Isotropic Zero Thermal Expansion and Local Vibrational Dynamics in (Sc,Fe)F3

Article abstract of DOI:10.1021/acs.inorgchem.7b01234

Scandium fluoride (ScF₃) exhibits a pronounced negative thermal expansion (NTE), which can be suppressed and ultimately transformed into an isotropic zero thermal expansion (ZTE) by partially substituting Sc with Fe in (Sc_0.8Fe_0.2)F₃ (Fe20). The latter displays a rather small coefficient of thermal expansion of -0.17 × 10^-6/K from 300 to 700 K. Synchrotron X-ray and neutron pair distribution functions confirm that the Sc/Fe-F bond has positive thermal expansion (PTE). Local vibrational dynamics based on extended X-ray absorption fine structure indicates a decreased anisotropy of relative vibration in the Sc/Fe-F bond. Combined analysis proposes a delicate balance between the counteracting effects of the chemical bond PTE and NTE from transverse vibration. The present study extends the scope of isotropic ZTE compounds and, more significantly, provides a complete local vibrational dynamics to shed light on the ZTE mechanism in chemically tailored NTE compounds.

Full text of DOI:10.1021/acs.inorgchem.7b01234

Communication
pubs.acs.org/IC
Isotropic Zero Thermal Expansion and Local Vibrational Dynamics in
(Sc,Fe)F3
Feiyu Qin,† Jun Chen,*,† Umut Aydemir,‡,§ Andrea Sanson,∥ Lu Wang,† Zhao Pan,† Jiale Xu,†
Chengjun Sun,⊥ Yang Ren,⊥ Jinxia Deng,† Ranbo Yu,† Lei Hu,†,‡ G. Jeffrey Snyder,‡ and Xianran Xing†
†Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, China
‡Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
§Department of Chemistry, Koc University, Sariyer, Istanbul 34450, Turkey
∥Department of Physics and Astronomy, University of Padova, I-35131 Padova, Italy
⊥X-ray Science Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
S
* Supporting Information
strong temperature fluctuations using isotropic ZTE structural
ABSTRACT: Scandium fluoride (ScF3) exhibits a pro-
nounced negative thermal expansion (NTE), which can be
suppressed and ultimately transformed into an isotropic
zero thermal expansion (ZTE) by partially substituting Sc
with Fe in (Sc0.8Fe0.2)F3 (Fe20). The latter displays a
rather small coefficient of thermal expansion of −0.17 ×
10−6/K from 300 to 700 K. Synchrotron X-ray and
neutron pair distribution functions confirm that the Sc/
Fe−F bond has positive thermal expansion (PTE). Local
vibrational dynamics based on extended X-ray absorption
fine structure indicates a decreased anisotropy of relative
vibration in the Sc/Fe−F bond. Combined analysis
proposes a delicate balance between the counteracting
effects of the chemical bond PTE and NTE from
transverse vibration. The present study extends the scope
of isotropic ZTE compounds and, more significantly,
provides a complete local vibrational dynamics to shed
light on the ZTE mechanism in chemically tailored NTE
compounds.
materials. However, such compounds are documented in only a
few species: e.g., Fe[Co(CN)6],10 Zr1−xSnxMo2O8,11 nano
Mn3Cu0.5Ge0.5N,12 (Sc0.85Ga0.05Fe0.15)F3,7b TaO2F,13 and
Zn4B6O13.14
The strong NTE of ScF3 tends to be weakened after chemical
substitutions of Sc with Ga/Fe,7b Ti, Zr, etc.15 Specifically, an
isotropic ZTE with a larger temperature range (0.23 × 10−6/K,
300−900 K) has been achieved in (Sc0.85Ga0.05Fe0.1)F3
presumably because of a short-range structure distortion.7b
However, the local vibrational dynamics of Sc and substituted
metal atoms is equally essential and critical to elucidating the
ZTE mechanism.
Here we present an isotropic ZTE compound, (Sc0.8Fe0.2)F3
(Fe20), displaying an extremely low coefficient of thermal
expansion (CTE) of −0.17 × 10−6/K over a wide temperature
range of 300−700 K. The direct experimental evidence for the
ZTE mechanism is validated by a joint analysis of synchrotron X-
ray and neutron pair distribution functions (XPDF and NPDF),
as well as extended X-ray absorption fine structure (EXAFS). In
particular, a delicate balance is observed between the weakened
PTE of the chemical bonds and also the suppressed thermal
vibration of the Sc/Fe−F atoms, ultimately giving rise to ZTE.
The present work not only broadens the scope of high-
temperature isotropic ZTE materials but also provides a
comprehensive understanding of the local vibrational dynamics
leading to ZTE behavior.
he overwhelming majority of materials exhibit positive
Tthermal expansion (PTE) because of the nearly universal
increase in the bond length with temperature due to increasing
atomic vibration amplitude. Negative thermal expansion (NTE)
is counterintuitive and typically results from some other
processes. The physical phenomenon leading to NTE is often
related to magnetic or electric polarization effects, such as in an
Invar alloy,1 antiperovskite manganese nitrides,2 and La-
Scandium fluoride (ScF3) crystallizes in a cubic structure with
the Pm3m space group (Figure 1a). It is comprised of corner-
̅
shared ScF6 octahedra. With increasing temperature, coupled
vibrations occur in these fluorine-linked ScF6 octahedra, which
brings them closer together and results in an overall NTE in ScF3
(Figure 1b).16
3
(Fe,Si,Co)13 related closely to magnetic order variation, in
BiNiO3,4 attributed to intermetallic charge-transfer transition, in
PbTiO3-based solid solutions5 originating from spontaneous
polarization, etc. NTE framework solids are inherently different
because NTE arises only from atomic vibrations. The NTE in
these materials is explained by the rigid unit mode model, which
involves low-frequency phonon modes intimately coupled with
polyhedron motion as found in, e.g., ZrW2O8,6 ScF3,7 and
CaZrF6.8
A series of (Sc1−xFex)F3 solid solutions (x = 0, 0.05, 0.10, 0.15,
and 0.20) were synthesized by a conventional solid-state reaction
method.7b,c Rietveld structure refinement on powder X-ray
diffraction (XRD) shows that Fe occupies the Sc crystallographic
site (0, 0, 0) and all of the (Sc1−xFex)F3 solid solutions share the
same cubic structure with ScF3 (Figure S1). High-temperature
Zero thermal expansion (ZTE) compounds are rare but
critical for practical applications.9 For example, high-precision
optical instruments requiring 3D stability can accommodate
Received: May 13, 2017
© XXXX American Chemical Society
A
DOI: 10.1021/acs.inorgchem.7b01234
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Inorganic Chemistry
Communication
K),11 nano Mn3Cu0.5Ge0.5N (0.12 × 10−6/K, 12−230 K),12
TaO2F (0.29 × 10−6/K, 300−773 K),13 Zn4B6O13 (0.28 × 10−6/
K, 13−110 K),14 and (Sc0.85Ga0.05Fe0.15)F3 (0.23 × 10−6/K, 300−
900 K).7b Similar to the above compounds, Fe20 shows a
relatively small CTE value (−0.17 × 10−6/K) in a wide
temperature range up to 700 K. It is difficult to achieve such a
steady isotropic ZTE value because the lower-energy phonon
modes are generally overwhelmed by the high-energy counter-
parts.
Partial substitution of Sc with heterogeneous atoms like Ga/
Fe,7b Ti, or Zr15 is demonstrated to suppress the NTE of ScF3.
Here our motivation is to unveil the physical picture captured
from a local structural perspective. Temperature-dependent
synchrotron XPDF and NPDF were analyzed on Fe20. The G(r)
functions of Fe20 XPDF are presented in Figure 3a. The blue and
Figure 1. (a) Cubic crystal structure of ScF3. (b) ScF6 octahedral
rotation with increasing temperature, as indicated by the red arrows,
thus causing shrinkage of the lattice volume.
XRD data of (Sc1−xFex)F3 solid solutions were collected to
investigate the lattice thermal expansion. As depicted in Figure
2a, ScF3 demonstrates a strong NTE. Its lattice constant
Figure 2. (a) Lattice constants of (Sc1−xFex)F3 solid solutions (x = 0,
0.05, 0.10, 0.15 and 0.20; for clarity, they are denoted as ScF3, Fe5, Fe10,
Fe15, and Fe20, respectively). (b) Contour plots of the (100) peaks of
ScF3 and Fe20 as a function of the temperature. The color bar indicates
the normalized intensity. Black and blue arrows demonstrate variation of
the peak positions with increasing temperature.
Figure 3. (a) G(r) functions of Fe20 with increasing temperature (blue,
room temperature; red, high temperature). Atomic peaks are marked by
dashed lines. (b) M−F and M−M atomic peaks (M represents Sc and
Fe). Red and black arrows indicate peak shifts with increasing
temperature. Distance changes in (c) Sc−F and M−F and (d) Sc−Sc
and M−M. Black squares indicate atomic pairs of ScF3. Red circles and
blue diamonds demonstrate M−F and M−M in Fe20 from XPDF and
NPDF.
decreases smoothly upon heating with a linear CTE of −3.46
× 10−6/K (300−800 K).7 By the substitution of Sc with Fe, the
strong NTE in pure ScF3 is gradually weakened in (Sc0.95Fe0.05)F3
(Fe5), (Sc0.9Fe0.1)F3 (Fe10), and (Sc0.85Fe0.15)F3 (Fe15), with
CTEs of −2.78, −1.79, and −0.99 (all ×10−6/K, 300−800 K).
Further, the lattice constant of Fe20 remains basically unchanged
over a wide temperature range (300−700 K), exhibiting an
obvious ZTE with a very small CTE value of −0.17 × 10−6/K
(Figure 2a). The obvious increase in the lattice constant above
700 K presumably comes from the PTE contribution of the
chemical bonds. The atomic displacement parameters (APDs) of
the F atoms of Fe20 also increase more slowly than those of ScF3,
implying a weakened transverse motion (Figure S3). Contour
plots of the (100) peaks of pure ScF3 and Fe20 are presented in
Figure 2b. With rising temperature, the (100) peak position of
ScF3 shifts to higher 2θ angles. In sharp contrast, a small
movement occurs in the (100) peak of Fe20 upon heating,
visually confirming its isotropic ZTE property.
red G(r) functions indicate room and high temperatures,
respectively. Atomic peaks at 2, 4.5, and 5.7 Å correspond to
the nearest, second-nearest, and distinct M−F neighbor
interatomic distances (here M indicates Sc and Fe). The atomic
peak located at around 2.6−3.1 Å, marked by the black box,
demonstrates the F−F atomic pair, and the peak at 4 Å indicates
the M−M atomic interactions. For clarity, the temperature
dependence of the G(r) functions of M−F and M−M are
enlarged and are presented in Figure 3b. The M−F peak shifts to
a higher distance region marked by the red arrow, while the M−
M distance barely changes, as shown by the black arrow.
Quantitatively, the M−F distance in Fe20 slowly expands with
increasing temperature, accompanying a weak CTE of 4.36 ×
10−6/K (300−700 K), as demonstrated by the XPDF (red
circles) and NPDF (blue diamonds) results. This implies that the
PTE contribution is significantly suppressed. Note that there is a
considerable PTE of Sc−F (black squares) in ScF3 (CTE of 13.85
× 10−6/K, 300−700 K;16 Figure 3c). The M−M interatomic
distances in Fe20 remain almost the same during the whole
Isotropic ZTE materials are best for applications requiring
strict thermal stability. Otherwise, a large temperature variation
would cause stress concentration and thus material fatigue or
even failure. So far, some chemically modified isotropic ZTE
materials have been reported like Fe[Co(CN)6] (−1.47 × 10−6/
K, 4.2−300 K),10 Zr1−xSnxMo2O8 (−0.06 × 10−6/K, 12−600
B
DOI: 10.1021/acs.inorgchem.7b01234
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Communication
temperature range, revealing a ZTE behavior in accordance with
its macroscopic lattice ZTE.
local thermal dynamics based on the EXAFS study elucidates that
M−F bonds become stiffer with respect to bending, which gives
rise to a highly reduced anisotropy of relative thermal vibration.
The NTE contribution is simultaneously suppressed to macro-
scopic framework expansion. Consequently, a delicate balance is
constructed between both repressed PTE, originating from
atomic potential anharmonicity, and NTE components,
attributed to the lower frequency modes. Ultimately, the
isotropic ZTE is achieved in the composition of Fe20. The
introduction of heterogeneous atoms into ScF3 inevitably
produces a certain degree of local distortion, which moves the
F atoms away from its midpoint site.7b This distortion ultimately
impacts the thermal motions of F atoms in both the transverse
and longitudinal directions, which correlates closely with the
weakened transverse motion and suppressed chemical bond PTE
in heterogeneous atom-doped ScF3 solid solutions.
The magnitudes of the Fourier transforms of Sc and Fe K-edge
EXAFS signals, k2χ(k), are presented in Figure 4a as a function of
In summary, an isotropic ZTE was achieved in (Sc1−xFex)F3
solid solutions. The CTE decreases to a small value of −0.17 ×
10−6/K. A joint analysis of PDF and EXAFS shows isotropic ZTE
stemming from a balanced competition between the chemical
bond PTE and local NTE contribution, both suppressed
compared to ScF3. The present work not only reports a new
isotropic ZTE compound but also provides an unambiguous and
comprehensive insight into the local thermal dynamics of the
host and substituted atomic correlations, which could shed light
on the thermal expansion of chemically engineered NTE
framework solids.
Figure 4. (a) Fourier transforms of Sc and Fe K-edge EXAFS signals.
Isolated thermal (b) MSRD∥, (c) MSRD⊥, and (d) γ = MSRD⊥/MSRD∥
of Sc−F in ScF3 (black squares), Sc−F (red circles), and Fe−F (blue
squares) of Fe20. Solid lines are the best fits based on the Einstein
model.
ASSOCIATED CONTENT
■
S
* Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.inorg-
chem.7b01234.
the temperature. Local vibration dynamics of Sc−F and Fe−F in
Fe20 were analyzed separately by solely considering the first
coordination shell. The parallel mean-square relative displace-
ment (MSRD∥) values of Sc−F and Fe−F in Fe20 and Sc−F in
pure ScF3 show comparable temperature response (Figure 4b),
which implies the similar stretching bond force constants of Sc/
Fe−F and Sc−F. The perpendicular MSRD⊥ value of Sc−F in
ScF3 is strongly sensitive to the temperature. However, an
apparent discrepancy between the MSRD⊥ values of Sc/Fe−F in
Fe20 and Sc−F in ScF3 is observed. The former ones reveal a
highly suppressed temperature dependence (Figure 4c), which
demonstrates that Sc−F in ScF3 bends more flexibly than Sc/
Fe−F in Fe20. The value of γ = MSRD⊥/MSRD∥ represents the
degree of anisotropy of relative thermal vibration. The γ value of
Sc−F in ScF3 reaches a higher value of ∼19 at high
temperatures,16 close to that of high NTE compounds, such as
22 in Ag2O,17 24.2 in CuScO2,18 and 26 in ZrW2O8.19 It is
interesting to note that the anisotropy of Sc−F in Fe20 decreases
approximately by a factor of 2 (γ = 11.4) and that of Fe−F
remains as 8.8, similar to 6 and 11 in extremely weak NTE
compounds of Ge and CuCl, respectively.20 The reduced γ values
of Sc/Fe−F in Fe20 depict a clear physical scenario in which the
Sc/Fe−F bond is much stiffer with respect to the bending of Sc−
F in ScF3. This anisotropy of relative thermal vibration, related
closely to the low frequency phonon modes and responsible for
NTE, is highly suppressed in (Sc1−xFex)F3 solid solutions, in
contrast to the highly vibrating Sc−F atomic correlation found in
ScF3.
Experimental details, structure refinement, and EXAFS
analysis (PDF)
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: junchen@ustb.edu.cn.
ORCID
Jun Chen: 0000-0002-7330-8976
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This work was supported by the National Natural Science
Foundation of China (Grants 91422301, 21231001, and
21590793), the Changjiang Young Scholars Award, the National
Program for Support of Top-notch Young Professionals, and the
Fundamental Research Funds for the Central Universities, China
(Grant FRF-TP-14-012C1). This research used resources of the
Advanced Photon Source, a U.S. Department of Energy (DOE),
Office of Science, User Facility operated for the DOE, Office of
Science, by Argonne National Laboratory under Contract DE-
AC02-06CH11357. U.A. and G.J.S. acknowledge funding from
the Solid-State Solar-Thermal Energy Conversion Center
(S3TEC), an Energy Frontier Research Center funded by the
U.S. DOE, Office of Science, Basic Energy Sciences (Grant DE-
SC0001299).
By the substitution of Sc with heterogeneous atoms, the
nearest-neighbor M−F interactions exhibit weakened PTE, as
determined by XPDF and NPDF, which results in a decreased
PTE contribution to lattice expansion. On the other side, the
C
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structure study of CuScO2 and CuLaO2. Phys. Rev. B: Condens. Matter
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