Chemistry of Materials 1989, 1, 19-26
19
Articles Short- and Long-Range Order in Na(1)-Eu(I1) @"-Alumina Michael A. Saltzberg,tJ John 0. Thomas,s and Gregory C. Farrington*$? Department of Materials Science, University of Pennsylvania, 3231 Walnut Street, Philadelphia, Pennsylvania 19104, and Institute of Chemistry, University of Uppsala, Box 531, S-751 21 Uppsala, Sweden Received M a y 13, 1988 When the Na(1) content of the two-dimensional fast ionic conductor Na(1) @"-aluminais partially or fully replaced with Eu(II), the mobile cations in the resulting isomorphous materials have varying degrees of short- and long-range order. Single-crystalX-ray structure refinements of four such compositions are reported here. These results, as well as data from TEM and optical spectroscopy studies, can be interpreted in terms of a model in which the mobile ion distribution in the materials is determined by mobile ionframework interactions, mobile ion-mobile ion interactions,and kinetic effects related to the thermal history of the samples. Introduction The @"-aluminas are solid electrolytes with high ionic but negligible electronic conductivities. The parent compound, Na(1) @"-alumina, is nonstoichiometric and has a typical composition of Na1~mMgo.mAllo.~017. A wide variety of isomorphs of @"-alumina can be easily synthesized by the ion exchange of the Na(1) content with mono-, di-, and trivalent cations. The resulting mixed compositions are elegant systems for investigating ionic-orderingphenomena and also of considerable interest for a variety of technological applications. The structure of Na(1) @"-alumina is shown in Figure 1.' Close-packed layers consisting of aluminum ions, some of which are replaced by Mg(II), and oxygen ions separate more open regions that contain the mobile Na(1) ions. The close-packed blocks have a structure similar to that of the mineral spinel and are thus referred to as "spinel blocks". The "conduction planes" separating the spinel blocks contain both oxygen ions ("column oxygens") as well as mobile Na(1) ions. Together, the spinel blocks and the column oxygens form a rigid crystalline framework. There are two well-defined sites for the mobile cations in the conduction planes (Figure 2): the tetrahedral Beevers-Ross (BR) site and the eight-coordinate midoxygen (mO) site. In Na(1) @"-alumina, the Na(1) ions occupy five-sixthsof the available BR sites, and conduction occurs by a vacancy mechanism.' The Na(1) sublattice is highly disordered a t room temperature.2 The ion-exchange properties of Na(1) @"-alumina are quite unusual. As mentioned earlier, the Na(1) content can be partially or completely replaced by a wide variety of mono-, di-, and trivalent ion^.^-^ In all cases, the @"alumina framework is retained (albeit often with some distortion), but the structure of the conduction planes varies greatly with the nature of the mobile cation.6 Single-crystal X-ray studies of a large number of the divalent isomorphs of @"-aluminahave shown that, at room
temperature, the mobile divalent ions occupy both mO and BR sites. The specific cation distributions and site occupancies vary from isomorph to isomorph.6 Recently, it has been proposed that the structures and properties of the di- and trivalent @"-aluminasdepend on the thermal history of the material^.^ It is clear that in the Eu(I1) system long-range ordered structures form during low-temperature annealing.8 The kinetics of the ordering process are slow, and the degree of ordering depends on the composition and possibly on the degree to which a sample is h ~ d r o t e d . ~ The P-alumina framework is an excellent model system for investigating many of the factors that influence the structure and properties of partially disordered materials. Isomorphous samples of @"-aluminacan be prepared over a wide composition range and can include mono-, di-, and trivalent ions. In addition, the two-dimensionality of the structure simplifies the interpretation of the experimental results. In this paper, we present the results of singlecrystal X-ray diffraction studies of the Na(1)-Eu(I1) @"alumina system from the pure Na(1) to the pure Eu(I1) composition. This system was chosen because Na(1) and Eu(I1) have similar ionic radii and because Eu(I1) is fluorescent and thus provides a spectroscopic probe of the immediate surroundings of the Eu(I1) ions. The goal of the study was to determine the factors that control the structure of Na-Eu(I1) p'-alumina as the charge and the total number of cations in the conduction planes are varied.
'University of Pennsylvania. 'Present address: E. I. du Pont de Nemours Inc., Central Research and Development Department, Experimental Station, Wilmington, DE 19898. *University of Uppsala. * To whom correspondence should be addressed.
1983, 9, 301. (7) Davies, P. K.; Petford, A.; O'Keeffe, M. Solid State Ionics 1986, 18, 624.
0897-4756/89/2801-0019$01.50/0
Experimental Procedures Na(1) r-alumina single crystals were grown by a flux evaporation method that has been described previously.10 Well-formed, (1) Bettman, M.; Peters, C. R. J. Phys. Chem. 1969, 73, 1774. (2) Frase, K. G.; Thomas. J. 0.: Farrington. - . G. C. Solid State Ionics 1983, 9,307. (3) Briant, J. L.; Farrington, G. C. J. Solid State Chem. 1980,33,385. (4) Dunn, B.; Farrington, G. C. Mater. Res. Bull. 1980, 15, 1773. (5) Farrington, G. C.; Dunn, B. Solid State Zonics 1982, 7, 267. (6) Thomas, J. 0.;Aldbn, M.; Farrington, G. C. Solid State Ionics
(8)Saltzberg, M. A.; Davies, P. K.; Farrington, G. C. Mater. Res. Bull. 1986, 21, 1533.
( 9 ) Saltzberg,, M. A.; Davies, P. K.; Garzon, F. H.; Farrington, G. C. Solid State Ionics, in press.
0 1989 American Chemical Society
Saltzberg et al.
20 Chemistry of Materials, Vol. 1, No. I , 1989
Table I. Cell Parameters of Na(1)-Eu(I1) p'-Alumina exchange, % a, A c, A cell vol, A3 33.513 (13) 917.38 (60) 0 5.622 (1) 33.644 (3) 921.96 (15) 23 5.625 (1) 33.616 (6) 919.86 (27) 40 5.621 (1) 33.541 (3) 920.32 (15) 75 5.629 (1) 33.539 (6) 918.86 (26) 100 5.624 (1)
A C
"T A
t
11.3A
I
B I
A
33.85 A
~~~
B
B
Oxygen
A
@
Sodium
Table 11. Data Parameters for the Refinements Na(1) replaced by Eu(I1) 23% 40% 75% 100% 4357" 3468" total reflctns coll 1396 4335" no. of independent reflctns 1396b 1399 1398 1128 no. used in refinement (>2a(R2)) 1234 1071 1126 987 1.076 1.076 1.076 0.994 (sin e&/, A-l N/A 1.15% 1.01% 1.10% R factor for equiv refs
C
"Each reflection measured three times (at \k = -0.5, 0.0, +0.5). All measured reflections treated as independent, including small number of Friedel pairs. graphite monochromatized Mo K a radiation. Essentially symmetry-independent sets of reflections of type +h,+lz,&Z(h 5 lz) were collected out to 6 = 50". The R-translation condition -h k Z = 3n was imposed on the hexagonal indexing system used. Sets of test reflections were monitored a t regular intervals; all four data sets exhibited small monotonic variations that were subsequently corrected for prior to the correction for Lp factor and absorption. The latter were made by using pdd values arrived a t assuming nominal 23%, 40%, 75%, and 100% Na(1) exchange. Mean transmission values of 90%, 75%, 65%, and 45% were obtained for increasing Eu(I1) content. The cell parameters (Table I) were determined from the least-squares refinement of approximately 25 observed Q values. These were measured on the diffractometer for Friedel pairs of reflections from the actual crystals used for the data collections. A description of the data collected for the four refinements is given in Table 11. The computer programs used in the refinements are described in ref 11. The scattering factors used were taken from ref 12. All refinements involved the minimization of the function Cw(F,2 - IFc12)2,where the weighting function (w)used is of the form w = l/a2(Fo2),and a2(F;) = a2co,t(F2)+ (kF2)2; k is an empirical constant set to 0.04. Reflections with F 2 < 2a(F;) were removed from the refinements and the calculation of the subsequent Fourier syntheses.
+ +
Figure 1. Structure of Na(1) p'-alumina.
Figure 2. p-Alumina conduction "plane". Light gray circles are oxygens below plane; open circles are oxygens above plane; dark gray circles are column oxygens in plane. Triangles mark BR sites; stars mark mO sites. optically clear crystals, typically 4 X 4 X 0.5 mm, were cut and polished by using standard methods. The samples were labeled with radioactive 22Naby ion exchange in molten NaN03, so that the extent of Na(1) replacement in later exchanges with Eu(I1) could be easily monitored. After being annealed to homogenize the tracer, the crystals were sealed with Eu12 under vacuum in quartz ampules. The extent of ion exchange was controlled by varying the time and temperature of the reaction. After exchange, the samples were clear and undamaged and intense yellow-green. They were annealed at 500 "C under vacuum for 3 days to ensure compositional homogeneity and then for 3-30 days a t 150-200 "C to allow the ions to attain or at least approach their equilibrium microstructures (see ref 8 and 9). Compositionscorrespondingto 23%, 40%, 75%; and 100% of Na(1) replaced by Eu(I1) were selected for single-crystal X-ray diffraction studies. The crystals used for the data collections (maximum dimensions ~ 0 . 2mm) were obtained from the larger annealed samples. Equivalent procedures were followed for the four data sets to minimize the relative effects of systematic experimental error. The X-ray diffraction intensity data were measured a t 23 "C by using an automated NONIUS CAD4-F diffractometer with (10) Kummer, J. T. Prog. Solid State Chem. 1972, 7,141.
Description of the Refinements Traditional crystallography assumes that the structure of a crystalline material can be fully characterized by describing the content of a single unit cell. However, in a partially disordered, nonstoichiometric material such as r-alumina, the structural characterization derived in this way is not complete. It is thus important to state just what information a crystallographic study of a disordered material can provide. If the mobile ion sublattice in @"-aluminawere completely disordered, the structure of the material could be adequately described by calculating average site occupations in the framework unit cell. However, if the positions of the mobile ions are correlated, this type of description is incomplete. For example, it has been shown that in many divalent @"-aluminasthere is short-range ordering among the mobile cations, and the structural refinement improves if the occupations of adjacent BR sites are refined inde~endent1y.l~This requires lowering the space-group ~~~~~
~
~~
(11)Lundgren, J. 0. Crystallographic Computer Programs, Report No. UUIC-B13-04-05, Institute of Chemistry, University of Uppsala,
Sweden, 1982.
(12) International Tables for X-ray Crystallography; Kynoch Press: Birmingham, AL, 1974; Vol. IV. (13) Thomas, J. 0.;AldBn, M.; McIntyre, G. J.; Farrington, G. C. Acta. Crystallogr., Sect. B 1984, 40, 208.
Chemistry of Materials, Vol. I , No. 1, 1989 21
Order in Na(I)-Eu(II) p”-Alumina Table 111. Summary of actual actual refined exchange, mobile exchange, % % charge 23 40 75 100
1.67 1.67 1.67 1.67
24 40 81 100
and 100% structures, the fit was significantly improved by the use of a more sophisticated thermal model (yjjk’s for ions in BR sites and bijk;s for ions in mO sites). In the 75% exchanged sample, very weak extra reflections corresponding to a tripling of the R3m unit cell were observed. This indicates that some long-range ordering was present. These reflections were not included in the refinement, because the structure is known to contain ordered and disordered domains.8 Nevertheless, the description obtained with the R3m unit cell represents the correct auerage structure of the material within the coherence length of the experiment. In the Discussion, we have combined the information presented here with optical spectroscopy and transmission electron microscopy (TEM) results published p r e v i o ~ s l y . ~ ~ ~ From this combination of perspectives, a clearer picture of the complex structure of these materials emerges.
the Refined Models refined mobile R(F),” R,(F2),b % % charge 1.69 1.53 1.66 1.76
14.0 11.9 9.6 11.3
4.1 4.4 3.3 3.4
a ‘Conventional” R factor normally quoted in structure refinements. Weighted R factor based on F2.
symmetry from centrosymmetric RBm to noncentrosymmetric R3m for the mobile ions. Physically this process reflects the fact that there are only 0.833 divalent ions per formula unit (i.e., per two BR sites), and that minimizing coulombic repulsion requires that two adjacent BR sites are not occupied simultaneously. Note, however, that even though adjacent BR sites are refined independently, they Results are still crystallographically equivalent, so that the refined The mobile ion distributions in p”-alumina samples with relative occupationshave only limited physical significance as a qualitative expression of the extent of short-range 23%, 40%, 75%, and 100% of the Na(1) replaced with Eu(I1) are summarized in Table IV in terms of the refined order in the material. In the extreme case in which the mobile ion site occupations. As mentioned in the previous mobile ions form a structure with long-range order, the appropriate unit cell may be some multiple of the framesection, the Fobdelectron density plots derived from the refinements are more accurate than the site occupations work unit cell. Long-range structures of this type have been observed in highly exchanged Eu(I1) /3”-al~mina.~l~ in describing the mobile ion distribution in these compounds. Electron density plots of sections through the One of the most serious practical difficulties encountered conduction pathways, i.e., of planes parallel to the c axis in modeling a structure containing mobile ions is that the and running between BR sites, are shown in Figure 3. A fractional site occupations and the thermal parameters of schematic diagram of the framework structure of this these ions are highly coupled in the refinement. The total vertical section, which indicates the position of the mO number of mobile ions and the fraction of each ion in a mixed system such as Na(I)/Eu(II) can refine to unphysites, the BR sites, and the conduction pathway in the sical values if minimizing the R factor is the only criterion electron density plots, is also included so that the relationship between the mobile ion distributions and the used in the refinement. The results presented here rep@’-alumina framework is clear. resent a compromise between minimizing the R factor and maintaining a description of the structure that matches In Na(1) @”-alumina,it has been shown that the Na(1) density is centered on BR sites and is accompanied either the known composition. In all cases, the total refined by considerable relaxation of the Na(1) ions toward the mobile charge and the Na(I)/Eu(II) ratio were kept within adjacent mO sites or by significant occupation of mO sites about 8% of the actual values. It should be noted, howby Na(I).2 In contrast to the pure Na(1) material, the ever, that the electron density maps obtained from these samples with 23% and 40% of the Na(1) replaced by Eustudies are essentially invariant with respect to these small (11)show significant electron density at an intermediate differences in the refined models. This is because the calculated phases of the observed reflections used in the site in the conduction pathway, between the mO and BR Fourier syntheses are largely determined by the structure sites (see Figure 3 ) . The refinements indicate that these of the framework, which does not change from model to immediate 18h sites (R3m notation), of general coordinates (x,--x,z), are occupied by Eu(I1) ions, with the Na(1) ions model. occupying BR sites. The values of the 18h site coordinates Table I11 lists the refined total mobile charge, the were refined for these materials and are given in Table IV. Na(I)/Eu(II) ratios, and the R factors of the refinements. The 23% and 40% exchanged structures were refined When the Eu(I1) concentration increases from 23% to 40% within the harmonic approximation using anisotropic of the total mobile charge, the Eu(I1) ions occupy mO sites to a lesser extent, as shown by the diminished electron thermal parameters (Pij’s)for the mobile ions. In the 75%
exchange, % 23
40
75
100
ion Eu(I1) Eu(I1) Na(1)’ Na(1) Eu(I1) Eu(I1) NaU) Na(U Eu(I1) Eu(I1) Eu(I1) NaU) NaU) Eu(I1) Eu(I1) Eu(I1)
Table type of site 18h 18h BR BR 18h 18h BR BR
mO BR BR BR BR mO BR BR
IV. Refined Mobile Ion Site Occupations X
Y
0.9041 (2) -0.9041 (2) ., 0 0 0.9057 (10) -0.9057 (10) 0 0
-0.9041 (2) 0.9041 (2) . , 0 0 -0.9057 (10) 0.9057 (10) 0 0
0.1680 -0.1680 0.1730 4.1730 0.1686 -0.1686 0.1732 4.1732
6/6
‘16
‘16
0 0 0 0
0 0
0.1734 -0.1734 0.1734 -0.1734
=/e
0 0
0 0
occ
Z
(1) (1) i2j (2) (2) (2)
(1) (1) (1) (1) (1) (1)
I16
0
0
0.1731 (2) -0.1731 (2)
0.0116 (6) 0.0224 (8) 0.1010 i 6 j 0.1125 (6) 0.0353 (13) 0.0159 (13) 0.0725 (26) 0.0804 (26) 0.1022 (2) 0.0043 (4) 0.0060 (4) 0.0261 (3) 0.0261 (3) 0.1308 (8) 0.0060 (4) 0.0096 (4)
ions/formula unit 0.069 0.134 0.606 0.675 0.212 0.095 0.435 0.482 0.613 0.026 0.036 0.157 0.157 0.785 0.036 0.058
(4) (5) i4j (4) (8) (8)
(16) (16) (1) (3) (3) (2) (2) (6) (2) (2)
Saltzberg et al.
22 Chemistry of Materials, Vol. 1, No. I, 1989
b-axis
Spinel Block BR ‘’
I
I
Spinel Block a
b
\
Figure 3. FoMelectron density plots of Na(1)-Eu(I1) p”-alumina showing a section through the conduction pathway parallel to the c axis: (a) schematic diagram indicating the location of the plots
in the r-alumina framework; (b) 23% exchanged; (c) 40% exchanged; (d) 75% exchanged; (e) 100% exchanged.
density at these sites. The shape of the Na(1) distribution is virtually the same from 23% and 40% exchanged. A radical change in the structure of the conduction planes occurs between 40% and 75% exchange. The Eu(11) ions occupy well-defined mO sites in the 75% exchanged sample with only a small amount of Eu(I1) in BR sites. Na(1) ions continue to occupy BR sites, but the intermediate 18h site is essentially empty. The 100% structure is very similar to the 75% structure, with Eu(I1) ions occupying predominantly mO sites and a small amount of Eu(I1) in well-defined BR sites. Again, the 18h site is unoccupied. The electron density plots through the plane of the column oxygens (the conduction plane, z = 1/6) give another view of the structural trends with changes in composition. These are shown in Figure 4, along with a schematic diagram of the framework at this position in the structure that shows the position of the column oxygens, the mO sites, zind the BR sites in the electron density plots. The maxima of the Eu(I1) electron density in the 18h sites are slightly above and below the plane of the column oxygens (see Table IV), but the evolution of the site occupations is apparent. As the Eu(I1) concentration increases from 23% to 40% of the total charge, the Eu(I1) distribution centered between BR and mO sites becomes more diffuse and fills the center of the conduction pathway. As the Eu(I1) concentration increases further and the total number of mobile ions decreases, the Eu(I1) ions occupy well-defined mO sites. As before, no dramatic change in
\
\ O
\
‘\\
0
‘\
Figure 4. FoMelectron density plots of Na(1)-Eu(I1) p”-alumina through the conduction plane a t z = (a) schematic diagram indicating the location of the plots in the @”-aluminaframework; (b) 23% exchanged; (c) 40% exchanged; (d) 75% exchanged; (e) 100% exchanged.
the structure is apparent when the Eu(I1) concentration is increased from 75% to 100% of the total mobile charge.
Discussion Structure of the Conduction Planes. As the results presented in the last section show, the structure of the conduction planes of Na(1)-Eu(I1) p’-alumina varies greatly with composition. The Eu(I1) ions reside in sites between the mO and BR sites in the samples with 23%
Order i n Na(I)-Eu(II) p - A l u m i n a and 40% of the Na(1) replaced by Eu(I1) but shift to well-defined mO sites by 75% exchange. The structure changes little between 75% and 100% exchange. It should be stressed that these diffraction experiments give reliable information about the average structure of the materials but do not provide all of the information needed to describe the mobile ion distribution, particularly a t high Eu(I1) levels where long-range ordering is important. Nevertheless, by combining the diffraction results with previously published results on long-range ordering phenomena in Na(1)-Eu(I1) @”-alumina, it is possible to identify the principal factors that determine the arrangements of ions in these materials. We propose that the structure of Na(1)-Eu(I1) p”-alumina (and by analogy certain other partially disordered materials) is principally influenced by three factors: (1) mobile ion-framework interactions, specifically, the preferential occupations of BR sites by Na(1) ions and of mO sites by Eu(I1) ions, which result from maximizing the integrated bond strengths between the cations and the surrounding framework oxygen ions; (2) mobile ion-mobile ion interactions, of which Na(1)-Eu(I1) and Eu(I1)-Eu(I1) repulsions are the most important; (3) kinetic effects related to the thermal history of the samples, which can partially preserve metastable high-temperature microstructures at room temperature. A model in which the relative contributions from these factors vary with composition can explain the site occupations of the mobile ions and the degree of short- and long-range order among these ions as the p’-alumina system evolves from the pure Na(1) form to the pure Eu(I1) form. Each of these factors will be discussed in turn, beginning with mobile ion-framework interactions. In each of the structures refined in this study, Na(1) ions are found exclusively (within the quality of the refinement) in or near the distorted tetrahedral BR sites. This is not surprising, since alkali ions are often found in four-coordinate sites. As mentioned earlier, one-sixth of these sites are vacant in pure Na(1) @”-alumina. The ionic distribution around the BR sites indicates that the Na(1) ions relax considerably toward neighboring vacant sites.2 The Na(1) ions appear to be more localized when Eu(I1) is present in the structure than in pure Na(1) @”-alumina,but it is impossible from the electron density data to assess how this effect varies with composition, because the average distributions of the Na(1) ions and the stronger scattering Eu(I1) ions are superimposed. In contrast to alkali ions, lanthanide ions are almost never observed in four-coordinate sites and normally occupy eight-coordinate sites in oxide structures. It is thus reasonable to expect that Eu(I1) ions would have a tendency to occupy mO sites in @”alumina, and indeed, Eu(I1) ions occupy mO sites almost exclusively a t high concentrations. At lower Eu(I1) concentrations,however, it appears that the dominant interactions that determine the conduction plane structure are those between the mobile ions. This is evidenced by the fact that the Eu(I1) ions do not occupy their favored sites, the eight-coordinate mO sites, in the 23% and 40% exchanged compounds. We propose that they are shifted from these sites by Coulombic repulsion from other mobile ions. When the Eu(I1) concentration is less than about 40% of the total mobile charge (25% of the mobile ion population), the Eu(I1) ions are, on average, quite distant from each other. We can thus consider that, to a first approximation, only Na(1)-Eu(I1) interactions are important in determining the Eu(I1) shift from mO sites at low Eu(I1) concentrations. The occupation of the 18h site can be seen as a compromise between the
Chemistry of Materials, Vol. 1, No. 1, 1989 23
Full cell
314 Cell
112 Cell
Figure 5. Schematic diagrams illustrating the model used for the calculation of the Na(1)-Eu(I1) interaction probabilities in Na(1)-Eu(I1) p”-alumina. The arrows indicate the probable directions for Eu(I1)relaxation from the mO site. The model does not include the relaxation of the Na(1) ions.
preference of Eu(I1) ions for mO sites and the minimizing of Na(1)-Eu(I1) repulsion. Recently, Collin et al. discussed the role of Na(1)-Na(1) interactions in the structure of Na(1) @”-alumina.14 Their calculations and experiments indicate these interactions, rather than Na(1)-framework interactions, principally determine the mobile ion distribution in the material. Our results support this analysis and extend it to mixed monovalent-divalent systems in which the population of divalent ions is low. Since Na(1)-Eu(I1) repulsion appears so influential a t low Eu(I1) concentrations, we have attempted in a qualitative way to determine the relative importance of this repulsion as a function of composition by the use of a simple model that considers one conduction pathway, i.e., two adjacent BR sites with one mO site between them. When a Eu(I1) ion is present in the mO site, simple Coulombic considerations should prevent the adjacent BR sites from being occupied by Na(1) ions. If we make the simplifying assumption that the Coulombic repulsion preventing Eu(I1) and Na(1) ions from occupying adjacent mO and BR sites does not influence the Na(1) occupation of the next nearest BR sites, then the probability that the four BR sites closest to this pathway are occupied (see Figure 5 ) can be determined by assuming a random distribution of the Na(1) ions over all the remaining available BR sites in the structure. Clearly, this model takes into account only the local structure around the Eu(I1) ions (short-range order) and is not applicable when long-range Eu(I1)-Eu(I1) interactions become important. What then are the consequences of this model? At one extreme of composition, when less than 1% of the Na(1) is replaced by Eu(II), it predicts that on average about 67% of the Eu(I1) ions are surrounded by four Na(1) ions in the next nearest BR sites (these can be termed “full cells”), and about 33% are surrounded by three Na(1) ions distributed over the four next nearest BR sites (“3/4 cells”). As the Eu(I1) concentration increases, the vacancy concentration in the conduction planes also increases, and the average environment of the Eu(I1) ions changes. Table V shows the probability of finding Eu(I1) ions in full, 3/4, and 1/2 cells, as a function of composition, assuming that all (14) Collin, G.; Boilot, J. P.; Colomban, P.; Comes, R. Solid State lonics, in press.
24 Chemistry of Materials, Vol. 1, No. 1, 1989
Saltzberg et al.
Table V. Calculated Na(1)-Eu(I1) Interaction Probabilities Eu(I1) in Eu(I1) in Eu(1I) in exchange, “full cells”, “ 3 / 4 cells”, “l/z cells”, 70 % 70 70 10 27 73 0 20 20 80 0 30 11 89 0 40 50
0 0
60 70 80
0 0 0
100
86 67 40
0
Nail) ion Euill) ion
0 14
33 60 100
of the Na(1) ions, except those adjacent to Eu(I1) ions, are on BR sites. At 80% exchange, where Eu(I1)-Eu(I1) interactions are important, each Eu(I1) ion need be surrounded by only two Na(1) ions. In fact, just below this composition, Eu(I1) ions are seen to occupy well-defined, undistorted mO sites almost exclusively, and the intermediate 18h sites are empty. We can also, in a qualitative way, link the occupation of undistorted mO sites by Eu(I1) ions with the appearance of the ‘/z cells. Our model predicts that some Eu(I1) ions should begin to occupy undistorted mO sites just above 40% exchange; the mO occupation should increase from roughly 33% of the Eu(I1) ions at 60% exchange to 100% of these ions a t 80% exchange. We have not studied the structure of a sample with a composition between 40% and 75% exchange, but our experimental results show a small occupation of mO sites by Eu(I1) ions in the 40% exchanged structure. Undue credence should not be placed on this simplified picture of Na(1)-Eu(I1) p”-alumina, but it suggests that Na(1) ions do have an important influence on the Eu(1I) distribution, a t least up to 40% exchange. Above this level, Na(1)-Eu(I1) interactions quickly become less important and, by 80% exchange, have little influence on the position of the Eu(I1) ions. Up to this point, we have considered only the local Na(1) structure around each Eu(I1) ion and ignored Eu(I1)-Eu(I1) interactions because, at low concentrations, the Eu(I1) ions are quite distant from each other. However, at Eu(1I) concentrations in excess of 40-607’0 of the total mobile ion charge, Eu(I1)-Eu(I1) repulsions become important and long-range ordering effects must be considered. This conclusion is validated by results we have previously published regarding long-range ordering of the mobile ions in Na(1)-Eu(I1) p”-alumina as a function of compo~ition.~ In that study, extra reflections in TEM diffraction patterns indicated a long-range ordered structure for the mobile cations over a range of compositions. No measurable tendency to order was observed in samples with 40% or less of the total charge replaced by Eu(II), but samples with greater than 70% of the Na(1) replaced all showed some degree of long-range order. In the samples examined, the microstructure was heterogeneous, with coexisting ordered and disordered domains. The kinetics of the ordering process are strongly influenced by composition. In the 100% exchanged samples, the degree of ordering varies greatly with thermal history, and annealing times of about 10 days are necessary to create a measurable fraction of the ordered structure. Samples with 70-80% of the Na(1) replaced order more easily, and samples generally have a greater volume fraction of the ordered structure and are much less sensitive to thermal history. For example, a 70-80% exchanged sample develops a measurable fraction of ordered structure even upon rapid cooling from 600 “C by quenching in oil. These data show that at high temperatures configurational entropy produces a conduction plane structure that is highly disordered. Fast-cooling from temperatures above
Figure 6. Schematic diagrams of the proposed models for the conduction plane structures of (A) 20% exchanged and (B) 80% exchanged Na(1)-Eu(I1) @”-alumina. These two compositions are typical of the regimes in which short- and long-range order, respectively, are dominant.
300 “C partially preserves the high-temperature structure in the highly exchanged (>75% Na(1) replaced) samples. In the fast-cooled structure, a small percentage of Eu(I1) ions are trapped in BR sites. These ions relax back into mO sites when the ordered structure is re-formed by annealing under vacuum at 150-200 0C.8,9 The variation in the amount of long-range ordering with composition can be understood by considering that at low Eu(I1) concentrations the presence of the Na(1) ions precludes the formation of an ordered structure by forcing Eu(I1) ions off mO sites. A t intermediate Eu(I1) concentrations (60-80% exchange), the Na(1) concentration is reduced sufficiently to allow the Eu(I1) ions to occupy undistorted mO sites, and the formation of a long-range ordered structure is favored a t low temperatures because it minimizes Eu(I1)-Eu(I1) and Na(1)-Eu(I1) repulsions. At still higher Eu(I1) concentrations, the total ion population is lower and the average distance between mobile cations larger so that the tendency to order is decreased. We suggest that this is why samples with 70-80% of the Na(1) replaced by Eu(I1) order more readily than fully exchanged samples. The kinetics of the formation of the ordered structure are obviously quite slow in the fully exchanged samples. The presence of a small amount of Na(1) ions appears to enhance the rate of the ordering process and thus lead to a greater fraction of the ordered structure in mixed samples. Figure 6 shows schematic representations of our model of the conduction plane structures of 12 in-plane unit cells for 20% and 80% exchanged Na(1)-Eu(I1) @”-aluminaand summarizes the points made in this discussion. These two compositions correspond to conditions in which short (Figure 6A) and long-range (Figure 6B) order are dominant. The 20% structure (Figure 6A) shows no long-range order; the Eu(I1) ions occupy the intermediate 18h sites observed in the electron density data, and the Eu(I1) ions relax toward adjacent vacant BR sites and are shifted off the mO sites. The model for the 80% exchanged sample (Figure 6B) does show long-range ordering and is consistent with the electron diffraction patterns obtained from samples of this composition. The Eu(I1) ions occupy undistorted mO sites, with a unit cell based on a tripling of the Na(1) @”-aluminaunit cell in one in-plane direction and a doubling in the other. This 3 X 2 cell contains four Eu(I1) ions and two Na(1) ions. Other compositions must, of course, have slightly different ordered structures, simply on the basis of stoichiometry. The 3 X 2 cell shown here
Chemistry of Materials, Vol. 1, No. 1, 1989 25
Order in Na(I)-Eu(II) @”-Alumina
550
460
500 540 580 WAVELENGTH ( n m )
620
Figure 7. Eu(I1) fluorescence in samples of Na(1)-Eu(I1)@”alumina: (a) 1%;(b) 23%; (c) 100%. Intensitieswere normalized to the same value. Actual intensities were in the order a > b >
C.
for highly exchanged Na(1)-Eu(I1) @”-aluminais the most reasonable (though not the only) unit cell for the ordered structure that is consistent with the experimental data. Optical Property/Structure Relationships. The fluorescence spectra of Na(1)-Eu(I1) @”-aluminahave been previously reported, but without detailed ana1y~is.l~ Representative spectra are reproduced in Figure 7, and the peak positions vs composition for a large number of samples are plotted in Figure 8, top. The peak position shifts smoothly from about 550 nm to about 500 nm as the Eu(I1) concentration is increased from
