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Perturbed-angular-correlation spectroscopy: evidence for probe-dopant interactions in Ca-doped barium titanate
Materials Science and Engineering, B15 ( 1992) 209 -216
209
Perturbed-angular-correlation spectroscopy: evidence for probe-dopant interactions in Ca-doped barium titanate James M. Adams and Gary L. Catchen Department of Nuclear Engineering and Materials Research Laboratory, The Pennsylvania State University, University Park, PA 16802 (USA) (Received April 18, 1992; in revised form June 13, 1992)
Abstract To investigate dopant- and defect-probe interactions, we have performed perturbed-angular-correlation (PAC) spectroscopy on Ca-doped barium titanate ceramics. Polycrystalline samples of barium titanate were prepared using the resinintermediate process, and the samples were doped with Ca according to the formula (Ba 1_xCax)(Til _yCay)O3_y, where 0 < x< 0.05 and 0 < y< 0.05. All of the samples were doped with approximately 0.1 at.% Hf, which was substituted into the Ti sites and carded the lalHf-* lalTa PAC probe radioactivity. Measurements were performed over a temperature range from laboratory temperature to approximately 1100 K. In the ferroelectric phases, at Ca concentrations of several percent, the doping produces an increase in the Ti-site electric-field-gradient (efg) asymmetry and in the extent of spectral linebroadening. At higher Ca concentrations, the linebroadening increases further and the ferroelectric-to-paraelectric transition is not discemable. The changes in efg symmetry and spectral linebroaderting, which are essentially temperature invariant, could be attributed to preferential substitution of the Ca dopant into Ba coordination spheres that are near the probe sites. In the paraelectric phase, doping at 2 at.% produces a weak perturbation that is several times stronger than the corresponding weak perturbation that non-doped samples show over the same temperature range. This result strongly suggests that O vacancies do not cause these weak perturbations.
1. Introduction
During the past several years, we have been using a nuclear technique, perturbed-angular-correlation (PAC) spectroscopy, to investigate the effects of local fields in ferroelectric, ternary-metal-oxide ceramics [1-5]. The research has focused on primarily ABO3 perovskites such as PbTiO3 [2] and BaTiO 3 (for a review of PAC measurements performed on ABO3 perovskites see ref. 1) and related compounds such as L i N b O a and LiTaO 3 [3, 4]. These materials are particularly well suited for PAC spectroscopy, because the radioactive 18~Hf--, 181Ta PAC probe can be substituted into these crystals in small amounts, less than 1 at.%. A primary research objective has been to better understand the mechanisms that give rise to the ferroelectricto-paraelectric transitions. In particular, we have been using PAC spectroscopy to delineate dynamic order-disorder and static displacive aspects of these phase transitions [1-4]. In nonmagnetic materials, the PAC technique can measure the electric-field-gradient (efg) tensor at the lattice site of a radioactive probe ion that was substituted into the crystal [5]. Specifically, the technique measures the interaction of the nuclear-electric quad0921-5107/92/$5.00
rupole moment of an exited nuclear level in the probeion nucleus with extranuclear efgs produced by all of the electrons and nuclei that surround the probe nucleus. This excited nuclear level is populated by the emission of an initial ),-ray, and it is depopulated by the emission of a final )'-ray. During the lifetime of the intermediate level, the quadrupole moment of the level can interact with the extranuclear efgs. This interaction changes the nuclear orientation prior to the emission of the final ),-ray. Because the nuclear orientation changed, the direction in space where the final )'-ray is emitted is different than where it would have been had no interaction occurred. To describe this process, we say that the nuclear-quadrupole interaction perturbs the angular correlation, i.e. spatial correlation of the )'-)' cascade. This effect is indeed measurable, and it is the basis of the PAC technique. Because the chemistry of the Hf 4 + ion is very similar to that of the Ti 4~ ion and nearly identical to that of the Zr 4+ ion, the 181I-If/lalTa probe is well suited to investigating perovskites that contain Group IV elements such as B a Z i O 3. Because the )'-)' cascade that involves the hyperfine interaction takes place between excited states in the lSlTa nucleus, the actual interaction involves a Ta impurity at the site of interest, which is © 1992--Elsevier Sequoia. All rights reserved
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J. M. Adams, G. L. Catchen
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Probe-dopant interactions in Ca-doped barium titanate
the Ti site in B a l t O 3. However, the process of substituting the probe depends on the chemical properties of Hf, which subsequently decays by t - emission to populate excited states in 18~Ta. Nuclear-quadrupole interactions fall into two categories, static and time-varying. During a static interaction, the efg appears experimentally to be essentially a time-averaged quantity. For example, in a crystal lattice, the vibrational motions of the atoms in the lattice are usually much more rapid than the time scale of the y - y cascade, which can range from approximately 0.1 ns to several hundred nanoseconds. As a result of this "motional narrowing" effect, efgs produced by vibrating atoms fixed to their lattice sites give rise to static interactions. Time-varying interactions arise when the efg fluctuates either in magnitude or in symmetry during the intermediate-level lifetime, i.e. motion on a slower timescale. Because detecting the initial y-ray selects nuclei in specific orientations, these fluctuations cause the nuclear-spin orientation of the intermediate level to become random, i.e. to relax. This effect, which can be caused by effects such as ions "hopping" in and out of lattice sites, attenuates the measured angular correlation. The specific experimental difficulty arises when the spectral lines measured in a PAC experiment show either broadening or attenuation. In general, linebroadening can occur when static point defects are trapped at locations that are near the PAC-probe site. Similarly linebroadening and attenuation can occur when dynamic disordering produces fluctuating efgs near the probe site. For ferroelectric BaTiO 3 and PbTiO 3, at temperatures below the tetragonal-to-cubic transition temperature Tc, the PAC measurements show well-defined nuclear-quadrupole interactions that are characterized by highly-broadened lines [1, 2]. At temperatures above To, the measurements show a very weak interaction that has no temperature sensitivity [1]. This weak interaction is quantitatively similar to interactions measured on the cubic non-ferroelectric perovskites SrTiO 3 and B a H f O 3 at laboratory temperature [1]. In the cubic, non-ferroelectric structures, because of symmetry, the nuclear-quadrupole iteractions at the Ba sites should vanish and the correlation should be nonperturbed, if the structures were truly cubic. Moreover, if the probes would tend to trap defects such as O vacancies in the cubic phases, then the measured weak perturbations should show temperature sensitivities that correspond to thermally-activated detrapping of these defects. Thus, on these perovskites, the linebroadening at temperatures below T~ and the weak perturbations at temperatures above T~ remain anomalous and unexplained [5]. To interpret these anomalous results, we need to identify the origins of the linebroadening that occurs at
temperatures below 7~ and the weak perturbation that occurs at temperatures above Tc. For this reason, we performed a series of PAC measurements on CAdoped barium titanate, in which we varied the Ca concentrations from 0 to 10 at.%. We expected the measurements to be sensitive to two effects. At low Ca concentrations, when Ca 2+ ions substituted into primarily the Ba sites, no additional oxygen vacancies should be produced and the major effect should involve interactions between Ca 2+ dopants at Ba sites and Ta 5+ probe ions at the Ti sites. At higher Ca concentrations, when Ca 2+ ions substitute into both the Ba and Ti sites, additional oxygen vacancies should be produced. The major effect then should involve interactions of the LSiTa5 + probe ions between both the oxygen vacancies and the Ca z+ dopants. However, we can explain the results of the experiments primarily in terms of interactions between Ca 2÷ ions and the Ta 5÷ probe ions. Moreover, we do not need to introduce the effects of O vacancies to explain the measured spectral lineshapes. This interpretation has a particularly significant implication for the measurements on nondoped BaTiO3, because it strongly suggests that the well-known linebroadening observed in the ferroelectric phase and the weak perturbation observed in the paraelectric phase arise from effects other than O vacancies trapped in the vicinity of the probe ions.
2. Experimental details 2.1. Sample preparation
Polycrystalline samples of BaTiO 3 were prepared using a variation of the resin-intermediate method, which is described elsewhere [1, 2]. To perform the PAC measurements, 1-2 g of sample material that typicaUy contained 15-30/aCi of 18~Hfactivity were sealed in fused-silica tubes. Small amounts of powder from these samples were used for X-ray powder diffraction to check the phase purity of the samples. From the powder patterns, we estimated that the samples were at least 95% phase pure. The nominal Hf concentrations were 0.1-0.2 at.% of the Ti-ion concentration. These Hf concentrations were kept as small as was practical, because adding small amounts of t-If, i.e. several percent or less, causes the c/a ratio of the BaTiO 3 lattice to change sigrfificantly [6]. Additiormily, the samples were sintered at temperatures of 1570 K or higher. Although these high temperatttres are not necessary to produce the BaTiO3 structure via resin-intermediateproduced powders, these temperatures are necessary to assure that the HI dopant comt~letely substitutes into the structure. The levels of Ca doping ranged from 2 to 10 at.%. The Ba and Ti concentrations were adjusted according to the formula: (Bal_xCax)(Ti~_yCay)O3_y,
J. M. Adams, G. L. Catchen
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Probe-dopant interactions in Ca-doped barium titanate
in which 0~
(1) in which r is the intermediate-level lifetime. To analyze the experimental perturbation functions, a one-site model was used to fit the data: -A22GE2(t~)=A,
So(ri)+
Sk(ri)
X exp( -½ 8tOktt) COS(tOktl)] +A2 J
(2)
A1 is the normalization factor that represents the probes that undergo the static interaction. A 2 repre-
211
sents the effects of ),-rays that are absorbed in the sample en route to the detector and the contributions from probes that are not in well-defined chemical environments such as either at grain boundaries or in secondary phases. In this application, A1 ~'A2. The frequencies tok and the Sk(r/) coefficients describe a static interaction in a polycrystalline source. Once the interaction frequencies are determined from the experimental perturbation function, tOo, Vzz,and r/are calculated using a procedure that ref. 8 describes in detail. The factor exp(--½6tOkti) represents the effects of a Lorentzian distribution of interaction frequencies that produces inhomogeneous linebroadening in which 6 is the lineshape parameter. The parameter 6 gives a measure of the relative width of the distribution, in which 6 = AtOk/tOk 0 and tOk° refers to the interaction frequency that would occur at a non-defective probe site.
3. Results
Figure 1 presents the perturbation functions for Cadoped samples of barium titanate that were measured at laboratory temperature. Figure 2 summarizes the parameters derived from the fits to the data. For the case of zero Ca-doping, the perturbation function fields well-defined frequencies, and the line is extensively broadened. As a result of the broadening, the asymmetry parameter r/= 0.16 + 0.05 is small but it is nonzero. Although a zero asymmetry would be consistent with the tetragonal symmetry of the lattice, the small but nonvanishing r/value is expected from the distribution of interaction frequencies that the broad line and the associated large dt parameter indicate. As the Ca-doping concentrations increase, the lines broaden further. The perturbation functions are nonetheless sufficiently well defined that unique interaction frequencies could be determined. We see that the efgs are significantly more asymmetric (r/= 0.32 + 0.03 for 2% Ca and r / = 0 . 4 1 + 0 . 0 3 for 4% Ca) than is the corresponding efg in the non-doped case. Because the perturbation functions for samples doped with larger Ca concentrations are highly broadened, the derived asymmetry parameters may not be unique. For each of the Ca concentrations, 2, 4, 5, 6, and 10 at.%, we performed a series of measurements at several elevated temperatures, typically over a range from 400 to 1100 K. For these paraelectric phases, the resulting perturbation functions are highly broadened, and the associated lineshapes show no discernible temperature dependence. As an example, Fig. 3 presents the perturbation functions for a 10% Ca-doped sample of barium titanate that was measured at the indicated temperatures. Each of these perturbation functions is
212
J. M. Adams, G. L. Catchen /
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Probe-dopant interactions in Ca-doped barium titanate 1.0
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k
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I , .
40
t(nsec)
Fig. 1. Perturbation functions measured at laboratory temperature on ceramic, Ca-doped barium titanate samples. The Ca concentrations are indicated in atomic percent. The solid lines represent fits of eqn. (2) to the data. The dashed lines represent constrained two-site-model fits to the data.
0,I
0.00 . . . . . . . . .
highly broadened. As a result, the derived efg parameters may not be unique. However, despite the limitations of these data, all of these perturbation functions appear to be alike. Because 10% Ca-doping is known to lower the Curie temperature to approximately laboratory temperature [7], the sample was in the paraelectric phase for all four of the measurements. Thus, these perturbation functions represent ternperatureinvariant interactions that took place in the paraelectric phase, which are characterized by a broad distribution of interaction frequencies. Figure 4 presents the perturbation functions for a non-doped sample measured at a temperature above
, ......... I0
I .... , .... J ......... 20 30 I (nsec)
.
J..
40
Fig. 3. Perturbation functions measured at the indicated temperatures on barium titanate samples doped with 10 at.% Ca. The solid lines represent fits of eqn. (2) to the data; and the pertinent, derived parameters are indicated. The dotted lines indicate the "hard-core", i.e. AlSo, values that represent the limiting case of strong, inhomogeneous linebroadening.
Tc and for a 2% Ca-doped sample measured at two temperatures above To; within the experimental errors, the derived Vu-parameters are the same for the two functions representing the 2% Ca-doped sample.
J. M. Adams, G. L. Catchen
/
Probe-dopant interactions in Ca-doped barium titanate
value--A22S0~0.04 for long times, t > 2 0 n s . The
4. Discussion To determine the effects of Ca doping at laboratory temperature, we consider the perturbation functions that Fig. 1 shows and the associated summaries of derived parameters that Fig. 2 shows. As the concentration of Ca increases, the perturbation functions indicate more asymmetric interactions, i.e. ~1 increases, and the lines broaden. At highest Ca concentrations, 10%, the peak in the perturbations function is gone, and the function approaches the so-called "hard core"
02
! ~N,~,
Vzz = 0.6 + O.I x IO17 Vcrn-
i%.
2
8=1.6±0.3 ~,A~
ml~r..
2 */. Co 780K
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o.2'
2*/*Co 4 4 0 K
xt "
. . . .
0
,
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L . . . . . . . . .
I0
½.
m . . . . . . . . .
20 I' (nse¢)
O%Co410K
"
I . . . . . . . . .
50
'
I . . .
40
Fig. 4. Perturbation function measured at the indicated temperatures for non-doped and 2 at.% Ca-doped barium titanate. The solid lines represent fits of eqn. (2) to the data; and the pertinent, derived parameters are indicated. At these measurement temperatures, the samples were in the respective paraelectric phases. The dotted lines indicate the non-perturbed values. These lines represent the limiting case of a vanishing probe-site efg, to which pure cubic local-site symmetry is expected to give rise. Notice that the perturbation functions for the Ca-doped samples indicate much more strongly perturbed correlations than does the perturbation function for non-doped samples.
perturbation function approaches the hard-core value when the distribution of interaction-frequency sets, tok in eqn. (2), is broad, i.e. ~ in the exponent (½&Okti) is large. In this context, a broad distribution of interaction-frequency sets can arise when each of the probes undergoes a slightly different interaction. If, for example, the first and second metal-ion coordination spheres around the probe ion were to have a significant ~umber of dopants substituted in place of the native Ba and Ti ions, we would expect the measured interaction to represent an average of many slightly-different probe environments. Hence, we would expect to observe large 6-values that would reflect the presence of Ca dopants in the vicinity of the probe ion. This information suggests two hypotheses that could explain the data. One possibility is that the Ca substitution is random among the Ba sites. The other possibility is that Ca substitutes preferentially into Ba sites that are in the coordination spheres nearest to the ~8~Hf--, ~8~Ta probe ions. Since all of the Ca concentrations, 2-10 at.%, are much greater than the probe concentration, 0.1-0.2 at.%, substitution of several Ca ions into a Ba coordination sphere is not limited by the magnitude of any of the Ca concentrations being too small, ie. similar in magnitude to the Hf concentrations. To test the random-substitution hypothesis, we determine the probability that a Ca 2÷ ion would substitute into the Ba coordination sphere in the vicinity of the probe ion. Table 1 gives the probability that k dopant Ca 2÷ ions would be found in the nearestneighbor Ba coordination sphere of eight ions for several different Ca 2÷ concentrations, x. These probabilities indicate that the effects of only zero, one, and two dopant ions need to be considered and that the effects of two dopant ions are only significant for x>0.05. Additionally, for x > 0 . 0 2 , the occupancy probability for k - - 0 and 1 changes very slowly with dopant concentrations. The appendix presents the details of these probability calculations. According to the random-substitution hypothesis, we expect either two or perhaps three distinct nuclear-quadrupole interactions at the 181Taprobe sites. To test this hypothesis, we tried to fit some of the perturbation functions for Ca concentrations of 2, 4, and 5% using a two-site model, which is a generalization of eqn. (2). We 1 8 1 H f " *
TABLE 1. Dopant occupancy probabilities for eight coordination k
x --0.02
x -- 0.04
x ==0.06
x = 0.08
x = 0.10
0 1 2 3
0.85 0.14 0.01 --
0.72 0.24 0.04 --
0.61 0.31 0.07 0.01
0.51 0.36 0.11 0.02
0.43 0.38 0.15 0.03
214
J. M. Adams, G. L. Catchen
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Probe-dopant interactions in Ca-doped barium titanate
selected these particular Ca concentrations, because they represent doping levels for which the randomsubsitution model indicates that either one or two Ca 2÷ ions is likely to substitute into any particular Ba coordination sphere. If the random-substitution hypothesis holds, then we expect to observe two distinct, welldefined nuclear-quadrupole interactions. One should appear to be very similar to the interaction observed in non-doped BaTiO3, i.e. a pristine interaction, and the other should be different. The associated site-occupancy fractions should be determined according to the random-substitution model. For example, for the 2% Ca-doped sample, we expect 85% of the measured anisotropy to arise from the interaction at the pristine probe site and 15% to arise from the interaction in which a Ca 2÷ ion is located in the nearest-neighbor Ba coordination sphere. To fit the perturbation functions, we constrained the normalization factors A i in the fitting function to correspond to the associated siteoccupancy fractions. We also fixed the parameters o)~, o)2, and 61 that describe the primary pristine interaction. We allowed the parameters o)4, o)5, and d2 that describe the secondary interaction to vary. Figure 1 shows the resulting fits along with the corresponding one-site fits. We see that these two-site fits provide a poorer representation of the data than the one-site fits provide, which differences in the respective chisquared values support quantitatively. Moreover, when we performed two-site fits that did not employ the aforementioned constraints, the fitting program converged to a fit that represented only one site, the pristine probe site. Thus, the two-site fits based on the random-substitution hypothesis are not as consistent with the experimental results as are the one-site fits. However, the one-site fits also do not provide completely accurate representation of the perturbation functions in all regions of time. A possible explanation is that the preferential substitution of Ca 2÷ ions into the nearest-neighbor Ba coordination sphere may involve random numbers of Ca 2÷ ions. This effect could produce multiple distributions of frequency sets that would give rise to the observed discrepancies. Because this model of the random-substitution hypothesis falls, we need to consider the preferential substitution of the Ca 2÷ ions into the Ba coordination spheres in the vicinity of the probe ions. We base this preferential-substitution hypothesis on the following considerations. The ionic radii of Ca 2+ ion and the Ba 2÷ ion, which are 1.14/k and 1.50 A respectively, differ significantly [10]. The Hf 4+ probe-ion radius is 0.85/k, and it is larger than the 0.745/k radius of the native Ti n÷ ion, for which it substitutes [10]. Thus, the presence of the I-If4 ÷ ion could create local strain, and this strain could provide an energetically favorable pathway for the smaller Ca 2÷ ions to substitute for the
larger Ba 2+ ions in the nearest coordination sphere in the vicinity of the H f 4 + probe ion. Since the Ca 2+ and Ba 2+ ions have the same formal charge, their actual charges should be similar, and any small differences in electrostatic energy should not be important. Hence, ionic size differences allow us to make a plausible case for the preferential-substitution hypothesis. Now, if Ca 2+ ion substitution were preferentially into the Ba coordination spheres in the vicinity of the probe ions, then we would expect to observe a single, well-defined nuclear-quadrupole interaction. In comparison to the corresponding interaction in pristine BaTiO3, this interaction would have a larger asymmetry, i.e. tl would be larger, and it would have a broader distribution of frequency sets, i.e. 6 would be larger. The larger asymmetry would arise because differences in size and charge between the Ca 2+ ions and the Ba 2+ ions would break the local axial symmetry of the probe site. The broader frequency distribution would arise because several chemically inequivalent but electrostatically similar configurations of Ca 2+ and Ba 2+ ions in the Ba configuration may be accessible. We return to the measured perturbation functions in Fig. 1. We observe that for perturbation functions representing Ca concentrations of 2, 4, and 5 at.%, the asymmetries are higher than that for the non-doped case and that the d-values increase with increasing Ca concentration. This behavior is qualitatively consistent with the preferential-substitution hypothesis. (In an extended abstract published earlier, we state an explanation somewhat differently [5].) Moreover, the perturbation functions representing Ca concentrations of 6 and 10 at.%, are reasonably similar in shape. This similarly suggests either that the preferential substitution of Ca 2+ ions into the nearest-neighbor Ba coordination sphere may saturate or that substitution into the Ti sites may compete at these large Ca concentrations. These possibilities are not mutually exclusive, and they both may be operative. The consistency of the preferential-substitution hypothesis, therefore, does not depend on the accuracy of the report that Ca 2+ ions substitute into the Ba sites at concentrations below approximately 5 at.% and into the Ti sites at higher concentrations [7]. To consider the Ca 2÷ substitution further, we observe that the perturbation functions shown in Fig. 3 for the 10% Ca-doped barium titanate sample do not change significantly with increasing temperature. Since we believe that the sample was in the paraelectric phase for all of the indicated measurement temperatures [7], we should not and do not observe any changes in the perturbation functions that indicate a phase transition. This insensitivity to temperature change strongly suggests that the measured interactions were purely static and not time-varying. The stoichiometry that we
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Probe-dopant interactions in Ca-doped barium titanate
assumed [7], if it were correct, requires that the 10% Ca doping produces approximately a 5% concentration of vacancies. We expect this level of O vacancies to produce nuclear-spin relaxation at elevated temperatures via an O-vacancy hopping mechanism. The absence of temperature sensitivity that these perturbation functions show strongly suggests that either the O vacancies were immobile on the PAC timescale at the measurement temperatures, or that the Ca substitution did not produce appreciable O vacancies. We do not have sufficient information to distinguish between these two possibilities. Now, we focus on the paraelectric-phase perturbation functions for 2% Ca-doped barium titanate, that Fig. 4 presents. For the 2% Ca-doped samples, V~z=0.9+0.1 x 10 7 V c m -2, and for the non-doped sample, Vzz=0.2+0.1xl017 V cm -2. These results suggest that the cause of the weak perturbation that arises in the non-doped case is not static O vacancies. We estimate the effect on the probe-site efg of a single O vacancy in the nearest-neighbor oxygen coordination of the probe by considering the O vacancy as a point charge. The contribution to the probe-site efg produced by a single point charge is proportional to q(3z 2 - r 2 ) / r 5, in which q is the point charge and z and r are the charge coordinates (r 2 = x 2 +y2 +z2). If we arbitrarily pick the O vacancy to be on the z-axis, then the associated point charge contribution to the efg is proportional to q/r 3. Suppose that the weak perturbation, which the non-doped samples showed in the paraelectric phase, were caused by a single, static O vacancy, then we would associate an efg proportional to A q / r 3 with the weak perturbation characterized by Vu = 0.2 _+0.1 x 1017 W c m -2 in which Aq would be the charge difference indicated in the reaction V o + ½02 + 2e' = Oo and r would be the T i - O bond length. If the stronger perturbation, which the 2% Ca-doped samples showed, were caused by a single Ca 2÷ ion in a Ba site, then we would associate a similar term Aq(z 2 - r 2 ) / r 5 with the stronger perturbation characterized by Vzz-- 0.9 __0.1 x 1017 V c m -2, in which z and r are the coordinates of the nearest Ba site to the probe. Since the nearest Ba site is much further away than the Ti-O bond length and since the actual charge difference Aq between the Ca 2÷ and the Ba 2÷ ions is small, we could expect the contribution of a Ca dopant to the probe site efg to be much smaller than the corresponding contribution produced by a single static O vacancy. But, exactly the opposite is the case. Therefore, the stronger perturbation that appeared in the paraelectric phase of the 2% Ca-doped barium titanate sample strongly suggests that the weak perturbation that appeared in the non-doped sample was not caused by static O vacancies. The origin of this weak perturbation most likely lies elsewhere.
215
5. Conclusions The effects of Ca doping on the static Ti-site efgs in barium titanate are consistent with the preferentialsubstitution hypothesis. Because the Ca 2÷ ion is smaller than the Ba 2÷ ion and the I-If4÷ ion is larger than the Ti 4÷ ion, substitution of Ca 2÷ into the Bacoordination sphere nearest to the probe ion may be energetically favorable. Thus, the nuclear-quadrupole interactions measured by the 181Ta5÷ nucleus at the Ti site may include contributions from nearest-neighbor Ca 2 ÷ ions. Because, at Ca concentrations greater than 5 at.%, the Ca 2÷ ions were expected to partially substitute into the Ti sites to produce an equal concentration of O vacancies, temperature-sensitive, time-varying interactions were expected but not observed. This result suggests that these higher Ca 2÷ concentrations do not produce mobile O vacancies. The PAC measurements made on the paraelectric phase of 2 at.% Ca-doped barium titanate showed a weak perturbation that was significantly stronger than the corresponding perturbations exhibited by the non-doped barium titanate samples. This result, when interpreted using simple point-charge estimates, strongly suggests that the weak perturbation observed in paraelectric (non-doped) barium titanate was not caused by O vacancies.
Acknowledgments We thank Dr. Ian D. Williams of the Materials Research Laboratory for sharing his insights into the solid-state chemistry of barium titanate with us. We thank Professor Robert L. Rasera of the University of Maryland Baltimore County for his critical comments on the research. We acknowledge the encouragement and guidance that Professor Stewart K. Kurtz of the Materials Research Laboratory provided. We thank the Office of Naval Research (Grant No. N00014-90-J4112) for supporting this investigation.
References 1 G. L. Catchen, S. J. Wukitch,E. M. Saylor, W. Huebner and M. Blaszkiewicz,Ferroelectrics, 117(1991) 175. 2 G. L. Catchen, S. J. Wukitch, D. M. Spaar and M. Blaszkiewicz, Phys. Rev. B, 42 (1990) 1885. 3 G. L. Catchen and D. M. Spaar, Phys. Rev. B, 44 (1991) 12137. 4 G. L. Catchen, J. M. Adams, T. M. Rearick, Phys. Rev. B, in press. 5 G. L. Catehen and R. L. Rasera, Ferroelectrics, 120 (1991) 33. 6 W. H. Payne and V. J. Termery, J. Am. Ceram. Soc., 48 (1965)413.
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Probe-dopant interactions in Ca-doped barium timnaw
7 Z. Q. Zhuang, M. P. Harmer, D. M. Smyth and R. E. Newnham, Mat. Res. Bull., 22 (1987) 1329. 8 G.L. Catchen, J. Mater. Educ., 12 (1991) 253. 9 G. L. Catchen, L. H. Menke, Jr., K. Jamil, M. Blaszkiewicz and B. E. Scheetz, Phys. Rev. B, 39 (1989) 3826. 10 O. Muller and R. Roy, The Major Ternary Structural Families, Springer, Berlin, 1974, p. 487.
To compute specific values, we use:
(n+m-r)(n+m-r-1 (n+m-r-2 I n~mm ] n+m-1 I n+m-2 ]
P(0)=~
(n+m-r-(n-l)]
(4)
•" \
Appendix To calculate the probability that a Ca 2÷ ion substitutes into a Ba site that is part of the Ba coordination nearest to the probe, we consider an analogous problem in manufacturing. In particular, we consider selecting r items from a collection of n defective items and m non-defective items. The number of r-subsets of n + m items is (n +rm ). The number of ways of selecting k defective items from n defective items is (~), and the number of ways of selecting r - k non-defective items from rn non-defective items is (r~k). Hence, the probability of interest is given by:
p(k) -
m)
(3)
in which there are n factors, and
p(k)
= ~-1
m-7~+l
(5)
For a specific case, (Bal _xCax)TiO3, since the Ba coordination contains 8 Ba 2÷ ions, r = 8. We can choose n and m as arbitrarily large numbers that represent n Ca 2+ ions and m Ba 2+ ions, respectively. For example, for x = 0.02, n = 20 and m = 980; alternatively, n = 200 and m = 9800, and so forth. The arbitrary choice of values for n and m does not affect significantly the magnitude of the calculated probabilities. We use eqns. (4) and (5) to calculate values of for successively larger pairs of n and m values, and the resulting probabilities converge to acceptable values.
p(k)
209
Perturbed-angular-correlation spectroscopy: evidence for probe-dopant interactions in Ca-doped barium titanate James M. Adams and Gary L. Catchen Department of Nuclear Engineering and Materials Research Laboratory, The Pennsylvania State University, University Park, PA 16802 (USA) (Received April 18, 1992; in revised form June 13, 1992)
Abstract To investigate dopant- and defect-probe interactions, we have performed perturbed-angular-correlation (PAC) spectroscopy on Ca-doped barium titanate ceramics. Polycrystalline samples of barium titanate were prepared using the resinintermediate process, and the samples were doped with Ca according to the formula (Ba 1_xCax)(Til _yCay)O3_y, where 0 < x< 0.05 and 0 < y< 0.05. All of the samples were doped with approximately 0.1 at.% Hf, which was substituted into the Ti sites and carded the lalHf-* lalTa PAC probe radioactivity. Measurements were performed over a temperature range from laboratory temperature to approximately 1100 K. In the ferroelectric phases, at Ca concentrations of several percent, the doping produces an increase in the Ti-site electric-field-gradient (efg) asymmetry and in the extent of spectral linebroadening. At higher Ca concentrations, the linebroadening increases further and the ferroelectric-to-paraelectric transition is not discemable. The changes in efg symmetry and spectral linebroaderting, which are essentially temperature invariant, could be attributed to preferential substitution of the Ca dopant into Ba coordination spheres that are near the probe sites. In the paraelectric phase, doping at 2 at.% produces a weak perturbation that is several times stronger than the corresponding weak perturbation that non-doped samples show over the same temperature range. This result strongly suggests that O vacancies do not cause these weak perturbations.
1. Introduction
During the past several years, we have been using a nuclear technique, perturbed-angular-correlation (PAC) spectroscopy, to investigate the effects of local fields in ferroelectric, ternary-metal-oxide ceramics [1-5]. The research has focused on primarily ABO3 perovskites such as PbTiO3 [2] and BaTiO 3 (for a review of PAC measurements performed on ABO3 perovskites see ref. 1) and related compounds such as L i N b O a and LiTaO 3 [3, 4]. These materials are particularly well suited for PAC spectroscopy, because the radioactive 18~Hf--, 181Ta PAC probe can be substituted into these crystals in small amounts, less than 1 at.%. A primary research objective has been to better understand the mechanisms that give rise to the ferroelectricto-paraelectric transitions. In particular, we have been using PAC spectroscopy to delineate dynamic order-disorder and static displacive aspects of these phase transitions [1-4]. In nonmagnetic materials, the PAC technique can measure the electric-field-gradient (efg) tensor at the lattice site of a radioactive probe ion that was substituted into the crystal [5]. Specifically, the technique measures the interaction of the nuclear-electric quad0921-5107/92/$5.00
rupole moment of an exited nuclear level in the probeion nucleus with extranuclear efgs produced by all of the electrons and nuclei that surround the probe nucleus. This excited nuclear level is populated by the emission of an initial ),-ray, and it is depopulated by the emission of a final )'-ray. During the lifetime of the intermediate level, the quadrupole moment of the level can interact with the extranuclear efgs. This interaction changes the nuclear orientation prior to the emission of the final ),-ray. Because the nuclear orientation changed, the direction in space where the final )'-ray is emitted is different than where it would have been had no interaction occurred. To describe this process, we say that the nuclear-quadrupole interaction perturbs the angular correlation, i.e. spatial correlation of the )'-)' cascade. This effect is indeed measurable, and it is the basis of the PAC technique. Because the chemistry of the Hf 4 + ion is very similar to that of the Ti 4~ ion and nearly identical to that of the Zr 4+ ion, the 181I-If/lalTa probe is well suited to investigating perovskites that contain Group IV elements such as B a Z i O 3. Because the )'-)' cascade that involves the hyperfine interaction takes place between excited states in the lSlTa nucleus, the actual interaction involves a Ta impurity at the site of interest, which is © 1992--Elsevier Sequoia. All rights reserved
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J. M. Adams, G. L. Catchen
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Probe-dopant interactions in Ca-doped barium titanate
the Ti site in B a l t O 3. However, the process of substituting the probe depends on the chemical properties of Hf, which subsequently decays by t - emission to populate excited states in 18~Ta. Nuclear-quadrupole interactions fall into two categories, static and time-varying. During a static interaction, the efg appears experimentally to be essentially a time-averaged quantity. For example, in a crystal lattice, the vibrational motions of the atoms in the lattice are usually much more rapid than the time scale of the y - y cascade, which can range from approximately 0.1 ns to several hundred nanoseconds. As a result of this "motional narrowing" effect, efgs produced by vibrating atoms fixed to their lattice sites give rise to static interactions. Time-varying interactions arise when the efg fluctuates either in magnitude or in symmetry during the intermediate-level lifetime, i.e. motion on a slower timescale. Because detecting the initial y-ray selects nuclei in specific orientations, these fluctuations cause the nuclear-spin orientation of the intermediate level to become random, i.e. to relax. This effect, which can be caused by effects such as ions "hopping" in and out of lattice sites, attenuates the measured angular correlation. The specific experimental difficulty arises when the spectral lines measured in a PAC experiment show either broadening or attenuation. In general, linebroadening can occur when static point defects are trapped at locations that are near the PAC-probe site. Similarly linebroadening and attenuation can occur when dynamic disordering produces fluctuating efgs near the probe site. For ferroelectric BaTiO 3 and PbTiO 3, at temperatures below the tetragonal-to-cubic transition temperature Tc, the PAC measurements show well-defined nuclear-quadrupole interactions that are characterized by highly-broadened lines [1, 2]. At temperatures above To, the measurements show a very weak interaction that has no temperature sensitivity [1]. This weak interaction is quantitatively similar to interactions measured on the cubic non-ferroelectric perovskites SrTiO 3 and B a H f O 3 at laboratory temperature [1]. In the cubic, non-ferroelectric structures, because of symmetry, the nuclear-quadrupole iteractions at the Ba sites should vanish and the correlation should be nonperturbed, if the structures were truly cubic. Moreover, if the probes would tend to trap defects such as O vacancies in the cubic phases, then the measured weak perturbations should show temperature sensitivities that correspond to thermally-activated detrapping of these defects. Thus, on these perovskites, the linebroadening at temperatures below T~ and the weak perturbations at temperatures above T~ remain anomalous and unexplained [5]. To interpret these anomalous results, we need to identify the origins of the linebroadening that occurs at
temperatures below 7~ and the weak perturbation that occurs at temperatures above Tc. For this reason, we performed a series of PAC measurements on CAdoped barium titanate, in which we varied the Ca concentrations from 0 to 10 at.%. We expected the measurements to be sensitive to two effects. At low Ca concentrations, when Ca 2+ ions substituted into primarily the Ba sites, no additional oxygen vacancies should be produced and the major effect should involve interactions between Ca 2+ dopants at Ba sites and Ta 5+ probe ions at the Ti sites. At higher Ca concentrations, when Ca 2+ ions substitute into both the Ba and Ti sites, additional oxygen vacancies should be produced. The major effect then should involve interactions of the LSiTa5 + probe ions between both the oxygen vacancies and the Ca z+ dopants. However, we can explain the results of the experiments primarily in terms of interactions between Ca 2÷ ions and the Ta 5÷ probe ions. Moreover, we do not need to introduce the effects of O vacancies to explain the measured spectral lineshapes. This interpretation has a particularly significant implication for the measurements on nondoped BaTiO3, because it strongly suggests that the well-known linebroadening observed in the ferroelectric phase and the weak perturbation observed in the paraelectric phase arise from effects other than O vacancies trapped in the vicinity of the probe ions.
2. Experimental details 2.1. Sample preparation
Polycrystalline samples of BaTiO 3 were prepared using a variation of the resin-intermediate method, which is described elsewhere [1, 2]. To perform the PAC measurements, 1-2 g of sample material that typicaUy contained 15-30/aCi of 18~Hfactivity were sealed in fused-silica tubes. Small amounts of powder from these samples were used for X-ray powder diffraction to check the phase purity of the samples. From the powder patterns, we estimated that the samples were at least 95% phase pure. The nominal Hf concentrations were 0.1-0.2 at.% of the Ti-ion concentration. These Hf concentrations were kept as small as was practical, because adding small amounts of t-If, i.e. several percent or less, causes the c/a ratio of the BaTiO 3 lattice to change sigrfificantly [6]. Additiormily, the samples were sintered at temperatures of 1570 K or higher. Although these high temperatttres are not necessary to produce the BaTiO3 structure via resin-intermediateproduced powders, these temperatures are necessary to assure that the HI dopant comt~letely substitutes into the structure. The levels of Ca doping ranged from 2 to 10 at.%. The Ba and Ti concentrations were adjusted according to the formula: (Bal_xCax)(Ti~_yCay)O3_y,
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Probe-dopant interactions in Ca-doped barium titanate
in which 0~
(1) in which r is the intermediate-level lifetime. To analyze the experimental perturbation functions, a one-site model was used to fit the data: -A22GE2(t~)=A,
So(ri)+
Sk(ri)
X exp( -½ 8tOktt) COS(tOktl)] +A2 J
(2)
A1 is the normalization factor that represents the probes that undergo the static interaction. A 2 repre-
211
sents the effects of ),-rays that are absorbed in the sample en route to the detector and the contributions from probes that are not in well-defined chemical environments such as either at grain boundaries or in secondary phases. In this application, A1 ~'A2. The frequencies tok and the Sk(r/) coefficients describe a static interaction in a polycrystalline source. Once the interaction frequencies are determined from the experimental perturbation function, tOo, Vzz,and r/are calculated using a procedure that ref. 8 describes in detail. The factor exp(--½6tOkti) represents the effects of a Lorentzian distribution of interaction frequencies that produces inhomogeneous linebroadening in which 6 is the lineshape parameter. The parameter 6 gives a measure of the relative width of the distribution, in which 6 = AtOk/tOk 0 and tOk° refers to the interaction frequency that would occur at a non-defective probe site.
3. Results
Figure 1 presents the perturbation functions for Cadoped samples of barium titanate that were measured at laboratory temperature. Figure 2 summarizes the parameters derived from the fits to the data. For the case of zero Ca-doping, the perturbation function fields well-defined frequencies, and the line is extensively broadened. As a result of the broadening, the asymmetry parameter r/= 0.16 + 0.05 is small but it is nonzero. Although a zero asymmetry would be consistent with the tetragonal symmetry of the lattice, the small but nonvanishing r/value is expected from the distribution of interaction frequencies that the broad line and the associated large dt parameter indicate. As the Ca-doping concentrations increase, the lines broaden further. The perturbation functions are nonetheless sufficiently well defined that unique interaction frequencies could be determined. We see that the efgs are significantly more asymmetric (r/= 0.32 + 0.03 for 2% Ca and r / = 0 . 4 1 + 0 . 0 3 for 4% Ca) than is the corresponding efg in the non-doped case. Because the perturbation functions for samples doped with larger Ca concentrations are highly broadened, the derived asymmetry parameters may not be unique. For each of the Ca concentrations, 2, 4, 5, 6, and 10 at.%, we performed a series of measurements at several elevated temperatures, typically over a range from 400 to 1100 K. For these paraelectric phases, the resulting perturbation functions are highly broadened, and the associated lineshapes show no discernible temperature dependence. As an example, Fig. 3 presents the perturbation functions for a 10% Ca-doped sample of barium titanate that was measured at the indicated temperatures. Each of these perturbation functions is
212
J. M. Adams, G. L. Catchen /
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Probe-dopant interactions in Ca-doped barium titanate 1.0
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Fig. 2. Dependence of the electric-field-gradient and line-shape parameters on Ca concentration. The lines are drawn to guide the eye.
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k
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I , .
40
t(nsec)
Fig. 1. Perturbation functions measured at laboratory temperature on ceramic, Ca-doped barium titanate samples. The Ca concentrations are indicated in atomic percent. The solid lines represent fits of eqn. (2) to the data. The dashed lines represent constrained two-site-model fits to the data.
0,I
0.00 . . . . . . . . .
highly broadened. As a result, the derived efg parameters may not be unique. However, despite the limitations of these data, all of these perturbation functions appear to be alike. Because 10% Ca-doping is known to lower the Curie temperature to approximately laboratory temperature [7], the sample was in the paraelectric phase for all four of the measurements. Thus, these perturbation functions represent ternperatureinvariant interactions that took place in the paraelectric phase, which are characterized by a broad distribution of interaction frequencies. Figure 4 presents the perturbation functions for a non-doped sample measured at a temperature above
, ......... I0
I .... , .... J ......... 20 30 I (nsec)
.
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40
Fig. 3. Perturbation functions measured at the indicated temperatures on barium titanate samples doped with 10 at.% Ca. The solid lines represent fits of eqn. (2) to the data; and the pertinent, derived parameters are indicated. The dotted lines indicate the "hard-core", i.e. AlSo, values that represent the limiting case of strong, inhomogeneous linebroadening.
Tc and for a 2% Ca-doped sample measured at two temperatures above To; within the experimental errors, the derived Vu-parameters are the same for the two functions representing the 2% Ca-doped sample.
J. M. Adams, G. L. Catchen
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Probe-dopant interactions in Ca-doped barium titanate
value--A22S0~0.04 for long times, t > 2 0 n s . The
4. Discussion To determine the effects of Ca doping at laboratory temperature, we consider the perturbation functions that Fig. 1 shows and the associated summaries of derived parameters that Fig. 2 shows. As the concentration of Ca increases, the perturbation functions indicate more asymmetric interactions, i.e. ~1 increases, and the lines broaden. At highest Ca concentrations, 10%, the peak in the perturbations function is gone, and the function approaches the so-called "hard core"
02
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½.
m . . . . . . . . .
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Fig. 4. Perturbation function measured at the indicated temperatures for non-doped and 2 at.% Ca-doped barium titanate. The solid lines represent fits of eqn. (2) to the data; and the pertinent, derived parameters are indicated. At these measurement temperatures, the samples were in the respective paraelectric phases. The dotted lines indicate the non-perturbed values. These lines represent the limiting case of a vanishing probe-site efg, to which pure cubic local-site symmetry is expected to give rise. Notice that the perturbation functions for the Ca-doped samples indicate much more strongly perturbed correlations than does the perturbation function for non-doped samples.
perturbation function approaches the hard-core value when the distribution of interaction-frequency sets, tok in eqn. (2), is broad, i.e. ~ in the exponent (½&Okti) is large. In this context, a broad distribution of interaction-frequency sets can arise when each of the probes undergoes a slightly different interaction. If, for example, the first and second metal-ion coordination spheres around the probe ion were to have a significant ~umber of dopants substituted in place of the native Ba and Ti ions, we would expect the measured interaction to represent an average of many slightly-different probe environments. Hence, we would expect to observe large 6-values that would reflect the presence of Ca dopants in the vicinity of the probe ion. This information suggests two hypotheses that could explain the data. One possibility is that the Ca substitution is random among the Ba sites. The other possibility is that Ca substitutes preferentially into Ba sites that are in the coordination spheres nearest to the ~8~Hf--, ~8~Ta probe ions. Since all of the Ca concentrations, 2-10 at.%, are much greater than the probe concentration, 0.1-0.2 at.%, substitution of several Ca ions into a Ba coordination sphere is not limited by the magnitude of any of the Ca concentrations being too small, ie. similar in magnitude to the Hf concentrations. To test the random-substitution hypothesis, we determine the probability that a Ca 2÷ ion would substitute into the Ba coordination sphere in the vicinity of the probe ion. Table 1 gives the probability that k dopant Ca 2÷ ions would be found in the nearestneighbor Ba coordination sphere of eight ions for several different Ca 2÷ concentrations, x. These probabilities indicate that the effects of only zero, one, and two dopant ions need to be considered and that the effects of two dopant ions are only significant for x>0.05. Additionally, for x > 0 . 0 2 , the occupancy probability for k - - 0 and 1 changes very slowly with dopant concentrations. The appendix presents the details of these probability calculations. According to the random-substitution hypothesis, we expect either two or perhaps three distinct nuclear-quadrupole interactions at the 181Taprobe sites. To test this hypothesis, we tried to fit some of the perturbation functions for Ca concentrations of 2, 4, and 5% using a two-site model, which is a generalization of eqn. (2). We 1 8 1 H f " *
TABLE 1. Dopant occupancy probabilities for eight coordination k
x --0.02
x -- 0.04
x ==0.06
x = 0.08
x = 0.10
0 1 2 3
0.85 0.14 0.01 --
0.72 0.24 0.04 --
0.61 0.31 0.07 0.01
0.51 0.36 0.11 0.02
0.43 0.38 0.15 0.03
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Probe-dopant interactions in Ca-doped barium titanate
selected these particular Ca concentrations, because they represent doping levels for which the randomsubsitution model indicates that either one or two Ca 2÷ ions is likely to substitute into any particular Ba coordination sphere. If the random-substitution hypothesis holds, then we expect to observe two distinct, welldefined nuclear-quadrupole interactions. One should appear to be very similar to the interaction observed in non-doped BaTiO3, i.e. a pristine interaction, and the other should be different. The associated site-occupancy fractions should be determined according to the random-substitution model. For example, for the 2% Ca-doped sample, we expect 85% of the measured anisotropy to arise from the interaction at the pristine probe site and 15% to arise from the interaction in which a Ca 2÷ ion is located in the nearest-neighbor Ba coordination sphere. To fit the perturbation functions, we constrained the normalization factors A i in the fitting function to correspond to the associated siteoccupancy fractions. We also fixed the parameters o)~, o)2, and 61 that describe the primary pristine interaction. We allowed the parameters o)4, o)5, and d2 that describe the secondary interaction to vary. Figure 1 shows the resulting fits along with the corresponding one-site fits. We see that these two-site fits provide a poorer representation of the data than the one-site fits provide, which differences in the respective chisquared values support quantitatively. Moreover, when we performed two-site fits that did not employ the aforementioned constraints, the fitting program converged to a fit that represented only one site, the pristine probe site. Thus, the two-site fits based on the random-substitution hypothesis are not as consistent with the experimental results as are the one-site fits. However, the one-site fits also do not provide completely accurate representation of the perturbation functions in all regions of time. A possible explanation is that the preferential substitution of Ca 2÷ ions into the nearest-neighbor Ba coordination sphere may involve random numbers of Ca 2÷ ions. This effect could produce multiple distributions of frequency sets that would give rise to the observed discrepancies. Because this model of the random-substitution hypothesis falls, we need to consider the preferential substitution of the Ca 2÷ ions into the Ba coordination spheres in the vicinity of the probe ions. We base this preferential-substitution hypothesis on the following considerations. The ionic radii of Ca 2+ ion and the Ba 2÷ ion, which are 1.14/k and 1.50 A respectively, differ significantly [10]. The Hf 4+ probe-ion radius is 0.85/k, and it is larger than the 0.745/k radius of the native Ti n÷ ion, for which it substitutes [10]. Thus, the presence of the I-If4 ÷ ion could create local strain, and this strain could provide an energetically favorable pathway for the smaller Ca 2÷ ions to substitute for the
larger Ba 2+ ions in the nearest coordination sphere in the vicinity of the H f 4 + probe ion. Since the Ca 2+ and Ba 2+ ions have the same formal charge, their actual charges should be similar, and any small differences in electrostatic energy should not be important. Hence, ionic size differences allow us to make a plausible case for the preferential-substitution hypothesis. Now, if Ca 2+ ion substitution were preferentially into the Ba coordination spheres in the vicinity of the probe ions, then we would expect to observe a single, well-defined nuclear-quadrupole interaction. In comparison to the corresponding interaction in pristine BaTiO3, this interaction would have a larger asymmetry, i.e. tl would be larger, and it would have a broader distribution of frequency sets, i.e. 6 would be larger. The larger asymmetry would arise because differences in size and charge between the Ca 2+ ions and the Ba 2+ ions would break the local axial symmetry of the probe site. The broader frequency distribution would arise because several chemically inequivalent but electrostatically similar configurations of Ca 2+ and Ba 2+ ions in the Ba configuration may be accessible. We return to the measured perturbation functions in Fig. 1. We observe that for perturbation functions representing Ca concentrations of 2, 4, and 5 at.%, the asymmetries are higher than that for the non-doped case and that the d-values increase with increasing Ca concentration. This behavior is qualitatively consistent with the preferential-substitution hypothesis. (In an extended abstract published earlier, we state an explanation somewhat differently [5].) Moreover, the perturbation functions representing Ca concentrations of 6 and 10 at.%, are reasonably similar in shape. This similarly suggests either that the preferential substitution of Ca 2+ ions into the nearest-neighbor Ba coordination sphere may saturate or that substitution into the Ti sites may compete at these large Ca concentrations. These possibilities are not mutually exclusive, and they both may be operative. The consistency of the preferential-substitution hypothesis, therefore, does not depend on the accuracy of the report that Ca 2+ ions substitute into the Ba sites at concentrations below approximately 5 at.% and into the Ti sites at higher concentrations [7]. To consider the Ca 2÷ substitution further, we observe that the perturbation functions shown in Fig. 3 for the 10% Ca-doped barium titanate sample do not change significantly with increasing temperature. Since we believe that the sample was in the paraelectric phase for all of the indicated measurement temperatures [7], we should not and do not observe any changes in the perturbation functions that indicate a phase transition. This insensitivity to temperature change strongly suggests that the measured interactions were purely static and not time-varying. The stoichiometry that we
J. M. Adams, G. L. Catchen
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Probe-dopant interactions in Ca-doped barium titanate
assumed [7], if it were correct, requires that the 10% Ca doping produces approximately a 5% concentration of vacancies. We expect this level of O vacancies to produce nuclear-spin relaxation at elevated temperatures via an O-vacancy hopping mechanism. The absence of temperature sensitivity that these perturbation functions show strongly suggests that either the O vacancies were immobile on the PAC timescale at the measurement temperatures, or that the Ca substitution did not produce appreciable O vacancies. We do not have sufficient information to distinguish between these two possibilities. Now, we focus on the paraelectric-phase perturbation functions for 2% Ca-doped barium titanate, that Fig. 4 presents. For the 2% Ca-doped samples, V~z=0.9+0.1 x 10 7 V c m -2, and for the non-doped sample, Vzz=0.2+0.1xl017 V cm -2. These results suggest that the cause of the weak perturbation that arises in the non-doped case is not static O vacancies. We estimate the effect on the probe-site efg of a single O vacancy in the nearest-neighbor oxygen coordination of the probe by considering the O vacancy as a point charge. The contribution to the probe-site efg produced by a single point charge is proportional to q(3z 2 - r 2 ) / r 5, in which q is the point charge and z and r are the charge coordinates (r 2 = x 2 +y2 +z2). If we arbitrarily pick the O vacancy to be on the z-axis, then the associated point charge contribution to the efg is proportional to q/r 3. Suppose that the weak perturbation, which the non-doped samples showed in the paraelectric phase, were caused by a single, static O vacancy, then we would associate an efg proportional to A q / r 3 with the weak perturbation characterized by Vu = 0.2 _+0.1 x 1017 W c m -2 in which Aq would be the charge difference indicated in the reaction V o + ½02 + 2e' = Oo and r would be the T i - O bond length. If the stronger perturbation, which the 2% Ca-doped samples showed, were caused by a single Ca 2÷ ion in a Ba site, then we would associate a similar term Aq(z 2 - r 2 ) / r 5 with the stronger perturbation characterized by Vzz-- 0.9 __0.1 x 1017 V c m -2, in which z and r are the coordinates of the nearest Ba site to the probe. Since the nearest Ba site is much further away than the Ti-O bond length and since the actual charge difference Aq between the Ca 2÷ and the Ba 2÷ ions is small, we could expect the contribution of a Ca dopant to the probe site efg to be much smaller than the corresponding contribution produced by a single static O vacancy. But, exactly the opposite is the case. Therefore, the stronger perturbation that appeared in the paraelectric phase of the 2% Ca-doped barium titanate sample strongly suggests that the weak perturbation that appeared in the non-doped sample was not caused by static O vacancies. The origin of this weak perturbation most likely lies elsewhere.
215
5. Conclusions The effects of Ca doping on the static Ti-site efgs in barium titanate are consistent with the preferentialsubstitution hypothesis. Because the Ca 2÷ ion is smaller than the Ba 2÷ ion and the I-If4÷ ion is larger than the Ti 4÷ ion, substitution of Ca 2÷ into the Bacoordination sphere nearest to the probe ion may be energetically favorable. Thus, the nuclear-quadrupole interactions measured by the 181Ta5÷ nucleus at the Ti site may include contributions from nearest-neighbor Ca 2 ÷ ions. Because, at Ca concentrations greater than 5 at.%, the Ca 2÷ ions were expected to partially substitute into the Ti sites to produce an equal concentration of O vacancies, temperature-sensitive, time-varying interactions were expected but not observed. This result suggests that these higher Ca 2÷ concentrations do not produce mobile O vacancies. The PAC measurements made on the paraelectric phase of 2 at.% Ca-doped barium titanate showed a weak perturbation that was significantly stronger than the corresponding perturbations exhibited by the non-doped barium titanate samples. This result, when interpreted using simple point-charge estimates, strongly suggests that the weak perturbation observed in paraelectric (non-doped) barium titanate was not caused by O vacancies.
Acknowledgments We thank Dr. Ian D. Williams of the Materials Research Laboratory for sharing his insights into the solid-state chemistry of barium titanate with us. We thank Professor Robert L. Rasera of the University of Maryland Baltimore County for his critical comments on the research. We acknowledge the encouragement and guidance that Professor Stewart K. Kurtz of the Materials Research Laboratory provided. We thank the Office of Naval Research (Grant No. N00014-90-J4112) for supporting this investigation.
References 1 G. L. Catchen, S. J. Wukitch,E. M. Saylor, W. Huebner and M. Blaszkiewicz,Ferroelectrics, 117(1991) 175. 2 G. L. Catchen, S. J. Wukitch, D. M. Spaar and M. Blaszkiewicz, Phys. Rev. B, 42 (1990) 1885. 3 G. L. Catchen and D. M. Spaar, Phys. Rev. B, 44 (1991) 12137. 4 G. L. Catchen, J. M. Adams, T. M. Rearick, Phys. Rev. B, in press. 5 G. L. Catehen and R. L. Rasera, Ferroelectrics, 120 (1991) 33. 6 W. H. Payne and V. J. Termery, J. Am. Ceram. Soc., 48 (1965)413.
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Probe-dopant interactions in Ca-doped barium timnaw
7 Z. Q. Zhuang, M. P. Harmer, D. M. Smyth and R. E. Newnham, Mat. Res. Bull., 22 (1987) 1329. 8 G.L. Catchen, J. Mater. Educ., 12 (1991) 253. 9 G. L. Catchen, L. H. Menke, Jr., K. Jamil, M. Blaszkiewicz and B. E. Scheetz, Phys. Rev. B, 39 (1989) 3826. 10 O. Muller and R. Roy, The Major Ternary Structural Families, Springer, Berlin, 1974, p. 487.
To compute specific values, we use:
(n+m-r)(n+m-r-1 (n+m-r-2 I n~mm ] n+m-1 I n+m-2 ]
P(0)=~
(n+m-r-(n-l)]
(4)
•" \
Appendix To calculate the probability that a Ca 2÷ ion substitutes into a Ba site that is part of the Ba coordination nearest to the probe, we consider an analogous problem in manufacturing. In particular, we consider selecting r items from a collection of n defective items and m non-defective items. The number of r-subsets of n + m items is (n +rm ). The number of ways of selecting k defective items from n defective items is (~), and the number of ways of selecting r - k non-defective items from rn non-defective items is (r~k). Hence, the probability of interest is given by:
p(k) -
m)
(3)
in which there are n factors, and
p(k)
= ~-1
m-7~+l
(5)
For a specific case, (Bal _xCax)TiO3, since the Ba coordination contains 8 Ba 2÷ ions, r = 8. We can choose n and m as arbitrarily large numbers that represent n Ca 2+ ions and m Ba 2+ ions, respectively. For example, for x = 0.02, n = 20 and m = 980; alternatively, n = 200 and m = 9800, and so forth. The arbitrary choice of values for n and m does not affect significantly the magnitude of the calculated probabilities. We use eqns. (4) and (5) to calculate values of for successively larger pairs of n and m values, and the resulting probabilities converge to acceptable values.
p(k)