Ca K-edge X-ray absorption fine structure in BaTiO3-CaTiO3 solid solutionsV. Krayzman, I. Levin, J. C. Woicik, F. Bridges, E. J. Nelson, and D. C. Sinclair Citation: Journal of Applied Physics 113, 044106 (2013); doi: 10.1063/1.4784226 View online: http://dx.doi.org/10.1063/1.4784226 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/113/4?ver=pdfcov Published by the AIP Publishing Advertisement:

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Ca K-edge X-ray absorption fine structure in BaTiO3-CaTiO3 solid solutions

V. Krayzman,1,2 I. Levin,1,a) J. C. Woicik,1 F. Bridges,3 E. J. Nelson,4 and D. C. Sinclair5

1Ceramics Division, National Institute of Standards and Technology, Gaithersburg Maryland 20899, USA2Department of Materials Science and Engineering, University of Maryland, College Park,Maryland 20742, USA3Department of Physics, University of California, Santa Cruz, California 95064, USA4Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory,Menlo Park, California 94025, USA5Department of Materials Science and Engineering, University of Sheffield, Sheffield S1 3JD, United Kingdom

(Received 9 November 2012; accepted 2 January 2013; published online 24 January 2013)

Ca K-edge extended X-ray absorption fine structure (EXAFS) has been used to analyze local

coordination of Ca in (Ba,Ca)TiO3 and Ba(Ti,Ca)O3�d solid solutions. EXAFS reveals the average

Ca-O distance in (Ba1�xCax)TiO3 (0< x� 0.3) is significantly larger compared to CaTiO3, which

suggests a relatively limited relaxation of the oxygen framework around Ca in the solid solutions;

nevertheless, the [CaO12] coordination environment appears to be strongly distorted. No significant

differences in Ca-O distances were observed among the solid-solution samples with different

x-values. For BaTi0.97Ca0.03O3�d sample, EXAFS indicates that Ca is predominantly located on the

B-sites with a Ca-O distance of 2.28 A. X-ray absorption near-edge structure, which is different for

A and B-site Ca, has been interpreted using phenomenological considerations. VC 2013 AmericanInstitute of Physics. [http://dx.doi.org/10.1063/1.4784226]

INTRODUCTION

BaTiO3-based perovskite-like dielectrics are utilized in

ubiquitous multilayer ceramic capacitors (MLCC)1,2 and posi-

tive-temperature-coefficient resistors (PTCR).2 Commercial

formulations employ various chemical-doping strategies on

the Ba (A) and/or Ti (B) sites to optimize the dielectric and

electrical properties of these materials. The role of doping as

a tool for the control of point defects and electrical carriers

becomes particularly important in the case of Ni electrodes

that require sintering under reduced conditions. A list of dop-

ants used to improve the performance of BaTiO3 includes

various rare-earth and transition-metal cations that are substi-

tuted into either the larger A (12-coordinated) or smaller B

(6-coordinated) sites.1–3 Calcium is another promising dopant

which inhibits the reduction of Ti and can be used to control

TC.4–6 However, the crystal-chemical behavior of Ca is com-

plex because it can occupy both the A and B sites in the per-

ovskite structure. The solubility limits for Ca in Ba1�xCax

TiO3 and BaTi1�xCaxO3�d solid solutions have been esti-

mated as x � 0.25 (Refs. 7 and 8) and x � 0.04,8 respectively,

although these limits vary somewhat with processing condi-

tions. According to previous studies,10 substitution of Ca for

Ti is manifested in increased lattice volumes and lower TC

values. In contrast, substitution of Ca for Ba yields smaller

lattice volumes with little effect on TC.10 Comparison of ex-

perimental lattice parameters with those expected from

Vegard’s law suggested that samples with nominal Ca substi-

tution on the Ba sites still feature a certain fraction of Ca on

the Ti sites.11 Conversely, samples with the nominal Ca sub-

stitution on the Ti sites have been proposed to exhibit a

small Ca occupancy on the Ba sites.11 Raman spectra of

Ba(Ti,Ca)O3�d revealed a well-defined breathing-mode peak

at 830 cm�1, whereas this peak was absent in the spectra of

(Ba,Ca)TiO3.12 The breathing-mode peak, which becomes

Raman-active only if oxygen atoms are simultaneously

bonded to distinct B-cations, provides a sensitive, if qualita-

tive, probe of the B-site occupancy by Ca. Raman measure-

ments lent no support for the presence of Ca on the B-sites in

the (Ba,Ca)TiO3 samples; however, the detection limits for

the breathing-mode peak have not been established.

X-ray absorption fine structure (XAFS) spectroscopy is

a standard technique for quantitative determination of local

coordination of dopant species. Surprisingly, no XAFS stud-

ies of the coordination of Ca in perovskites, apart from the

recent analysis of Ca K near-edge XAFS (XANES) in

CaTiO3,13 have been reported. In the present contribution we

describe a study of the Ca K-edge XAFS in Ca-substituted

(on both the Ba and Ti sites) BaTiO3 and in CaTiO3, which

is used as a reference. Both XANES and extended XAFS

(EXAFS) parts of XAFS spectra were analyzed. Our results

provide direct evidence for Ca occupancy on the B-sites in

Ba(Ti,Ca)O3 samples. In the (Ba,Ca)TiO3 samples, the aver-

age Ca-O bond length is found to be appreciably longer com-

pared to CaTiO3, which suggests that the A-site volume

around Ca in the solid solutions remains relatively large.

EXPERIMENTAL

The ceramic samples for this study were prepared using

conventional solid-state methods. The CaTiO3 sample was

the same as that used in previous neutron diffraction stud-

ies.14 Ba1�xCaxTiO3 (x¼ 0.05, 0.1, 0.2, 0.3) samples were

synthesized from BaCO3 (99.99%), CaCO3 (99.99%), and

TiO2 (<10 ppm P2O5), which were mixed for 20 min under

acetone using an agate mortar and pestle. Mixtures were

pressed into pellets and calcined at 1000 �C. The resulting

a)Author to whom correspondence should be addressed. Electronic mail:

igor.levin@nist.gov.

0021-8979/2013/113(4)/044106/7/$30.00 VC 2013 American Institute of Physics113, 044106-1

JOURNAL OF APPLIED PHYSICS 113, 044106 (2013)

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powders were heated repeatedly at 1450 �C (with intermedi-

ate grinding for 15 min) until no changes in the detailed

X-ray diffraction (XRD) patterns could be observed; typi-

cally, equilibrium was attained after 3 heatings for a total of

72 h. The BaTi0.97Ca0.03O2.97 sample was the same as that

used in previous Raman studies.12 Samples were character-

ized using XRD in a powder diffractometer equipped with a

Ge incident beam monochromator (Cu Ka1 radiation) and a

solid-state position sensitive detector.

XAFS measurements of the Ca K-edge (4038 eV) were

performed at ambient temperature at the beamline 4-3 of the

Stanford Synchrotron Light Source. For these measurements,

the powders were dispersed on a sulfur-free sticky tape. The

double-crystal monochromator was operated with a pair of

Si (111) crystals. The data were collected in fluorescence

and transmission modes for dilute and concentrated samples,

respectively. A four-element Si-drift detector was used for

the fluorescence measurements. The detector count-range

was adjusted to minimize dead-time correction effects.

Transmission data for the Ca K-edge in CaTiO3 were used

for energy calibration. The fluorescence data were corrected

for the dead-time of the detector. All data were processed

using ATHENA.15 Fitting was accomplished using the

ARTEMIS software.15 Scattering amplitudes and phases

were calculated using FEFF8.16

The cluster used to calculate the Ca EXAFS signal in

CaTiO3 was constructed from the structural parameters of this

compound.12 For (Ba,Ca)TiO3, a tetragonal BaTiO3-like

structure with lattice parameters determined using XRD was

adopted. The model for Ba(Ti,Ca)O3 was constructed by

placing an absorbing Ca atom in the center of an oxygen octa-

hedron in the BaTiO3 structure and then shifting the 6

nearest-neighbor oxygen atoms away to achieve Ca-O bond

distances of RCa-O¼ 2.26 A. More distant atoms in this cluster

were displaced from the central Ca atom by d¼DR(RTi-O/r)3,

where DR¼RCa-O�RTi-O (RTi-O is the Ti-O distance in

BaTiO3), and r is the distance from the particular neighbor to

the absorbing Ca atom.

RESULTS AND DISCUSSION

Fig. 1 compares Ca XANES for CaTiO3 and (Ba,Ca)

TiO3 solid solutions. According to Ref. 13, the pre-edge peak

A in the spectrum of CaTiO3 is associated with excitation of

the Ca 1s electron to the Ca p-states which are hybridized

with both the “excitonic” Ca 3d states and the Ti 3d states.

Ca contains no d electrons but exhibits d resonance scattering

of a photoelectron; an attractive core-hole potential reduces

the energy of these d-resonance states by several eV thereby

transforming them into the so-called “excitonic” states.

Hybridization of the Ca p states with the “excitonic” Ca 3dstates can be attributed to distortions of the A-site [CaO12]

coordination polyhedra caused by octahedral tilting and Ca

displacements. Hybridization of the Ca p states with Ti 3dstates occurs through the oxygen 2p states. The XANES spec-

tra for Ca in CaTiO3 and (Ba,Ca)TiO3 solid solutions differ

primarily by the intensity of feature B, which increases pro-

gressively with increasing fraction of Ba atoms around the

absorbing Ca. Therefore, this feature can be attributed to

hybridization of the Ca p-states with the 5d states of Ba

(through oxygen atoms).

CaTiO3 exhibits octahedral tilting that yields ortho-

rhombic Pnma symmetry.14,17 This tilting, which is driven

by the bonding requirements of the relatively small Ca cati-

ons, distorts the [CaO12] coordination environment; the Ca-

O distances in the average structure are split approximately

into 3 groups of distances �2.39 A (�4), 2.64 A (�4), and

3.14 A (�4) (Table I). Additionally, Ca cations are displaced

from the high-symmetry central positions. Ca EXAFS in

CaTiO3 (Fig. 2) can be fitted successfully using a model with

three Ca-O (�4) distances and single Ca-Ti (�8) and Ca-Ca

(�6) distances; the fitting range was limited to encompass

these three coordination shells. The E0 value was found to

correspond to the inflection point of the main absorption

peak. The amplitude reduction factor S02 was fixed at the

theoretical value of 0.924 calculated by FEFF. The structural

parameters obtained from EXAFS are summarized in Table

I. The refined short Ca-O distances are somewhat longer

than the corresponding average distances obtained from

Rietveld refinements.14 Obviously, the model that fits the

EXAFS data provides a rather approximate picture of distor-

tions around Ca; specifically, it gives no indication of the

shortest Ca-O distances of �2.37 A (see footnote to Table I)

in the average structure. The existence of such short distan-

ces in the local structure of CaTiO3 has been corroborated by

a previous analysis of a pair-distribution function (PDF)

measured using neutron total scattering,18 which revealed a

well-defined peak at �2.40 A (inset in Fig. 3(a)). Attempts to

describe the EXAFS data using the average-structure coordi-

nation yielded a relatively poor fit. In fact, the distortion of

the [CaO12] coordination polyhedra, as inferred from

EXAFS, appears to be smaller than that deduced from the

neutron diffraction data.

We checked whether the EXAFS data are consistent

with the neutron total scattering data for CaTiO3 by per-

forming simultaneous fitting of the neutron PDF (Ref. 18)

and Ca EXAFS using a reverse Monte Carlo (RMC) algo-

rithm implemented in the RMCPROFILE software;19–21

both datasets were recorded from the same sample. A

FIG. 1. Ca K XANES spectra of CaTiO3 (x¼ 1) and Ba1�xCaxTiO3

(x¼ 0.05, 0.1, 0.2, and 0.3) solid solutions.

044106-2 Krayzman et al. J. Appl. Phys. 113, 044106 (2013)

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neutron Bragg profile was also included in the fit to con-

strain the average structure. Details of the procedure for

such combined refinements have been described previ-

ously.20,21 Unlike highly parameterized fits in Artemis,

RMC refinements use no effective parameters and all the

FIG. 2. k-space EXAFS (a) and its FT (b, red line) for Ca in CaTiO3. The

result of the real-space fit is shown in (b) using a blue line. The k-range used

in the FT was from k¼ 2.7 A�1 to k¼ 9.5 A�1. The k-weighted EXAFS sig-

nal was multiplied by the Hanning window (Dk¼ 1) prior to the FT.

FIG. 3. Results of simultaneous fitting of the neutron PDF (a), Ca EXAFS

(b), and neutron Bragg profile (not shown) for CaTiO3. The fitting was

accomplished using a RMC algorithm implemented in the RMCPROFILE

software. The inset shows a magnified view of a low-R portion of the PDF.

The peak corresponding to the short Ca-O distances (labeled as (Ca-O)1 as

in Table I) is relatively well separated; however, the remaining Ca-O dis-

tance distribution overlaps with that for the O-O distances. The y-axis in (b)

differs from that in Fig. 2(b) by a multiplicative factor because of the differ-

ent forms of the FT used by RMCPROFILE and Artemis; this difference has

no effect on the refined parameters. In both figures, the experimental and

calculated signals are indicated using red and blue lines, respectively.

TABLE I. Parameters of the Ca coordination environment in CaTiO3 obtained by fitting different types of experimental data. Coordination numbers (N), aver-

age distances (R), and the associated Debye-Waller factors (r2) for each coordination shell around Ca are specified. The units of R and r2 values are A and A2,

respectively.

EXAFS PDFþEXAFS (RMC fit)a Rietveldb

Coordination shell Nc R r2 N R r2 N R D

(Ca-O)1 4 2.46(2) 0.008(3) 4.23(9) 2.400(2) 0.0103(1) 4 2.394 0.003

(Ca-O)2 4 2.71(3) 0.005(3) 3.81(9) 2.671(2) 0.010(1) 4 2.642 0.001

(Ca-O)3 4 2.95(7) 0.03(2) 3.96(7) 3.147(3) 0.031(1) 4 3.137 0.013

(Ca-Ti) 8 3.35(2) 0.017(2) 8 3.310(2) 0.021(2) 8 3.314 0.015

aThese parameters were obtained by fitting a partial Ca-O PDF obtained from the RMC refinements with a sum of symmetric Gaussian peaks.bThe Ca-O and Ca-Ti distances were calculated from the atomic coordinates reported in Ref. 14. The Ca-O distances, grouped according to individual coordi-

nation shells, are {2. 36, 2.37 (�2), 2.48}, {2.62 (�2), 2.66 (�2)}, {3.03, 3.05, 3.23) (�2)}. The Ca-Ti distances are 3.17 (�2), 3.27 (�2), 3.33 (�2), and 3.48

(�2). The R and D parameters quoted in the table correspond to the average and variance values calculated for each group of the Rietveld-refined distances,

respectively.cThe coordination numbers for this model were kept fixed during the fit.

044106-3 Krayzman et al. J. Appl. Phys. 113, 044106 (2013)

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atomic displacements are modeled explicitly. In these fits,

the value of S02 was adjusted to 0.84, which improved the

fit relative to a theoretical value of 0.924 without any sig-

nificant effect on the resulting partial PDFs. The E0 value

was fixed at a value obtained from the EXAFS fit, as

described above. Good quality fits (Fig. 3) were obtained

for both the total scattering and EXAFS data;22 in fact, the

quality of the EXAFS fit (Fig. 3(b)) is only marginally

worse compared to that obtained by fitting the EXAFS

alone (Fig. 2(b)). Inclusion of the single-scattering paths

that involve oxygen atoms from the 2nd Ca-O coordination

shell at �4.9 A was essential for obtaining a good fit for the

EXAFS. Thus, both neutron total scattering and Ca EXAFS

appear to be consistent with each other. The interatomic

distances calculated from the average atomic positions in

the RMC-refined configuration agreed (within 0.02 A) with

those obtained from conventional Rietveld refinements

using the same neutron diffraction dataset.

Fig. 4 displays partial Ca-O PDFs for CaTiO3 obtained

by fitting the neutron total scattering data alone and by si-

multaneous fitting of the total scattering and the EXAFS.

Both partial Ca-O PDFs can be modeled satisfactorily using

sums of three Gaussian peaks; the individual-peak charac-

teristics are summarized in Table I. The primary differences

between the two Ca-O distributions are in the effective

coordination numbers for the short and intermediate Ca-O

distances. The result of the combined PDF/EXAFS fit rela-

tive to a fit of the PDF alone is to increase the number of

the shorter Ca-O distances (from 4 to �4.2) at the expense

of the number of the intermediate distances (decreases from

4 to 3.8); this redistribution causes the centers of both the

short- and the intermediate-distance peaks to shift to longer

distances and modifies the widths of these two peaks.23 The

distribution of the Ca-Ti distances deviates significantly

from the Gaussian shape. The assumption of a Gaussian

shape for this distribution could have biased the results of

the EXAFS fit in Artemis, especially because signals from

the Ca-O and Ca-Ti scattering paths overlap closely. Addi-

tionally, including single-scattering paths for the 2nd Ca-O

coordination sphere in the parametric model used in Arte-

mis is difficult because of the large number of structural

variables used; yet, the contribution of these paths was

found to be significant. Conversely, the intermediate Ca-O

distance peak in the total neutron PDF overlaps completely

with the strong O-O peak and, therefore, cannot be reliably

determined from the PDF. Interference effects in EXAFS

make it much more sensitive to split distances compared to

diffraction PDF. Thus, simultaneous fitting of both datasets,

which mitigates errors associated with each technique,

FIG. 4. The partial Ca-O (red) and Ca-Ti (orange) PDFs (multiplied by R2)

derived from the combined PDF/EXAFS refinements are compared to the

corresponding partial distributions (blue: Ca-O, green: Ca-Ti) obtained by

fitting the neutron total scattering data alone.

FIG. 5. (a) k-space EXAFS spectra for

Ca in Ba1�xCaxTiO3 [x¼ 0.05 (black),

0.1 (red), 0.2 (blue), and 0.3 (purple)]

along with the real (b) and imaginary (c)

parts of the EXAFS FT. The spectra for

these solid-solution samples are similar

to each other but different from the

spectrum for CaTiO3 (green line). (d)

Magnitude of the EXAFS FT. An

upshift of the real and imaginary parts

of the FT for (Ba,Ca)TiO3 relative to

those for CaTiO3 is evident in (b) and

(c).

044106-4 Krayzman et al. J. Appl. Phys. 113, 044106 (2013)

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facilitates accurate determination of the strongly distorted

local coordination environment of Ca.

Ca EXAFS spectra for the Ba1�xCaxTiO3 solid solutions

are similar for 0.05� x� 0.3 (Fig. 5(a)). The real and imagi-

nary parts of the EXAFS Fourier transform (FT) for the solid-

solution samples are shifted by �0.16 A to longer distances

relative to those for CaTiO3 (Figs. 5(b) and 5(c)); the distance

shift is obscured in the plot of the magnitude of the FT (Fig.

5(d)). This suggests that the average Ca-O and Ca-Ti distan-

ces around Ca in (Ba,Ca)TiO3 are elongated relative to

CaTiO3; that is, the volumes of the oxygen cube-octahedra

around Ca in the solid-solution samples remain significantly

larger than those in CaTiO3. This inference from the EXAFS

spectra correlates with a weaker intensity of the pre-edge fea-

ture A in the Ba1�xCaxTiO3 (Fig. 1) samples relative to its in-

tensity in CaTiO3, because hybridization of the Ca 2p states

with the “excitonic” Ca 3d and Ti 3d states will be dimin-

ished for larger oxygen cages around Ca. Such longer average

Ca-O distances are consistent with the lattice volume of

Ba1�xCaxTiO3 (0< x� 0.3) (e.g., V¼ 62.21 A3 for x¼ 0.3)

being considerably larger than the lattice volume of CaTiO3

(V¼ 55.85 A3). This limited relaxation around Ca contrasts

with nearly ideal octahedral volumes acquired by relatively

small B-cations placed in a large host lattice, as reported, for

example, for Ti dopants in BaZrO3 and Mn in SrTiO3;24,25

the difference can be attributed at least in part to distinct

metal-oxygen bond strengths for the A- and B-cations.

Detailed comparison of the real and imaginary parts of the

FT for the solid-solution samples (not shown) also revealed a

small but systematic decrease of the average Ca-O distances

with increasing x, which concurs with the trend in the lattice

volumes for the Ba1�xCaxTiO3 samples (the unit-cell volume

decreases from 64.05 A3 for x¼ 0.05 to 62.21 A3 for x¼ 0.3).

Attempts to fit a CaTiO3-like model to the Ca EXAFS data

for the solid-solution samples were unsuccessful. Accurate

determination of a distorted Ca coordination environment in

these samples from the EXAFS data alone is difficult, if pos-

sible, given the issues encountered in CaTiO3. Refinements

of local structure in (Ba,Ca)TiO3 using a combined fit of neu-

tron total scattering and EXAFS data are in progress and the

results will be reported separately.

Ca EXAFS spectra for the BaTi0.97Ca0.03O2.97 (Fig. 6)

differs markedly from that for (Ba,Ca)TiO3 (Fig. 5). Fitting

the first peak in the EXAFS FT for BaTi0.97Ca0.03O2.97 using

a model with Ca atoms residing on the B-sites yields a Ca-O

distance of 2.28(1) A with a Debye-Waller (D-W) factor of

0.006(1) A2. This distance and the D-W factor are entirely

consistent with Ca coordinated six-fold by oxygen; for

example, similar Ca(B-site)-O distances have been reported

from Rietveld refinements of Ca(Ca1/3Nb2/3)O3.26 However,

attempts to the fit an extended distance range in the EXAFS

FT indicated that this sample features Ca atoms on both the

B- and A-sites. Then, l(E)¼ (1�f)lB(E) þ flA(E), where

l(E) is the spectrum measured, lB(E) and lA(E) refer to the

contributions of Ca on the B- and A-sites, respectively, and fis a fraction of the A-site Ca. We isolated lB(E) by using

a spectrum for Ba0.95Ca0.05TiO3 as lA(E). The B-site

EXAFS was fitted using a typical B-site model that included

single-scattering Ca-O, Ca-Ti, and Ca-Ba paths as well as

double- and triple-scattering Ca-O-Ti paths and a single-

scattering Ca-O (distant) path; the effects of non-180�

scattering angles in the multiple-scattering paths were

accommodated by the Debye-Waller factors. A satisfactory

fit (the residual of 3%) was obtained for the A-site fraction f� 0.3. All the structural parameters refined to sensible values

with S02¼ 0.924. For comparison, the residual of the fit with-

out the A-site subtraction was 6% and several D-W factors

refined to negative values; in this case, the S02 value

obtained by fitting just the first peak was 0.65. Thus, our

results suggest that the actual occupancy of Ca on the B-sites

is �0.02, instead of the nominal 0.03, and the remaining Ca

occupies the A-sites. Such mixed-site occupancy concurs

with the results reported from the previous study of the lat-

tice parameters in Ba(Ti,Ca)O3.9 Table II summarizes struc-

tural parameters refined for the B-site Ca coordination. The

Ti-O distance in the Ca(B)-O-Ti triplets is calculated to be

1.77 A, which is much shorter than the shortest Ti-O distance

in BaTiO3 (1.9 A); that is, the oxygen coordination environ-

ments of Ti atoms adjacent to the B-site Ca appear to be

strongly distorted.

FIG. 6. k-space EXAFS (a) and its FT (b) for the B-site Ca in BaTi0.97

Ca0.03O2.97. The blue and red traces in (a) correspond to the data as meas-

ured and after isolating the B-site contribution, respectively. The blue and

red traces in (b) correspond to the experimental (B-site) and fitted EXAFS

FT, respectively. The k-range used in the FT is from k¼ 2.7 A�1 to

k¼ 10.9 A�1. The k2-weighted EXAFS signal was multiplied by the Han-

ning window (Dk¼ 1) prior to the FT. The quality of the fit and the refined

structural parameters were invariant with respect to the k-weight used.

044106-5 Krayzman et al. J. Appl. Phys. 113, 044106 (2013)

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The XANES for the B-site Ca also differs from that for

Ca in the (Ba,Ca)TiO3 solid solutions (Fig. 7). An upshift of

the main peak by 5 eV can be interpreted using the Natoli

rule27 because the Ca(B-site)-O distance (2.28 A) is signifi-

cantly shorter than the typical average Ca(A-site)-O distance

(�2.7 A). Fig. 7 compares the B-site Ca XANES with the Ti

K XANES in BaTiO3. This comparison is justified because

Ca (Z¼ 20) and Ti (Z¼ 22) exhibit similar atomic numbers

and coordination environments (B-sites). Clear similarities

between the two spectra are observed. Feature C in the Ti

XANES spectra corresponds to excitation of the Ti 1s electron

to the Ti p states that are hybridized with the Ba 4f band.13

These Ba 4f bands are expected to be similar in BaTiO3 and

BaTi0.97Ca0.03O2.97; therefore, feature B in the Ca spectrum

likely originates from the excitation of the Ca 1s electron to

the Ca p states that are hybridized with the Ba 4f band.

The pre-edge features in the Ca and Ti spectra are some-

what different. The Ti pre-edge structure (Fig. 7(b)) exhibits

several features/peaks13 that are associated with (i) p-dhybridization for the absorbing atom (feature A), (ii) hybrid-

ization of the Ti p states with the 3d states of the neighboring

Ti atoms and with Ba 5d states via the O 2p orbitals (a group

of features B). In case of Ca, no p-d mixing occurs on the

absorbing atom, because Ca, which is significantly larger than

Ti, resides in the centers of oxygen octahedra. The energy of

the “excitonic” Ca d states is closer to the energies of the Ti

3d and Ba 5d states than the energy of the “excitonic” Ti 3dstates and, therefore, the corresponding hybridization is much

stronger for Ca. This explains a prominent pre-edge feature A

in the Ca spectrum (Fig. 7(a)) as opposed to the relatively

weak pre-edge structure for Ti (Fig. 7(b)).

CONCLUSIONS

We employed Ca K-edge XAFS to study the local coordi-

nation of Ca in BaTiO3-CaTiO3 solid solutions with Ca sub-

stitutions on both the Ba and Ti sites. Accurate determination

of the distorted coordination of Ca in CaTiO3 (used as a refer-

ence) from EXAFS alone proved difficult. Simultaneous fit-

ting of Ca EXAFS and the total PDF derived using neutron

total scattering provides a model that is consistent with both

types of data. According to this model, the local distortion of

Ca-O coordination in CaTiO3 deviates from the average in the

relative fractions of the short and intermediate distances; how-

ever, these differences could not be established from fitting ei-

ther the EXAFS or total PDF separately. For example, a

simple model of distorted Ca coordination provides an excel-

lent fit to the EXAFS data but the degree of distortion appears

to be smaller than that indicated by the neutron diffraction

data. The local distortions around Ca in (Ba1�xCax)TiO3

appear to be similar for 0< x� 0.3, and the average Ca-O dis-

tances in all the solid-solution samples are appreciably longer

than the average Ca-O distance in CaTiO3. This observation

contrasts with the local-structure relaxation around the B-site

substitutions, which, when placed in a large host perovskite

lattice, commonly attain nearly-ideal local-coordination vol-

umes. The details of Ca coordination in the solid solutions

cannot be determined from EXAFS alone and their determina-

tion is pending combined EXAFS/PDF refinements. Analysis

of Ca EXAFS in BaTi0.97Ca0.03O2.97 sample provides a direct

proof of Ca occupancy on the Ti sites. The actual concentra-

tion of the B-site Ca appears to be less than the nominal value.

The origins of the main features of the Ca K XANES spectra

in samples with Ca occupancy on the A- and B-sites have

been interpreted using phenomenological arguments.

ACKNOWLEDGMENTS

Portions of this research were carried out at the Stanford

Synchrotron Radiation Lights Source, a Directorate of the

SLAC National Accelerator Laboratory and an Office of

FIG. 7. (a) Ca K XANES spectra for the B-site Ca in BaTi0.97Ca0.03O2.97

(blue – as measured, red – after removing the A-site contribution); (b) Ti KXANES spectrum for BaTiO3.

TABLE II. Parameters of the B-site Ca coordination in BaTi0.97Ca0.03O2.97

obtained by fitting the EXAFS data. Coordination numbers (N), average dis-

tances (R), and the associated Debye-Waller factors (r2) for each coordina-

tion shell around Ca are specified. The units of R and r2 values are A and

A2, respectively.

Parameters

Coordination shell Na R r2

Ca-O 6 2.28(2) 0.006(1)

Ca-Ti 6 4.0(1) 0.005a

Ca-Ba 4 3.55(2) 0.008(2)

aKept fixed during fitting.

044106-6 Krayzman et al. J. Appl. Phys. 113, 044106 (2013)

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Science User Facility operated for the U.S. Department of

Energy Office of Science by Stanford University. The work

of FB was supported by NSF Grant DMR1005568. DCS

thanks the EPSRC (Grant No. EP/G005001/11) for funding.

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