The peak splitting in FT
moduli of EXAFS spectra at Yb L
3
-edge is weaker. Similar effects of the Ln–O coordination
shell splitting were observed by us earlier for some Ln titanates [
54
,
64
], zirconates [
64
], and
hafnates [43].
If we compare the local disordering trends observed in Pr and Yb L
3
-edge XANES and
EXAFS spectra (Figures 4and 5) and the best-fit values of antisite defect concentrations
calculated from powder diffraction (see Table S1), one can assume that the emerging
fluorite phase should be enriched with Yb while Pr remains preferably in the pyrochlore
phase. This means that the cation sublattice disordering upon the “pyrochlore
→
fluorite”
transformation is initiated by a rearrangement involving the Yb sites.

Crystals 2023,13, 1405 10 of 23
0 1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
a
Pr
2
Zr
2
O
7
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
(Pr
0.25
Yb
0.75
)
2
Zr
2
O
7
Yb
2
Zr
2
O
7
K
-Zr
1400
o
C
|FT(
c
(k
2
)k)|, Å
-3
r, Å
012345
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
b
|FT(
c
(k
2
)k)|, Å
-3
r, Å
Yb
2
Zr
2
O
7
(Pr
0.25
Yb
0.75
)
2
Zr
2
O
7
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7
L
3
-Yb
1400
o
C
012345
0.0
0.1
0.2
0.3
0.4
0.5
c
Pr
2
Zr
2
O
7
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
|FT(
c
(k
2
)k)|, Å
-3
r, Å
L
3
-Pr
1400 °C
Figure 5.
FT moduli of EXAFS spectra measured at K-Zr (
a
), L
3
-Yb (
b
), and L
3
-Pr (
c
) edges for the
series of (Pr1−xYbx)2Zr2O7-1400 complex oxides.
Table 3.
EXAFS fitting results for the Zr–O, Yb–O, and Pr–O shells of (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400
powders.
K-Zr Edge
Sample R(Zr–O), Å σ2(Zr–O), Å2N (sp. gr.) Rdis , % RXRD , Å
Pr2Zr2O72.12(1) 0.007(1) 6 (Fd¯
3m) 16 2.09(1)
(Pr0.75Yb0.25 )2Zr2O72.11(1) 0.006(1) 6 (Fd¯
3m) 15 2.10(1)
(Pr0.5Yb0.5 )2Zr2O72.13(1) 0.006(1) 6.4 (Fd¯
3m13 2.07(1)
+Fm¯
3m) 2.27(1)
(Pr0.25Yb0.75 )2Zr2O72.15(1) 0.010(1) 7 (Fm¯
3m) 17 2.26(1)
Yb2Zr2O72.24(1) 0.008(1) 6 (R¯
3) 15 2.13(1)
L3-Yb edge
Sample R(Yb–O), Å σ2(Yb–O), Å2N (sp. gr.) Rdis , % RX R D, Å
(Pr0.75Yb0.25 )2Zr2O72.14(1) 0.008(1) 2 (Fd¯
3m) 9 2.05(1)
2.31(1) 0.004(1) 6 2.31(1)
(Pr0.5Yb0.5 )2Zr2O72.23(1) 0.012(1) 6.2 (Fd¯
3m12 2.07(1)
+Fm¯
3m) 2.27(1)
(Pr0.25Yb0.75 )2Zr2O72.25(1) 0.010(1) 7 (Fm¯
3m) 16 2.26(1)
Yb2Zr2O72.23(1) 0.013(1) 6 (R¯
3) 9 2.28(2)
L3-Pr edge
Sample R(Pr–O), Å σ2(Pr–O), Å2N (sp. gr.) Rdis , % RX RD , Å
Pr2Zr2O72.28(2) 0.015(2) 2 (Fd¯
3m) 15 2.32(1)
2.53(2) 0.022(2) 6 2.61(1)
(Pr0.75Yb0.25 )2Zr2O72.16(2) 0.015(2) 2 (Fd¯
3m) 16 2.30(1)
2.44(2) 0.019(2) 6 2.55(1)
(Pr0.5Yb0.5 )2Zr2O72.39(2) 0.011(2) 2 (Fd¯
3m) 18 2.29(1)
2.56(2) 0.020(2) 6 2.58(1)
(Pr0.25Yb0.75 )2Zr2O7∗2.26(1)
Values given in parentheses correspond to the estimated standard deviations (esd); N is the fixed coordination
number; R is the interatomic distance from EXAFS;
σ2
is the Debye–Waller factor (DWF); R
dis
is the discrepancy
index; RXR D is the interatomic distance from XRD; and ∗—only XRD data available.

Crystals 2023,13, 1405 11 of 23
3.2. Catalytic Properties
According to the literature data [
65
,
66
], M (metal)-O (oxygen) bond lengths, the pres-
ence of oxygen vacancies, and the active metal type are the three main factors determining
catalytic properties of complex oxide compounds. As it was mentioned before in Section 3.1,
the progressive Yb
3+
substitution for Pr
3+
in (Pr
1−x
Yb
x
)
2
Zr
2
O
7
(0
≤x≤
1) polycrystalline
materials induces prominent changes both in crystallographic and local-structure parame-
ters. This means that all three aforementioned factors are involved. Therefore, it might be
anticipated that all (Pr
1−x
Yb
x
)
2
Zr
2
O
7
polycrystalline materials would manifest different
catalytic activities.
Based on earlier studies of catalytic propane dehydration, active sites in (Pr
1−x
Yb
x
)
2
Zr
2
O
7
were envisaged as a couple of coordinatively unsaturated cations (Pr
3+
/Yb
3+
and Zr
4+
)
bound to an adjacent oxygen vacancy and lattice oxygen. Unfortunately, such a sug-
gestion was not supported by structural studies of the catalytic systems, prepared at
1000
◦
C [
26
]. This temperature is not high enough for phase transitions to take place in
Ln zirconates [
27
,
28
], and the studied samples obviously had a disordered defect–fluorite
structure.
The canonical mechanism of alkane cracking implies the detachment of a hydrogen
atom from the alkane-derived carbocation, giving rise to another carbocation, which is
further decomposed via the
β
-scission (i.e., the scission of the C–C bond in the
β
-position
with respect to the carbon atom bearing the positive charge in the carbocation). In this
process, carbocations act as chain carriers. Typically, carbocations formed from components
of the crude feedstock are prominently stable. In particular, carbocations can be formed
upon the catalyst-assisted protonation of alkenes. Alkenes can be present in the feedstock
as admixtures. Alternatively, alkenes can be generated from alkanes via the free radical
cracking (provided that the reaction temperature is sufficiently high) or via the hydrogen
detachment by Lewis acid sites of the catalyst (dehydrogenation) [23,67].
Herewith, we elucidate the catalytic properties of (Pr
1−x
Yb
x
)
2
Zr
2
O
7
polycrystalline
materials prepared by the calcination at 1400 ◦C.
According to previous reports, the thermally activated propane cracking starts above
500
◦
C. The apparent propane conversion is as low as 2% at 600
◦
C, but it increases to 20%
at 700
◦
C. The major reaction products were identified as methane and ethane [
68
]. In the
presence of (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 catalysts, the propane conversion increases from 65%
to 94% at 700 ◦C on going from Pr2Zr2O7to Yb2Zr2O7(Figure 6).
400 500 600 700 800 900
0
20
40
60
80
100
a
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
Conversion of propane (%)
Temperature (°C)
x=0
x=0.25
x=0.5
x=0.75
x=1
0.00 0.25 0.50 0.75 1.00
0
10
20
30
40
50
60
70
80
90
100
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
Conversion of propane (%)
x
b
700 °C
Figure 6.
Temperature dependence of conversion of propane for (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 catalysts
with different values of x(a); propane conversion at the optimum cracking temperature (b).
As it can be seen in Figure 6a, the propane conversion reaches the values of 100%
at 850
◦
C for all catalytic systems under study. If we compare these results with earlier
studies of thermally activated cracking [
68
], the same level of conversion is achieved at
systematically lower temperatures. Furthermore, the selectivity to ethylene and propylene
is also altered (Figure 7).

Crystals 2023,13, 1405 12 of 23
Opposite trends in ethylene and propylene selectivity are observed on going from
Pr
2
Zr
2
O
7
to Yb
2
Zr
2
O
7
(Figure 7a–d). The decrease in ethylene selectivity along the series
Pr
2
Zr
2
O
7>
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7>
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7>
(Pr
0.25
Yb
0.75
)
2
Zr
2
O
7>
Yb
2
Zr
2
O
7
strongly implies that the pyrochlore-type structure primarily catalyzes the propane de-
composition to methane and ethylene (Figure 7a,b). Meanwhile, the increase in the
propylene yield along the series Pr
2
Zr
2
O
7<
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7<
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7
<
(Pr
0.25
Yb
0.75
)
2
Zr
2
O
7<
Yb
2
Zr
2
O
7
suggests that propane dehydrogenation predominantly
proceeds over defect fluorite and
δ
-phase (Figure 7c,d). Therefore, distinctly different types
of catalytically active sites towards the propane cracking emerge in the complex oxide
systems under study, which are characterized by specific features of the crystal and local
atomic structures.
To gain more insight into the nature of catalytic activity of the systems under study,
the electron acceptor properties of the catalysts’ surface were evaluated. The mean number
(N) and strength (E
0
) of Lewis acid sites were calculated based on kinetics pyridine accu-
mulation (Table 4). The bimodal character of pyridine adsorption curves is of note. This
evidently means that there are several distinct adsorption sites. We tentatively assign them
to Zr–O, Pr–O, and Yb–O active sites. The number of electron acceptor sites increases along
the series Pr
2
Zr
2
O
7<
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7<
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7<
(Pr
0.25
Yb
0.75
)
2
Zr
2
O
7<
Yb2Zr2O7(see Table 4).
400 500 600 700 800 900
0
20
40
60
80
100
a
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
x=0
x=0.25
x=0.5
x=0.75
x=1
Selectivity to C
2
H
4
(%)
Temperature (°C)
0.00 0.25 0.50 0.75 1.00
0
20
40
60
700 °C
b
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
Selectivity to C
2
H
4
(%)
x
400 500 600 700 800 900
0
20
40
60
80
100
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
Selectivity to C
3
H
6
(%)
Temperature (°C)
x=0
x=0.25
x=0.5
x=0.75
x=1
c
0.00 0.25 0.50 0.75 1.00
0
10
20
30
40
50
d
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
Selectivity to C
3
H
6
(%)
x
700 °C
Figure 7.
Selectivity to ethylene (
a
,
b
) and to propylene (
c
,
d
) for complex oxide catalysts
(Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 with different values of
x
; (
b
,
d
)-selectivity at the optimum cracking temperature.

Crystals 2023,13, 1405 13 of 23
Table 4. Surface morphology characteristics of (Pr1−xYbx)2Zr2O7-1400 catalysts.
Catalyst PAC, N, µmol/g WC3H8E0, kJ/mol SBE T , m2/g r, nm
mmol/g cm3/g
Pr2Zr2O763.3 288 0.004 27.2 11 11.7
(Pr0.75Yb0.25)2Zr2O755.8 298 0.007 31.1 7 10.0
(Pr0.5Yb0.5)2Zr2O748.5 304 0.008 33.1 6 9.6
(Pr0.25Yb0.75)2Zr2O744.1 309 0.008 35.7 5 9.0
Yb2Zr2O741.3 311 0.009 37.7 3 8.3
PAC is the number of primary adsorption centers calculated from comparative isotherm of water vapor adsorption;
N is the total number of electron acceptor centers (Lewis acid sites) calculated from pyridine adsorption curves;
W
C3H8
is the volume of adsorbed propane calculated according to the Barrett, Joyner, and Halenda (BJH) method;
E
0
is the characteristic adsorption energy calculated according to the Dubinin-Astakhov method; S
BET
is the
BET specific surface area; and
r
is the mean pore size in the capillary condensation mode determined by the
BJH method.
Primary adsorption centers (or PAC) were quantified in order to establish the dominant
mechanism of propane catalytic conversion. The number of primary adsorption centers
and total number of oxygen-containing centers were determined using the adsorption of
water vapor from the gaseous phase (Table 4). The latter value increases along the series
Pr
2
Zr
2
O
7<
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7<
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7<
(Pr
0.25
Yb
0.75
)
2
Zr
2
O
7<
Yb
2
Zr
2
O
7
.
The textural properties of the (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 catalysts were analyzed using
the N
2
adsorption–desorption isotherms with the explicit account for the pore size distribu-
tion. All of the materials under study were characterized by a non-porous surface with a
moderately low concentration of mesopores. The mean pore size decreases along the series
Pr
2
Zr
2
O
7<
(Pr
0.75
Yb
0.25
)
2
Zr
2
O
7<
(Pr
0.5
Yb
0.5
)
2
Zr
2
O
7<
(Pr
0.25
Yb
0.75
)
2
Zr
2
O
7<
Yb
2
Zr
2
O
7
(Table 4).
The (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 catalysts exhibiting high activity and selectivity towards
propane cracking possess active sites constructed of pairs of zirconium and lanthanoid
cations bound to oxygen vacancies and lattice oxide anions. These sites are capable of
efficient C–H bond activation, which is actually the rate-limiting step in light alkane
dehydrogenation [25].
Typically, the specific surface area strongly affects the activity of heterogeneous cata-
lysts. In our case, the total propane conversion demonstrates a prominent tend to increase
with a decrease in the specific surface area of the catalysts from 11 m
2
/g down to 3 m
2
/g
on going from Pr
2
Zr
2
O
7
to Yb
2
Zr
2
O
7
(Figure 8a). This clearly implies that the available
surface exerts the minimum influence on the apparent activity of the catalysts towards the
propane dehydrogenation. Such behavior is very unusual and thus should be elucidated in
more detail. We assert that the total and specific activities pass through the maxima with a
very small degree of filling. Each real surface of these catalytic systems is characterized by
a blocky, mosaic structure, as a result of which isolated migration regions may appear on
the surface, separated from each other by energy or geometric barriers. They can be similar
to real cells, for example, faces of elementary crystals adjacent to adsorption centers with
an increased adsorption potential characteristic of an energetically inhomogeneous surface.
Cracks and other surface disturbances, crystal defects, and stoichiometric composition
disorders can also cause migration areas. This leads to the appearance of random catalytic
centers. If there were a large number of them, we would not be able to unambiguously
characterize the mechanism of the processes taking place. For the formation of active
centers in the form of a cluster of n-atoms, it does not matter what the origin and nature of
these inhomogeneities are. It is important that when forming a layer of catalytic centers,
the surface (which is very insignificant) allows for the free migration of particles only in
limited areas. These surface disturbances are an obstacle to free movement through the
volume of the catalyst, forming potential pits where additional catalytic centers should
accumulate. In our case, their number is very small. The catalyst surface is a collection of
closed migration regions. Experimental data on the sintering of catalysts were a confirma-
tion of these ideas. The rate of deactivation of catalysts obeys the first-order equation for

Crystals 2023,13, 1405 14 of 23
the concentration of additional centers on the surface. Consequently, the additional centers
on the surface do not depend on each other and do not interact with each other. The size
of the migration areas significantly exceeds the radius of action of molecular forces (by
tens of times). Consequently, the formation of additional centers of catalytic cents is an
independent event. The distribution of these cents over the surface of the catalyst obeys the
law of chance and tends to a minimum. Thus, we can make an unambiguous conclusion
that the main catalytic centers are precisely the Lewis acid centers.
2 4 6 8 10 12
50
60
70
80
90
100
a
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
x=0
x=0.25
x=0.5
x=0.75
x=1
Conversion of propane (%)
Specific surface (m
2
/g)
280 290 300 310
30
40
50
60
70
80
90
100
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
x=0
x=0.25
x=0.5
x=0.75
x=1
Conversion of propane (%)
Total number of Lewis acid sites (
m
mol/g)
b
Figure 8.
Apparent conversion of propane as a function of (
a
) specific surface area of the catalysts
and (b) total number of Lewis acid sites.
Meanwhile, an increase in the number of Lewis acid sites with increasing Yb content
in (Pr
1−x
Yb
x
)
2
Zr
2
O
7
gives rise to a virtually linear increase in the propane conversion.
Therefore, it is the number of Lewis acid sites that plays a decisive role in determining the
activity of the catalytic systems under study (Figure 8b).
According to Jeon et al. [
69
], for the non-oxidative dehydrogenation of propane on
metal oxides the propane molecules are adsorbed on M
x+
surface sites. Then, hydrogen
from the adsorbed propane molecule is abstracted by surface oxygen, forming a hydroxyl
group and a propyl species.
Proceeding to the analysis of product ratio, we should note that the Zr
4+
transition
metal cations are capable of propane activation due to the completely filled 3
d10
orbitals
and unoccupied 4th electronic shell. The metal ion’s electron affinity becomes maximized
when the 4th electronic shell is completely empty. In addition to Zr
4+
, the complex oxides
(Pr
1−x
Yb
x
)
2
Zr
2
O
7
contain rare-earth cations with different configurations of 4
f
electrons.
The empty shells are prone to electron capture from adsorbates, which can serve as a
mechanism of adsorption activation over this metal ion active site. It is important that the
dominant phase switches from pyrochlore through defect fluorite to
δ
-phase on going from
Pr
2
Zr
2
O
7
to Yb
2
Zr
2
O
7
, which is accompanied by specific changes in the crystal and local
atomic structures of the materials (vide supra, Section 3.1). In particular, pyrochlore phases
are abundant with oxygen vacancies. Probably, these vacancies can also act as acceptors of
the electron density of adsorbate molecules.
The established correlation between catalytic behavior and structural features of the
(Pr1−xYbx)2Zr2O7complex oxides can be rationalized in the following way.
Carbon atoms in the propane molecule bear an excessive electron density due to the
induction effect. The C
3
H
8
molecules become adsorbed at the gas–solid interface on the
Lewis-cationic (Pr
3+
/Yb
3+
) and Zr
4+
sites of the catalysts. An increase in the fraction
of Yb
3+
cations (characterized by a higher ion potential (Z/r) with respect to Pr
3+
in
(Pr
1−x
Yb
x
)
2
Zr
2
O
7
increases both the number (N) and strength (E
0
) of Lewis acid surface
sites, which promotes propane adsorption (W
C3H8
) (see Table 4). This ultimately results in
enhanced propane conversion, i.e., catalytic activity (see Figures 6and 8b).
The selectivity to C
2
H
4
decreases from 60% to 28% on shifting from Pr
2
Zr
2
O
7
to
Yb
2
Zr
2
O
7
(see Figure 7a,b), i.e., the tendency of propane decomposition via the C–C bond

Crystals 2023,13, 1405 15 of 23
scission is weakened. A tentative mechanism of propane decomposition yielding ethylene
is shown in Figure 9. Such a scheme is well supported by the structural parameters
of Pr
2
Zr
2
O
7
. The size factor (metal–oxygen bond length R(Pr–O(1)) = 2.53(2) Å), the
abundance of oxygen vacancies (8
a
sites in the pyrochlore structure), and the availability of
vacant 4
f
orbitals in Pr
3+
(4
f2
) together promote the horizontal orientation of adsorbed
propane molecules, in which the distance between terminal carbon atoms is 2.51 Å. The
decomposition of propane occurs via the C–C bond scission over Pr
2
Zr
2
O
7
. Regarding
Yb
2
Zr
2
O
7
, the metal–oxygen bonds (Pr/Yb)–O become shorter, which gives rise to a switch
of the dominant propane cracking mechanism to the C-H on scission, i.e., dehydrogenation
(Figure 10).
According to Figure 7c,d discussed earlier, the selectivity to C
3
H
6
increases from
20% to 47% on going from Pr2Zr2O7to Yb2Zr2O7. This means that the C–H bond scission
yielding propylene tends to dominate. A tentative mechanism of the dehydrogenation in
that case is shown in Figure 10. The propane dehydrogenation predominance is probably
due to a specific orientation of the adsorbed propane molecule on active sites of the
(Pr
1−x
Yb
x
)
2
Zr
2
O
7
complex oxide catalysts. For instance, the metal–oxygen bond lengths are
R(Zr–O) = 2.15(1) Å, R(Pr–O) = 2.26(1) Åand R(Yb–O) = 2.25(1) Å in the (Pr
0.25
Yb
0.75
)
2
Zr
2
O
7
-
1400 sample characterized by the defect fluorite structure. Moreover, analogous values are
R(Zr–O) = 2.24(1) Åand R(Yb–O) = 2.23(1) Å for Yb
2
Zr
2
O
7
, which features the
δ
-phase (see
Table 3). In both the above cases, the size factor prevents the horizontal adsorption of the
propane molecule. Instead, the propane molecule is obliged to adsorb vertically. Such an
adsorbate orientation on Zr–O and (Pr/Yb)–O active sites promotes efficient C–H bond
scission in C
3
H
8
to afford M–C
3
H
7
and O–H surface complexes. Ultimately, gaseous C
3
H
6
and H
2
are released as a result of the
β
-hydrogen elimination from M–C
3
H
7
(Figure 10).
It should be noted that the proposed propane dehydrogenation mechanism is in good
agreement with that described in the literature [69].
Figure 9. The mechanism of propane decomposition yielding ethylene.

Crystals 2023,13, 1405 16 of 23
Figure 10. The mechanism of propane decomposition yielding propylene.
Therefore, all of the surface atoms of the catalyst could similarly promote dehydro-
genation. Meanwhile, only specific configurations with enlarged interatomic separations
could activate side reactions (e.g., decomposition through the C–C bond scission). Thus, the
geometrical and electronic factors of the catalyst surface structure govern its activity. This
could be rationalized recoursing to the concept of non-specific (structure-insensitive) and
specific (structure-sensitive) reactions. Dehydrogeation reactions, being typical structure-
insensitive ones, could be just as efficiently catalyzed by active sites with either short or
very long interatomic distances. On the contrary, propane decomposition via the C–C bond
scission is a typical structure-sensitive reaction that could proceed only on appropriately
organized active sites with specific geometry featuring interatomic distances of ca. 2.5 Å.
Apparent activation energies of the reaction were calculated for all the complex oxide
catalysts under study (Table 5), postulating that the propane cracking is the first-order
reaction [
68
]. The catalyst-free thermally activated propane cracking is characterized by the
activation energy of 104 kJ/mol [
68
]. The activation energy is decreased in the presence of
catalysts by a few tens kJ/mol, which facilitates the process a lot.
Table 5. Major catalysis-relevant characteristics of (Pr1−xYbx)2Zr2O7-1400 materials.
Catalyst TON ×106Ea, kJ/mol/g CB, %
Pr2Zr2O74 89 97
(Pr0.75Yb0.25)2Zr2O72.7 87 97
(Pr0.5Yb0.5)2Zr2O72.5 86 98
(Pr0.25Yb0.75)2Zr2O72.1 79 98
Yb2Zr2O72 77 97
TON-turnover number; Ea—propane cracking activation energy; and CB—carbon balance.
Importantly, the activation energy for the catalysts under study remain essentially
constant over the entire temperature range, which means that the reaction obeys the same
carbenium mechanism and proceeds in the catalyst-assisted heterogeneous mode rather
than switching to the homogeneous gas-phase mode.
The propane cracking could yield not only C
x
H
y
radicals but free carbon as well,
which could in its turn react with hydrogen, affording methane and other hydrocarbons.

Crystals 2023,13, 1405 17 of 23
With an increase in temperature, the reaction between free carbon atoms starts to prevail,
which gives rise to the coking of available catalytic sites (Figure 11).
Figure 11. The mechanism of coking of (Pr1−xYbx)2Zr2O7-1400 catalysts.
The experimentally observed decrease in the activity of the cracking catalysts can
be due to the shielding of the active surface with soot deposits (Figure 12). Accord-
ing to
Figure 12
, the most prominent loss of activity occurs after the 5th cycle for all
(Pr1−xYbx)2Zr2O7catalysts under study.
0.00
0.25
0.50
0.75
1.00
0
10
20
30
40
50
60
70
80
90
100
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
Cycle no.
1
2
3
4
5
6
7
8
9
10
Conversion of propane (%)
x
Figure 12.
Catalytic performance degradation of the (Pr
1−x
Yb
x
)
2
Zr
2
O
7
-1400 systems under cycling.
As it can be judged from Figure 11, the propane molecule should be adsorbed vertically
on an active site in order to enable the coke formation process. This suggestion is further

Crystals 2023,13, 1405 18 of 23
supported by experimentally observed stronger changes in the propylene selectivity than
the ethylene selectivity, upon cycling on going from Pr2Zr2O7to Yb2Zr2O7(Figure 13).
0.00
0.25
0.50
0.75
1.00
0
10
20
30
40
50
a
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
Selectivity to C
3
H
6
(%)
Cycle no.
1
2
3
4
5
6
7
8
9
10
x
0.00
0.25
0.50
0.75
1.00
0
10
20
30
40
50
60
70
(Pr
1-x
Yb
x
)
2
Zr
2
O
7
Selectivity to C
2
H
4
(%)
Cycle no.
1
2
3
4
5
6
7
8
9
10
b
x
Figure 13.
Changes in the propylene (
a
) and ethylene (
b
) selectivity upon cycling for the
(Pr1−xYbx)2Zr2O7-1400 catalysts.
This poisoning or surface blocking is non-specific. The catalyst activity can be restored
via oxidative regeneration, aimed at the removal of blocking soot deposits but avoiding the
decomposition of the catalyst structure and the degradation of appropriate active sites. The
choice of regeneration conditions at a temperature of 750
◦
C for 100 h after every 10 cycles
allows for carbon combustion to work according to the mechanism of a heterogeneous
process. The specificity of the process lies in the fact that the chemical stage cannot be
considered in isolation from the process of transferring a gaseous oxidizer (air oxygen)
from the surrounding space to the surface of a burning solid. The combustion rate depends
on the chemical properties of carbon and the regeneration characteristics. Oxygen supply
to the combustion zone is carried out by diffusion and, therefore, depends on many factors:
the shape and size of the coking hearth, the movement of the gas medium, the diffusion
coefficients of oxygen, and the reaction products in the space above the surface of the
catalyst and in cracks or pores. For this reason, we performed regeneration after 10 cycles.
This avoids the formation of a solid resin, which permanently blocks the catalytic center.
For the same reason, we do not increase the processing temperature with the possibility of
reducing its time.
At the initial moment of burnout, this will happen due to oxygen being near its surface.
After its use, a layer of combustion products –CO
2
is formed around the incandescent
surface. The combustion rate will decrease, and the process may stop if there is no oxygen
supply from more distant areas of the gas space. This flow occurs due to diffusion, and the
combustion rate will be determined by the magnitude of the diffusion flow. The intensity of
diffusion largely depends on the intensity and nature of the movement of the gas medium
near the surface. The rate of a chemical reaction is determined mainly by temperature and
obeys the Arrhenius law.
At high temperature, the carbon oxidation reaction proceeds very quickly, and the
overall speed of the process will be limited by the diffusion of oxygen to the surface. Thus,
we do not reduce the regeneration temperature, and the value of 750
◦
C is optimal. Thus,
the process consists of two processes that are different in nature: the process of oxygen
transfer from the gas space to the coking site and the process of its chemical interaction with
the surface of solid carbon. Both of these processes are interrelated, but each of them has its
own patterns. The most important of these processes is the process of oxygen consumption,
which is characterized by many chemical reactions.
The mechanism of the complex reaction of an oxygen–carbon compound consists in the
formation of two oxides of CO and CO
2
simultaneously through an intermediate physico-

Crystals 2023,13, 1405 19 of 23
chemical complex of the C
x
O
y
type, which is then split into CO and CO
2
. Accordingly, the
equation of the carbon combustion reaction can be written as follows:
hC+uO2→mCO +nCO2
Then, a homogeneous combustion reaction proceeds with the release of carbon monoxide:
2CO +O2→2CO2
This reaction can occur both near the surface of coal and inside the coal mass, in
its pores and cracks. Another reaction is a heterogeneous reaction between hot coal and
carbon dioxide:
C+CO2↔2CO
This happens at a noticeable rate in places where there is a shortage of oxygen but
where the carbon temperature is high enough. We found that the treatment of the catalysts
in an air flow for 100 h at 750
◦
C gives rise to the full recovery of catalytic activity and
complete removal of undesired soot, which is evidenced by a nearly 100% carbon balance
(Table 5). The amount of free carbon formed and burned out was determined by weighing
the reactor. Since the “carbon balance” has good convergence, this allowed us to consider
this method very accurate.
4. Conclusions
The local atomic and crystal structures of praseodymium/ytterbium zirconates with
the common formula (Pr
1−x
Yb
x
)
2
Zr
2
O
7
(0
≤x≤
1) synthesized via the coprecipitation
followed by the calcination are elucidated in detail with the use of a set of diffraction,
spectroscopic, and electron microscopy techniques. All of the precipitated precursors are
found to be hydrated basic carbonates (Ln/Zr)(OH)
5
(CO
3
)
·n
H
2
O (1.5
<n<
2.5). They are
all X-ray amorphous irrespective of the metal cation composition. The initial crystallization
of the precursors at 600–800
◦
C results in the formation of nanocrystalline powders with the
defect fluorite structure. The calcination at a higher temperature 1100–1200
◦
C gives rise to
the complete removal of carbonates, which induces a chain of phase transitions fluorite (sp.
gr.
Fm ¯
3m
)
→
pyrochlore (sp. gr.
Fd ¯
3m
) at 0
≤x≤
0.5. The (Pr
0.25
Yb
0.75
)
2
Zr
2
O
7
sample
retains the defect fluorite structure up to the maximum calcination temperature 1400
◦
C.
A complex oxide with a specific structure differing from cubic fluorite is formed in the
case of Yb
2
Zr
2
O
7
calcined at 800
◦
C. Its calcination at even higher temperature affords the
emergence of the rhombohedral δ-phase (sp. gr. R¯
3).
We clearly demonstrate that the peculiarities of crystal and the local atomic structures
of the (Pr
1−x
Yb
x
)
2
Zr
2
O
7
(0
≤x≤
1) samples prepared by calcination at 1400
◦
C/3 h exert
an essential influence on their catalytic activity as regards the catalytic cracking of propane.
The catalytic activity quantified via the conversion of propane is strongly affected by the
total number and strength of accessible Lewis acid surface sites on (Pr
1−x
Yb
x
)
2
Zr
2
O
7
as
identified by the pyridine adsorption measurements. More specifically, the progressive
replacement of Pr
3+
with Yb
3+
cations leads to an increase in the number of electron
acceptor centers, which results in increased propane conversion. Meanwhile, an opposite
trend in the product selectivity (ethylene vs. propylene) is observed with variation of
the catalysts’ composition and structure. Indeed, the ethylene (formed due the propane
decomposition via the C–C bond scission) selectivity is decreased and the propylene
(formed due to the propane dehydrogenation) is increased on going from Pr
2
Zr
2
O
7
(sp. gr.
Fd ¯
3m
) to Yb
2
Zr
2
O
7
(sp. gr.
R¯
3
). We elaborate a tentative mechanism stating that it is the
geometry match between the metal–oxygen (Pr–O, Yb–O, and Zr–O) bond lengths in the
active sites and the adsorbed propane molecule size that is the key factor governing the
dominant route of catalytic propane cracking.

Crystals 2023,13, 1405 20 of 23
Supplementary Materials:
The following supporting information can be downloaded at https:
//www.mdpi.com/article/10.3390/cryst13091405/s1, Figure S1: SEM images of PrZrOH-prec (a),
Pr
0.5
Yb
0.5
ZrOH-prec (b) and YbZrOH-prec (c) particles; Figure S2: The STA curves of lanthanide zir-
conate precursors; Figure S3: FT-IR spectra of Pr
2
Zr
2
O
7
powders prepared at different temperatures;
Figure S4: Raman spectra Pr2Zr2O7(a), (Pr0.5Yb0.5)2Zr2O7(b), and Yb2Zr2O7(c) powders prepared
at different temperatures; Table S1: The results of XRD Rietveld refinement for (Pr
1−x
Yb
x
)
2
Zr
2
O
7
pre-
pared at different temperatures; and Table S2: Fractional atomic coordinates, isotropic displacement
parameters, and fractions of antisite defects (Ln
Zr
+Zr
Ln
) for (Pr
1−x
Yb
x
)
2
Zr
2
O
7
samples calcined at
1400 ◦C.
Author Contributions:
Conceptualization, V.V.P. and E.B.M.; methodology, V.V.P. and E.B.M.; vali-
dation, V.V.P., A.P.M., E.B.M. and Y.V.Z.; formal analysis, A.A.Y., B.R.G., O.V.C., S.G.R. and E.B.M.;
investigation, V.V.P., E.B.M., Y.V.Z., S.G.R., M.M.B., A.A.P., E.S.K., N.A.K., E.V.K., V.N.K., I.V.S., N.A.T.,
O.N.S. and N.V.O.; resources, V.V.P.; data curation, A.A.Y., B.R.G. and O.V.C.; writing—original
draft preparation, V.V.P., E.B.M. and Y.V.Z.; writing—review and editing, V.V.P., E.B.M., Y.V.Z. and
A.A.I.; visualization, E.B.M., A.A.Y., B.R.G., O.V.C., S.G.R. and A.A.I.; supervision, A.P.M.; project
administration, V.V.P. and A.P.M.; and funding acquisition, A.P.M. All authors have read and agreed
to the published version of the manuscript.
Funding:
The synthesis, synchrotron XRD, and XAFS measurements were partially supported by the
Ministry of Science and Higher Education of the Russian Federation (Agreement No. 75-15-2021-1352).
Raman and FT-IR measurements, SEM-EDS, ICP-AES, and STA were partially supported by the Ministry
of Science and Higher Education of the Russian Federation (project number FSWU-2023-0070).
Data Availability Statement: Data sharing not applicable.
Acknowledgments:
The authors acknowledge The European Synchrotron Radiation Facility (ESRF)
for providing the opportunity of XAFS measurements and G.R. Castro (BM25-SpLine ESRF) person-
ally for his help with the XAFS experiments.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Subramanian, M.; Aravamudan, G.; Rao, G.S. Oxide pyrochlores—A review. Prog. Solid State Chem.
1983
,15, 55–143. [CrossRef]
2.
Blanchard, P.E.; Clements, R.; Kennedy, B.J.; Ling, C.D.; Reynolds, E.; Avdeev, M.; Stampfl, A.P.; Zhang, Z.; Jang, L.Y. Does Local
Disorder Occur in the Pyrochlore Zirconates? Inorg. Chem. 2012,51, 13237–13244. [CrossRef] [PubMed]
3.
Karthik, C.; Anderson, T.J.; Gout, D.; Ubic, R. Transmission electron microscopic study of pyrochlore to defect–fluorite transition
in rare-earth pyrohafnates. J. Solid State Chem. 2012,194, 168–172. [CrossRef]
4.
Blanchard, P.E.R.; Liu, S.; Kennedy, B.J.; Ling, C.D.; Avdeev, M.; Aitken, J.B.; Cowie, B.C.C.; Tadich, A. Investigating the Local
Structure of Lanthanoid Hafnates Ln
2
Hf
2
O
7
via Diffraction and Spectroscopy. J. Phys. Chem. C
2013
,117, 2266–2273. [CrossRef]
5.
Farmer, J.M.; Boatner, L.A.; Chakoumakos, B.C.; Du, M.H.; Lance, M.J.; Rawn, C.J.; Bryan, J.C. Structural and crystal chemical
properties of rare-earth titanate pyrochlores. J. Alloys Compd. 2014,605, 63–70. [CrossRef]
6.
Thorogood, G.J.; Finkeldei, S.C.; Lang, M.K.; Simeone, D. (Eds.) Ordered and Disordered Cubic Systems: Pyrochlore to Fluorite, Now
and the Horizon; Frontiers Media SA: Lausanne, Switzerland, 2022. [CrossRef]
7.
Blanchard, P.E.R.; Liu, S.; Kennedy, B.J.; Ling, C.D.; Zhang, Z.; Avdeev, M.; Cowie, B.C.C.; Thomsen, L.; Jang, L.Y. Investigating
the order–disorder phase transition in Nd
2−x
Y
x
Zr
2
O
7
via diffraction and spectroscopy. Dalton Trans.
2013
,42, 14875. [CrossRef]
8.
Shamblin, J.; Feygenson, M.; Neuefeind, J.; Tracy, C.L.; Zhang, F.; Finkeldei, S.; Bosbach, D.; Zhou, H.; Ewing, R.C.; Lang, M.
Probing disorder in isometric pyrochlore and related complex oxides. Nat. Mater. 2016,15, 507–511. [CrossRef]
9.
Simeone, D.; Thorogood, G.J.; Huo, D.; Luneville, L.; Baldinozzi, G.; Petricek, V.; Porcher, F.; Ribis, J.; Mazerolles, L.; Largeau,
L.; et al. Intricate disorder in defect fluorite/pyrochlore: A concord of chemistry and crystallography. Sci. Rep.
2017
,7, 3727.
[CrossRef]
10.
Kimura, K.; Nakatsuji, S.; Wen, J.J.; Broholm, C.; Stone, M.B.; Nishibori, E.; Sawa, H. Quantum fluctuations in spin-ice-like
Pr2Zr2O7.Nat. Commun. 2013,4, 1934. [CrossRef]
11.
Gingras, M.J.P.; McClarty, P.A. Quantum spin ice: A search for gapless quantum spin liquids in pyrochlore magnets. Rep. Prog.
Phys. 2014,77, 056501. [CrossRef]
12. Winter, M.R.; Clarke, D.R. Oxide Materials with Low Thermal Conductivity. J. Am. Ceram. Soc. 2007,90, 533–540. [CrossRef]
13.
Pan, W.; Phillpot, S.R.; Wan, C.; Chernatynskiy, A.; Qu, Z. Low thermal conductivity oxides. MRS Bull.
2012
,37, 917–922.
[CrossRef]
14.
Liu, D.; Shi, B.; Geng, L.; Wang, Y.; Xu, B.; Chen, Y. High-entropy rare-earth zirconate ceramics with low thermal conductivity for
advanced thermal-barrier coatings. J. Adv. Ceram. 2022,11, 961–973. [CrossRef]

Crystals 2023,13, 1405 21 of 23
15.
Yamamura, H.; Nishino, H.; Kakinuma, K.; Nomura, K. Electrical conductivity anomaly around fluorite–pyrochlore phase
boundary. Solid State Ionics 2003,158, 359–365. [CrossRef]
16.
Shlyakhtina, A.V.; Shcherbakova, L.G. New solid electrolytes of the pyrochlore family. Russ. J. Electrochem.
2012
,48, 1–25.
[CrossRef]
17.
Ewing, R.C.; Weber, W.J.; Lian, J. Nuclear waste disposal–pyrochlore (A
2
B
2
O
7
): Nuclear waste form for the immobilization of
plutonium and “minor” actinides. J. Appl. Phys. 2004,95, 5949–5971. [CrossRef]
18.
Wang, Z.; Zhu, C.; Wang, H.; Wang, M.; Liu, C.; Yang, D.; Li, Y. Preparation and irradiation stability of A
2
B
2
O
7
pyrochlore
high-entropy ceramic for immobilization of high-level nuclear waste. J. Nucl. Mater. 2023,574, 154212. [CrossRef]
19.
Risovany, V.; Varlashova, E.; Suslov, D. Dysprosium titanate as an absorber material for control rods. J. Nucl. Mater.
2000
,
281, 84–89. [CrossRef]
20.
Risovany, V.; Zakharov, A.; Muraleva, E.; Kosenkov, V.; Latypov, R. Dysprosium hafnate as absorbing material for control rods.
J. Nucl. Mater. 2006,355, 163–170. [CrossRef]
21.
Uno, M.; Kosuga, A.; Okui, M.; Horisaka, K.; Muta, H.; Kurosaki, K.; Yamanaka, S. Photoelectrochemical study of lanthanide
zirconium oxides, Ln2Zr2O7(Ln = La, Ce, Nd and Sm). J. Alloys Compd. 2006,420, 291–297. [CrossRef]
22.
Xu, J.; Xi, R.; Xu, X.; Zhang, Y.; Feng, X.; Fang, X.; Wang, X. A
2
B
2
O
7
pyrochlore compounds: A category of potential materials for
clean energy and environment protection catalysis. J. Rare Earths 2020,38, 840–849. [CrossRef]
23.
Chen, S.; Chang, X.; Sun, G.; Zhang, T.; Xu, Y.; Wang, Y.; Pei, C.; Gong, J. Propane dehydrogenation: Catalyst development, new
chemistry, and emerging technologies. Chem. Soc. Rev. 2021,50, 3315–3354. [CrossRef]
24.
Monai, M.; Gambino, M.; Wannakao, S.; Weckhuysen, B.M. Propane to olefins tandem catalysis: A selective route towards light
olefins production. Chem. Soc. Rev. 2021,50, 11503–11529. [CrossRef] [PubMed]
25.
Al-Sultan, F.S.; Basahel, S.N.; Narasimharao, K. Yttrium Oxide Supported La
2
O
3
Nanomaterials for Catalytic Oxidative Cracking
of n-Propane to Olefins. Catal. Lett. 2019,150, 185–195. [CrossRef]
26.
Markova, E.B.; Cherednichenko, A.G.; Smirnova, S.S.; Sheshko, T.F.; Kryuchkova, T.A. Features of the Catalytic Cracking of
Propane with a Step-Wise Change PrxYb2−xZr2O7.Catalysts 2023,13, 396. [CrossRef]
27.
Popov, V.V.; Menushenkov, A.P.; Gaynanov, B.R.; Zubavichus, Y.V.; Svetogorov, R.D.; Yastrebtsev, A.A.; Pisarev, A.A.; Arzhatkina,
L.A.; Ponkratov, K.V. Features of formation and evolution of crystal and local structures in nanocrystalline Ln
2
Zr
2
O
7
(Ln = La
−
Tb). J. Phys. Conf. Ser. 2017,941, 012079. [CrossRef]
28.
Yastrebtsev, A.; Popov, V.; Menushenkov, A.; Beskrovnyi, A.; Neov, D.; Shchetinin, I.; Ponkratov, K. Comparative neutron and
X-ray diffraction analysis of anionic and cationic ordering in rare-earth zirconates (Ln = La, Nd, Tb, Yb, Y). J. Alloys Compd.
2020
,
832, 154863. [CrossRef]
29.
Stanek, C.R.; Jiang, C.; Uberuaga, B.P.; Sickafus, K.E.; Cleave, A.R.; Grimes, R.W. Predicted structure and stability of A
4
B
3
O
12
δ-phase compositions. Phys. Rev. B 2009,80, 174101. [CrossRef]
30.
Andrievskaya, E. Phase equilibria in the refractory oxide systems of zirconia, hafnia and yttria with rare-earth oxides. J. Eur.
Ceram. Soc. 2008,28, 2363–2388. [CrossRef]
31.
Grima, L.; Peña, J.; Sanjuán, M. Pyrochlore-like ZrO
2
-PrO
x
compounds: The role of the processing atmosphere in the stoichiometry,
microstructure and oxidation state. J. Alloys Compd. 2022,923, 166449. [CrossRef]
32.
Bonville, P.; Guitteny, S.; Gukasov, A.; Mirebeau, I.; Petit, S.; Decorse, C.; Hatnean, M.C.; Balakrishnan, G. Magnetic properties
and crystal field in Pr2Zr2O7.Phys. Rev. B 2016,94, 134428. [CrossRef]
33.
Wang, Y.; Gao, B.; Wang, Q.; Li, X.; Su, Z.; Chang, A. A
2
Zr
2
O
7
(A = Nd, Sm, Gd, Yb) zirconate ceramics with pyrochlore-type
structure for high-temperature negative temperature coefficient thermistor. J. Mater. Sci. 2020,55, 15405–15414. [CrossRef]
34.
Clements, R.; Hester, J.R.; Kennedy, B.J.; Ling, C.D.; Stampfl, A.P. The fluorite–pyrochlore transformation of Ho
2−y
Nd
y
Zr
2
O
7
.
J. Solid State Chem. 2011,184, 2108–2113. [CrossRef]
35.
Sayed, F.N.; Jain, D.; Mandal, B.; Pillai, C.G.S.; Tyagi, A.K. Tunability of structure from ordered to disordered and its impact on
ionic conductivity behavior in the Nd2−yHoyZr2O7(0.0 ≤y≤2.0) system. RSC Adv. 2012,2, 8341. [CrossRef]
36.
Heremans, C.; Wuensch, B.J.; Stalick, J.K.; Prince, E. Fast-Ion Conducting Y
2
(Zr
y
Ti
1−y
)
2
O
7
Pyrochlores: Neutron Rietveld
Analysis of Disorder Induced by Zr Substitution. J. Solid State Chem. 1995,117, 108–121. [CrossRef]
37.
Hess, N.J.; Begg, B.D.; Conradson, S.D.; McCready, D.E.; Gassman, P.L.; Weber, W.J. Spectroscopic Investigations of the Structural
Phase Transition in Gd2(Ti1−yZry)2O7Pyrochlores. J. Phys. Chem. B 2002,106, 4663–4677. [CrossRef]
38.
Moreno, K.J.; Fuentes, A.F.; Maczka, M.; Hanuza, J.; Amador, U. Structural manipulation of pyrochlores: Thermal evolution of
metastable Gd2(Ti1−yZry)2O7powders prepared by mechanical milling. J. Solid State Chem. 2006,179, 3805–3813. [CrossRef]
39.
Lu, X.; Fan, L.; Shu, X.; Su, S.; Ding, Y.; Yi, F. Phase evolution and chemical durability of co-doped Gd
2
Zr
2
O
7
ceramics for nuclear
waste forms. Ceram. Int. 2015,41, 6344–6349. [CrossRef]
40.
Wang, J.; Wang, J.X.; Zhang, Y.B.; Wei, Y.F.; Zhang, K.B.; Tan, H.B.; Liang, X.F. Order-disorder phase structure, microstructure and
aqueous durability of (Gd, Sm)2(Zr, Ce)2O7ceramics for immobilizing actinides. Ceram. Int. 2019,45, 17898–17904. [CrossRef]
41.
Popov, V.; Menushenkov, A.; Yastrebtsev, A.; Rudakov, S.; Ivanov, A.; Gaynanov, B.; Svetogorov, R.; Khramov, E.; Zubavichus, Y.;
Molokova, A.; et al. Multiscale study on the formation and evolution of the crystal and local structures in lanthanide tungstates
Ln2(WO4)3.J. Alloys Compd. 2022,910, 164922. [CrossRef]
42.
Brahlek, M.; Gazda, M.; Keppens, V.; Mazza, A.R.; McCormack, S.J.; Mielewczyk-Gry´n, A.; Musico, B.; Page, K.; Rost, C.M.;
Sinnott, S.B.; et al. What is in a name: Defining “high entropy” oxides. APL Mater. 2022,10, 110902. [CrossRef]

Crystals 2023,13, 1405 22 of 23
43.
Popov, V.V.; Menushenkov, A.P.; Yaroslavtsev, A.A.; Zubavichus, Y.V.; Gaynanov, B.R.; Yastrebtsev, A.A.; Leshchev, D.S.; Chernikov,
R.V. Fluorite-pyrochlore phase transition in nanostructured Ln
2
Hf
2
O
7
(Ln = La
−
Lu). J. Alloys Compd.
2016
,689,
669–679.
[CrossRef]
44.
Svetogorov, R.D.; Dorovatovskii, P.V.; Lazarenko, V.A. Belok/XSA Diffraction Beamline for Studying Crystalline Samples at
Kurchatov Synchrotron Radiation Source. Cryst. Res. Technol. 2020,55, 1900184. [CrossRef]
45.
Petricek, V.; Dusek, M.; Palatinus, L. Crystallographic computing system JANA2006: General features. Z. Krist.
2014
,229, 345–352.
[CrossRef]
46.
Castro, G.R. Optical design of the general-purpose Spanish X-ray beamline for absorption and diffraction. J. Synchrotron Radiat.
1998,5, 657–660. [CrossRef]
47.
Chernyshov, A.; Veligzhanin, A.; Zubavichus, Y. Structural Materials Science end-station at the Kurchatov Synchrotron Radiation
Source: Recent instrumentation upgrades and experimental results. Nucl. Instrum. Methods Phys. Res. Sect. A
2009
,603, 95–98.
[CrossRef]
48.
Klementev, K.V. Extraction of the fine structure from x–ray absorption spectra. J. Phys. D Appl. Phys.
2001
,34, 209–217. [CrossRef]
49. Newville, M. IFEFFIT: Interactive XAFS analysis and FEFF fitting. J. Synchrotron Radiat. 2001,8, 322–324. [CrossRef]
50.
Rehr, J.J.; Kas, J.J.; Vila, F.D.; Prange, M.P.; Jorissen, K. Parameter-free calculations of X-ray spectra with FEFF9. Phys. Chem. Chem.
Phys. 2010,12, 5503–5513. [CrossRef]
51.
Teplonogova, M.; Yapryntsev, A.; Baranchikov, A.; Ivanov, V. High-Entropy Layered Rare Earth Hydroxides. Inorg. Chem.
2022
,
61, 19817–19827. [CrossRef]
52.
Du, H.; Williams, C.T.; Ebner, A.D.; Ritter, J.A. In Situ FTIR Spectroscopic Analysis of Carbonate Transformations during
Adsorption and Desorption of CO2in K-Promoted HTlc. Chem. Mater. 2010,22, 3519–3526. [CrossRef]
53.
Nakamoto, K. Infrared and Raman Spectra of Inorganic and Coordination Compounds. Part A: Theory and Applications in Inorganic
Chemistry, 6th ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2009.
54.
Popov, V.; Menushenkov, A.; Gaynanov, B.; Ivanov, A.; d’Acapito, F.; Puri, A.; Shchetinin, I.; Zheleznyi, M.; Berdnikova, M.;
Pisarev, A.; et al. Formation and evolution of crystal and local structures in nanostructured Ln
2
Ti
2
O
7
(Ln = Gd
−
Dy). J. Alloys
Compd. 2018,746, 377–390. [CrossRef]
55.
Popov, V.; Menushenkov, A.; Zubavichus, Y.; Dubyago, F.; Yastrebtsev, A.; Ivanov, A.; Rudakov, S.; Svetogorov, R.; Khramov, E.;
Kolyshkin, N.; et al. Control over crystal, local atomic and electronic structures of cerium chromates/chromites via the synthesis
conditions. Mater. Chem. Phys. 2023,296, 127269. [CrossRef]
56.
Shlyakhtina, A.V.; Vorobieva, G.A.; Leonov, A.V.; Shchegolikhin, A.N.; Chernyak, S.A.; Baldin, E.D.; Streletskii, A.N. Kinetics
of Formation and Crystallization of Ln
2
Ti
2
O
7
(Ln = Gd, Lu) Pyrochlores from Nanoparticulate Precursors. Inorg. Mater.
2022
,
58, 964–982. [CrossRef]
57.
Chernyshev, V.A. Structure and Lattice Dynamics of La
2
Zr
2
O
7
Crystal: Ab Initio Calculation. In Computational Science and Its
Applications–ICCSA 2019; Springer International Publishing: Berlin/Heidelberg, Germany, 2019; pp. 625–638. [CrossRef]
58.
Kushwaha, A.; Mishra, S.; Vishwakarma, M.; Chauhan, S.; Jappor, H.R.; Khenata, R.; Omran, S.B. Theoretical study of thermal
conductivity, mechanical, vibrational and thermodynamical properties of Ln
2
Zr
2
O
7
(Ln = La, Nd, Sm, and Eu) pyrochlore. Inorg.
Chem. Commun. 2021,127, 108495. [CrossRef]
59.
Bai, Y.; Lu, L.; Bao, J. Synthesis and Characterization of Lanthanum Zirconate Nanocrystals Doped with Iron Ions by a
Salt-Assistant Combustion Method. J. Inorg. Organomet. Polym. Mater. 2011,21, 590–594. [CrossRef]
60.
Tang, Z.; Huang, Z.; Qi, J.; Guo, X.; Han, W.; Zhou, M.; Peng, S.; Lu, T. Synthesis and characterization of Gd
2
Zr
2
O
7
defect fluorite
oxide nanoparticles via a homogeneous precipitation-solvothermal method. RSC Adv. 2017,7, 54980–54985. [CrossRef]
61.
Lee, Y.H.; Chen, J.M.; Lee, J.F.; Kao, H.C.I. XANES Spectroscopic Studies of the Phase Transition in Gd
2
Zr
2
O
7
.J. Chin. Chem. Soc.
2009,56, 543–548. [CrossRef]
62.
Nandi, C.; Poswal, A.; Jafar, M.; Kesari, S.; Grover, V.; Rao, R.; Prakash, A.; Behere, P. Effect of Ce
4+
-substitution at A and B sites
of Nd2Zr2O7: A study for plutonium incorporation in pyrochlores. J. Nucl. Mater. 2020,539, 152342. [CrossRef]
63.
Luo, Q.H.; Howell, R.C.; Dankova, M.; Bartis, J.; Williams, C.W.; Horrocks, W.D.; Young, V.G.; Rheingold, A.L.; Francesconi, L.C.;
Antonio, M.R. Coordination of Rare-Earth Elements in Complexes with Monovacant Wells-Dawson Polyoxoanions. Inorg. Chem.
2001,40, 1894–1901. [CrossRef]
64.
Popov, V.; Menushenkov, A.; Ivanov, A.; Gaynanov, B.; Yastrebtsev, A.; d’Acapito, F.; Puri, A.; Castro, G.; Shchetinin, I.; Zheleznyi,
M.; et al. Comparative analysis of long- and short-range structures features in titanates Ln
2
Ti
2
O
7
and zirconates Ln
2
Zr
2
O
7
(Ln =
Gd, Tb, Dy) upon the crystallization process. J. Phys. Chem. Solids 2019,130, 144–153. [CrossRef]
65.
Gao, Y.; Liu, Y.; Yu, H.; Zou, D. High-entropy oxides for catalysis: Status and perspectives. Appl. Catal. A
2022
,631, 118478.
[CrossRef]
66.
Pan, Y.; Liu, J.X.; Tu, T.Z.; Wang, W.; Zhang, G.J. High-entropy oxides for catalysis: A diamond in the rough. Chem. Eng. J.
2023
,
451, 138659. [CrossRef]
67.
Panchenkov, G.M.; Kolesnikov, I.M. On the Relationship between the Composition and Structure of Catalysts and Catalytic
Properties. Russ. J. Phys. Chem. A 1970,44, 900–903.

Crystals 2023,13, 1405 23 of 23
68.
Markova, E.B.; Lyadov, A.S.; Kurilkin, V.V. Features of propane conversion in the presence of SmVO
3
and SmVO
4
.Russ. J. Phys.
Chem. A 2016,90, 1754–1759. [CrossRef]
69.
Jeon, N.; Choe, H.; Jeong, B.; Yun, Y. Propane dehydrogenation over vanadium-doped zirconium oxide catalysts. Catal. Today
2020,352, 337–344. [CrossRef]
Disclaimer/Publisher’s Note:
The statements, opinions and data contained in all publications are solely those of the individual
author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to
people or property resulting from any ideas, methods, instructions or products referred to in the content.