A Novel, Layered Phase in Ti&#x26;#x02010;Rich SrTiO<sub>3</sub> Epitaxial Thin Films


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Title
A novel, layered phase in Ti-rich SrTiO3 epitaxial thin films.

Permalink
https://escholarship.org/uc/item/3h43d3xp

Journal
Advanced materials (Deerfield Beach, Fla.), 27(5)

ISSN
0935-9648

Authors
Lee, Sungki
Damodaran, Anoop R
Gorai, Prashun
et al.

Publication Date
2015-02-01

DOI
10.1002/adma.201403602
 
Peer reviewed

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 A Novel, Layered Phase in Ti-Rich SrTiO 3  Epitaxial Thin Films 

   Sungki    Lee     ,        Anoop R.    Damodaran     ,        Prashun    Gorai     ,        Nuri    Oh     ,        Jarrett A.    Moyer     ,    
    Ji-Hwan    Kwon     ,        Naheed    Ferdous     ,        Amish    Shah     ,        Zuhuang    Chen     ,        Eric    Breckenfeld     ,        
R. V. K.    Mangalam     ,        Paul V.    Braun     ,        Peter    Schiffer     ,        Moonsub    Shim     ,        Jian-Min    Zuo     ,    
    Elif    Ertekin     ,       and        Lane W.    Martin*   

  S. Lee, Dr. A. R. Damodaran, Dr. Z. Chen, 
Prof. L. W. Martin 
 Department of Materials Science and Engineering 
 University of California
Berkeley,    Berkeley  ,   California    94720  ,   USA   
E-mail:  lwmartin@berkeley.edu    
 Dr. P. Gorai, N. Ferdous, Prof. E. Ertekin 
 Department of Mechanical Science and Engineering 
 University of Illinois
Urbana-Champaign,    Urbana  ,   Illinois    61801  ,   USA    
 N. Oh, Dr. J.-H. Kwon, Dr. A. Shah, Dr. E. Breckenfeld, 
Dr. R. V. K. Mangalam, Prof. P. V. Braun, Prof. M. Shim, Prof. J.-M. Zuo 
 Department of Materials Science and Engineering 
and Materials Research Laboratory 
 University of Illinois
Urbana-Champaign,    Urbana  ,   Illinois    61801  ,   USA    
 Dr. J. A. Moyer, Prof. P. Schiffer 
 Department of Physics 
 University of Illinois 
 Urbana-Champaign,    Urbana  ,   Illinois    61801  ,   USA   

DOI: 10.1002/adma.201403602

characterization methods, these approaches push the edge of 
materials control. Using these techniques it is possible to pro-
duce exotic new phases that do not exist in the bulk, [ 20,21 ]  syn-
thesize artifi cial heterostructures, [ 22,23 ]  and control materials at 
the unit-cell level to enable new states of matter. [ 24,25 ]  Although 
these approaches provide unprecedented control, they are lim-
ited in the geometries of phases that can be created (i.e., lay-
ered heterostructures) and the cost, complexity, and lack of 
scalability of the continuous in situ monitoring makes large 
scale use challenging. 

 In this work, we explore a new, self-assembly route to produce 
novel phases, whereby we combine systems with a tendency for 
spontaneous phase separation with non-equilibrium deposi-
tion techniques and thin-fi lm epitaxy. The goal is to explore the 
evolution of a classical equilibrium concept (i.e., eutectic mate-
rials) under non-equilibrium growth conditions that are kineti-
cally limited and infl uenced by epitaxial relationships. To do 
this, we focus on a model oxide eutectic system: SrTiO 3 –TiO 2 . 
The equilibrium SrTiO 3 –TiO 2  eutectic phase diagram has been 
known for decades, [ 26 ]  but this work is motivated by a number 
of recent studies. First, directional solidifi cation of this eutectic 
system has produced exotic, split-ring resonator-like TiO 2  fea-
tures embedded in a SrTiO 3  matrix. 

[ 16 ]  Second is the use of 
complex shuttered thin-fi lm deposition processes and epitaxy 
to study new members of the Sr  n +1 Ti  n  O 3 n +1   Ruddlesden–Popper 
(RP) homologous series and their properties. [ 27,28 ]  It should 
be noted that most work on the Ti-rich side of the phase dia-
gram has been done in the context of bulk eutectic systems and 
what little work has been done on the Ti-rich materials as fi lms 
has shown only the production of amorphous TiO  x   inclusions 
in a SrTiO 3  matrix. 

[ 29 ]  Most thin-fi lm work in this system has 
focused on nearly stoichiometric SrTiO 3  or Sr-excess phases. 
This begs the question of whether non-equilibrium growth 
techniques and thin-fi lm epitaxy can be used to produce novel 
phases and/or nanostructures akin to those observed in Sr-rich 
SrTiO 3  on the Ti-rich side of the phase diagram. Here, we study 
the growth, structure, and properties of the Ti-rich portion of 
the SrTiO 3 –TiO 2  phase diagram in and around the eutectic 
composition. We observe that the non-equilibrium nature of 
the growth process results in fi lms that greatly exceed the ther-
modynamic solubility limit of Ti in SrTiO 3  (≈0.5 mol% of Ti in 
bulk SrTiO 3  

[ 30 ]  as compared with ≈130 mol% of Ti in SrTiO 3  in 
the current study) and the eventual formation of a layered, Ti-
rich phase with nominal chemical formula Sr 2 Ti 7 O 14 . Scanning 
transmission electron microscopy (STEM)-based studies map 
out the structure and valence state of this phase, fi rst-principles 

  Self-assembled oxide nanostructures produced, for example, 
via eutectic phase separation, spinodal decomposition-like 
routes, and other pathways [ 1–8 ]  have drawn considerable 
interest for their varied properties. Such approaches leverage 
innate chemical and thermodynamic driving forces that favor 
the spontaneous separation of two phases into an equilibrium 
state characterized by potentially complex micro- and nano-
structures (i.e., layered structures, vertically aligned rods in a 
matrix, etc.) and exotic composite properties. [ 4,7,9 ]  Researchers 
have demonstrated the ability to control the geometry, shape, 
and size of such phase-separated structures by tuning material 
composition, [ 10 ]  growth temperature, [ 11 ]  strain state, [ 12 ]  growth, 
and cooling rates. [ 3,13–17 ]  Deterministic and ordered materials 
self-assembly in these systems is, however, a challenge. In 
particular, it is diffi cult to access submicron feature sizes in 
eutectic systems due to the high processing temperatures and 
fast cooling rates that must be used. [ 1    –4 ]  Although spinodal 
decomposition-like routes have been used to produce nanoscale 
features, producing long-range ordered arrays of features via 
this approach is diffi cult. [ 10 ]  

 On the other hand, non-equilibrium approaches, including 
modern thin-fi lm growth techniques, can be applied to sys-
tems to produce atomically and chemically precise artifi cial 
heterostructures and nanostructures. [ 18,19 ]  Leveraging advances 
in deposition techniques and the development of in situ 

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approaches explore the phase stability and electronic properties, 
and studies of the dielectric, optical, thermal, and magnetic 
properties reveal diminished dielectric permittivity (and low 
dielectric loss), an enhanced bandgap, glass-like thermal con-
ductivity, and the potential for 2D anti-ferromagnetism. 

 In the equilibrium phase diagram ( Figure    1  a), [ 26 ]  the eutectic 
composition for the SrTiO 3 –TiO 2  system is located at 21 mol% 
SrO/79 mol% TiO 2 . Films of the SrTiO 3 –TiO 2  system were 
grown on SrTiO 3  (001), (110), and (111) substrates via pulsed-
laser deposition from targets of the following compositions 
(where the fi rst and second numbers refer to the mole per-
centage of SrO and TiO 2 , respectively): 43:57, 33:67, 30:70, 
25:75, 23:77, 21:79, 17:83, 10:90, and 0:100. Details of the growth 
process are provided in the Supporting Information. X-ray dif-
fraction studies of all fi lms (focusing on ≈100 nm thick fi lms 
on SrTiO 3  (111) substrates) reveal only a single set of diffraction 
peaks and no evidence of phase separation or multiple phases 
(Figure S1, Supporting Information). Atomic-force microscopy 
studies reveal no evidence of phase separation with the surface 
remaining relatively smooth across all compositions (Figure S2, 
Supporting Information). Only upon in-depth cross-sectional 
high-angle annular dark-fi eld (HAADF)-STEM imaging of the 
atomic structure of the fi lms did clear differences emerge (see 
Figure S3, Supporting Information for details) and only when we 
reach the eutectic composition of 21 mol% SrO/79 mol% TiO 2  
does the STEM imaging reveal the presence of an unexpected 
layered phase with an out-of-plane periodicity of ≈0.91 nm 
(Figure  1 b). Such a layered phase was observed on (111)-ori-
ented versions of SrTiO 3 , (LaAlO 3 ) 0.3 –(Sr 2 AlTaO 6 ) 0.7  (LSAT), 
LaAlO 3 , and Nb-doped SrTiO 3  substrates, but not on (001)- and 
(110)-oriented substrates (where complex and disordered struc-
tures are observed, Figure S3, Supporting Information). 

  High-resolution HAADF-STEM imaging ( Figure    2  a) and 
nano-area electron diffraction (NAED) (Figure  2 b) were com-
pleted to assess the atomic structure of the phase (see Sup-
porting Information for details). Both the STEM imaging and the 
NAED patterns reveal a periodicity of ≈0.91 nm along the out-of-
plane direction (ca. 4 times longer than that of the SrTiO 3  {111} 

d-spacing). Along the in-plane direction, fi rst- and second-order 
diffraction peaks (Figure  2 b) reveal periodicities of ≈0.487 and 
≈0.243 nm that correspond to Sr–Sr and Sr–O interatomic spac-
ings, respectively. Comparison with the SrTiO 3  substrate (inset, 
Figure  2 a,b) reveals that the layered phase is composed of layers 
with local coordination akin to that in SrTiO 3  that are separated 
by a monolayer of periodically aligned Ti- and O-ions (that exhibit 
reduced Z-contrast and are consistent with the highly Ti-rich 
nature of the fi lm composition). 

  Average structural information about the layered phase 
was obtained using on-axis (about the 222-diffraction peak of 
the substrate) and off-axis (about the 113- and 042-diffraction 
peaks of the substrate) X-ray reciprocal space mapping (RSM) 
studies (Figure  2 c–e). Here, we index the fi lm assuming that 
the  a ,  b , and  c  lattice parameters are parallel to the [112], [110], 
and [111] of the substrate, respectively. The order of the diffrac-
tion condition is determined by comparison to the measured 
periodicities from the STEM imaging and NAED patterns. 
On-axis RSM studies (Figure  2 c) show the presence of a fi lm 
peak (indexed as the 008-diffraction condition) that reveals an 
out-of-plane lattice spacing  c  ≈ 0.915 nm (commensurate with 
the 0.91 nm obtained from the STEM and NAED analysis). 
Off-axis RSM studies about the 042-diffraction condition of the 
substrate (Figure  2 d) show the presence of a fi lm peak indexed 
to be the 048-diffraction condition that enables calculation of 
the in-plane spacing  b  ≈ 0.569 nm (≈3.1% expanded as com-
pared with the substrate in the same direction). Off-axis RSM 
studies about the 113-diffraction condition of the substrate 
(Figure  2 e) reveal the presence of a set of fi lm peaks indexed 
to be the 4 07- and 406-diffraction conditions that enables cal-
culation of the in-plane lattice spacing  a  ≈ 0.987 nm (≈3.1% 
expanded as compared with the substrate lattice spacing in the 
same direction).  φ -scans about the 042- and 048-diffraction con-
ditions of the substrate and fi lm (Figure  2 f), respectively, reveal 
the epitaxial relationship to be [100] f //[112] s  and [010] f //[ 110] s  
and, from STEM/NAED, the out-of-plane [001] f  is found to be 
tilted by ≈10.2° from the [111] s  (where f and s refer to fi lm and 
substrate, respectively). In summary, the unit cell of the layered 

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 Figure 1.    Self-assembled, layered eutectic SrTiO 3 –TiO 2  fi lm. a) Equilibrium eutectic phase diagram of SrO–TiO 2  system (Adapted with per-
mission. [26]  Copyright 1969, American Ceramic Society. Printed with permission of the American Ceramic Society (www.ceramics.org).). 
b) HAADF-STEM image of the resulting fi lm of eutectic composition (21 mol% SrO/79 mol% TiO 2 ) grown on a SrTiO 3  (111) substrate. Inset shows 
alignment of the structure. 



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phase is:  a  = 0.987 nm,  b  = 0.569 nm,  c  = 0.929 nm,  α  =  γ  = 90°, 
and  β  = 100.2°. Note that this unit cell corresponds to two for-
mula units (i.e., Sr 4 Ti 14 O 28 ) to fully encompass the complex 
symmetry of the system. 

 From the STEM imaging, it is possible to extract the atomic 
positions (of the cations) and to produce a model of the pro-
posed structure. Although it is not possible to resolve all of the 
O-ions, the cation arrangement suggests that all Ti–O bonding 
should occur within octahedra (TiO 6 ) and that all O-sites are 
fully occupied to both compensate charge and coordination 
(a detailed discussion of the atomic model and simulated diffrac-
tion patterns is provided in Table S1 and Figure S4 and S5 in the 
Supporting Information). Based on the extracted inter atomic dis-
tances, an atomic model can be constructed and the simulated 
diffraction pattern [ 31 ]  for this initial model matches that obtained 
in the NAED studies well, suggesting a good initial under-
standing of the structure (Figure S5c, Supporting Information). 

 Disambiguation of the structure, however, requires addi-
tional steps. Briefl y, the STEM imaging provides a projection 
of the atomic columns, but does not reveal the density or exact 
make-up of atoms in those columns. Thus, there were a number 

of potential candidate structures consistent with the image. We 
reiterate that no Ti-rich SrTiO 3  phases are reported within the 
vicinity of the eutectic composition in the equilibrium phase 
diagram. Although not reported on the equilibrium phase dia-
gram, two Ti-rich phases have been reported in the literature: 
Sr 2 Ti 5 O 12  

[ 32 ]  (corresponding to 29 mol% SrO/71 mol% TiO 2 ) 
and Sr 2 Ti 6 O 13  

[ 33 ]  (corresponding to 25 mol% SrO/75 mol% 
TiO 2 ). Both phases are known to exist only as minor phases, 
are thought to be metastable, and are off in composition 
(8 and 4 mol% defi cient in TiO 2 , respectively) from the eutectic 
composition studied herein. Nonetheless, we have considered 
the possibility that these phases (or a phase possessing these 
nominal chemical formulas and a structure commensurate 
with that observed here) could be the novel, layered phase. 
A detailed description of these candidate phases is provided 
(Figure S6, Supporting Information). 

 Differentiation of the potential structures for the layered 
phase is achieved by chemical analyses. First, from Rutherford 
backscattering spectrometry (Figure S7, Supporting Informa-
tion) the Sr:Ti ratio for the fi lms is determined to be ≈1:3.6 that 
matches (within the experimental error) the Sr 2 Ti 7 O 14  phase. 

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 Figure 2.    Structural characterization of the novel, layered phase. a) HAADF-STEM image after smoothing process (along the [110] zone axis of the 
substrate) of the novel, layered phase. Inset shows a corresponding image along the same zone axis for the SrTiO 3  substrate. b) NAED pattern from 
the novel, layered phase. Inset shows a corresponding NAED pattern along the same zone axis for the SrTiO 3  substrate. RSM studies about the 
c) 222-, d) 042-, and e) 113-diffraction conditions of the substrate. f )  φ -scans about the 042- and 048-diffraction conditions of the substrate and fi lm, 
respectively, revealing the epitaxy of the fi lm/substrate system.



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N Thus, from the atomic-level imaging, X-ray diffraction, and 
chemical analyses, the novel, layered phase produced during 
the growth of the eutectic composition materials is determined 
to be a new phase – Sr 2 Ti 7 O 14 . The proposed unit cell for this 
phase is highlighted by the presence of layers with local coor-
dination akin to that in SrTiO 3  that are separated by a mono-
layer of periodically aligned Ti- and O-ions. We also note that 
in the unit cell of this structure that there are three types of 
octahedral bonding including two corner-, four edge-, and eight 
face-sharing octahedra (Figure S5b, Supporting Information). 
This specifi c complex and close-packed TiO 6  octahedra arrange-
ment is not reported in any published TiO  x   phase, but corner-, 
edge-, and face-sharing octahedra are all possible in TiO  x   sys-
tems. The appropriate charge balance of this structure could 
be achieved (theoretically, assuming nearly complete oxidation) 
with three possible combinations of Ti 2+ :Ti 3+ :Ti 4+  species occur-
ring in ratios of 2:0:5, 1:2:4, and 0:4:3. Previous studies suggest 
that face-sharing octahedra in Ti-based systems require the 
presence of Ti 3+  [ 34 ]  and since eight of the total 14 octahedra in 
the unit cell are face-sharing, we expect that Ti 3+  must populate 
the majority of the Ti-sites, suggesting that the structure should 
possess a 0:4:3 ratio of Ti 2+ :Ti 3+ :Ti 4+ . 

 The average valence state of Ti in Sr 2 Ti 7 O 14  was probed via 
STEM-based electron energy loss spectroscopy (EELS) studies 
of the Ti– L 2,3   and O– K  edge spectra ( Figure    3  a). We observe a 
shift (to lower energies) and broadening of the Ti– L 2,3   peaks for 
the novel, layered phase as compared with the SrTiO 3  substrate 
consistent with what has been observed in oxygen-defi cient 
SrTiO 3−δ  

[ 35 ]  and Ti 2 O 3  (that possess only Ti 
3+  valence states) [ 36 ]  

thereby confi rming the presence of a mixed Ti 3+ /Ti 4+  valence 
state. We also note that the intensity of the  α  peak from the 
O– K  edge spectra is signifi cantly diminished indicating that the 
Sr–O bonding contributes less to the spectra [ 37 ]  which is, again, 
consistent with Sr 2 Ti 7 O 14  (especially the TiO  x   inter-layers) pos-
sessing less Sr–O bonding compared with SrTiO 3 . 

  Armed with this detailed structural and chemical data, we 
further explored the structure and stability of the Sr 2 Ti 7 O 14  

phase via density functional theory (DFT) using hybrid func-
tionals (see Supporting Information for details). Considering 
the possibility of several valence states for the Ti-ions within 
the structure, it is possible that the TiO 6  octahedra may be sus-
ceptible to energetically favorable internal distortions. Small 
perturbations of the TiO 6  octahedra may not be resolvable via 
experiment alone and we used the DFT approaches to assess 
the lowest energy structure of the Sr 2 Ti 7 O 14  phase. The simu-
lations reveal that the structure is locally stable, and confi rm 
the presence of slight octahedral distortions, for which we fi nd 
an energy recovery of ≈3.4 eV per unit cell in comparison to 
the undistorted structure. This is a reasonably large energy 
recovery in comparison to the atomization energy, which we 
fi nd to be ≈196 eV per unit cell. Several distinct distortions are 
present, corresponding to the various Ti 3+  and Ti 4+  environ-
ments for the octahedra. A schematic illustrating the lowest-
energy structure is provided (Figure  3 b,c). From this experi-
mentally and DFT-optimized structure, we can thus compare 
the experimentally observed atomic structure (Figure  3 d) to a 
simulated Z-contrast STEM image (Figure  3 e), as well as a sim-
ulated selective area diffraction pattern (Figure  3 f) to the actual 
NAED pattern. This comparison shows excellent and nearly 
ideal matching (including matched modulation of the intensity 
across the diffraction pattern); thereby confi rming the extracted 
and optimized structure is representative of the real structure 
of the material. 

 Based on the structural analysis that suggests a new struc-
ture and phase, it is important to understand the mechanism 
for and nature of the evolution of this exotic phase. Clearly 
the structure that is formed deviates, somewhat dramatically, 
from the traditional eutectic system from which it was grown, 
and thus it warrants comparison with other exotic structures 
observed in materials – namely crystallographic shear struc-
tures (CSS). CSS can be considered as an example of so-called 
non-conservative defect structures – or defect structures that 
change the composition of the parent material – and have been 
found in a range of materials. [ 38–42 ]  In transition metal oxides, 

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 Figure 3.    Atomic models and spectroscopy of the novel, layered phase. a) EELS profi le from the novel, layered phase (orange) and SrTiO 3  substrate 
(blue) revealing the presence of a mixture of Ti 3+ /Ti 4+  in the former. Schematic illustrations of b) multiple unit cells (along the [110]) and c) a 3D 
view of a single unit cell of the proposed (experimentally and DFT-optimized) structure for Sr 2 Ti 7 O 14  revealing the various types of TiO 6  octahedra 
bonding including corner- (blue), edge- (violet), and face-sharing (cyan). d) Smoothed  Z -contrast STEM image of the novel layered phase. e) Simulated 
Z-contrast STEM image of the same area of the novel layered phase confi rming excellent matching of the extracted structure. f ) Simulated diffraction 
pattern for the model structure overlaid on the top of the NAED diffraction pattern revealing excellent matching. The blue circle marks the 000 diffrac-
tion condition.



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special non-conservative defect structures occur whereby a 
reduction of the oxygen content results in a disruption of the 
underlying structural framework whence the structure is effec-
tively cleaved, a fraction of the oxygen ions are removed, and 
the structure is placed back together, now sheared (or shifted) 
with respect to one another thereby creating a so-called crystal-
lographic shear plane. [ 38,43 ]  While early work on CSS focused 
on binary oxide materials, more recent work has explored CSS 
in ternary, anion-defi cient perovskites [ 42,44–47 ]  and others have 
gone on to extend the idea to cation-excess systems such as the 
RP homologous series. [ 48–50 ]  In a similar spirit, it is possible to 
discuss Sr 2 Ti 7 O 14  within the confi nes of CSS. Assuming that 
the parent material is in fact SrTiO 3  and noting that the full 
unit cell for our system has been determined to be Sr 4 Ti 14 O 28 , 
we would then want to compare this to 14 unit cells of the 
parent SrTiO 3  (i.e., Sr 14 Ti 14 O 42 ). Sr 2 Ti 7 O 14  could be produced 
upon the removal of 10 Sr- and 14 O-ions from the 14 unit cells 
of SrTiO 3  (or 0.71 Sr and 0.33 O per unit cell of SrTiO 3 ). The 
Sr and O are preferentially removed from (111) in the structure 
(producing layers of TiO  x   with no Sr atoms) and the remaining 
perovskite layers are sheared by ½[112]. 

 Such a comparison with CSS may provide an alternative way 
of thinking about this system, but is important to point out a 
number of ways that the Sr 2 Ti 7 O 14  differs from traditional CSS 
systems. First, as noted from the analysis above, Sr 2 Ti 7 O 14  
is a fully oxidized system (i.e., with the exception of a small, 
equilibrium density of oxygen vacancies common to all oxide 
materials, all available oxygen sites in the structure are fully 
occupied) like in the case of the RP phases. In Sr 2 Ti 7 O 14  the 
mixed Ti 3+  and Ti 4+  valence state originates from the coor-
dination environment of the Ti-ions in the TiO  x  -layers, not 
from large-scale oxygen defi ciency. This is different from the 
vast majority of work on CSS that has focused on signifi cantly 
anion-defi cient systems. Second, the nature of the non-stoichi-
ometry is both opposite to and vastly larger in magnitude in 
Sr 2 Ti 7 O 14  than in previously examined systems. In the RP sys-
tems, for instance, there is  A -site excess and in the worst case 
that excess is only 2:1  A : B  ratio whereas in Sr 2 Ti 7 O 14  there is 
 B -site excess with a much larger 2:7  A : B  ratio. Finally, typical 
CSS systems lack long-range order to the CSS since there is 
a degenerate family of shear planes. This typically causes the 
material to possess complex rotations of the CSS giving rise to 
what some have called waves, hairpins, and Γ-shapes as in the 
case of the  A n B n  O 3 n −2  homologous series of perovskite-based 
CSS. [ 42 ]  In the Sr 2 Ti 7 O 14  phase, however, we have observed only 
one variant of the potential CSS that runs parallel to the growth 
plane of the fi lm in a highly ordered, periodic fashion across 
the sample. 

 In the end, articulation of the structure within the parlance 
of CSS may help shed some light on the mechanism under-
lying the formation of this structure. Ultimately it appears to be 
an extreme type of CSS that is likely infl uenced by a number of 
factors. First, thin-fi lm epitaxy and substrate orientation appear 
to play a critical role since growth of fi lms simultaneously on 
SrTiO 3  (001), (110), and (111) substrates reveals that only the 
(111)-oriented substrates give rise to the Sr 2 Ti 7 O 14  phase. This 
likely arises from the fact that the TiO  x   layers in the structure, 
which possess sixfold symmetry, would be diffi cult to form on 
the fourfold or twofold symmetric cubic and rectangular lattices 

of (001)- and (110)-oriented substrates (in other words, the (111) 
surface is the only orientation that can accommodate the CSS). 
Second, the fi lm composition is found to be important since 
a deviation of only ≈3 mol% in TiO 2  composition can destroy 
the phase (Figure S3, Supporting Information). Finally, the 
kinetics of the growth process appear to play a role. Truly this 
is a non-equilibrium structure and the degree of order in the 
Sr 2 Ti 7 O 14  increases as the growth rate is reduced suggesting 
that the formation of the phase requires suffi cient time for the 
diffusion/rearrangement of the constituent ions. The system is 
likely metastable in the sense that the Sr 2 Ti 7 O 14  was found to 
be stable at growth temperatures <850 °C, above which the fi lm 
decomposes into two phases (rutile TiO 2  and SrTiO 3 ). 

 Having established the structure, we proceed to explore 
the electronic structure and physical properties of Sr 2 Ti 7 O 14  
including optical absorption, dielectric permittivity and loss, 
thermal conductivity, and magnetism. Again, due to the pres-
ence of mixed-valence cations [Ti 3+  (3 d  1 ) and Ti 4+  (3 d  0 )], special 
attention was given to probing the electronic structure and 
potential for spin ordering. In structures with face-, edge-, and 
corner-sharing octahedra, superexchange and direct exchange 
mechanisms compete with each other and the prevailing spin 
confi guration is determined by a competition between different 
exchange interactions that are affected by electron occupancy of 
orbitals, bond angles, and cation–cation separation. [ 51–53 ]  From 
inspection of the crystal structure, two spin confi gurations are 
possible. In the fi rst, direct exchange interactions within both 
pairs of Ti-ions participating in face-sharing octahedra drive 
localization of the excess electrons. In this confi guration, a 
direct exchange interaction  J  is expected to be large within a 
pair of face-sharing octahedra, but weaker from one pair to 
the next. In the second, the Ti-ions (in the TiO  x   plane) par-
ticipating in edge-sharing octahedra carry the excess electrons 
and superexchange mechanisms support a 2D ordered spin 
confi guration. 

 Conventional DFT simulations [ 54 ]  predict that the structure 
is not spin-polarized and, although there is a large gap between 
the nominal valence and conduction bands, the Fermi level 
is located above the conduction band edge and the system is 
predicted to be metallic (which it is not). Additionally, rather 
than distinct Ti 3+ -and Ti 4+ -ions, the extra electrons are shared 
equally amongst all Ti-ions (in the TiO  x   plane) in a metallic 
state. Moving to hybrid DFT calculations, which we expect to be 
more accurate in this case, we are able to assess the possibility 
of charge and spin ordering. For a standard choice of hybrid 
parameters, [ 55 ]  we predict that an anti-ferromagnetic check-
erboard-like spin confi guration, in which the excess electrons 
are localized on the Ti-ions within the TiO  x   plane ( Figure    4  a), 
is more stable than the non-magnetic one by ≈0.2 eV/unit cell. 
Examination of the distribution of up- and down-spin electron 
density within the TiO  x   plane (Figure  4 b) shows the nature of 
the anti-ferromagnetic order and how the oxygen ions along 
the octahedral shared edges mediate the anti-ferromagnetic 
Ti confi guration via superexchange, indicating that the second 
scenario considered above prevails. It should also be noted, that 
the spin-down electron distributions are observed to extend 
asymmetrically out of the plane toward the neighboring Ti 
atoms across the shared octahedral face, suggesting that mild 
elements of the fi rst scenario (a ferromagnetic coupling across 

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face sharing octahedra due to direct exchange) are also present, 
but weaker than the anti-ferromagnetic order within the plane. 

  Finally, the electronic density of states (Figure  4 c) reveals 
three distinct sets of states are present in the vicinity of the 
Fermi energy. The lower set of states (nominally the valence 
band), exhibits an oxygen 2 p  character while the intermediate 
and upper (nominally conduction band) exhibit a Ti 3 d  char-
acter. The intermediate states are highly localized to the edge-
sharing Ti atoms in the TiO  x   plane and likely are states offset 
from the conduction bands, stabilized in part by exchange 
interactions leading to the anti-ferromagnetic confi guration. [ 56 ]  
The primary gap is calculated to be 3.7–3.8 eV. 

 Subsequent experimental study confi rms many of these 
observations. Magnetic measurements of the sample cooled 
from 550 K in a magnetic fi eld and in zero fi eld reveal no fer-
romagnetic ordering either in- or out-of-the-plane of the fi lm 
from 4 to 550 K, but a broad peak in the magnetic susceptibility 
was observed in both fi eld cooled and zero fi eld cooled measure-
ments around 400 K, which could be indicative of anti-ferromag-
netic ordering in the material and is consistent with the predic-
tions of anti-ferromagnetic order from the hybrid DFT studies. 
Transmittance and refl ectance studies of Sr 2 Ti 7 O 14 /LaAlO 3  (111) 
heterostructures also confi rm the predictions of the hybrid DFT 
studies. A linear fi t of  αhv  2  (where  α  is the absorption coeffi -
cient,  h  is Planck constant, and  υ  is the frequency of photon) as 
a function of the photon energy ( hυ ) ( Figure    5  a) reveals a direct 
bandgap for Sr 2 Ti 7 O 14  of ≈3.87 eV. The decreased transmittance 
in Sr 2 Ti 7 O 14  between 360 and 660 nm is due to the LaAlO 3  sub-
strate with complex twin structures that refl ect the visible light 
diffusively and decreases the transmittance. See the Supporting 
Information for details of these measurements. 

  Likewise, probes of electronic conduction reveal a highly 
insulating material (albeit with some anisotropy). When 
measured in the out-of-plane geometry, 100 nm thick fi lms 
revealed low leakage current densities of <0.01 µA cm –2  even 
under applied electric fi elds in excess of 200 kV cm –1  while 
measurements in the in-plane geometry revealed leakage 

currents at least 10 2 -times larger, but still 
indicative of an insulating material (Figure 
S8, Supporting Information). Such obser-
vations are consistent with what might be 
expected based on the highly anisotropic 
structure, which could limit conduction out-
of-the-plane of the fi lm and based on what 
has been observed mixed Ti 3+ /Ti 4+  TiO  x   com-
pounds where the conductivity can be larger 
than in purely Ti 4+  systems. [ 57 ]  Subsequent 
probes of the out-of-plane dielectric per-
mittivity ( ε  r ) and loss tangent of Sr 2 Ti 7 O 14 /
Nb-doped SrTiO 3  (111) heterostructures at 
room temperature as a function of frequency 
have also been completed (Figure  5 b). The 
dielectric permittivity of the Sr 2 Ti 7 O 14  fi lms 
was found to be essentially frequency-inde-
pendent with a value of 48 with low loss 
tangents (0.002 at 10 kHz) in the frequency 
range 1–100 kHz. This low dielectric per-
mittivity may be expected considering that 
the Sr 2 Ti 7 O 14  phase consists of SrTiO 3 -like 

layers ( ε  r  ≈ 300) and layers of face-sharing octahedra TiO  x   layers 
(which are structurally similar to Ti 2 O 3  that has a  ε  r  ≈ 45) [ 58 ]  that 
effectively produce a nanoscale, layered dielectric. 

 Lastly, the thermal conductivity ( κ ) of the Sr 2 Ti 7 O 14  fi lms 
was measured in the fi lm-normal direction by time-domain 
thermorefl ectance (TDTR) [ 59 ]  (see Figure S9, Supporting 
Information for details). We note that the thermal conduc-
tivity of the Sr 2 Ti 7 O 14  fi lms shows a signifi cantly lower value 
of  κ  ≈ 1.3 W m-K –1  compared with parent phases SrTiO 3  
and TiO 2  that range between 8.8 and 11.2 W m 

–1  K –1  [ 60,61 ]  
whereas the speed of sound of the layered fi lm remains 
essentially the same as the parent phases. Previously, low 
 κ  has been observed in artifi cially synthesized SrTiO 3 -superla-
ttice systems ( κ  ≥ 2.8 W m –1  K –1  for (SrTiO 3 ) m /(CaTiO 3 )  n   and 
 κ  ≥ 1.8 W m –1  K –1  for (SrTiO 3 ) m /(BaTiO 3 )  n   superlattices) [ 62 ]  and 
in Sr  n +1 Ti  n  O 3 n +1   RP-phases ( κ  ≥ 4.5 W m –1  K –1 ), [ 63 ]  but not as 
low as that observed in the Sr 2 Ti 7 O 14  fi lms. We hypothesize 
that the glass-like thermal conductivity arises from two main 
contributions: i) signifi cant phonon scattering at the bounda-
ries between SrTiO 3 -like and TiO  x   layers in this phase and ii) 
a low contribution of electronic thermal conductivity from low 
free electron concentration. This is not surprising considering 
that Sr 2  Ti 7 O 14  has a periodic spacing of 0.91 nm in the out-of-
plane direction (excellent for scattering portions of the heat car-
rying phonons) and that the electrical conductivity is extremely 
low as we observed from the leakage experiment. The ability 
to produce highly ordered layered structures with subnanom-
eter length-scales could open up many opportunities for low 
thermal transport applications. 

 In conclusion, we have synthesized a new phase Sr 2 Ti 7 O 14  
that self-assembled into a highly ordered, layered structure that 
consists of layers with local order akin to that of SrTiO 3  sepa-
rated by close-packed, TiO  x   layers by combining non-equilib-
rium growth techniques, thin-fi lm epitaxy, and a system with 
an innate chemical/structural instability. We observe that the 
layered Sr 2 Ti 7 O 14  phase is realized only at the eutectic composi-
tion of the SrTiO 3 –TiO 2  system, when growth takes place on 

Adv. Mater. 2015, 27, 861–868

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www.MaterialsViews.com

 Figure 4.    Spin confi guration, orbital charge density, and electronic density of states of the 
novel, layered phase. Schematic illustration of a) the proposed spin confi guration in which 
the edge-sharing, planar TiO 6  octahedra exhibit a 3 d  

1  electron valence and a checkerboard 
anti-ferromagnetic spin confi guration and b) the charge density of the orbitals corresponding 
to this confi guration according to hybrid DFT calculations, showing the occupation of orbitals 
to minimize electron overlap. c) Corresponding electronic density of states for the system.



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(111)-oriented perovskite substrates, and when the kinetics of 
the growth process are appropriately controlled. It should be 
noted, however, that although the phase is found to form at the 
eutectic composition, the role of the innate eutectic tendency of 
this system in stabilizing this layered phase is not fully under-
stood at this point and is clearly a matter for future studies in 
other systems. In-depth X-ray and electron diffraction studies 
and imaging have allowed for the precise identifi cation of the 
structure and unit cell of this phase. Subsequent chemical and 
spectroscopic studies were used to confi rm these studies. The 
Sr 2 Ti 7 O 14  phase possesses properties that are unique from 
the parent SrTiO 3  and TiO 2  phases including a larger optical 
bandgap of 3.87 eV, reduced dielectric constant of 48, low dielec-
tric loss, and a glass-like thermal conductivity of 1.3 W m –1  K –1 . 

This unique approach to the formation of high-ordered lay-
ered materials could represent a new modality to achieve novel 
states of matter in other systems possessing similar chemical/
structural instabilities and can provide new insights into the 
design of hierarchical structures by self-assembly.  

  Supporting Information 
 Supporting Information is available from the Wiley Online Library or 
from the author.  

  Acknowledgements 
 S.L., Z.C., P.V.B., and L.W.M. acknowledge the support of the Air Force 
Offi ce of the Scientifi c Research under grant FA9550–12–1–0471. A.R.D. 
acknowledges support from the Army Research Offi ce under grant 
W911NF-14–1–0104. E.B. acknowledges support from the National 
Science Foundation under grant DMR-1124696. P.G, N.F, and E.E. 
acknowledge support from the Strategic Research Initiatives Program 
of the College of Engineering at the University of Illinois at Urbana-
Champaign. N.O. and M.S. acknowledge support from the National 
Science Foundation under grant CHE-1153081. The work was carried 
out, in part, in the Materials Research Laboratory Central Research 
Facilities, University of Illinois.   

Received:  August 7, 2014 
Revised:  October 20, 2014 

Published online:  December 18, 2014   

[1]     R. L.    Ashbrook  ,  J. Am. Ceram. Soc.    1977 ,  60 ,  428 .  
[2]     V. S.    Stubican  ,   R. C.    Brandt  ,  Annu. Rev. Mater. Sci.    1981 ,  11 ,  267 .  
[3]     Y.    Waku  ,   N.    Nakagawa  ,   T.    Wakamoto  ,   H.    Ohtsubo  ,   K.    Shimizu  , 

  Y.    Kohtoku  ,  Nature    1997 ,  389 ,  49 .  
[4]     J. L.    Llorca  ,   V. M.    Orera  ,  Prog. Mater. Sci.    2006 ,  51 ,  711 .  
[5]     H.    Zheng  ,   J.    Wang  ,   S. E.    Lofl and  ,   Z.    Ma  ,   L.    Mohaddes-Ardabili  , 

  T.    Zhao  ,   L.    Salamanca-Riba  ,   S. R.    Shinde  ,   S. B.    Ogale  ,   F.    Bai  , 
  D.    Viehland  ,   Y.    Jia  ,   D. G.    Schlom  ,   M.    Wuttig  ,   A.    Roytburd  , 
  R.    Ramesh  ,  Science    2004 ,  303 ,  661 .  

[6]     B. S.    Guiton  ,   P. K.    Davies  ,  Nat. Mater.    2007 ,  6 ,  586 .  
[7]     J. L.    MacManus-Driscoll  ,  Adv. Funct. Mater.    2010 ,  20 ,  2035 .  
[8]     S. A.    Harrington  ,   J.    Zhai  ,   S.    Denev  ,   V.    Gopalan  ,   H.    Wang  ,   Z.    Bi  , 

  S. A. T.    Redfem  ,   S.-H.    Baek  ,   C. W.    Bark  ,   C.-B.    Eom  ,   Q.    Jia  , 
  M. E.    Vickers  ,   J. L.    MacManus-Driscoll  ,  Nat. Nanotechnol.    2011 ,  6 ,  491 .  

[9]     W.    Zhang  ,   A.    Chen  ,   Z.    Bi  ,   Q.    Jia  ,   J. L.    MacManus-Discoll  ,   H.    Wang  , 
 Curr. Opin. Solid State Mater. Sci.    2013 ,  18 ,  6 .  

[10]     M.    Muralidhar  ,   N.    Sakai  ,   M.    Nishiyama  ,   M.    Jira  ,   T.    Machi  , 
 Appl. Phys. Lett.    2003 ,  82 ,  943 .  

[11]     L.    Mohaddes-Ardabili  ,   H.    Zheng  ,   S. B.    Ogale  ,   B.    Hannoyer  ,   W.    Tian  , 
  J.    Wang  ,   S. E.    Lofl and  ,   S. R.    Shinde  ,   T.    Zhao  ,   Y.    Jia  ,   L.    Salamanca-
Riba  ,   D. G.    Schlom  ,   M.    Wuttig  ,   R.    Ramesh  ,  Nat. Mater.    2004 ,  3 ,  533 .  

[12]     J. L.    MacManus-Driscoll  ,   P.    Zerrer  ,   H.    Wang  ,   H.    Yang  ,   J.    Yoon  , 
  A.    Fouchet  ,   R.    Yu  ,   M. G.    Blamire  ,   Q.    Jia  ,  Nat. Mater.    2008 ,  7 ,  314 .  

[13]     Y.    Lu  ,   C.    Wang  ,   Y.    Gao  ,   R.    Shi  ,   X.    Liu  ,   Y.    Wang  ,  Phys. Rev. Lett.    2012 , 
 109 ,  086101 .  

[14]     M.    Parlier  ,   R.    Valle  ,   L.    Perrière  ,   S.    Lartigue-Korinek  ,   L.    Mazerolles  , 
 J. Aerosp. Lab.    2011 ,  AL03 .  

[15]     A.    Revcolevschi  ,   G.    Dhalenne  ,  Adv. Mater.    1993 ,  5 ,  657 .  
[16]     D. A.    Pawlak  ,   S.    Turczynski  ,   M.    Gajc  ,   K.    Kolodziejak  ,   R.    Diduszko  , 

  K.    Rozniatowski  ,   J.    Smalc  ,   I.    Vendik  ,  Adv. Funct. Mater.    2010 ,  20 , 
 1116 .  

Adv. Mater. 2015, 27, 861–868

www.advmat.de
www.MaterialsViews.com

 Figure 5.    Optical, dielectric, and thermal properties of the novel, layered 
phase. a) The dependence of α hv  2  on photon energy ( hv ) and (inset) 
transmittance of the Sr 2 Ti 7 O 14  phase. b) Dielectric permittivity ( ε  r ) and 
loss tangent (tanδ) of the Sr 2 Ti 7 O 14  phase measured at 10 mV of ac 
voltage bias with no dc bias as a function of frequency. c) Thermal con-
ductivity ( κ , top) and speed of sound ( υ , bottom) for SrTiO 3 , TiO 2 , and 
Sr 2 Ti 7 O 14  as measured by TDTR.



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[17]     R. M.    White  ,   J. M.    Kunkle  ,   A. V.    Polotai  ,   E. C.    Dickey  ,  J. Eur. Ceram. 
Soc.    2011 ,  31 ,  1227 .  

[18]     H. M.    Christen  ,   G.    Eres  ,  J. Phys.: Condens. Matter    2008 ,  20 , 
 264005 .  

[19]     D. G.    Schlom  ,   L.-Q.    Chen  ,   X.    Pan  ,   A.    Schmehl  ,   M. A.    Zurbuchen  ,  J. 
Am. Ceram. Soc.    2008 ,  91 ,  2429 .  

[20]     L. W.    Martin  ,   Q.    Zhan  ,   Y.    Suzuki  ,   R.    Ramesh  ,   M.    Chi  ,   N.    Browning  , 
  T.    Mizoguchi  ,   J.    Kreisel  ,  Appl. Phys. Lett.    2007 ,  90 ,  062903 .  

[21]     R. J.    Zeches  ,   M. D.    Rossell  ,   J. X.    Zhang  ,   A. J.    Hatt  ,   Q.    He  , 
  C.-H.    Yang  ,   A.    Kumar  ,   C. H.    Wang  ,   A.    Melville  ,   C.    Adamo  ,   G.    Sheng  , 
  Y.-H.    Chu  ,   J. F.    Ihlefeld  ,   R.    Erni  ,   C.    Ederer  ,   V.    Gopalan  ,   L.-Q.    Chen  , 
  D. G.    Schlom  ,   N. A.    Spaldin  ,   L. W.    Martin  ,   R.    Ramesh  ,  Science    2009 , 
 326 ,  977 .  

[22]     M.    Dawber  ,   N.    Stucki  ,   C.    Lichtensteiger  ,   S.    Gariglio  ,   P.    Ghosez  , 
  J.-M.    Triscone  ,  Adv. Mater.    2007 ,  19 ,  4153 .  

[23]     E.    Bousquet  ,   M.    Dawber  ,   N.    Stucki  ,   C.    Lichtensteiger  ,   P.    Hermet  , 
  S.    Gariglio  ,   J.-M.    Triscone  ,   P.    Ghosez  ,  Nature    2008 ,  452 ,  732 .  

[24]     J.    Chakhalian  ,   A. J.    Millis  ,   J.    Rondinelli  ,  Nat. Mater.    2012 ,  11 ,  92 .  
[25]     H. Y.    Hwang  ,   Y.    Iwasa  ,   M.    Kawasaki  ,   B.    Keimer  ,   N.    Nagaosa  , 

  Y.    Tokura  ,  Nat. Mater.    2012 ,  11 ,  103 .  
[26]     M. K.    Reser  ,  Phase Diagrams for Ceramists ,  American Ceramic 

Society ,  Columbus, OH, USA    1969 .  
[27]     J. H.    Haeni  ,   C. D.    Theis  ,   D. G.    Schlom  ,   W.    Tian  ,   X. Q.    Pan  , 

  H.    Chang  ,   I.    Takeuchi  ,   X.-D.    Xiang  ,  Appl. Phys. Lett.    2001 ,  78 ,  3292 .  
[28]     C.-H.    Lee  ,   N. D.    Orloff  ,   T.    Birol  ,   Y.    Zhu  ,   V.    Goian  ,   E.    Rocas  , 

  R.    Haislmaier  ,   E.    Vlahos  ,   J. A.    Mundy  ,   L. F.    Kourkoutis  ,   Y.    Nie  , 
  M. D.    Biegalski  ,   J.    Zhang  ,   M.    Bernhagen  ,   N. A.    Benedek  ,   Y.    Kim  , 
  J. D.    Brock  ,   R.    Uecker  ,   X. X.    Xi  ,   V.    Gopalan  ,   D.    Nuzhnyy  ,   S.    Kamba  , 
  D. A.    Muller  ,   I.    Takeuchi  ,   J. C.    Booth  ,   C. J.    Fennie  ,   D. G.    Schlom  , 
 Nature    2013 ,  502 ,  532 .  

[29]     T.    Suzuki  ,   Y.    Nishi  ,   M.    Fujimoto  ,  Philos. Mag. A    2000 ,  80 ,  621 .  
[30]     S.    Witek  ,   D. M.    Smyth  ,  J. Am. Ceram. Soc.    1984 ,  67 ,  372 .  
[31]     J.-M.    Zuo  ,   J. C.    Mabon  ,  Microsc. Microanal.    2004 ,  10 ,  S02 .  
[32]     B.    Peplinski  ,   Th.    Hübert  ,   M.    Willfahrt  ,   U.    Banach  ,  Mater. Sci. Forum   

 1996 ,  228 ,  531 .  
[33]     C. M.    Liu  ,   X. T.    Zu  ,   W. L.    Zhou  ,  J. Phys. D: Appl. Phys.    2007 ,  40 ,  7318 .  
[34]     M. G.    Vincent  ,   K.    Yvon  ,   A.    Grüttner  ,  Acta Crystallogr.    1980 ,  36 ,  803 .  
[35]     D. A.    Muller  ,   N.    Nakagawa  ,   A.    Ohtomo  ,   J. L.    Grazul  ,   H. Y.    Hwang  , 

 Nature    2004 ,  430 ,  657 .  
[36]     E.    Stoyanov  ,   F.    Langenhorst  ,   G.    Steinle-Neumann  ,  Am. Mineral.   

 2006 ,  92 ,  577 .  
[37]     Z.    Zhang  ,   W.    Sigle  ,   M.    Rühle  ,  Phys. Rev. B    2002 ,  66 ,  094108 .  
[38]     L. A.    Bursill  ,   B. G.    Hyde  ,  Prog. Solid State Chem.    1972 ,  7 ,  177.   
[39]     J. C.    Ruiz-Morales  ,   J.    Canales-Vazquez  ,   C.    Savaniu  ,   D.    Marrero-

Lopez  ,   W.    Zhou  ,   J. T. S.    Irvine  ,  Nature    2006 ,  439 ,  568 .  

[40]     G.    Van Tendeloo  ,   O. I.    Lebedev  ,   M.    Hervieu  ,   B.    Raveau  ,  Rep. Prog. 
Phys.    2004 ,  67 ,  1315 .  

[41]     E. D.    Sprecht  ,   A.    Goyal  ,   J.    Li  ,   P. M.    Martin  ,   X.    Li  ,   M. W.    Rupich  , 
 Appl. Phys. Lett.    2006 ,  89 ,  162510 .  

[42]     M.    Batuk  ,   S.    Turner  ,   A. M.    Abakumov  ,   D.    Batuk  ,   J.    Hadermann  , 
  G.    Van Tendeloo  ,  Inorg. Chem.    2014 ,  53 ,  2171 .  

[43]     J. S.    Anderson  ,   J. M.    Browne  ,   A. K.    Cheetham  ,   R.    Von Dreele  , 
  J. L.    Hutchison  ,   F. J.    Lincoln  ,   D. J. M.    Bevan  ,   J.    Straehle  ,  Nature   
 1973 ,  243 ,  81 .  

[44]     A. M.    Abakumov  ,   J.    Hadermann  ,   G.    Van Tendeloo  ,   E. V.    Antipov  , 
 J. Am. Chem. Soc.    2008 ,  91 ,  1807 .  

[45]     A. M.    Abakumov  ,   J.    Hadermann  ,   S.    Bals  ,   I. V.    Nikolaev  ,   E. V.    Antipov  , 
  G.    Van Tendeloo  ,  Angew. Chem. Int. Ed.    2006 ,  45 ,  6697 .  

[46]     A. M.    Abakumov  ,   J.    Haderman  ,   M.    Batuk  ,   H.    D’Hondt  , 
  O. A.    Tyablikov  ,   M. g.    Rozova  ,   K. V.    Pokholok  ,   D. S.    Filimonov  , 
  D. V.    Sheptyakov  ,   A. A.    Tsirlin  ,   D.    Niermann  ,   J.    Hemberger  , 
  G.    Van Tendeloo  ,   E. V.    Antipov  ,  Inorg. Chem.    2010 ,  49 ,  9508 .  

[47]     J.    Hadermann  ,   A. M.    Abakumov  ,   I. V.    Nikolaev  ,   E. V.    Antipov  ,   G.    Van 
Tendeloo  ,  Solid State Sci.    2008 ,  10 ,  382 .  

[48]     R. J. D.    Tilley  ,  J. Solid State Chem.    1977 ,  21 ,  293 .  
[49]     M. A.    McCoy  ,   R. W.    Grimes  ,   W. E.    Lee  ,  Philos. Mag. A    1997 ,  75 ,  833 .  
[50]     A. P.    Tomsia  ,   A. M.    Glaeser  ,  Ceramic Microstructures: Control at the 

Atomic Level ,  Plenum Press ,  New York    1998 .  
[51]     J.    Kanamori  ,  Prog. Theor. Phys.    1957 ,  17 ,  177 .  
[52]     J.    Kanamori  ,  Prog. Theor. Phys.    1957 ,  17 ,  197 .  
[53]     J. B.    Goodenough  ,  J. Phys. Chem. Solids    1958 ,  6 ,  287 .  
[54]     J.    Perdew  ,   K.    Burke  ,   M.    Ernzerhof  ,  Phys. Rev. Lett.    1996 ,  77 ,  3865 .  
[55]     A. V.    Krukau  ,   O. A.    Vydrov  ,   A. F.    Izmaylov  ,   G. E.    Scuseria  ,  J. Chem. 

Phys.    2006 ,  125 ,  224106 .  
[56]     P.    Gori  ,   N.    Ferdous  ,   E.    Ertekin  ,  unpublished .  
[57]     F. J.    Morin  ,  Phys. Rev. Lett.    1959 ,  3 ,  34 .  
[58]     G.    Lucovsky  ,   R. J.    Sladek  ,   J. W.    Allen  ,  Phys. Rev. B    1977 ,  16 ,  5452 .  
[59]     D. G.    Cahill  ,   W. K.    Ford  ,   K. E.    Goodson  ,   G. D.    Mahan  ,   A.    Majumdar  , 

  H. J.    Maris  ,   R.    Merlin  ,   S. R.    Phillpot  ,  J. Appl. Phys.    2003 ,  93 ,  793 .  
[60]     E.    Breckenfeld  ,   R.    Wilson  ,   J.    Karthik  ,   A. R.    Damodaran  ,   D. G.    Cahill  , 

  L. W.    Martin  ,  Chem. Mater.    2012 ,  24 ,  331 .  
[61]     D. J.    Kim  ,   D. S.    Kim  ,   S.    Cho  ,   S. W.    Kim  ,   S. H.    Lee  ,   J. C.    Kim  ,  Int. J. 

Thermophys.    2004 ,  25 ,  281 .  
[62]     J.    Ravichandran  ,   A. K.    Yadav  ,   R.    Cheaito  ,   P. B.    Rossen  , 

  A.    Soukiassian  ,   S. J.    Suresha  ,   J. C.    Duda  ,   B. M.    Foley  ,   C.-H.    Lee  , 
  Y.    Zhu  ,   A. W.    Lichtenberger  ,   J. E.    Moore  ,   D. A.    Muller  ,   D. G.    Schlom  , 
  P. E.    Hopkins  ,   A.    Majumdar  ,   R.    Ramesh  ,   M. A.    Zurbuchen  , 
 Nat. Mater.    2014 ,  13 ,  168 .  

[63]     K. H.    Lee  ,   S. W.    Kim  ,   H.    Ohta  ,   K.    Koumoto  ,  J. Appl. Phys.    2006 ,  100 , 
 063717 .