A non-zero electric field gradient tensor, detected by probes that occupy sites with cubic point group symmetry, was observed in many ABO3 perovskite-type compounds. This breakdown of local cubic symmetry is commonly associated with the presence of oxygen vacancies around the probe. This effect in BaTixHf1-xO3 with x = 0.7, 0.5, 0.3, 0.1, 0.05 and 0.01 is studied in this work. The cell parameters were obtained at laboratory temperature using XRD spectroscopy. The hyperfine parameters were measured at a 181Ta probe in the B site using Perturbed Angular Correlations (PAC) spectroscopy as a function of both temperature and composition. As a common trend, a static asymmetric and distributed quadrupolar interaction, strongly dependent on composition has been observed. The results, together with those corresponding to 1 > x ≥ 0.75, are analyzed using the point-charge model in terms of polarized oxygen vacancies, different covalence of the Ti-O and Hf-O bonds with computational simulation for the lattice positions of cations and oxygen vacancies.Facultad de Ciencias Exacta

Alonso, Roberto Emilio

López García, Alberto Raúl

Zeitschrift für Naturforschung A

SEDICI - Repositorio de la UNLP

Charge Distribution Model in Cubic Perovskite-type Compounds 
R. E. Alonso and A. López-García 
Departamento de Ffsica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CC. 67, 
1900 La Plata, Repüblica Argentina 
Reprint requests to Prof. A. L.-G.; fax: +54-221-425-2006, e-mail: abeti@venus.fisica.unlp.edu.ar 
Z. Naturforsch. 55 a, 261-266 (2000); received August 25, 1999 
Presented at the XVth International Symposium on Nuclear Quadrupole Interactions, 
Leipzig, Germany, July 25 - 30, 1999. 
A non-zero electric field gradient tensor, detected by probes that occupy sites with cubic point 
group symmetry, was observed in many AB03 perovskite-type compounds. This breakdown of 
local cubic symmetry is commonly associated with the presence of oxygen vacancies around the 
probe. This effect in BaT^Hfi-^O-, with x = 0.7, 0.5, 0.3, 0.1, 0.05 and 0.01 is studied in this 
work. The cell parameters were obtained at laboratory temperature using XRD spectroscopy. The 
hyperfine parameters were measured at a 1X1 Ta probe in the B site using Perturbed Angular Correla-
tions (PAC) spectroscopy as a function of both temperature and composition. As a common trend, 
a static asymmetric and distributed quadrupolar interaction, strongly dependent on composition 
has been observed. The results, together with those corresponding to 1 > x > 0.75, are analyzed 
using the point-charge model in terms of polarized oxygen vacancies, different covalence of the 
Ti-0 and Hf-0 bonds with computational simulation for the lattice positions of cations and oxygen 
vacancies. 
Key words: Perovskites; Ferroelectrics Materials; Defects; Polarized Oxygen Vacancies; Electric 
Field Gardient. 
Introduction 
Perovskite-type compounds AA'BB'03 can contain 
a large number of oxygen vacancies [ 1 ] which depend 
strongly on the preparation method and the subse-
quent thermal treatment. Some macroscopic physical 
properties are closely related with such defects. 
Microscopic studies of perovskites have been done 
through the determination of the electric field gradi-
ent tensor (EFG) at probes located at A and B sites. 
However, the presence of oxygen vacancies does not 
allow a direct interpretation of the hyperfine parame-
ters because the contribution of the oxygen vacancies 
to the EFG is still unknown. 
Symmetry considerations show that at the position 
of the B cation in the cubic phase of stoichiomet-
ric perovskites the EFG is zero. This brings about a 
straightforward relation between the EFG in a non-
stoichiometric cubic phase at probes placed in B-sites 
and the distribution of oxygen vacancies. Therefore 
we have studied in this work the hyperfine interactions 
in the cubic phase of BaTi^Hfi-zC^ with various 
values of x. The experimental results were obtained 
by X-ray diffraction (XRD) and Perturbed Angular 
Correlation (PAC) spectroscopy. Once these data are 
obtained, computational calculations using the point-
charge model (PCM) are used to interpret the charac-
teristics of the EFG measured. 
PAC Measurements 
The samples were irradiated with a flux (1013/s 
cm2) of thermal neutrons at 300 K in order to activate 
the 18'Ta probe obtained from 180Hf. 
In this section the results of measurements on cu-
bic BaTi IHfi_ : r03 with x = 0.7, 0.5, 0.3, 0.1, 0.05; 
and 0.01 as a function of temperature are reported. 
These data will be added to previous ones obtained 
for x > 0.75 [2]. 
In all samples the perturbation factors measured 
were fitted with a static, asymmetric and disordered 
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262 R. E. Alonso and A. Löpez-Garci'a • Charge Distribution Model in Cubic Perovskite-type Compounds 262 
32 
24 
C/3 
TO 
16 
1: 
5 I I I I - L IL 
J . E 
i 1 i 1 
I b x f 
i 
i 1 
5 5 
I i I 
5 5 5 
X 2£_ 
I 
- 5 I 
5 5 5 
£ 
a x= 0.70 
0.50 
± 0.30 
0.10 
• 0.05 
0.01 
i * 
1 . 
1 
1 £ 
5 
4 0 0 600 1200 800 1000 
Temperature [KJ 
Fig. 1. Quadrupolar frequency as a function of temperature for the compositions measured. 
electric quadrupole interaction. Figure 1 shows the fit-
ted quadrupolar frequencies as functions of tempera-
ture and composition. The decrease of these with tem-
perature is commonly associated with cell expansion. 
The asymmetry parameter (mean value 77 = 0.42) is 
almost independent of temperature and composition. 
The distribution width 6 is large and independent of 
temperature: for x = 0.7, 0.5, 0.3, 0.1, 0.05 and 0.01 
resulted 6 = 32, 35, 35, 38,40, and 75%, respectively. 
The existence of a finite quadrupolar frequency at 
all measured compositions is not compatible with the 
cubic symmetry of the B- or the A-site. On the other 
hand, 181Tacan occupy neither an O nor an interstitial 
site. 
Figure 2 shows the dependence of U>Q, 77 and 6 
on the composition, obtained with values fitted or 
extrapolated (for x > 0.75) to room temperature. 
The quadrupolar frequency u;Q has a maximum for 
x ~ 0.7. At a first glance, this behavior of CJQ can-
not be explained only in terms of oxygen vacancies 
because all samples were prepared in the same way, 
i.e., as a first approximation it can be expected that 
all samples had the same oxygen vacancy content. 
EFG Produced by Oxygen Vacancies 
The Point Charge Model (PCM) of the EFG gives 
results that are only usable in a comparative sense 
between similar samples. Although in general the 
calculated EFG tensor does not agree with the ex-
perimental one, the relative trends of ujq and 77, when 
varying some parameter, are of interest. On the other 
hand, the PCM is a simple method that can deal in 
a straightforward way with disordered systems with 
many atoms (2000 and more). For dealing with such 
systems with ab-initio molecular dynamics or Monte 
Carlo methods the computational work must be enor-
mous. 
As mentioned previously, the solid state reaction 
technique used for sample preparation can gener-
ate distinct concentrations of oxygen vacancies. The 
amount of these defects is expected to be greater than 
2% in perovskites prepared by this method. Such va-
cancies produce long range fields. 
A low EFG would indicate that the oxygen vacan-
cies are randomly distributed and are not attracted by 
the 181Ta PAC probe. 
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R. E. Alonso and A. Löpez-Garci'a • Charge Distribution Model in Cubic Perovskite-type Compounds 263 
30 
cn 
^ 20 
o 10 
<D 
E 
E > 
(TJ 
•D 
<J 
«rt 
~o 
0 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
75 
60 
45 
30 
15 
-> r 
J i I . L 
I 
I 
I 
iL 
I 
20 40 60 80 
mole % of BaHfO 
100 
Fig. 2. The hyperfine 
parameters vs. x. The 
open squares correspond 
to room temperature ex-
trapolated values (See 
text). 
The calculation of the EFG was performed on sam-
ples of 10x10x10 unit cells. The calculation was 
done by dividing the lattice into shells. The central 
shell is a cube with Ta at the center, 6 O's (2-) at 
the center of the faces and 8 Ba's (2+) at the corners. 
The first shell consists of 26 cubes surrounding the 
central one, that have Ti (4+) or Hf (4+) at B sites 
randomly distributed according to the value of x. The 
second shell consists of 98 unit cubes covering the 
first one, and so on. Then, for a given concentra-
tion of oxygen vacancies, random vacancy positions 
were generated. The as produced configuration rep-
resents a possible neighborhood at each PAC probe, 
and the EFG tensor was calculated. This process was 
repeated 50000 times to generate a corresponding his-
togram. The cell parameter in the cubic structure was 
a = 1, so the results for Vzz are scaled by a factor 
l/47r£0a3. 
One way to take into account the 181Ta-oxygen va-
cancy interaction is by changing the charge of the 
vacancies around the probe. The oxygen vacancies 
are created during the synthesis process. The mean 
life of the 181Ta is too short to enable anion diffu-
sion during the life time of the metastable state. Two 
electrons appear for each oxygen vacancy. If these 
electrons are trapped by a vacancy, the oxygen octa-
hedra will have almost cubic symmetry and no EFG 
would be produced. On the other hand, if one or no 
electron is trapped, EFG's can be created. Due to the 
great mobility of the electrons they may rearrange in 
order to minimize the total energy. Thus, the original 
random distribution of oxygen vacancies has charge 
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264 R. E. Alonso and A. Löpez-Garci'a • Charge Distribution Model in Cubic Perovskite-type Compounds 264 
0.0 0.5 1.0 1.5 2.0 2.5 
V^ [a34rog 
Fig. 3. Vzz distribution functions for a sample with 3% 
oxygen vacancy content and polarisation profiles of type a) 
1/r3, b) 1/r. The frequency is the number of times that a 
calculated value of Vzz is obtained. 
states that depend on the distance to the Ta probe. The 
boundary conditions taken here are q = - 2 e for va-
cancies in the octahedron surrounding the probe and 
q = 0 for vacancies far away from this octahedron. 
In Fig. 3 the V2Z distribution functions are shown 
for 3% randomly distributed oxygen vacancies with 
electric charges modulated by the functions 1/r and 
1/r3 and with the above boundary conditions. Both 
curves show that the peaks corresponding to vacancies 
present in the first, second and third shells overlap, 
forming an asymmetric and broad unique peak. The 
figure shows the different profiles of the distribution 
that can be obtained with different polarizing func-
tions. The distribution width for a) and b) is nearly 
100% and greater than 200%, respectively. Broad dis-
tributions have been observed experimentally in sev-
eral perovskites [3 - 5]. This simple picture gives a 
reasonable explanation of their origin. 
In order to find the curve that reproduces the experi-
mental results, several parameters must be determined 
(the precise amount of oxygen vacancies, the actual 
function that describes the charge distribution of oxy-
gen vacancies, etc.). The interesting issue is that with 
a very simple hypothesis two observed experimental 
results can be explained: the presence of a non-zero 
EFG and the broad Vzz distribution widths in sites 
with cubic symmetry in perovskites. From the above 
discussion it can be concluded that the origin of the 
EFG in B-sites in perovskites is related to the presence 
300 
150 
0 
300 
150 
0 
300 
150 
0 
300 
150 
0 
300 
150 
0 
3 0 0 
1 5 0 
•• 1 1 — i — i — i i > i > ' i » i —•—i—• i ' i 
x= 0 7 0 • 
x= 0 . 5 0 ~ 
y , . 0 , 6 5 . , 7 7 ^ 
x= 0 3 0 • 
r , ps? . , 
x= 0 . 1 0 -
: 
J j . i 
x= 0 . 0 5 " 
: / 
j . i 
T \ 
0 . 3 9 ^ S u 
x= 0 . 0 1 • 
0 . 0 0 . 3 0 . 6 0 . 9 1 .2 1 .5 1 .8 2 .1 2 4 2 . 7 
V [a347is ] 
z z 1 <r 
Fig. 4. Vzz distribution for 8 = 0.3 e and 3% oxygen vacan-
cies for distinct values of x. The arrows indicate the position 
of the maximum. 
of oxygen vacancies, and the distribution widths of CJq 
observed are due to the charge polarization around the 
181 Ta probes (contributions to polarization of cations 
A and B were discarded for simplicity). The PAC 
spectra fitted with a unique distributed site (see PAC 
section) would mean that the probe is surrounded by 
several vacancies with different charge depending on 
their distance from the probe atom. 
Disorder Introduced by B-cation Substitutions 
The insulating perovskites AB0 3 are known to be 
almost ionic compounds. However, in a previous the-
oretical work about the cubic phases of SrTi03 and 
SrHf03 it was shown that the covalence of oxygen 2p 
electrons is bigger for the Ti-3d electrons than for Hf-
5d electrons [6]. The difference ammounts to about 
0.7 e, while the Sr ion has a purely ionic electronic 
shell structure. According to this hypothesis, in the 
present case, where there is Ba in place of Sr in the 
A-site, the Ti-0 bond would be more covalent than 
the Hf-0 bound. 
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R. E. Alonso and A. Löpez-Garci'a • Charge Distribution Model in Cubic Perovskite-type Compounds 265 
In the PCM it is normally assumed that the charges 
are concentrated at the ion's site with a charge equal to 
its nominal valence. But if the compound is covalent, 
the charge is distributed in space and the PCM is not 
applicable. Thus, for simulating the partial covalence 
of a bond we assume as a first approximation that 
the ionic charge is reduced from its nominal value. In 
order to study the variation of the EFG with the molar 
percentage of BaHf03 , the Ti ions were charged with 
+4 e - 6 and the Hf ions with +4 e. 
If Ti and Hf covalence is added to the EFG pro-
duced by polarized oxygen vacancies, the Vzz dis-
tribution function changes drastically. In Fig. 4 the 
results obtained for 6 = 0.3 e, 3% oxygen vacancies 
content and a charge polarization of the type Mr for 
different Ti:Hf ratios are shown. The Vzz distribution 
curves now have one broad peak whose maximum 
position depends on composition as is observed ex-
perimentally. 
The asymmetry parameter ij measured (see Fig. 2) 
is ~ 0.45 for x = 0.7, 0.5, 0.3 and 0.1 and tending to 
zero as a: —• 1. In samples with x = 0.05 and 0.01 the 
fitted 77's have big relative errors. This model predicts 
a mean asymmetry parameter of about 0.5, indepen-
dent of Ti:Hf ratio. 
In this family of compounds the measured relative 
width depends strongly on the Ti-Hf composition. For 
the richest Ti or Hf compositions 6 increases up to 
~ 80%, while for middle compositions 6 « 30% and 
almost constant. The values predicted by the model 
do not reproduce this fact because 6 is maximum for 
x = 0.5 and diminishes for x close to 0 and 1. This 
is expected. As was shown in Fig. 3 and the related 
discussion, the width of the EFG distribution func-
tion is strongly dependent on the profile selected for 
the polarisation of oxygen vacancies. Moreover, the 
tests performed on changing the difference of charge 
between Hf and Ti by distinct values (0.2 e, 0.4 e, 
etc.) show that again the width of the distribution 
varies with this parameter. In the real compound it 
is expected that the polarisation profile and the grade 
of covalence depend on the local disorder. Thus, the 
experimental distribution width dependence on com-
position can be reproduced by adjusting these two 
quantities. 
From the maximum values of the Vzz distribution 
functions shown in Fig. 4 and the lattice constants 
measured by XRD, the values of Vzz = A-k£qq?Vzz 
1 1 > 1 • 1 > 1 • 1 
30 -
• • 
25 - • 
M1 20 -
m 
i 15 -O • 3 
10 - • -
5 - I 1 I 1 1 I 1 1 
0 20 40 60 80 100 
% molar of BaHfO 3 
Fig. 5. Comparison between experimental (circles) and cal-
culated (triangles) data. The calculated data have been nor-
malised for coinciding both values at x = 0.70. 
can be calculated and compared with the experimental 
results. In Fig. 5 the measured and calculated Vzz 
values are shown. Taking into account the simplicity 
of the model and the hypothesis used, the agreement 
is reasonable. Thus, it can be concluded that the EFGs 
measured in the BaTixHfi_x03 family depend mainly 
on polarized, randomly distributed oxygen vacancies 
and on the different covalence of the B-O bonds. 
Conclusions 
For several compositions of the compounds 
BaTixHfi_x03 the lattice constant at room temper-
ature and the hyperfine interactions at the B-sites as 
functions of the temperature were measured. Above 
room temperature all the crystals were cubic. In each 
sample a non-zero, asymmetric and disordered EFG 
was obtained. This fact was previously observed in 
other perovskite-type compounds. The EFG at room 
temperature depends strongly on x. Using some sim-
ple assumptions and the PCM, we conclude that 
EFG's are related with the presence of oxygen va-
cancies. The behavior of the distribution width can be 
explained by the polarization of the oxygen vacancy 
charge as a function of the distance from the PAC 
probe atom. The dependence of the EFG on the mole 
percentage of BaHf03 can be reproduced taking into 
account the different degree of covalence of the Ti-0 
and Hf-0 bonds. 
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266 R. E. Alonso and A. Löpez-Garci'a • Charge Distribution Model in Cubic Perovskite-type Compounds 266 
[1] M. A. Bunin, S. A. Prosandeyev, I. I. Gegusin, and 
I. M. Tennenboum, Rad. Eff. Def. Solids 134, 75 
(1996). M. V. Raymond and D. M. Smyth, J. Phys 
Chem. Solids 57, 1507 (1996). W. L Warren, K. Van-
heusden, D. Dimos, G. E. Pike, and B. A. Tuttle, 
J. Amer. Ceram. Soc. 79, 536 (1996). 
[2] A. Ayala, PhD Thesis, Universidad de La Plata, 1996. 
[3] R. E. Alonso, P. de la Presa, A. Ayala, and A. Lopez 
Garcia, J. Physics: Cond. Mat. 10, 2139 (1998). 
[4] G. Catchen, S. Wokitch, D. Spaar, and M. Bla-
szkiewicz, Phys. Rev. B42, 1885 (1990). 
[5] G. Catchen, E. Hollinger, and T. Rearick, Z. Natur-
forsch. 51a, 411 (1996). 
[6] G. Fabricius, E. L. Peltzer y Bianca, C. O. Rodriguez, 
A. P. Ayala, P. de la Presa, and A. Lopez Garcia, Phys. 
Rev. B55, 41 (1997). 
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English

Charge distribution model in cubic perovskite-type compounds

Servicio de Difusión de la Creación Intelectual

Charge Distribution Model in Cubic Perovskite-type Compounds R. E. Alonso and A. López-García Departamento de Ffsica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, CC. 67, 1900 La Plata, Repüblica Argentina Reprint requests to Prof. A. L.-G.; fax: +54-221-425-2006, e-mail: abeti@venus.fisica.unlp.edu.ar Z. Naturforsch. 55 a, 261-266 (2000); received August 25, 1999 Presented at the XVth International Symposium on Nuclear Quadrupole Interactions, Leipzig, Germany, July 25 - 30, 1999. A non-zero electric field gradient tensor, detected by probes that occupy sites with cubic point group symmetry, was observed in many AB03 perovskite-type compounds. This breakdown of local cubic symmetry is commonly associated with the presence of oxygen vacancies around the probe. This effect in BaT^Hfi-^O-, with x = 0.7, 0.5, 0.3, 0.1, 0.05 and 0.01 is studied in this work. The cell parameters were obtained at laboratory temperature using XRD spectroscopy. The hyperfine parameters were measured at a 1X1 Ta probe in the B site using Perturbed Angular Correla-tions (PAC) spectroscopy as a function of both temperature and composition. As a common trend, a static asymmetric and distributed quadrupolar interaction, strongly dependent on composition has been observed. The results, together with those corresponding to 1 > x > 0.75, are analyzed using the point-charge model in terms of polarized oxygen vacancies, different covalence of the Ti-0 and Hf-0 bonds with computational simulation for the lattice positions of cations and oxygen vacancies. Key words: Perovskites; Ferroelectrics Materials; Defects; Polarized Oxygen Vacancies; Electric Field Gardient. Introduction Perovskite-type compounds AA'BB'03 can contain a large number of oxygen vacancies [ 1 ] which depend strongly on the preparation method and the subse-quent thermal treatment. Some macroscopic physical properties are closely related with such defects. Microscopic studies of perovskites have been done through the determination of the electric field gradi-ent tensor (EFG) at probes located at A and B sites. However, the presence of oxygen vacancies does not allow a direct interpretation of the hyperfine parame-ters because the contribution of the oxygen vacancies to the EFG is still unknown. Symmetry considerations show that at the position of the B cation in the cubic phase of stoichiomet-ric perovskites the EFG is zero. This brings about a straightforward relation between the EFG in a non-stoichiometric cubic phase at probes placed in B-sites and the distribution of oxygen vacancies. Therefore we have studied in this work the hyperfine interactions in the cubic phase of BaTi^Hfi-zC^ with various values of x. The experimental results were obtained by X-ray diffraction (XRD) and Perturbed Angular Correlation (PAC) spectroscopy. Once these data are obtained, computational calculations using the point-charge model (PCM) are used to interpret the charac-teristics of the EFG measured. PAC Measurements The samples were irradiated with a flux (1013/s cm2) of thermal neutrons at 300 K in order to activate the 18'Ta probe obtained from 180Hf. In this section the results of measurements on cu-bic BaTi IHfi_ : r03 with x = 0.7, 0.5, 0.3, 0.1, 0.05; and 0.01 as a function of temperature are reported. These data will be added to previous ones obtained for x > 0.75 [2]. In all samples the perturbation factors measured were fitted with a static, asymmetric and disordered 0932-0784 / 2000 / 0100-0261 $ 06.00 © Verlag der Zeitschrift für Naturforschung, Tübingen • www.znaturforsch.com UnauthenticatedDownload Date | 8/23/19 8:29 PM262 R. E. Alonso and A. Löpez-Garci'a • Charge Distribution Model in Cubic Perovskite-type Compounds 262 32 24 C/3 TO 16 1: 5 I I I I - L IL J . E i 1 i 1 I b x f i i 1 5 5 I i I 5 5 5 X 2£_ I - 5 I 5 5 5 £ a x= 0.70 0.50 ± 0.30 0.10 • 0.05 0.01 i * 1 . 1 1 £ 5 4 0 0 600 1200 800 1000 Temperature [KJ Fig. 1. Quadrupolar frequency as a function of temperature for the compositions measured. electric quadrupole interaction. Figure 1 shows the fit-ted quadrupolar frequencies as functions of tempera-ture and composition. The decrease of these with tem-perature is commonly associated with cell expansion. The asymmetry parameter (mean value 77 = 0.42) is almost independent of temperature and composition. The distribution width 6 is large and independent of temperature: for x = 0.7, 0.5, 0.3, 0.1, 0.05 and 0.01 resulted 6 = 32, 35, 35, 38,40, and 75%, respectively. The existence of a finite quadrupolar frequency at all measured compositions is not compatible with the cubic symmetry of the B- or the A-site. On the other hand, 181Tacan occupy neither an O nor an interstitial site. Figure 2 shows the dependence of U>Q, 77 and 6 on the composition, obtained with values fitted or extrapolated (for x > 0.75) to room temperature. The quadrupolar frequency u;Q has a maximum for x ~ 0.7. At a first glance, this behavior of CJQ can-not be explained only in terms of oxygen vacancies because all samples were prepared in the same way, i.e., as a first approximation it can be expected that all samples had the same oxygen vacancy content. EFG Produced by Oxygen Vacancies The Point Charge Model (PCM) of the EFG gives results that are only usable in a comparative sense between similar samples. Although in general the calculated EFG tensor does not agree with the ex-perimental one, the relative trends of ujq and 77, when varying some parameter, are of interest. On the other hand, the PCM is a simple method that can deal in a straightforward way with disordered systems with many atoms (2000 and more). For dealing with such systems with ab-initio molecular dynamics or Monte Carlo methods the computational work must be enor-mous. As mentioned previously, the solid state reaction technique used for sample preparation can gener-ate distinct concentrations of oxygen vacancies. The amount of these defects is expected to be greater than 2% in perovskites prepared by this method. Such va-cancies produce long range fields. A low EFG would indicate that the oxygen vacan-cies are randomly distributed and are not attracted by the 181Ta PAC probe. UnauthenticatedDownload Date | 8/23/19 8:29 PMR. E. Alonso and A. Löpez-Garci'a • Charge Distribution Model in Cubic Perovskite-type Compounds 263 30 cn ^ 20 o 10 <D E E > (TJ •D <J «rt ~o 0 0.8 0.7 0.6 0.5 0.4 0.3 0.2 75 60 45 30 15 -> r J i I . L I I I iL I 20 40 60 80 mole % of BaHfO 100 Fig. 2. The hyperfine parameters vs. x. The open squares correspond to room temperature ex-trapolated values (See text). The calculation of the EFG was performed on sam-ples of 10x10x10 unit cells. The calculation was done by dividing the lattice into shells. The central shell is a cube with Ta at the center, 6 O's (2-) at the center of the faces and 8 Ba's (2+) at the corners. The first shell consists of 26 cubes surrounding the central one, that have Ti (4+) or Hf (4+) at B sites randomly distributed according to the value of x. The second shell consists of 98 unit cubes covering the first one, and so on. Then, for a given concentra-tion of oxygen vacancies, random vacancy positions were generated. The as produced configuration rep-resents a possible neighborhood at each PAC probe, and the EFG tensor was calculated. This process was repeated 50000 times to generate a corresponding his-togram. The cell parameter in the cubic structure was a = 1, so the results for Vzz are scaled by a factor l/47r£0a3. One way to take into account the 181Ta-oxygen va-cancy interaction is by changing the charge of the vacancies around the probe. The oxygen vacancies are created during the synthesis process. The mean life of the 181Ta is too short to enable anion diffu-sion during the life time of the metastable state. Two electrons appear for each oxygen vacancy. If these electrons are trapped by a vacancy, the oxygen octa-hedra will have almost cubic symmetry and no EFG would be produced. On the other hand, if one or no electron is trapped, EFG's can be created. Due to the great mobility of the electrons they may rearrange in order to minimize the total energy. Thus, the original random distribution of oxygen vacancies has charge UnauthenticatedDownload Date | 8/23/19 8:29 PM264 R. E. Alonso and A. Löpez-Garci'a • Charge Distribution Model in Cubic Perovskite-type Compounds 264 0.0 0.5 1.0 1.5 2.0 2.5 V^ [a34rog Fig. 3. Vzz distribution functions for a sample with 3% oxygen vacancy content and polarisation profiles of type a) 1/r3, b) 1/r. The frequency is the number of times that a calculated value of Vzz is obtained. states that depend on the distance to the Ta probe. The boundary conditions taken here are q = - 2 e for va-cancies in the octahedron surrounding the probe and q = 0 for vacancies far away from this octahedron. In Fig. 3 the V2Z distribution functions are shown for 3% randomly distributed oxygen vacancies with electric charges modulated by the functions 1/r and 1/r3 and with the above boundary conditions. Both curves show that the peaks corresponding to vacancies present in the first, second and third shells overlap, forming an asymmetric and broad unique peak. The figure shows the different profiles of the distribution that can be obtained with different polarizing func-tions. The distribution width for a) and b) is nearly 100% and greater than 200%, respectively. Broad dis-tributions have been observed experimentally in sev-eral perovskites [3 - 5]. This simple picture gives a reasonable explanation of their origin. In order to find the curve that reproduces the experi-mental results, several parameters must be determined (the precise amount of oxygen vacancies, the actual function that describes the charge distribution of oxy-gen vacancies, etc.). The interesting issue is that with a very simple hypothesis two observed experimental results can be explained: the presence of a non-zero EFG and the broad Vzz distribution widths in sites with cubic symmetry in perovskites. From the above discussion it can be concluded that the origin of the EFG in B-sites in perovskites is related to the presence 300 150 0 300 150 0 300 150 0 300 150 0 300 150 0 3 0 0 1 5 0 •• 1 1 — i — i — i i > i > ' i » i —•—i—• i ' i x= 0 7 0 • x= 0 . 5 0 ~ y , . 0 , 6 5 . , 7 7 ^ x= 0 3 0 • r , ps? . , x= 0 . 1 0 -: J j . i x= 0 . 0 5 " : / j . i T \ 0 . 3 9 ^ S u x= 0 . 0 1 • 0 . 0 0 . 3 0 . 6 0 . 9 1 .2 1 .5 1 .8 2 .1 2 4 2 . 7 V [a347is ] z z 1 <r Fig. 4. Vzz distribution for 8 = 0.3 e and 3% oxygen vacan-cies for distinct values of x. The arrows indicate the position of the maximum. of oxygen vacancies, and the distribution widths of CJq observed are due to the charge polarization around the 181 Ta probes (contributions to polarization of cations A and B were discarded for simplicity). The PAC spectra fitted with a unique distributed site (see PAC section) would mean that the probe is surrounded by several vacancies with different charge depending on their distance from the probe atom. Disorder Introduced by B-cation Substitutions The insulating perovskites AB0 3 are known to be almost ionic compounds. However, in a previous the-oretical work about the cubic phases of SrTi03 and SrHf03 it was shown that the covalence of oxygen 2p electrons is bigger for the Ti-3d electrons than for Hf-5d electrons [6]. The difference ammounts to about 0.7 e, while the Sr ion has a purely ionic electronic shell structure. According to this hypothesis, in the present case, where there is Ba in place of Sr in the A-site, the Ti-0 bond would be more covalent than the Hf-0 bound. UnauthenticatedDownload Date | 8/23/19 8:29 PMR. E. Alonso and A. Löpez-Garci'a • Charge Distribution Model in Cubic Perovskite-type Compounds 265 In the PCM it is normally assumed that the charges are concentrated at the ion's site with a charge equal to its nominal valence. But if the compound is covalent, the charge is distributed in space and the PCM is not applicable. Thus, for simulating the partial covalence of a bond we assume as a first approximation that the ionic charge is reduced from its nominal value. In order to study the variation of the EFG with the molar percentage of BaHf03 , the Ti ions were charged with +4 e - 6 and the Hf ions with +4 e. If Ti and Hf covalence is added to the EFG pro-duced by polarized oxygen vacancies, the Vzz dis-tribution function changes drastically. In Fig. 4 the results obtained for 6 = 0.3 e, 3% oxygen vacancies content and a charge polarization of the type Mr for different Ti:Hf ratios are shown. The Vzz distribution curves now have one broad peak whose maximum position depends on composition as is observed ex-perimentally. The asymmetry parameter ij measured (see Fig. 2) is ~ 0.45 for x = 0.7, 0.5, 0.3 and 0.1 and tending to zero as a: —• 1. In samples with x = 0.05 and 0.01 the fitted 77's have big relative errors. This model predicts a mean asymmetry parameter of about 0.5, indepen-dent of Ti:Hf ratio. In this family of compounds the measured relative width depends strongly on the Ti-Hf composition. For the richest Ti or Hf compositions 6 increases up to ~ 80%, while for middle compositions 6 « 30% and almost constant. The values predicted by the model do not reproduce this fact because 6 is maximum for x = 0.5 and diminishes for x close to 0 and 1. This is expected. As was shown in Fig. 3 and the related discussion, the width of the EFG distribution func-tion is strongly dependent on the profile selected for the polarisation of oxygen vacancies. Moreover, the tests performed on changing the difference of charge between Hf and Ti by distinct values (0.2 e, 0.4 e, etc.) show that again the width of the distribution varies with this parameter. In the real compound it is expected that the polarisation profile and the grade of covalence depend on the local disorder. Thus, the experimental distribution width dependence on com-position can be reproduced by adjusting these two quantities. From the maximum values of the Vzz distribution functions shown in Fig. 4 and the lattice constants measured by XRD, the values of Vzz = A-k£qq?Vzz 1 1 > 1 • 1 > 1 • 1 30 -• • 25 - • M1 20 -m i 15 -O • 3 10 - • -5 - I 1 I 1 1 I 1 1 0 20 40 60 80 100 % molar of BaHfO 3 Fig. 5. Comparison between experimental (circles) and cal-culated (triangles) data. The calculated data have been nor-malised for coinciding both values at x = 0.70. can be calculated and compared with the experimental results. In Fig. 5 the measured and calculated Vzz values are shown. Taking into account the simplicity of the model and the hypothesis used, the agreement is reasonable. Thus, it can be concluded that the EFGs measured in the BaTixHfi_x03 family depend mainly on polarized, randomly distributed oxygen vacancies and on the different covalence of the B-O bonds. Conclusions For several compositions of the compounds BaTixHfi_x03 the lattice constant at room temper-ature and the hyperfine interactions at the B-sites as functions of the temperature were measured. Above room temperature all the crystals were cubic. In each sample a non-zero, asymmetric and disordered EFG was obtained. This fact was previously observed in other perovskite-type compounds. The EFG at room temperature depends strongly on x. Using some sim-ple assumptions and the PCM, we conclude that EFG's are related with the presence of oxygen va-cancies. The behavior of the distribution width can be explained by the polarization of the oxygen vacancy charge as a function of the distance from the PAC probe atom. The dependence of the EFG on the mole percentage of BaHf03 can be reproduced taking into account the different degree of covalence of the Ti-0 and Hf-0 bonds. UnauthenticatedDownload Date | 8/23/19 8:29 PM266 R. E. Alonso and A. Löpez-Garci'a • Charge Distribution Model in Cubic Perovskite-type Compounds 266 [1] M. A. Bunin, S. A. Prosandeyev, I. I. Gegusin, and I. M. Tennenboum, Rad. Eff. Def. Solids 134, 75 (1996). M. V. Raymond and D. M. Smyth, J. Phys Chem. Solids 57, 1507 (1996). W. L Warren, K. Van-heusden, D. Dimos, G. E. Pike, and B. A. Tuttle, J. Amer. Ceram. Soc. 79, 536 (1996). [2] A. Ayala, PhD Thesis, Universidad de La Plata, 1996. [3] R. E. Alonso, P. de la Presa, A. Ayala, and A. Lopez Garcia, J. Physics: Cond. Mat. 10, 2139 (1998). [4] G. Catchen, S. Wokitch, D. Spaar, and M. Bla-szkiewicz, Phys. Rev. B42, 1885 (1990). [5] G. Catchen, E. Hollinger, and T. Rearick, Z. Natur-forsch. 51a, 411 (1996). [6] G. Fabricius, E. L. Peltzer y Bianca, C. O. Rodriguez, A. P. Ayala, P. de la Presa, and A. Lopez Garcia, Phys. Rev. B55, 41 (1997). UnauthenticatedDownload Date | 8/23/19 8:29 PM

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Charge distribution model in cubic perovskite-type compounds

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