Local structure of Ba(1-x)Sr(x)TiO3 and BaTi(1-y)Zr(y)O3 nanocrystals probed by X-ray absorption and X-ray total scattering.

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Local Structure of Ba1xSrxTiO3 and BaTi1yZryO3 Nanocrystals Probed by X‑ray Absorption and X‑ray Total Scattering Federico A. Rabuffetti and Richard L. Brutchey* Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States

ABSTRACT The eﬀect of isovalent chemical substitution on the magnitude and coherence length of

local ferroelectric distortions present in sub-20 nm Ba1xSrxTiO3 (x = 0.0, 0.30, 0.50, 1.0) and BaTi1yZryO3 (y = 0.0, 0.15, 0.50, 1.0) nanocrystals synthesized at room temperature is investigated using X-ray absorption near edge structure (XANES) and pair distribution function analysis of X-ray total scattering data (PDF). Although the average crystal structure of the nanocrystals is adequately described by a centrosymmetric, cubic Pm3m space group, local ferroelectric distortions due to the displacement of the titanium atom from the center of the perovskite lattice are observed for all compositions, except BaZrO3. The symmetry of the ferroelectric distortions is adequately described by a tetragonal P4mm space group. The magnitude of the local displacements of the titanium atom in BaTiO3 nanocrystals is comparable to that observed in single crystals and bulk ceramics, but the coherence length of their ferroelectric coupling is much shorter (e20 Å). Substitution of Sr2þ for Ba2þ and of Zr4þ for Ti4þ induces a tetragonal-to-cubic transition of the room temperature local crystal structure, analogous to that observed for single crystals and bulk ceramics at similar compositions. This transition is driven by a reduction of the magnitude of the local displacements of the titanium atom and/or of the coherence length of their ferroelectric coupling. Replacing 50% of Ba2þ with Sr2þ slightly reduces the magnitude of the titanium displacement, but the coherence length is not aﬀected. In contrast, replacing 15% of the ferroelectrically active Ti4þ with Zr4þ leads to a signiﬁcant reduction of the coherence length. Deviations from the ideal solid solution behavior are observed in BaTi1yZryO3 nanocrystals and are attributed to an inhom*ogeneous distribution of the barium atoms in the nanocrystal. Compositionstructure relationships derived for Ba1xSrxTiO3 and BaTi1yZryO3 nanocrystals demonstrate that the evolution of the room temperature local crystal structure with chemical composition parallels that of single crystals and bulk ceramics, and that chemical control over ferroelectric distortions is possible in the sub-20 nm size range. In addition, the potential of PDF analysis of total scattering data to probe compositional ﬂuctuations in nanocrystals is demonstrated. KEYWORDS: vapor diﬀusion SolGel . perovskite . nanoparticles . XANES . total scattering

erovskite solid solutions Ba1xSrxTiO3 and BaTi1yZryO3 span a broad range of dielectric phenomena that make them functional materials in complex oxidebased microelectronics. The end members of these solid solutions are BaTiO3, SrTiO3, and BaZrO3. Although they share an ABO3 perovskite crystal structure consisting of AO12 cuboctahedra (A = Ba, Sr) and BO6 octahedra (B = Ti, Zr) as a common feature, their phase diagrams and dielectric behavior diﬀer signiﬁcantly. BaTiO3 undergoes three structural phase transitions: rhombohedral (R3m) to orthorhombic (Amm2) at 183 K, orthorhombic to tetragonal (P4mm) at 278 K, and tetragonal to cubic (Pm3m) at RABUFFETTI AND BRUTCHEY

393 K.1 The three low temperature phases are ferroelectric, whereas the high temperature phase is paraelectric. SrTiO3 is a quantum paraelectric featuring a tetragonal (I4/mcm) to cubic (Pm3m) phase transition at 105 K.2 The stabilization of the paraelectric state in the low temperature phase is due to zero-point quantum ﬂuctuations of the atomic positions.3 Finally, BaZrO3 remains cubic (Pm3m) and paraelectric at all temperatures. The crystal structure and dielectric properties of ABO3 perovskites can be rationally tuned through isovalent chemical substitution in the A or B sites. For example, the room temperature crystal structure of VOL. 7

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* Address correspondence to [emailprotected]. Received for review October 28, 2013 and accepted November 26, 2013. Published online November 26, 2013 10.1021/nn405629e C 2013 American Chemical Society

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ARTICLE Figure 1. (a) XRD patterns of Ba1xSrxTiO3 and BaTi1yZryO3 nanocrystals. Diﬀraction maxima corresponding to BaCO3 are denoted with the asterisk (/) symbol. TEM images of (b) Ba0.70Sr0.30TiO3 and (c) BaTi0.85Zr0.15O3 nanocrystals. Size distribution histograms obtained by analyzing 100 nanocrystals and high-resolution TEM images of individual nanocrystals are shown in the insets.

Ba1xSrxTiO3 changes from tetragonal to cubic upon substitution of ca. 3050% of Sr2þ for Ba2þ.49 This is accompanied by a decrease in the Curie temperature of the ferroelectric-to-paraelectric transition along with an enhancement of the room temperature dielectric constant.5,6 Similarly, BaTi1yZryO3 has a multiphase point at y ≈ 0.15 in which rhombohedral, orthorhombic, tetragonal, and cubic phases coexist near room temperature; at this particular substitution level, an enhancement of the room temperature dielectric constant is also observed.912 This solid solution exhibits normal ferroelectric behavior for y e 0.10 and relaxor behavior for 0.25 e y e 0.40; the ferroelectric-to-relaxor crossover occurs via a diﬀuse phase transition for 0.10 e y e 0.25. Although the phase diagrams of Ba1xSrxTiO3 and BaTi1yZryO3 solid solutions are well established for single crystals and bulk ceramics, free-standing nanocrystals of these compositions have not been the subject of a systematic compositionstructure investigation. Indeed, extensive work has been carried out to understand the structural bases of the “size eﬀect” in ferroelectric BaTiO3.1326 Typically, this has been done by probing the atomic arrangement of a set of BaTiO3 nanocrystals of ﬁxed composition and varying size. However, to the best of our knowledge, no systematic structural studies of perovskite nanocrystals of varying composition and ﬁxed size have been reported. Petkov et al., for example, investigated the crystal structure of 5 nm Ba1xSrxTiO3 nanocrystals (x = 0, 0.5, 1), but structural parameters to support the presence (or absence) of local ferroelectric distortions were provided only for BaTiO3.22 As a consequence, it remains unclear how the bulk structural picture changes with chemical composition upon reduction of the grain size. Speciﬁcally, there is a need to understand how the magnitude and coherence of local ferroelectric distortions change with nanocrystal chemical composition. Indeed, high k nanodielectrics such as Ba1xSrxTiO3 and BaTi1yZryO3 solid solutions feature polar nanoregions whose dynamics determine the functionality of the nanomaterials.9,2731 Current interest in free-standing perovskite nanocrystals of complex composition arises RABUFFETTI AND BRUTCHEY

from the potential that high k nanodielectrics oﬀer in microelectronics, particularly in terms of device downscaling and integration.32 An area of major interest is the development of solution-based synthetic approaches to the preparation of high-quality thin ﬁlms showing nanometer-size grains and bulk-like dielectric properties.32,33 From this perspective, understanding compositional control of structureproperty relations in high k nanodielectrics synthesized using solutionbased approaches is of prime importance from both fundamental and applied standpoints. In this work, X-ray absorption spectroscopy and X-ray total scattering were employed to derive compositionstructure relationships for free-standing, sub-20 nm Ba1xSrxTiO3 (x = 0.0, 0.30, 0.50, 1.0) and BaTi1yZryO3 (y = 0.0, 0.15, 0.50, 1.0) nanocrystals synthesized at room temperature. Speciﬁc chemical compositions were selected to facilitate comparison with phase diagrams derived from structural investigations of single crystals and bulk ceramics. X-ray techniques were chosen to probe the atomic arrangement of the perovskite nanocrystals over complementary length scales. The local atomic environment of the ferroelectrically active Ti4þ cation was probed using Ti K edge X-ray absorption near edge structure spectroscopy (XANES). The average and local crystal structure were investigated using Rietveld and pair distribution function (PDF) analysis of X-ray total scattering data. From a structural standpoint, emphasis was placed on elucidating the dependence of the magnitude and coherence of local ferroelectric distortions in Ba1xSrxTiO3 and BaTi1yZryO3 nanocrystals on chemical composition. From a chemical standpoint, emphasis was placed on assessing the chemical hom*ogeneity of Ba1xSrxTiO3 and BaTi1yZryO3 nanocrystals, as compositional ﬂuctuations are known to play a crucial role in the dynamics of polar nanoregions. RESULTS AND DISCUSSION X-ray diﬀraction (XRD) patterns and transmission electron microscopy (TEM) images of Ba1xSrxTiO3 and BaTi1yZryO3 nanocrystals are shown in Figure 1. Diffraction maxima arising from the perovskite phase can VOL. 7

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Figure 2. Ti K edge XANES spectra of BaTiO3, Ba0.70Sr0.30TiO3, and BaTi0.85Zr0.15O3 nanocrystals. The ﬁne structure of the pre-edge region is shown in the inset.

dp hybridization occurs due to the displacement of the titanium atom from the instantaneous center of the octahedral oxygen cage. The magnitude of this displacement, defined here as ΔTiO6, can be extracted from the area under peak B (see Methods for details). ΔTiO6 values of 0.25(1), 0.23(1), and 0.24(1) Å were obtained for BaTiO3 , Ba0.70Sr0.30 TiO3 , and BaTi0.85Zr0.15O3, respectively. ΔTiO6 in BaTiO3 nanocrystals is comparable to that reported in previous X-ray absorption investigations of BaTiO 3 single crystals38,39 and bulk ceramics.38,39,41 This finding gives further support to the notion that the “size effect” in ferroelectric BaTiO3 does not result from a decrease in the magnitude of local dipoles upon decreasing the grain size, but originates from a reduction in the spatial coherence of their ferroelectric coupling.16,20,24 Reduced ΔTiO6 values obtained for Ba0.70Sr0.30TiO3 and BaTi0.85Zr0.15O3 nanocrystals indicate that isovalent substitution in the A or B sites reduces the magnitude of the titanium displacement. This reduction is comparable to that reported in previous XANES investigations of chemically substituted BaTiO3 bulk ceramics.4143 Rietveld Analysis. Rietveld analysis of XRD patterns was carried out using the cubic Pm3m space group. A BaCO3 phase was included when needed. For this phase, the scale factor and lattice constants were refined. Results from Rietveld analyses are given in Table 1. Fits for two selected compositions are shown in Figure 3 panels a and b; fits for other compositions are given in the Supporting Information. A plot of the cubic lattice constant a as a function of the chemical substitution in Ba1xSrxTiO3 and BaTi1yZryO3 nanocrystals is shown in Figure 3c. Low Rwp values and visual inspection of the fits show that the average (i.e., longrange) crystal structure of Ba1xSrxTiO3 and BaTi1yZryO3 nanocrystals is adequately described by a cubic unit cell with the titanium atom in the center. The lattice constant of Ba1xSrxTiO3 (BaTi1yZryO3) nanocrystals decreases (increases) upon increasing x (y), as expected on the basis of ionic radii (rBa2þ = 1.42 Å, rSr2þ = 1.26 Å, rTi4þ = 0.61 Å, rZr4þ = 0.72 Å). In the case of Ba1xSrxTiO3 nanocrystals, a increases linearly with x, indicating an ideal solid solution behavior in which the Ba2þ and Sr2þ cations are randomly distributed over the A site.

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be indexed to the centrosymmetric, cubic Pm3m space group. The presence of minor amounts of BaCO3 (ICSD No. 158378, orthorhombic Pmcn space group) is observed in the patterns of BaTiO3, BaTi0.85Zr0.15O3, and BaZrO3. This carbonate phase results from the chemisorption of atmospheric CO2 upon postsynthetic exposure of the nanocrystals to air.3436 Nanocrystals belonging to the Ba1xSrxTiO3 solid solution are 8.9 ( 1.5 (x = 0.0), 12.3 ( 1.7 (x = 0.30), 13.3 ( 2.2 (x = 0.50), and 14.8 ( 1.9 (x = 1.0) nm in diameter, while those belonging to the BaTi1yZryO3 solid solution possess diameters of 10.4 ( 1.3 (y = 0.15), 11.5 ( 1.5 (y = 0.50), and 11.4 ( 1.9 (y = 1.0) nm (see Supporting Information). High-resolution TEM images of individual nanocrystals show the presence of well-deﬁned lattice fringes corresponding to the {110} crystal planes of the perovskite phase. X-ray Absorption Near Edge Structure. Ti K edge XANES spectra of BaTiO3, Ba0.70Sr0.30TiO3, and BaTi0.85Zr0.15O3 nanocrystals are given in Figure 2. The fine structure of the pre-edge region spanning the 49654975 eV energy range provides qualitative and quantitative information about the local atomic environment of the titanium atom.3740 The pre-edge region consists of three peaks centered at ∼4966.9 (A), 4969.0 (B), and 4972.5 (C) eV. Important in the context of this work is peak B, arising from a Ti s f dp electronic transition;

TABLE 1. Rietveld Analysis of X-ray Diffraction Data of Ba1xSrxTiO3 and BaTi1yZryO3 Nanocrystals composition

a (Å)

V (Å3)

UA (Å2)a

UB (Å2)a

UO (Å2)a

BaCO3 wt %b

Rwp

BaTiO3 Ba0.70Sr0.30TiO3 Ba0.50Sr0.50TiO3 SrTiO3 BaTi0.85Zr0.15O3 BaTi0.50Zr0.50O3 BaZrO3

4.0356(2) 3.9998(2) 3.9785(2) 3.92056(12) 4.0716(3) 4.1117(5) 4.2107(2)

65.725(11) 63.990(9) 62.975(11) 60.0262(6) 67.498(16) 69.51(2) 74.657(13)

1.09(6) 1.09(6) 1.07(7) 0.85(4) 1.49(10) 1.42(16) 1.22(10)

1.56(9) 1.55(8) 1.59(10) 1.14(5) 1.61(13) 2.7(2) 1.25(12)

0.27(13) 0.53(11) 0.74(14) 0.95(7) 0.8(2) 0.5(3) 0.8(2)

9.0(2)

3.0 2.9 2.7 2.4 2.7 3.1 2.3

3.0(2) 12.1(4)

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Figure 5. Parameters extracted from the ﬁt of the tetragonal model to the experimental PDFs of Ba1xSrxTiO3 (black [2]) and BaTi1yZryO3 (red 1) nanocrystals in the 1.520 Å range. (a) Average lattice constant. Linear ﬁts to the calculated values are shown as dashed lines; the corresponding R2 values are given for each ﬁt. (b) Diﬀerence between the Rwp values of the ﬁts obtained using the cubic and tetragonal models. ΔRwp values for ﬁts performed in the full interatomic distance range are shown with 4 and 3 symbols for Ba1xSrxTiO3 and BaTi1yZryO3, respectively. (c) Degree of tetragonality of the perovskite unit cell. (d) Mean displacement of the B site cation along the c axis. Error bars for t and dB values of BaTi0.50Zr0.50O3 and BaZrO3 have been omitted; see text for details. Dashed lines in panels bd are guides-to-the-eye.

as low as 15%. Both compositions observed for these nanocrystals are in agreement with the phase diagrams of Ba1xSrxTiO3 and BaTi1yZryO3 derived from single crystals and bulk ceramics, which show the critical substitution levels to induce a tetragonalto-cubic phase transition are x ≈ 0.300.50 and y ≈ 0.100.20, respectively. This observation demonstrates the compositional dependence of the crystal structure is not aﬀected by size eﬀects. Dielectric measurements on these nanocrystals have also shown that the dependence of the dielectric constant on chemical composition also parallels that observed in bulk.34,35 Finally, we bring our attention to the case of SrTiO3, whose room temperature average crystal structure is described by a cubic Pm3m space group. In this work, it is observed that the diﬀerence between the ﬁts provided by the cubic and tetragonal models is marginal (ΔRw = 0.1%). However, unlike the case of BaZrO3, structural parameters extracted for the tetragonal model exhibit uncertainties that are in line with those observed for the other members of the Ba1xSrxTiO3 solid solution, ruling out overparametrization of the model. In addition, values of t (0.8(2) %) and dTi (0.07(3) Å) are the smallest observed accross the Ba1xSrxTiO3 solid solution, as expected. The presence of polar nanoregions in SrTiO3 is well-documented in Raman and dielectric studies of bulk ceramics,8,49 thin ﬁlms,50 and free-standing 60 nm nanocrystals.51 Inspection of Figure 4 reveals that the better ﬁt provided by the tetragonal model results from a more accurate description of the intensity of the peak at ∼5.7 Å and of the doublets at ∼6.7 and 6.9, ∼9.9 and 10.3, and 14.4 and 15.1 Å. Total PDFs calculated using the cubic and tetragonal models were decomposed into partial PDFs to clarify the origin of this result. Partial PDFs of all the atomatom pairs present in BaTiO3 nanocrystals are shown in Figure 6a. Partial PDFs corresponding to BB pairs (i.e., TiTi, TiZr, and ZrZr) present in all other chemical compositions studied in this work are shown in Figure 6b. Figure 6a reveals that the cubic and tetragonal models yield an identical description of the spatial distribution of the all atomatom pairs in BaTiO3 nanocrystals. However, PDF peaks arising from TiTi pairs appear sharper in the tetragonal model. Careful inspection of the temperature factors of the B site atom extracted for the cubic and tetragonal models (Table 2) shows the broader BB peaks observed in the cubic model result from UB values that are artiﬁcially enlarged to account for local displacive disorder due to the oﬀ-centering of the B atom. This deﬁciency of the cubic model is relieved in the tetragonal model by allowing the position of the B atom to vary along the c axis. This, in turn, leads to signiﬁcantly smaller UB values, sharper BB peaks, and to a better ﬁt to the experimental PDFs. We note that partial TiTi PDFs of the cubic and tetragonal

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ARTICLE Figure 6. (a) Partial PDFs of BaTiO3 nanocrystals. (b) BB partial PDFs of Ba1xSrxTiO3 and BaTi1yZryO3 nanocrystals. Partial PDFs were computed in the 1.520 Å range using the cubic (black line) and tetragonal models (thicker red line).

models of BaTiO3 diﬀer strongly in the r e 16 Å range, but become nearly indistinguishable upon approaching 20 Å. Therefore, the coherence length of the ferroelectric coupling between local displacements of the titanium atom along the polar direction can be estimated to be on the order of ∼1620 Å, in good agreement with results reported in earlier structural studies of free-standing BaTiO3 nanocrystals16,22,24 and ultrathin ﬁlms.52 The short coherence length helps to explain the exponential reduction of the dielectric constant of ferroelectric perovskite oxides such as BaTiO3 upon going from the bulk to the nanoscale.16 The estimated coherence length does not seem to be signiﬁcantly aﬀected upon substitution of Sr2þ for Ba2þ up to levels of 50%. On the basis of this result and the evolution of dTi (see Figure 5d), it appears that chemical substitution in Ba1xSrxTiO3 nanocrystals leads only to a slight reduction of the magnitude of the local displacement of the titanium atom. In contrast, both the average magnitude of the local displacement dB (Figure 5d) and its coherence length appear to be strongly aﬀected by the substitution of Zr4þ for Ti4þ in BaTi1yZryO3 nanocrystals. Indeed, partial BB PDFs of the cubic and tetragonal models of BaTi0.85Zr0.15O3 and BaTi0.50Zr0.50O3 nanocrystals become nearly indistinguishable at ∼15 and ∼12 Å, respectively. These estimates are in good agreement with those in BaTi1yZryO3 bulk powders reported by Jeong et al.53 Finally, we turn our attention to the deviations from the ideal solid solution behavior observed in BaTi1yZryO3 nanocrystals. Observation of the experimental PDFs for this solid solution reveals an anomalous behavior of the peak located at ∼2.8 Å, which corresponds to the BaO atomic pair. Indeed, the RABUFFETTI AND BRUTCHEY

Figure 7. Experimental PDFs (O) of BaTi1yZryO3 nanocrystals in the 1.53.3 Å range; peaks arising from Ti(Zr)O and BaO pairs are indicated.

average BaO bond distance remains nearly constant upon an increasing y, while all other interatomic distances increase as expected (Figure 7). In addition, the experimental BaO peak broadens upon increasing y, reﬂecting a broader distribution of BaO distances. The fact that the average coordination environment of the barium atom appears increasingly distorted upon increasing the zirconium content indicates an inhom*ogeneous distribution of the barium atoms, and thus explains the deviations from the ideal solid solution behavior observed in BaTi1yZryO3 nanocrystals. Such a distribution can result from the presence of barium atoms in the perovskite lattice with a heavily distorted coordination environment.54 Alternatively, it can result from the segregation of barium-rich secondary phases whose structural coherence is not large enough to allow detection by Rietveld analysis of X-ray diﬀraction VOL. 7

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CONCLUSION In summary, X-ray absorption and X-ray total scattering were employed to gain fundamental insight into the compositional dependence of polar nanoregions in sub-20 nm Ba1xSrxTiO3 and BaTi1yZryO3 nanocrystals synthesized at room temperature. The presence of local ferroelectric distortions due to the oﬀcentering of the titanium atom was demonstrated, and their symmetry was adequately described by a tetragonal P4mm space group. Substitution of Sr2þ for Ba2þ and of Zr4þ for Ti4þ induced a tetragonal-to-cubic transition of the local crystal structure, analogous to that observed for the average crystal structure of single crystals and bulk ceramics. This structural transition within polar nanoregions was driven by a reduction of the magnitude of the local displacements of the titanium atom and/or of the coherence of their ferroelectric coupling. A reduction of the magnitude of the titanium oﬀ-centering was observed upon replacing

METHODS Synthesis of Ba1xSrxTiO3 and BaTi1yZryO3 Nanocrystals. Ba1xSrxTiO3 (x = 0.0, 0.30, 0.50, 1.0) and BaTi1yZryO3 (y = 0.0, 0.15, 0.50, 1.0) nanocrystals were synthesized via a vapor diffusion solgel method described elsewhere.3436 This method relies on the hydrolysis and polycondensation of a mixture of liquid bimetallic alkoxides (i.e., BaTi(OR)6/SrTi(OR)6 or BaTi(OR)6/BaZr(OR)6, R = CH2CHCH3OCH3) upon slow diffusion of water vapor into the solution. Crystallization of the desired perovskite phase occurs at atmospheric pressure and room temperature, without the need for postsynthetic thermal treatment. Synchrotron X-ray Diffraction. X-ray diffraction (XRD) patterns were collected at the 11IDB line 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. Transmission Electron Microscopy. Transmission electron microscopy (TEM) images were obtained using a JEOL JEM2100F (JEOL Ltd.) electron microscope operating at 200 kV. Samples were dispersed in methanol and deposited on a 200 mesh Cu grid coated with a lacey carbon film (Ted Pella, Inc.). Nanocrystal size distribution histograms were constructed by analyzing 100 individual nanocrystals and assuming spherical shape. X-ray Absorption Near Edge Structure. X-ray absorption near edge structure (XANES) spectra were collected at the 20BMB line of the Advanced Photon Source at Argonne National Laboratory. The incident X-ray beam was monochromatized using a Si(111) double crystal. A harmonic rejection mirror was used to eliminate higher harmonics, and the beam intensity was detuned an additional 10% to further reduce any residual harmonics. Measurements at the Ti K edge (4966 eV) were performed in transmission mode using gas ionization chambers filled with N2 to monitor the incident and transmitted intensities. Samples were prepared by spreading a thin, uniform layer of powder on Kapton tape. The incident X-ray beam size was 1 mm 6 mm (unfocused). XANES spectra were collected at room temperature

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50% of Ba2þ with Sr2þ in Ba1xSrxTiO3 nanocrystals, but the coherence length remained unchanged. In contrast, a noticeable reduction in the coherence length was observed upon replacing 15% of the ferroelectrically active Ti4þ with Zr4þ in BaTi1yZryO3 nanocrystals. Results presented in this work show that the evolution of the room temperature local crystal structure with chemical composition mirrors that of single crystals and bulk ceramics, thus suggesting that compositional control over cooperative properties such as ferroelectricity should be possible at the nanoscale, even for nanocrystals as small as 10 nm. A random distribution of the Ba2þ and Sr2þ cations over the A site was achieved in Ba1xSrxTiO3 nanocrystals. In contrast, deviations from the ideal solid solution behavior were observed in BaTi1yZryO3 nanocrystals upon increasing substitution of Zr4þ for Ti4þ. Analysis of the evolution of experimental PDF peaks' position (bond distance) and width (atomic disorder) pointed to an increasingly inhom*ogeneous distribution of the barium atoms upon an increase in the zirconium content. This ﬁnding highlights the potential of PDF analysis of total scattering data as a tool to investigate compositional ﬂuctuations in nanocrystals synthesized using solution-based approaches and molecular precursors as building blocks.

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data.29,55 Therefore, this ﬁnding demonstrates the utility of total scattering as a tool to probe compositional ﬂuctuations in nanocrystals synthesized using solution-based approaches and molecular precursors as building blocks.

under flowing helium. Each spectrum was normalized by subtracting the pre-edge and applying an edge-jump normalization using the Athena software.56 The displacement of the titanium atom from the instantaneous center of the octahedral oxygen cage (ΔTiO6) was derived from the area under peak B (AB) in the pre-edge region of the XANES spectrum, according to ΔTi

(Å) ¼ [(3AB )=γ]1=2

(1)

2 38

where γ = 11.1 eV Å . The extraction of AB was performed by fitting peaks A, B, and C with three Lorentzians; the background was fit in the 49654980 eV energy range using a polynomial function. Rietveld Analysis. Rietveld structural refinements were carried out using the GSAS software.57 Experimental data and atomic X-ray scattering factors were corrected for sample absorption and anomalous scattering, respectively. Refinements of the perovskite phase were performed using a mean atom approach, in which substitution in the A or B sites was simulated by changing the occupation factor of the corresponding site and fixing it at the nominal composition. The 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 ThomsonCoxHasting pseudo-Voigt function,58 (4) lattice constants, (5) fractional atomic coordinates of the B site atom(s) when allowed by symmetry, and (6) an isotropic thermal parameter for each chemical species, regardless of their crystallographic site in the perovskite structure (i.e., UA, UB, and UO). The Rwp indicator was employed to assess the quality of the refined structural models.59 Pair Distribution Function Analysis. The pair distribution function (PDF) G(r) defined as Z G(r) ¼ 4πr[F(r) F0 ] ¼ (2=π)

Qmax

Q[S(Q) 1] sin(Qr) dQ

(2)

was employed for structural analysis. Here, r is the radial distance, F(r) and F0 are the local and average atomic number

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Q ¼ (4π=λ)sinθ

(3)

where 2θ is the angle between incident and scattered X-rays. The RAD software was employed to extract G(r) from the raw diffraction data.60 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). For all compositions a maximum scattering vector (Qmax) of 25 Å1 was employed in the Fourier transform; the two exceptions were BaTi0.85Zr0.15O3 and BaTi0.50Zr0.50O3, for which a maximum scattering vector of 23 Å1 was used. Structural refinements were carried out using the PDFgui software.61 Similar to Rietveld analysis, a mean atom approach was employed to simulate chemical substitution. The following parameters were refined: (1) scale factor, (2) lattice constants, (3) fractional atomic coordinates of the B site atom(s) when allowed by symmetry, and (4) an isotropic thermal parameter for each chemical species, regardless of their crystallographic site in the perovskite structure. The Rw indicator was employed to assess the quality of the refined structural models.22,45 The calculated total PDF G(r) was decomposed into partial PDFs Gij(r) according to G(r) ¼

∑ij wij Gij (r)

(4)

where the summation runs over all the atomic species contained in the sample, and wij are the weighting factors defined as

∑i

wij ¼ [ci fi (Q)][cj fj (Q)]=j ci fi (Q)j2

(5)

Here, ci and fi(Q) are the atomic concentration and X-ray scattering factor of the ith chemical species, respectively, and obey the sums Σci = 1 and Σwij = 1.45,62 In this work, fi(Q) values were corrected for anomalous scattering and evaluated at Q = 0. Conflict of Interest: The authors declare no competing ﬁnancial interest. Acknowledgment. This material is based on work supported by the Department of Energy Oﬃce of Basic Energy Sciences under Grant No. DE-FG02-11ER46826. The authors thank Dr. Dale Brewe, Dr. Karena Chapman, and Dr. Kevin Beyer from the Advanced Photon Source for their assistance with the collection of X-ray absorption and X-ray scattering data. Dr. Leopoldo Suescun from CryssmatLab/DETEMA, Facultad de Quimica, Universidad de la Republica (Uruguay) is also gratefully acknowledged for useful discussions. 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 No. DE-AC02-06CH11357. Supporting Information Available: (1) Structure functions S(Q); (2) additional TEM images and size distribution histograms; (3) additional Rietveld ﬁts to the experimental XRD patterns; (4) experimental PDFs; (5) additional ﬁts to the experimental PDFs in the 1.520 Å range; (6) ﬁts to the experimental PDFs in the full interatomic distance range; (7) calculated partial PDFs. This material is available free of charge via the Internet at http:// pubs.acs.org.

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Local structure of Ba(1-x)Sr(x)TiO3 and BaTi(1-y)Zr(y)O3 nanocrystals probed by X-ray absorption and X-ray total scattering. - PDF Download Free (2024)