Structural disorder in AMoO4 (A = Ca, Sr, Ba) scheelite nanocrystals

Article abstract of DOI:10.1021/ic4025348

The crystal structure of sub-15 nm AMoO₄ (A = Ca, Sr, Ba) scheelite nanocrystals has been investigated using a dual-space approach that combines Rietveld and pair distribution function (PDF) analysis of synchrotron X-ray diffraction data. Rietveld analysis yields an average crystal structure in which the Mo-O bond distance exhibits an anomalously large contraction (2.8%) upon chemical substitution of Ba²⁺ for Ca²⁺. Such a dependence on chemical composition contradicts the well-known rigid character of Mo^VI-O bonds and the resulting rigidity of MoO₄ tetrahedra in scheelites. Unlike Rietveld, PDF analysis yields a local crystal structure in which the Mo-O bond distance shows a negligible contraction (0.4%) upon going from Ba²⁺ to Ca²⁺ and, therefore, appears independent of the chemical composition. Analysis of the anisotropic displacement parameters of the oxygen atom reveals that the disagreement between the average and local structural models arises from the presence of static orientational disorder of the MoO₄ tetrahedra. Rietveld analysis averages the random rotations of the MoO₄ tetrahedra across the scheelite lattice yielding an apparent Mo-O bond distance that is shorter than the true bond distance. In contrast, PDF analysis demonstrates that the structural integrity of the MoO₄ tetrahedra remains unchanged upon chemical substitution of the alkaline-earth cation, and that their orientational disorder is accommodated through geometric distortions of the AO₈ dodecahedra.

Full text of DOI:10.1021/ic4025348

Article
pubs.acs.org/IC
Structural Disorder in AMoO (A = Ca, Sr, Ba) Scheelite Nanocrystals
4
†
†
‡
,†
Federico A. Rabuffetti, Sean P. Culver, Leopoldo Suescun, and Richard L. Brutchey*
†
Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
‡
Cryssmat−Lab/DETEMA, Facultad de Química, Universidad de la Repub
́
lica, Montevideo, Uruguay
*
S Supporting Information
ABSTRACT: The crystal structure of sub-15 nm AMoO (A = Ca, Sr, Ba) scheelite
4
nanocrystals has been investigated using a dual-space approach that combines Rietveld and
pair distribution function (PDF) analysis of synchrotron X-ray diffraction data. Rietveld
analysis yields an average crystal structure in which the Mo−O bond distance exhibits an
anomalously large contraction (2.8%) upon chemical substitution of Ba2+ for Ca . Such a
2+
VI
dependence on chemical composition contradicts the well-known rigid character of Mo −
O bonds and the resulting rigidity of MoO tetrahedra in scheelites. Unlike Rietveld, PDF
4
analysis yields a local crystal structure in which the Mo−O bond distance shows a
negligible contraction (0.4%) upon going from Ba2+ to Ca and, therefore, appears
independent of the chemical composition. Analysis of the anisotropic displacement
parameters of the oxygen atom reveals that the disagreement between the average and
local structural models arises from the presence of static orientational disorder of the
MoO tetrahedra. Rietveld analysis averages the random rotations of the MoO tetrahedra
2+
4
4
across the scheelite lattice yielding an apparent Mo−O bond distance that is shorter than
the true bond distance. In contrast, PDF analysis demonstrates that the structural integrity of the MoO tetrahedra remains
4
unchanged upon chemical substitution of the alkaline-earth cation, and that their orientational disorder is accommodated
through geometric distortions of the AO dodecahedra.
8
INTRODUCTION
investigated using Rietveld analysis of conventional X-ray
diffraction (XRD) data and galvanostatic cycling, respectively.
Our work was motivated by the need to understand
compositional control of structure−function relationships in
nanocrystals of molybdenum-containing scheelites, as these
have attracted attention as potential anode materials in lithium
■
Oxides with the formula AMO (A = Ca, Sr, Ba; M = Mo, W)
4
belonging to the scheelite family constitute an important class
of functional materials in the areas of energy conversion and
storage. Examples of applications include hosts for lanthanide
1
2,3
ions in solid state phosphors and lithium-ion batteries. The
3
archetypical AMoO scheelite structure is shown in Figure 1. It
ion batteries. Interestingly, an anomalously large contraction of
4
features a tetragonal unit cell with space group I4 /a (Z = 4).
Alkaline-earth and molybdenum atoms occupy special positions
a (0, 1/4, 1/8) and 4b (0, 1/4, 5/8) respectively, whereas the
oxygen atom sits in a general position 16f (x, y, z). The
scheelite structure can be visualized as the assembly of AO8
dodecahedra and MoO tetrahedra. Each AO dodecahedron is
connected to four other dodecahedra through edge-sharing,
resulting in zigzag chains that develop along the c axis. MoO4
the Mo−O bond distance in AMoO
4
nanocrystals was observed
1
upon going from CaMoO to SrMoO and finally to BaMoO .
4
4
4
VI
4
This result was particularly surprising considering that Mo −O
bonds are known to be extremely rigid; as a consequence,
7
−9
MoO tetrahedra in scheelites behave as nearly rigid units.
4
4
8
Structural changes induced by chemical substitution, in addition
to pressure and temperature changes, are primarily accom-
modated through geometric distortions of the AO dodecahe-
8
tetrahedra are isolated from each other and connected to AO8
dodecahedra via bridging oxygen atoms; each oxygen atom is
connected to two alkaline-earth atoms and one molybdenum
II
dra, since A −O bonds are significantly more flexible due to
their higher ionic character. Herein, we report an in-depth
8,9
structural investigation of sub-15 nm AMoO4 scheelite
nanocrystals using a dual-space approach that combines
Rietveld and pair distribution function (PDF) analysis of
synchrotron XRD data. Comparison of the average and local
crystal structures shows that the anomalous contraction of the
Mo−O bond distance observed by Rietveld analysis originates
atom. AO dodecahedra are described by two distinct A−O
8
distances and eight distinct O−A−O angles, while MoO
4
tetrahedra are described by a single Mo−O distance and two
4
distinct O−Mo−O angles. CaMoO , SrMoO , and BaMoO
4
4
4
form an isostructural series despite the large change in the ionic
2+
radius of the eight-coordinate alkaline-earth cation (rCa
=
.12 Å, rSr2 = 1.26 Å, and rBa = 1.42 Å).
+
2+
5
from static orientational disorder of the MoO tetrahedra across
4
1
the scheelite lattice. The significance of coupling Rietveld and
Recently, our group reported the low temperature (<100 °C)
synthesis of sub-15 nm AMoO scheelite nanocrystals using the
vapor diffusion sol−gel method. Additionally, the crystal
structure and lithium storage capacity of the nanocrystals were
4
6
Received: October 7, 2013
Published: November 22, 2013
©
2013 American Chemical Society
1056
dx.doi.org/10.1021/ic4025348 | Inorg. Chem. 2014, 53, 1056−1061

Inorganic Chemistry
Article
atmosphere for 24 h at 80 °C. The resulting gel was collected,
washed with absolute ethanol (3 × 10 mL), and vacuum-dried at room
temperature to recover an off-white fine powder consisting of AMoO4
nanocrystals. TEM analysis revealed that these nanocrystals exhibited a
quasispherical shape with an average diameter of 9.3 ± 2.7, 7.9 ± 1.9,
6
and 12.3 ± 2.8 nm for CaMoO , SrMoO , and BaMoO , respectively.
4
4
4
Synchrotron X-ray Diffraction. X-ray diffraction patterns were
collected at the 11−ID−B beamline of the Advanced Photon Source at
Argonne National Laboratory. An incident photon energy of 90.484
keV (λ = 0.137024 Å) was employed. Samples were loaded in Kapton
tubes and diffraction data were collected in transmission mode at room
temperature.
Rietveld Analysis. Rietveld structural refinements were carried out
1
0,11
using the GSAS software.
Experimental data and atomic X-ray
scattering factors were corrected for sample absorption and anomalous
scattering, respectively. The average crystal structure of AMoO4
nanocrystals was refined with the tetragonal I4 /a space group. The
1
following parameters were refined: (1) scale factor, (2) background,
which was modeled using a shifted Chebyschev polynomial function,
(
3) peak shape, which was modeled using a modified Thomson−
12
Cox−Hastings pseudo-Voigt function, (4) lattice constants (a and
c), (5) fractional atomic coordinates of the oxygen atom (x , y , z ),
O
O
O
and (6) atomic anisotropic displacement parameters constrained by
1
1
33
11
22
the site symmetry (U and U for Ca, Sr, Ba, and Mo, and U , U ,
Figure 1. AMoO scheelite structure (A = Ca, Sr, Ba). Blue, purple,
33
12
13
23
4
U , U , U , and U for O). The Rwp indicator was employed to
and red spheres represent alkaline-earth, molybdenum, and oxygen
atoms, respectively.
13
assess the quality of the refined structural models.
Pair Distribution Function Analysis. The pair distribution
function G(r) defined as:
PDF analysis to achieve an accurate description of the atomic
arrangement in nanocrystals is highlighted.
G(r) = 4πr[ρ(r) − ρ ]
0
Q
max
=
(2/π) ∫Q
Q[S(Q) − 1]sin(Qr)dQ
EXPERIMENTAL SECTION
■
Synthesis of AMoO Nanocrystals. AMoO nanocrystals were
4
4
synthesized via a vapor diffusion sol−gel method described in detail
was employed for structural analysis. Here, r is the radial distance, ρ(r)
and ρ are the local and average atomic number density, respectively,
6
elsewhere. Briefly, MoO (acac) (95%; Sigma Aldrich) was dissolved
2
2
0
in the corresponding A(OR) alkoxide (R = CH CH OCH for Ca
and Q is the magnitude of scattering vector. The RAD software was
2
2
2
3
14
and CH CHCH OCH for Sr and Ba; Gelest, Inc.) in a 1:1 molar
employed to extract G(r) from the raw diffraction data. These were
first corrected for background, sample absorption, and Compton
scattering. Then, normalized structure functions S(Q) were obtained;
these are given in the Supporting Information. Finally, S(Q) was
Fourier-transformed to yield G(r). A maximum scattering vector
2
3
3
ratio. The resulting solution was exposed to a controlled flow of water
vapor for 48 h at room temperature and atmospheric pressure.
Diffusion of water vapor into the solution resulted in the formation of
a cracked gel, which was subsequently aged under a nitrogen
Figure 2. (a) Rietveld and (b) PDF analysis of the XRD patterns of AMoO nanocrystals. Experimental (○) and calculated (red) patterns are shown
4
along with the difference curve (blue). Tickmarks (green) corresponding to the phase refined are given in a, and PDF peaks arising from A−O and
Mo−O pairs are indicated in b. Note the Mo−O interatomic distance does not change with chemical composition. Difference curves in b have been
offset for clarity.
1
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Inorganic Chemistry
Article
1
(
Qmax) of 25 Å− was employed in the Fourier transform. Structural
Table 2. Structural Parameters of AMoO Nanocrystals
Extracted From PDF Analysis
4
1
5
refinements were carried out using the PDFgui software. The local
crystal structure of AMoO4 nanocrystals was refined with the
tetragonal I4 /a space group. Fits of this structural model to the
CaMoO
4
SrMoO
4
BaMoO
4
1
experimental PDFs were performed in the 1.25−13 Å interatomic
distance range in order to account for all atom−atom pairs along the
largest dimension of the unit cell. The following parameters were
refined: (1) scale factor, (2) lattice constants (a and c), (3) fractional
atomic coordinates of the oxygen atom (x , y , z ), and (4) atomic
a (Å)
c (Å)
c/a
5.220(2)
5.390(2)
12.000(10)
2.23(20)
348.5(4)
0.630(5)
0.514(5)
0.208(3)
0.9(8)
5.571(3)
12.783(10)
2.30(20)
396.7(5)
0.605(11)
0.512(8)
0.204(4)
1.2(6)
1.1(9)
1.2(4)
1.2(7)
1.0(1.2)
1.1(5)
13(7)
11.407(10)
2.19(20)
310.8(4)
0.642(4)
0.507(3)
0.212(2)
0.9(2)
3
V (Å )
O
O
O
xO
anisotropic displacement parameters constrained by the site symmetry
1
1
33
11
22
33
12
13
yO
(
U
U and U for Ca, Sr, Ba, and Mo, and U , U , U , U , U , and
2
3
for O). The R indicator was employed to assess the quality of the
z
O
w
16
11
a
2
refined structural models.
Bond Distance Distortion Index. The bond distance distortion
index
A:
U
U
U
U
U
(Å )
3
3
2
(Å )
1.5(6)
1.0(1.7)
0.9(7)
17
2
(ΔAO8) was employed to quantitatively assess geometric
eq (Å )
1.1(2)
1
1
2
distortions of the AO dodecahedra. Δ is defined as:
Mo:
O:
(Å )
0.70(10)
0.90(2)
0.76(8)
3.8(1.1)
3.4(1.2)
2.5(9)
1.1(8)
8
AO
8
3
3
2
(Å )
1.1(1.7)
1.1(7)
8
i
ΔAO8 = 1
|d
− ⟨dA−O⟩|
2
A−O
Ueq (Å )
∑
8
⟨dA−O
⟩
11
2
U
U
U
U
U
U
(Å )
3.4(1.8)
9(4)
i=1
2
2
2
(Å )
9(5)
where ⟨dA−O⟩ is the average A−O bond distance.
33
2
(Å )
4.1(1.9)
−2.2(1.8)
−2.0(1.4)
2.5(1.7)
5(2)
2(3)
1
2
2
(Å )
0.2(7)
1.3(7)
2.7(3)
2(2)
RESULTS AND DISCUSSION
■
13
2
(Å )
−0.8(6)
0.16(7)
3(1)
Rietveld and PDF fits to the experimental XRD patterns of
AMoO4 nanocrystals are shown in Figure 2. Calculated
structural parameters are given in Tables 1 and 2. Bond
2
3
2
(Å )
Ueq (Å2)
8(3)
Rw (%)
9.7
8.3
7.0
a
ij
Atomic displacements parameters are given as 100 × U .
Table 1. Structural Parameters of AMoO Nanocrystals
4
Extracted From Rietveld Analysis
CaMoO4
SrMoO4
BaMoO4
a (Å)
c (Å)
c/a
5.2334(6)
11.4477(15)
2.19(4)
313.53(8)
0.6462(7)
0.5103(6)
0.2080(4)
0.74(11)
1.22(18)
0.90(8)
0.80(5)
0.90(8)
0.83(4)
1.1(3)
5.4039(4)
12.0392(10)
2.23(2)
351.57(6)
0.6337(7)
0.5188(7)
0.2048(4)
1.24(12)
1.03(19)
1.17(8)
0.44(9)
0.75(16)
0.54(7)
1.2(3)
5.5871(4)
12.8223(11)
2.29(2)
400.26(7)
0.6171(10)
0.5289(11)
0.2006(5)
1.82(12)
1.23(16)
1.62(8)
0.35(11)
0.58(16)
0.42(8)
1.7(2)
3
V (Å )
xO
yO
zO
A:
U11 (Å )
a
2
U33 (Å )
2
2
U
U
U
U
U
U
U
U
U
U
(Å )
eq
11
2
Mo:
O:
(Å )
33
2
(Å )
2
(Å )
eq
1
2
3
1
1
2
1
2
3
2
3
3
2
(Å )
2
(Å )
1.2(3)
2.5(3)
4.1(5)
2
(Å )
2.6(4)
2.1(3)
2.4(5)
2
(Å )
−0.2(2)
0.2(2)
−0.9(3)
0.6(2)
0.6(4)
2
(Å )
0.6(3)
2
(Å )
Ueq (Å2)
−0.5(2)
1.62(19)
2.8
0.2(2)
0.7(4)
Figure 3. (a) Lattice constants a and c/2, (b) A−O bond distances,
and (c) Mo−O bond distance extracted from Rietveld (black symbols)
1.95(17)
2.2
2.7(2)
and PDF (red symbols) analysis of the XRD patterns of AMoO
Rwp (%)
2.0
4
a
ij
nanocrystals. The percent contraction of the Mo−O bond distance in
Atomic displacements parameters are given as 100 × U .
SrMoO and BaMoO relative to CaMoO is indicated in c. Dashed
4
4
4
lines are guides for the eye.
lengths, bond angles, and bond distance distortion indices are
given in Tables 3 and 4. Calculated lattice constants a and c/2,
and A−O and Mo−O bond distances are plotted in Figure 3 as
function of the ionic radius of the alkaline-earth cation. Low
material and its form factor. In addition, inspection of Tables 1
and 2 reveals that a complete set of physically plausible
structural parameters can be extracted from the experimental
XRD patterns using both Rietveld and PDF analysis. Important
in the context of this investigation is the fact that positively
defined anisotropic mean-square displacements were obtained
for the oxygen atom in all cases (vide infra). Rietveld and PDF
Rwp and R values and visual inspection of the fits show that
w
both the average and local crystal structure of AMoO4
nanocrystals are adequately described by a tetragonal scheelite
structure with space group I4 /a. It is worth noting that Rw
1
values below 10% were obtained for the fits to the experimental
PDFs, whereas typical R values reported in the literature range
from 10 to 25%, depending on the chemical nature of the
analysis show the AMoO unit cell axes expand linearly upon
w
4
going from CaMoO to BaMoO , as expected on the basis of
4
4
1
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Inorganic Chemistry
Article
the ionic radii (Figure 3a). This expansion is slightly anisotropic
and occurs primarily along the c axis. As a result, the metrics of
the tetragonal unit cell changes: the c/a ratio increases from
Table 4. Bond Angles, Bond Distances, and Polyhedra
Distortion Indices Extracted From PDF Analysis
CaMoO4
SrMoO4
BaMoO4
2
.19 to 2.30 (Tables 1 and 2). The increased sensitivity of the c
AO8
axis to chemical composition, temperature, and pressure
changes has been extensively reported in structural studies of
bulk AMoO4.
A−O (Å)
2.4112(13)
2.5518(14)
2.6456(10)
149.7(3)
67.1(3)
2.6967(13)
2.8266(10)
145.4(4)
66.4(4)
7
−9
2
.5071(10)
Rietveld and PDF analysis also give a similar
O−A−O (deg)
152.2(3)
description of the evolution of the two distinct A−O bond
distances (denoted as A-O (1) and A-O (2) in Figure 3b) with
chemical composition. Both increase linearly and at the same
rate upon going from CaMoO to BaMoO (Figure 3b).
6
9
7
8.0(3)
9.0(3)
4.0(3)
98.2(3)
97.3(4)
74.3(4)
75.8(4)
4
4
1
33.5(3)
135.6(4)
78.3(3)
138.3(4)
79.8(4)
According to Rietveld (PDF) analysis, the average A−O
7
6.4(3)
distance increases by 13−14% (12−13%). Interestingly,
1
26.6(3)
127.9(3)
76.7(4)
131.3(4)
71.4(4)
however, the bond distance distortion of the AO dodecahedra
8
7
9.0(3)
appears much larger to PDF than to Rietveld analysis,
regardless of the chemical composition (Tables 3 and 4).
Bond distance distortion values in the 18−24 range are
obtained using the latter, while values in the 2.7−4.2 range are
obtained using the former. In other words, the AO8
dodecahedra appear more distorted on the local scale. When
it comes to the description of the evolution of the Mo−O
distance with chemical composition, both Rietveld and PDF
VAO8 (Å3)
(× 103)
26.49
31.33
37.72
Δ
19.5
18.0
23.5
AO
8
MoO4
Mo−O (Å)
O−Mo−O (deg)
1.7698(7)
108.3(4)
111.9(4)
2.84
1.7632(7)
108.7(5)
111.0(5)
2.81
1.7627(7)
109.0(6)
110.4(6)
2.81
VMoO4 (Å3)
analysis reveal a contraction upon going from CaMoO to
4
1
8
4
BaMoO (Figure 3c). As a result, the volume of the MoO4
calculated bond valence sums (BVS) using A−O and Mo−O
bond distances extracted from both approaches, and corre-
sponding results are given in Table 5. For comparison, we have
tetrahedra decreases (Tables 3 and 4). Thus, the expansion of
Table 3. Bond Angles, Bond Distances, and Polyhedra
Distortion Indices Extracted From Rietveld Analysis
Table 5. Bond Valence Sums in AMoO Nanocrystals
4
CaMoO4
SrMoO4
BaMoO4
a
a
a
A
Mo
O
AO8
CaMoO4
SrMoO4
BaMoO4
Rietveld
2.01
2.13
2.12
2.03
2.20
2.19
1.93
2.40
2.37
6.12
5.80
5.78
6.40
5.90
5.84
6.98
5.91
5.88
2.03
1.98
1.98
2.11
2.02
2.01
2.23
2.04
2.06
A−O (Å)
2.469(4)
2.614(4)
2.636(4)
148.77(15)
67.41(10)
97.62(6)
73.51(6)
137.28(17)
79.22(10)
127.95(12)
76.71(19)
32.22
2.804(6)
2.819(5)
145.6(2)
66.14(13)
96.78(6)
73.94(9)
139.8(2)
81.72(15)
129.54(18)
74.2(3)
PDF
2
.487(4)
b
b
b
Rietveld in bulk
Rietveld
O−A−O (deg)
151.18(15)
6
9
7
8.46(9)
8.39(6)
3.46(6)
PDF
Rietveld in bulk
Rietveld
1
35.10(17)
PDF
7
7.05(10)
Rietveld in bulk
1
26.85(11)
a
Bond valence parameters l for Ca (1.967), Sr (2.118), Ba (2.285),
and Mo (1.907) were taken from ref 18. The empirical constant b was
fixed at 0.37. Ref 19.
0
7
8.50(18)
27.07
VAO8 (Å3)
ΔAO8 (× 103)
39.49
b
3.6
4.2
2.7
MoO4
Mo−O (Å)
O−Mo−O (deg)
1.750(3)
1.734(3)
107.87(14)
112.7(3)
2.67
1.701(5)
108.9(2)
110.5(4)
2.53
included BVSs reported by Nassif et al. in a combined powder
107.14(14)
X-ray and neutron diffraction investigation of bulk BaMoO
4
19
1
14.2(3)
2.74
synthesized via solid state reaction. These authors also
computed BVSs using structural parameters derived by Gurmen
et al. and Hazen et al. in their structural investigations of single
VMoO4 (Å3)
4
,7
crystal CaMoO4 and SrMoO4.
The common features
the unit cell observed upon increasing the ionic radius of the
alkaline-earth cation is driven by the expansion of the AO8
dodecahedra. However, the Mo−O distance derived from
Rietveld analysis shows an abnormally large contraction of 2.8%
upon going from CaMoO to BaMoO . In contrast, the bond
observed in these structural investigations are the overbonded
and underbonded character of the alkaline-earth and
molybdenum cations, respectively, as well as the increasing
strength of the Mo−O bond upon increasing the radius of the
alkaline-earth cation. This crystallochemical picture for the bulk
materials has been validated by studying the relative thermal
stabilities of CaMoO , SrMoO , and BaMoO against reduction
4
4
distance derived from PDF analysis shows a negligible
contraction of 0.4%, in agreement with the well-known rigidity
4
4
4
8,9
19,20
of MoO tetrahedra in AMoO scheelites. This is clearly
under hydrogen atmosphere.
Interestingly, BVSs derived
4
4
noticeable in Figure 2b, where the peak corresponding to the
Mo−O pair remains at the same r value (∼1.76 Å) for
CaMoO , SrMoO , and BaMoO .
To further explore similarities and differences between the
structural models derived from Rietveld and PDF analysis, we
from PDF analysis of AMoO nanocrystals are in excellent
4
agreement with those reported for their bulk counterparts,
indicating the corresponding structural models are adequate. In
contrast, BVSs derived from Rietveld analysis yield an
overbonded character for the molybdenum atom, suggesting
4
4
4
1
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Inorganic Chemistry
Article
the corresponding structural models fail to accurately describe
disorder in AMoO scheelite nanocrystals. Specifically, they
4
Mo−O bonds within the MoO tetrahedra.
point to orientational disorder of the MoO tetrahedra; that is,
4
4
Results presented thus far demonstrate that PDF analysis
these tetrahedra are randomly rotated throughout the scheelite
lattice. Rietveld analysis averages this orientational disorder
yielding a structural model that differs from that provided by
PDF analysis, which probes the local crystal structure. The
presence of disorder in AMoO4 nanocrystals was further
confirmed by fits of the proposed structural model to the
experimental PDFs in the 1.25−80 Å interatomic distance
provides a crystallochemically sensible description of Mo−O
bonds in AMoO nanocrystals, whereas Rietveld analysis does
4
not. The origin of this deficiency can be understood by
inspecting the shape and orientation of the thermal ellipsoids of
the oxygen atoms as a function of the chemical composition
(
Figure 4). Thermal ellipsoids extracted from Rietveld analysis
range (see the Supporting Information). For these fits, R
w
values of 14.5, 14.5, and 12.0% were obtained for CaMoO4,
SrMoO , and BaMoO , respectively. These are systematically
4
4
larger than those obtained in fits performed in the 1.25−13 Å
interatomic distance range, thus reflecting the loss of coherence
in the assembly of AO and MoO polyhedra as atomic pairs
8
4
that are further apart are incorporated into the structural
refinement. Orientational disorder in AMoO scheelites is not
4
surprising considering these are open framework structures that
have a high degree of structural flexibility. Specifically in the
case of MoO tetrahedra, these share corners with neighboring
4
AO dodecahedra via a bridging oxygen atom. The presence of
8
A−O−Mo “hinges” provides the tetrahedra with significant
21
rotational freedom. A similar structural flexibility, coupled
with transverse lattice vibrations, is at the origin of the negative
thermal expansion (NTE) coefficients exhibited by oxides
Figure 4. MoO tetrahedra in AMoO nanocrystals as described by
4
4
Rietveld (top) and PDF (bottom) analysis of XRD data. Thermal
ellipsoids are drawn with a 95% probability. Ellipsoids derived from
Rietveld analysis exhibit a component perpendicular to the Mo−O
bond that increases upon going from CaMoO to BaMoO . This
containing (Mo,W)O and (Mo,W)O corner-sharing poly-
4
6
21−24
hedra.
Unlike NTE materials, however, MoO tetrahedra
4
in AMoO nanocrystals did not show any signs of concerted
4
4
4
change is best observed by looking at the ellipsoid indicated with an
arrow. In contrast, the largest component of the ellipsoids derived
from PDF analysis appears perpendicular to the Mo−O bond,
regardless of the chemical composition.
rotation. The hypothesis of orientational disorder can also be
invoked to explain the observation that AO dodecahedra
8
appear more distorted on the local scale. Indeed, such an
observation results from the fact that random rotations of
MoO tetrahedra are primarily accommodated through geo-
4
change their shape and orientation relative to the Mo−O bond
metric distortions of the AO dodecahedra rather than by
8
upon going from CaMoO to BaMoO . The component of the
affecting the structural integrity of the tetrahedra, as expected
on the basis of the relative rigidities of the A−O and Mo−O
4
4
ellipsoid perpendicular to the Mo−O bond increases from
9
CaMoO to BaMoO . In contrast, ellipsoids derived from PDF
bonds.
4
4
analysis appear elongated along a direction perpendicular to the
Mo−O bond, regardless of the chemical composition. This
observation explains why the Mo−O bond distance extracted
from Rietveld analysis is significantly shorter than that provided
by PDF analysis and why this disagreement becomes more
noticeable upon going from CaMoO to SrMoO and finally to
Finally, we comment on the significance of coupling Rietveld
and PDF analysis to achieve an accurate representation of the
atomic arrangement in nano- and microcrystals. Results
presented herein demonstrate the inability of Rietveld analysis
to provide a fully consistent crystallochemical description of
AMoO nanocrystals. This limitation of the Rietveld method
4
4
4
BaMoO . An ellipsoid elongated perpendicular to the Mo−O
arises from the reduced structural coherence of nanocrystals
relative to their bulk counterparts. Petkov et al. have shown that
the reduction of structural coherence in spatially confined
chemical systems results from an enhancement of atomic
4
bond axis leads to an apparent bond distance that is shorter
than the true bond distance, because the projection of the local
position of the oxygen onto the direction that connects the
molybdenum with the average position of the oxygen is shorter
than the actual bond distance. This effect is similar to
25
positional disorder. As mentioned earlier, the structural
flexibility of AMoO scheelites is intrinsic to their crystal
structure. Thus, it seems reasonable to assume that orienta-
tional disorder of the MoO tetrahedra occurs in both bulk and
4
2
1
libration, but in our case its origin appears to be mainly
static rather than dynamic as discussed hereafter. Indeed, the
PDF peak corresponding to the Mo−O pair features a nearly
constant full width at half-maximum: values of 0.19, 0.19, and
4
nanocrystalline form factors. The fact that Rietveld analysis
provides an adequate structural model for AMoO in bulk
4
19
0
.20 Å were obtained for CaMoO , SrMoO , and BaMoO ,
form but not in nanocrystalline form, indicates that random
4
4
4
respectively, upon fitting the Mo−O peak with a single
Gaussian. This observation and the nearly constant Mo−O
bond distance demonstrate that the dynamics and structural
rotations of the MoO tetrahedra occur to a much larger extent
4
in the latter, merely reflecting their enhanced atomic positional
disorder. Indeed, Nogueira and co-workers recently suggested
the presence of structural disorder in Ba1−xSr MoO micro-
integrity of the MoO tetrahedra does not change significantly
4
x
4
26
with chemical composition. In addition, the disagreement
between the average and local structural models provided by
Rietveld and PDF analysis, respectively, would not be such if
the effect responsible for it was dynamic in nature. Considered
all together, these findings indicate the presence of static
crystals synthesized by a coprecipitation method. However,
the use of Rietveld analysis as the unique quantitative probe of
the crystal structure prevented them from identifying the exact
origin and nature of the disorder. This observation, coupled to
results presented herein, demonstrates the significance of
1
060
dx.doi.org/10.1021/ic4025348 | Inorg. Chem. 2014, 53, 1056−1061

Inorganic Chemistry
Article
combining Rietveld and PDF analysis to achieve an accurate
description of the atomic arrangement in both nano- and
microcrystals of materials in which local structural distortions
are expected to occur.
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CONCLUSIONS
■
In summary, the average and local crystal structures of sub-15
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4
random rotations of the tetrahedra across the scheelite lattice,
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(
(
1
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ASSOCIATED CONTENT
■
(
*
S
Supporting Information
Structure functions S(Q); fits to the experimental PDFs of
(
AMoO nanocrystals in the 1.25−80 Å interatomic distance
4
range. This material is available free of charge via the Internet at
http://pubs.acs.org.
(
(
24) Lind, C. Materials 2012, 5, 1125−1154.
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Phys. Rev. B 2008, 78, 054107.
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(
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: brutchey@usc.edu.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This material is based on work supported by the Department of
Energy Office of Basic Energy Sciences under Grant DE−
FG02−11ER46826. S.P.C. acknowledges the National Science
Foundation for a Graduate Research Fellowship. The authors
thank Dr. Karena Chapman and Dr. Kevin Beyer from the 11−
ID−B beamline of the Advanced Photon Source for their
assistance with the collection of X-ray diffraction data. Use of
the Advanced Photon Source at Argonne National Laboratory
was supported by the U.S. Department of Energy, Office of
Science, Office of Basic Energy Sciences, under Contract DE−
AC02−06CH11357.
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dx.doi.org/10.1021/ic4025348 | Inorg. Chem. 2014, 53, 1056−1061