pellets were crushed in an agate mortar and then passed through a 140-mesh sieve for subsequent pellet preparation. For the samples of the HfO, system, the ...
Effective Ionic Radius of Y3+ Determined from Lattice Parameters of Fluorite-Type HfO, and ZrO, Solid Solutions Dae-Joon Kim* Ceramics Division, Korea Institute of Science and Technology, Seoul 136791, Korea
Sang-Hoon Hyun* and Seung-Goo Kim Department of Ceramic Engineering, Yonsei University, Seoul 120-749, Korea
Masatomo Yashima* Research Laboratory of Engineering Materials, Tokyo Institute of Technology, Yokohama 227, Japan
Fluorite-type HfO, and ZrO, solid solutions were prepared by doping with 8 to 14 mol% of Ho,O, and Y,O,, and their lattice parameters were determined. In both HfO, and ZrO, systems, the lattice parameters of the solid solutions containing Ho,O, were consistently greater than those containing the same amounts of Y,O,. This indicated that the ionic radius of Ho3' was larger than that of Y3+in the fluorite structure solid solutions. The effective ionic radius of Y 3 +in eightfold coordination was estimated to be 0.1011 nm by using the measured lattice parameters and the empirical equations to predict the lattice parameters of the fluoritetype solid solutions.
enthalpy of the HfO, solid solution containing 10 mol% Ho,O, was higher than that containing 10 mol% Y,O,, even though Shannon's compilation of ionic radii: which is the most frequently quoted set of ionic radii, lists the ionic radius of Ho3+as smaller than the radius of Y3+ for 8CN. The lattice constant measurements of the same solid solutions also showed that the lattice parameter of the solid solution doped with 10 mol% Ho,O, was larger than that doped with 10 mol% Y,O,. Thus, they suggested that the relative radius of Ho'+ might be slightly larger than the ionic radius of Y3+ in fluorite-type solid solutions, but they did not elaborate to determine the relative radii of Ho3+ and Y3+ in 8CN. Furthermore, the comparison was based only on the HfO, solid solutions containing the very limited dopant oxide content of 10 mol%. The purpose of this study is to clarify the relative ionic radii of Ho'+ and Y3+in 8CN by determining the lattice parameters of the fluorite-type HfO, and ZrO, solid solutions formed by doping with Ho,O, and Y,O, in extensive composition ranges.
I. Introduction N THE fluorite structure, cations are in eightfold coordination I ( ~ with ~ ~ their ) nearest neighbors, and each anion is surrounded tetrahedrally by four cations. The solid solutions of fluorite-type MO, oxides, such as HfO,, ZrO,, CeO,, and Tho,, have been known as ionic conductors and are frequently utilized as oxygen sensors, solid electrolytes in fuel cells, and electrochemical oxygen pumps.'.' The highest ionic conductivities of the MO, solid solutions are achieved by doping with lower-valent (divalent and trivalent) cations. The addition of these aliovalent cations results in the formation of oxygen vacancies, which act as charge carriers at elevated temperatures, to achieve electrical neutrality. A coulomb attraction between oxygen vacancies and dopant cations forms defect complexe~.~-~ At a given temperature the ionic conductivity of MO, oxides is governed mainly by the enthalpy for association of a defect complex which is determined by the elastic strain field around the ~ o m p l e x .Accordingly, ~.~ the dependence of the ionic conductivity on the dopant cation size has been related to the strain energy contribution, which can be estimated by the ionic size mismatch between dopant and host ~ a t i o n . ~ Thus, -~ the conductivity is maximized as the mismatch is minimized. Recently, Trubelja and Stubican6 investigated the ionic conductivity of Hf0,-R,O, solid solutions (R = Sc3+,Y 3 +and , the lanthanide cations) and showed that the activation enthalpy for conduction increased with dopant radius except for the solid solutions doped with Ho,O, and Y,O,. That is, the activation
11. Experimental Procedure Samples were prepared by mixing 99.95% pure HfO,, 99% pure ZrO,, 99.999% pure Ho,O,, and 99.99% pure Y,O, (Aldrich Chemical Co., Inc., Milwaukee, WI). The mixed powders were pressed and presintered at 1300°C for 24 h. The sintered pellets were crushed in an agate mortar and then passed through a 140-mesh sieve for subsequent pellet preparation. For the samples of the HfO, system, the sieved powders were pressed into pellets isostatically at 350 MPa and sintered at 1550°C for 2 h. The sintered pellets were broken into pieces of about 3 mm in diameter and were melted on a water-cooled copper plate in an arc-imaging furnace in air. The melted specimen was cooled by taking the focus away from the specimen (cooling rate was about 1000 Us).For the samples of the ZrO, system, the pellets pressed isostatically were sintered at 1650°C for 2 h in air. The arc-melted and sintered specimens were crushed and ground in an agate mortar for X-ray powder diffractometry (XRD) investigation. For the determination of lattice parameters at room temperature, XRD data were obtained from the ground powder specimens, mixed carefully with an Si internal standard (SRM 640b), using an automated X-ray diffractometer (Philips, EA Almdo, Netherlands) with CuKa radiation, X (CuKa,) = 1.54060 A. A scan speed of 0.6" 28/min was used in the 80" to 130" 28 range. After Ka, peak stripping, the peak positions were determined by profile refinement using the built-in PC-APD program. The observed peak positions of the HfO, and the ZrO, solid solutions were corrected for possible instrumental and sample mounting aberrations from a second-degree polynominal best
M. F. Trubelja-contributing editor
Manuscript No. 194152. Received October 5,1993; approved December I , 1993. Support for D.-I. Kim was provided by Korea Ministry of Science and Technology under Contract No. 6-2E12510. *Member, American Ceramic Society.
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fit of (Sisrand - Si,,) vs Si,,, peak positions, where Sistand is the standard Si peak position of the SRM 640b and Si,,, is the observed peak position of the internal standard embedded in the powder samples. The lattice parameters were refined by a version of the Appleman and Evans least-squares procedure.8 111. Results and Discussion
The lattice parameters of the fluorite-type solid solutions in the HfO, system and the ZrO, system are plotted as a function of the dopant concentration in Figs. 1 and 2, respectively. The lattice parameters increase linearly with an increase in dopant contents, which indicates that Vegard’s law is applicable in these composition ranges. As shown in Figs. 1 and 2, the lattice constants of the solid solutions containing Ho,03 are consistently larger than those containing the same amounts of Y,O!. These trends suggest that the relative ionic radius of Ho3+ is larger than that of Y3+in 8CN since the lattice constants of fluorite-type MO, oxide solid solutions are determined by dopant cation radii at a given dopant content.’ This is inconsistent with the prediction based on the ionic radii from Shannon’s compilation: where the radii of Ho’+ and Y3+ are 0.1015 nm and 0.1019 nm, respectively. Nevertheless, the relatively large radius of Ho’+ over Y3+ is supported by the observation of the activation enthalpy for ionic conduction in the HfO, solid solutiom6 The activation enthalpy of the HfO, solid solution doped with 10 mol% Ho,O, is higher than doped with 10 mol% Y,O,, since the enthalpy becomes higher as the ionic size mismatch between Hf4+(r = 0.083 nm) and dopant cation becomes greater. The lattice parameters of A,B,O, compounds containing Ho3+ and Y3+ offer further evidence that the ionic radius of Ho3+is larger than that of Y3+in 8CN, as illustrated in Table I.” In the A,B,O, compounds with pyrochlore structure, the A and B ions are in the eightfold and the sixfold coordination, respectively. The fact that the lattice constants of the compounds retaining Ho3+with the common B ions are larger than those retaining Y3+clearly indicates that the relative radius of Ho3+is larger t h q the radius of Y3+ in 8CN. Indeed, another set of ionic radii” shows that the ionic radius of Ho3+is 0.102 nm and that of Y3+ is 0.1015 nm for 8CN. Now, the remaining questions are what are the relative ionic radii of Ho3+and Y3+ in fluorite-type solid solutions. To determine the relative radii, it was assumed that either of the radii of Ho3+(0.1015 nm) and Y3+ (0.1019 nm) were correct values so that either the radius of Y3+ is smaller than 0.1015 nm or the radius of Ho3+is larger than 0.1019 nm to conform to the measurements presented in Figs. 1 and 2. It has been shown that the lattice parameters of the fluoritetype MO, solid solutions can be estimated successfully by
mol% of Ho(Y),O,
Fig. 1. Lattice parameters of fluorite-type HfO, solid solutions as a function of dopant content.
Fig. 2. Lattice parameters of fluorite-type ZrO, solid solutions as a function of dopant content.
Table I. Lattice Parameters of Pyrochlore-typeCompounds Retaining Ho3+and Y3+ in Eightfold Coordination* ComD0und
Lattice Darameter (nml
Ho,Ru,O,
1.0150 1.0144 1.0374 1.0371
y2Ru207
Ho2Sn,07 Y2Sn20, *Reference 10
applying empirical e q ~ a t i o n s . ~The , ~ ~equations -~~ for the HfO, and ZrO, solid solutions doped with trivalent cations are’
+ (0.0203Ar 0.00022)~~ = 0.5120 + (0.0212Ar - 0.00023)~~
a H f= 0.5098 a,,
-
(1)
(2) where aHT and a, are the lattice constants (in nanometers) of the fluorite-type HfO, and ZrO, solid solutions, respectively, Ar (in nanometers) is the difference in ionic radius of dopant cation and the host cation (e.g., Hf4+ and Zr“’), and m is the concentration of dopant cation (in mole percent) in the form of RO, (e.g., HoO, and YO, 5 ) . In Table I1 the lattice parameters plotted in Figs. 1 and 2 are compared with those calculated using Eqs. (1) and (2), where the ionic radii are from Shannon’s compilation for 8CN., Note that the ionic radius of Zr4+( r = 0.084 nm) is slightly larger than that of Hf4+( r = 0.083 nm). In Table I1 the deviations of the calculated lattice parameters from the measured values for the solid solutions doped with Y,03 are much greater than those doped with Ho,03 for all compositions. This implies that the Y3+radius of 0.1019 nm for 8CN, as found in Shannon’s table, is somewhat overestimated and the relative radius of Y3+ should be smaller than 0.1015 nm, which corresponds to the ionic radius of Ho3+in 8CN. The deviations in the lattice parameters of the solid solutions containing Ho,03 may result partially from the fact that regression analyses to obtain Eqs. ( 1 ) and (2) were performed by using data which include the lattice parameters doped with Y3+,whose ionic radius was determined as 0.1019 nm.9 Provided that the differences between the measured and the calculated lattice constants of the solid solutions containing Y,O, are about the same as those containing Ho,03, the ionic radius of Y3+ for 8CN can be calculated for each composition of Table I1 using Eqs. (1) and ( 2 ) . The calculated values are listed in Table 111and the average ionic radius of Y3+for 8CN is estimated to be 0.101 1 nm. Despite the considerable deviations
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Table 11. Measured and Calculated Lattice Parametersof Fluorite-typeHfO, and ZrO, Solid Solutions Lattice parameter (nm) HfO, solid solution
Dopant concentration (mol%)*
8 (14.81) lO(18.18) 12 (21.43) 14 (24.56)
Ho@,
ZIO, solid solution
HozQ
Y20,
Y20,
Meas.
Calc.
Meas.
Calc.
Meas.
Calc.
Meas.
Calc.
0.51217 +- 0.00008 0.51268 f0.00007 0.5 1317 ? 0.00008 0.51371 i0.00003
0.51210
0.51206 k 0.00004 0.51255 t0.00005 0.51305 k 0.00005 0.51353 k 0.00006
0.51222
0.51393 f0.00002 0.51450 rt 0.00001 0.51504 2 0.00001 0.51552 t0.00001
0.51409
0.51380 f0.00001 0.51437 rt 0.00002 0.51488 2 0.00003 0.51537 2 0.00001
0.51421
0.51263 0.51313 0.51362
0.51278 0.51331 0.51382
0.51456 0.51502 0.51546
0.5 1472 0.5 1520 0.5 1560
*Values in parentheses correspond to mol% of HoO, or YO, 5 .
Table 111. Effective Ionic Radius of Y3+for Eightfold Coordination Calculated from Lattice Parameters of Fluorite-typeHfO,-Y,O, and Zr0,-Y,O, Solid Solutions
-fa
References
Effective ionic radius of Y” (nm)
(YO, 5 ) concentration (mol%)
HfO, solid solution
ZrO- solid solution
8 (14.81) lO(18.18) 12 (21.43) 14 (24.56)
0.101 12 0.10115 0.10122 0.10114
0.10109 0.10115 0.10114 0.10121
of the calculated lattice parameters from the measured ones in the Hf0,-Y,O, and the ZrO,-Y,O, solid solutions in Table 11, if it is assumed that 0.1019 nm is the representative radius of Y3 in 8CN, the average radius of Ho3+for 8CN is calculated to be 0.1022 nm. When this new radius of Ho and the radii of the rest of the lanthanide cations for 8CN from Shannon’s set are plotted as a function of atomic number, the radii fall on a smoothly descending curve, which represents the lanthanide contraction, except for a cusp at Ho. The curve fits better with the ionic radius of 0.1015 nm for Ho3+.This further supports that the ionic radius of Y3+ for 8CN is smaller than 0.1015 nm. +
VI. Summary The effective ionic radius of Y3+for the eightfold coordination was estimated to be 0.101 1 nm from the accurate measurements of the lattice parameters of HfO, and ZrO, solid solutions doped with Ho,O, and Y,O,. This value is more reasonable than the value of 0.1019 nm from Shannon’s set of ionic radii for the lattice parameters and the reported activation enthalpy for ionic conduction of the fluorite-type oxide solid solutions, both of which are governed by dopant cation ionic size.
IT. H. Etsell and S. N. Flengas, “The Electrical Properties of Solid 0xide.Electrolytes,” Chem. Rev., 70 (31 339-76 (1970). ’E. C. Subbmao and H. S. Maiti, “Solid Electrolytes with Oxygen Ion Conduction,” Solid State Ionics, 11 (41 317-38 (1984). ’R. Gerhardt-Anderson and A. S. Nowick, “Ionic Conductivity of CeO, with Trivalent Dopants of Different Ionic Radii,” Solid State Ionics, 5 , 547-50 (1981). 4J. A. Kilner, “The Role of Dopant Size in Determining Oxygen Ion Conductivity in the Fluorite Structure Oxides”: pp. 189-92 in Solid State Chemistry 1982, Proceedings of the Second European Conference. Edited by R. Metselaar, H. J. M. Heijligers, and J. Schoonman. Elsevier, Amsterdam, Netherlands, 1983. ‘J. A. Kilner and R. J. Brook, “A Study of Oxygen Ion Conductivity in Doped Non-Stoichiometric Oxides,” Solid State tonics, 6 [3] 237-52 (1982). 6M. F. Trubelja and V. S. Stnbican, “Ionic Conductivity of the Fluorite-type Hafnia-R,O, Solid Solutions,” J . Am. Ceram. Soc., 74 [lo] 2489-94 (1991). ’R. D. Shannon, “Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides,” Acta Crystallogr.,Sect. A: Cryst. Phys. Diffr. Theor. Gen. Crystallojir., A32 [5] 75147 (1976). *D. E. Appleman and H. T. Evans, “Job 9214 Indexing and Least-Squares Refinement of Powder Diffraction Data”: p. 188 in U.S. Department of Commerce Publication No. 216. National Technical Information Service, Washington, DC, 1973. ’D.-J. Kim, “Lattice Parameters, Ionic Conductivities, and Solid Solubility Limits in Fluorite-Structure MO, Oxide (M = Hf4’, Zr4’, Ce“, Th4+,U“‘) Solid Solutions,” J . Am. Cerum. Soc., 72 181 1415-21 (1989). ‘OF. S.Galasso, “Structure and Properties of Inorganic Solids”; pp. 102-106 in International Series of Monographs in Solid-State Physics, Vol: 7. Pergamon Press, New York, 1970. “R. D. Shannon and C. T. F’rewitt, “Effective Ionic Radii in Oxides and Fluorides,” Acta Crystallogr., Sect. B : Struct. Crystallogr. Cryst. Chem., B25, 92546 (1969). ”D.-J. Kim and T. Y. Tien, “Phase Stability and Physical Properties of Cubic and Tetragonal ZrO, in the System ZrO,-Y,O,-Ta,O,,” J . Am. Cerum. Soc., 74 [I21 3061-65 (1991). I’M. Yashima, N. Ishizawa, and M.Yoshimura, “Application of an Ion-Packing Model Based on Defect Clusters to Zirconia Solid Solutions: I, Modeling and Local Structure of Solid Solutions,” J . Am. Ceram. Soc., 75 [6] 154149 (1992). “M. Ydshima, N. Ishizawa, and M. Yoshimura, “Application of an Ion-Packing Model Based on Defect Clusters to Zirconia Solid Solutions: 11, Applicability of Vegard’s Law,” J. Am. Cerum. Soc., 75 [6] 155Ck57 (1992). 0
