3)O3–PbZrO3 system

Journal of Physics and Chemistry of Solids 63 (2002) 15±22

www.elsevier.com/locate/jpcs

Structure re®nement of large domain relaxors in the Pb(Mg1/3Ta2/3)O3 ±PbZrO3 system W. Dmowski*, M.K. Akbas, T. Egami, P.K. Davies Department of Materials Science and Engineering and the Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, PA 19104, USA Received 21 October 1998; accepted 11 May 2000

Abstract The relaxor ferroelectric compound Pb(Mg0.3Ta0.6Zr0.1)O3 (PMT±PZ) was studied by X-ray, neutron and electron diffraction and transmission electron microscopy in the as-sintered and annealed states. The as-sintered sample was comprised of nanometer-sized 1:1 chemically ordered domains dispersed in a disordered matrix. After annealing at 13258C the domain size increased to ,30 nm and the degree of order exceeded 95% in terms of the volume fraction of the ordered domains, yet the sample retained its diffuse, frequency dependent relaxor characteristics. Re®nements of the chemically ordered structure using the Rietveld analysis revealed that the octahedral (B) site occupancies were in excellent agreement with a ªrandom siteº model for the chemical ordering. In this charge-balanced model for the 1:1 ordered Pb…b 01=2 b 001=2 †O3 structure the Ta cations predominantly occupy the b 00 site, while the b 0 site is populated by a random distribution of the Mg, Zr and remaining Ta cations. Large temperature factors for Pb and O atoms are observed in both as-sintered and annealed samples, indicating localized displacements of the Pb and O atoms. The mixed occupancy of the b 0 position appears to be responsible for the relaxor characteristics in the dielectric response in spite of the growth of the chemical domains. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Ceramics; D. Crystal structure; D. Ferroelectricity

1. Introduction Lead-based ferroelectric relaxor oxides are a technologically important class of materials. They are characterized by diffuse, frequency-dependent maxima in the real and imaginary parts of the dielectric permittivity upon transition from the ferroelectric to the paraelectric state. The crystal structure of the PMN family of relaxors is based on a simple perovskite cell PbBO3 with the general formula 51 21 Pb…B21 ˆ Mg, Co, Ni, Zn; B 51 ˆ Nb, Ta). 1=3 B2=3 †O3 (B The origin of the relaxor behavior is generally attributed to the structural frustration and heterogeneity due to the presence of mixed valent cations in the octahedral B site, but the detailed microscopic origin is yet to be fully understood. Transmission electron microscopy (TEM) studies of * Corresponding author. Tel.: 11-215-898-9645; fax: 11-215573-2128. E-mail address: [email protected] (W. Dmowski).

the PMN family relaxors revealed the formation of nanometer size chemically ordered domains with 1:1 Bsite ordering [1±3]. This 1:1 order doubles the basic perovskite unit cell and results in a Pb…b 01=2 b 001=2 †O3 structure where the b 0 and b 00 cation sites are arranged on a rocksalt type Bsite sub-lattice, see Fig. 1. Two different schemes have been proposed for the occupancies of the cation positions in the ordered 1:1 structure. In the ªspace-chargeº model, it was postulated that the sites are occupied exclusively by the B 21 and B 51 cations, 51 respectively leading to a composition Pb…B21 1=2 B1=2 †O3 : The negative net charge carried by the ordered domains was assumed to be compensated by a positively charged, B 51 rich, disordered matrix. The space charge in the ordered and disordered parts limits any growth of the ordered regions and results in a very small domain size for the chemically ordered phase. Indeed, the lack of domain coarsening upon long-term annealing was cited as indirect support of the space-charge model. An alternate charge

0022-3697/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0022-369 7(00)00197-9

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W. Dmowski et al. / Journal of Physics and Chemistry of Solids 63 (2002) 15±22

Fig. 1. Schematic picture of the double perovskite cell of 1:1 ordered Pb…b 01=2 b 001=2 †O3 . Oxygen atoms are shown only for one octahedra.

balanced, ªrandom layerº model was proposed, through rejected, in the early studies of PMN [4]. In this model the b 0 site is randomly populated by a 2:1 distribution of the B 21 and B 51 cations while the b 00 site is occupied exclusively by B 51. In the resulting structural formula, 51 51 Pb…‰B21 2=3 B1=3 Š1=2 ‰B Š1=2 †O3 ; the overall 1:2 stoichiometry of the B site is preserved in all regions of the sample and the ordered domains are charge balanced. In this case domain coarsening should be mainly limited by kinetics. Recently through studies of tantalate relaxors in the (1 2 x)Pb(Mg1/3Ta2/3)O3 ±(x)PbZrO3 (PMT±PZ) system, Akbas and Davies [5] have shown that extensive modi®cations in the degree of 1:1 order and the size of the chemical ordered domains can be induced through high temperature (,13258C) annealing treatments. The preparation of samples with almost complete 1:1 chemical order casts severe doubts on the validity of the space-charge model and supports the random site description for the chemical order in these systems. Moreover, the observation that these well-ordered samples retain their diffuse and frequencydependent dielectric response indicates that a phase separated nano-domain structure is not essential for the relaxor behavior. In this paper we present the results of X-ray and neutron Rietveld structure studies of a PMT relaxor containing 10 mol% PZ. Re®nements were conducted on samples after regular sintering and prolonged annealing at 13258C. The occupancies of the ordered cation positions are compared to those predicted by the random site and space-charge models, and we discuss how the chemical ordering affects the details of the atomic structure.

2. Experimental methods 2.1. Sample preparation Samples of (1 2 x)PMT±(x) PZ solid solutions with x ˆ 0:1; Pb(Mg0.3Ta0.6Zr0.1)O3, were prepared by solid state techniques from high purity oxides (.99.9%) via the ªcolumbite routeº [6]. Details are published elsewhere [7]. The ®nal sintering of the samples was conducted at 12258C for 1 h using an inverted crucible method. After sintering, some of the ceramics were annealed at 13258C for 48 h. These conditions had been previously shown to induce signi®cant chemical order. To minimize the loss of PbO and bulk decomposition during the high temperature treatment, the ceramics were buried in a ªsacri®cialº powder of the same composition, wrapped in platinum foil and placed into platinum crucibles that were closed with a tight-®tting lid. After annealing, small amounts of columbite and pyrochlore decomposition products were removed from the surface of the perovskite pellet. 2.2. Dielectric measurement The dielectric properties of the ceramics were determined as a function of frequency using a high-precision impedance±capacitance±resistance (LCR) meter (Model HP4284A, Hewlett±Packard, Palo Alto, CA). An environmental chamber (Model 9023, Delta Design, San Diego, CA) was used to study the temperature dependence of the dielectric properties from liquid nitrogen to room temperature.

W. Dmowski et al. / Journal of Physics and Chemistry of Solids 63 (2002) 15±22

17

Fig. 2. Temperature and frequency dependence of the real part of the dielectric permittivity and the dielectric loss of as-sintered (dashed line) and annealed (solid line) PMT-10% PZ ceramics.

2.3. TEM sample preparation

2.5. TOF neutron diffraction and GSAS procedures

TEM samples were prepared by grinding the ceramic pellets to a thickness of ,20 mm and polishing both sides with 5, 3, 1, and 0.25 mm Al2O3 powder. Final thinning was conducted using ion milling on thin sections supported by copper grids. Centered dark-®eld images were obtained from the (3/2, 3/2, 3/2) supercell re¯ections.

Neutron TOF diffraction patterns were collected at the Special Environment Powder diffractometer at the Intense Pulsed Neutron Source of the Argonne National Lab. Measurements were carried out at room temperature on powder samples contained in a vanadium can. The 908 detector bank was used for the Rietveld re®nement using the GSAS package [8]. The scale factor, background coef®cients, peak pro®le parameters, zero correction, oxygen position, occupancies, isotropic and anisotropic temperature factors were re®ned. Because the neutron scattering lengths of Mg, Zr and Ta are very similar, the chemical ordering of B-site cations cannot be observed by neutron diffraction. However, neutron scattering length of oxygen is comparable to the other high Z atoms, therefore it provided complementary information, particularly on the position of the oxygen ions. The analysis of the ordered sample used ®xed B cation occupancies obtained from the X-ray Rietveld re®nement.

2.4. X-ray diffraction and data analysis X-ray diffraction measurements were performed at the beamline X7A at the National Synchrotron Light Source, Brookhaven Nation Laboratory. Samples were mounted in a 0.33 mm diameter glass capillary. During the measurement the capillary was continuously rotated to improve orientational averaging. Diffraction intensities were collected at a wavelength of 0.05181 nm using a Position Sensitive Detector (PSD) with a 0:6 £ 10 mm2 ; receiving slit. The beam size was 0:8 £ 8 mm2 : The GSAS package was used for the Rietveld re®nement [8] in the range of d ˆ 0:08 , 0:5 nm: The asymmetric peak shape function #3 that is suitable for this setup was used [9] and the background was modeled using terms of 1/Q 2 and Q 2 expansions (#12 in GSAS). The as sintered sample was re®ned using a single set of pro®le parameters. Because the ordering peaks in the annealed sample were broader than those from the subcell, additional broadening terms for the supercell peaks were re®ned, with the sub-cell re¯ections described as set of stacking fault vectors in the GSAS procedure [8]. The scale factor, background coef®cients, peak pro®le parameters, zero correction, oxygen position, occupancies, isotropic and anisotropic temperature factors were all re®ned.

3. Results 3.1. Dielectric properties Fig. 2 presents the results of the dielectric measurements on the as-sintered and annealed samples. Both samples show diffuse and frequency-dependent maxima in the real and imaginary part of the relative permittivity characteristic of the relaxor behavior. The only effect of annealing is to reduce the amplitude of the permittivity maxima by about 12% and to shift the curve towards lower temperatures by a few degrees. It is clear from the data that the high

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W. Dmowski et al. / Journal of Physics and Chemistry of Solids 63 (2002) 15±22

Fig. 3. Centered dark-®eld TEM images of: (A) as-sintered; (B) annealed samples of PMT-10% PZ. The inset of each ®gure shows the corresponding [110] electron diffraction patterns.

temperature anneal does not affect the relaxor behavior of the PMT±PZ solid solution. 3.2. TEM studies Fig. 3 shows centered dark ®eld images of the PMT±PZ solid solution in the as-sintered and annealed state collected using the (3/2, 3/2, 3/2) ordering re¯ection. The corresponding [110] electron diffraction patterns are shown in the inset of each image. The as-sintered sample is comprised of 2± 3 nm sized 1:1 ordered domains dispersed in a disordered matrix. Annealing at temperatures below ,12758C does not

produce any signi®cant growth of the ordered domains. However, annealing at 13258C for 24±48 h produced significant increases in the volume fraction of the ordered phase (.95%) and the size of the chemically ordered regions. In the dark ®eld image the size of these regions approaches ,100 nm; however, higher resolution lattice imaging revealed that these regions do contain considerable substructure, primarily in the form of anti-phase boundaries, and that the typical size of a defect free ordered domain is approximately 30 nm. The very large change in the degree of ordering induced by the high temperature heat treatment demonstrates that in the as-sintered samples the

W. Dmowski et al. / Journal of Physics and Chemistry of Solids 63 (2002) 15±22

19

Fig. 4. Observed, calculated X-ray diffraction pro®les and difference curve for the as-sintered sample as a function of 2u . Inset shows same plot, but for smaller y range.

establishment of the chemical order on the B-site positions is limited by kinetics. 3.3. Rietveld re®nements Fig. 4 presents the X-ray Rietveld re®nement of the as sintered, partially ordered sample of PMT±PZ. Due to the small size and volume of the ordered domains in the assintered sample, these patterns only contain very weak and diffuse superlattice re¯ections at low angles. Therefore, the  space group of the aristotype data was re®ned in the Pm3m perovskite sub-cell with Mg, Ta, and Zr randomly occupying a single type of octahedral position and the sum of the B Table 1  X-ray Rietveld re®nement of PMT±PZ. As-sintered sample, Pm3m; wRp ˆ 3:43%; Rp ˆ 2:82% x Pb O

y

z

Ê 2] Ideal occupancy Re®ned fractions U [A

0.5 0.5 0.5 1.0 0.5 0 0 1.0

b Mg 0 Zr 0 Ta 0

0 0 0

0 0 0

0.3 0.1 0.6

0.995 0.968

0.052 0.019 0.028 0.028

0.305 0.105 0.590

0.0038 0.0038 0.0038

cation fractions was constrained to 1.0. Very weak re¯ections originating from traces of a pyrochlore contaminant were excluded from the re®nement. The ®nal results are summarized in Table 1. Although the oxygen concentration re®ned to a value slightly lower than 1.0, the overall R factors were almost the same for full oxygen occupancy. The temperature factor for Pb was large and corresponds Ê . Such a to an average displacement amplitude of 0.23 A large ªthermalº amplitude suggests that lead is locally displaced from its ideal position but that the correlation length of displacements is short, and this effect is incorporated into the Debye±Waller factor in the Rietveld re®nement. A similar large temperature factor was obtained for oxygen. The observed anisotropy in the temperature factor suggests that oxygen displacements are mostly transverse with respect to the B±O bond. The temperature factors for Ê ) and show no the B cations were small (amplitude ,0.06 A evidence for strong deviations from their ideal positions. The particle size determined from the Lorentzian broadening of the Bragg peak is 4 mm in the as-sintered sample. But the Lorentzian component of the Bragg peak is probably resolution limited, and the real size may be larger. There is signi®cant strain broadening of ,0.13% in the Gaussian pro®le, which most likely originates from the small volume fraction of chemically ordered nano-domains dispersed in the disordered matrix. Re®nements of the neutron TOF diffraction data were in good agreement with those obtained

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W. Dmowski et al. / Journal of Physics and Chemistry of Solids 63 (2002) 15±22

Fig. 5. Observed, calculated X-ray diffraction pro®les and difference curve for the annealed sample as a function of 2u . Inset shows same plot but for smaller y range.

from the X-ray data. While these did yield a smaller estimate of the particle size, 1.3 mm, it may again be resolution limited. For both re®nements there was no evidence for any rhombohedral distortion from cubic symmetry. The large degree of 1:1 ordering in the high temperature annealed sample was re¯ected by the signi®cantly sharper and stronger superlattice peaks in the X-ray patterns, as shown in Fig. 5. The extensive chemical order on the Bsite positions induced by the annealing produces a Pb…b 01=2 b 001=2 †O3 structure with a doubled cubic perovskite  and two discrete B-site positions, cell, space group Fm3m; 0 00 b and b . The experimental and ®nal calculated pro®les for Table 2 Neutron TOF Rietveld re®nement of PMT±PZ. As-sintered sample,  wRp ˆ 5:52%; Rp ˆ 3:92% Pm3m; x

y

z

FRAC

Ê 2] U [A

Pb O

0.5 0.5

0.5 0

0.5 0

1.004 1.01

0.053 0.009 0.026 0.026

b Mg Zr Ta

0 0 0

0 0 0

0 0 0

0.305 0.105 0.590

0.0066 0.0066 0.0066

the X-ray Rietveld re®nement of this sample are plotted in Fig. 5 and summarized in Table 3. During the structure re®nement the relative concentrations of the B-site cations were constrained to the overall bulk stoichiometry and the fraction of Ta on the two cation positions was allowed to vary against the sum of (Mg 1 Zr). The ®nal R factor …Rp ˆ 2:67%† was found to be insensitive to changes of ^0:03 in the ®nal occupancy of Ta. Table 3  X-ray Rietveld re®nement of PMT±PZ. Annealed sample, Fm3m; wRp ˆ 3:46%; Rp ˆ 2:67% x Pb O

b0 Mg Zr Ta b 00 Mg Zr Ta

y

z

Ê 2] Ideal occupancy, Re®ned U [A random site model fractions

0.25 0.25 0.25 1.0 0.252 0 0 1.0

0.957 0.951

0.035 0.0041 0.0195 0.0195

0 0 0

0 0 0

0 0 0

0.6 0.2 0.2

0.492 0.192 0.316

0.0035 0.0035 0.0035

0.5 0.5 0.5

0 0 0

0 0 0

0 0 1.0

0.108 0.008 0.884

0.0016 0.0016 0.0016

W. Dmowski et al. / Journal of Physics and Chemistry of Solids 63 (2002) 15±22 Table 4 Neutron TOF Rietveld re®nement of PMT±PZ. Annealed sample,  wRp ˆ 5:80%; Rp ˆ 3:90% Fm3m;

Pb O

b0 Mg Zr Ta b 00 Mg Zr Ta a

x

y

z

FRAC

Ê 2] U [A

0.25 0.252

0.25 0

0.25 0

0.995 1.003

0.051 0.0059 0.026 0.026

0 0 0

0 0 0

0 0 0

0.492 0.192 0.316

0.01 0.01 0.01

0.5 0.5 0.5

0 0 0

0 0 0

0.108 0.008 0.884

0.0012 0.0012 0.0012

a

a

Fixed from X-ray re®nement.

From the re®nement it is found that the Ta atoms preferentially partition themselves (,90% occupancy) onto the b 00 position in the Pb…b 01=2 b 001=2 †O3 structure (Fig. 1), while the Mg, Zr, and remaining Ta cations are randomly distributed on the b 0 site (see Table 2). The experimental cation occupancies are in very good agreement with those predicted by the ªrandom siteº model for the cation ordering, where the structure of this sample can be represented as Pb{(Mg0.6Zr0.2Ta0.2)1/2(Ta)1/2)}O3. Small differences in the predicted and observed cation distributions suggest that the structure show some degree of anti-site disorder. However, it should be recalled that the annealed sample is comprised of ordered 1:1 domains. Therefore, the re®ned occupancies necessarily include contributions from the locally disordered anti-phase boundaries that separate the different translational variants of the 1:1 random site structure. The size of the domains calculated from the width of the ordering peaks (30 nm) is in excellent agreement with the estimates from the TEM images. The particle size determined from the Lorentzian broadening is about 0.8 mm, and is smaller than that in the as-sintered sample. At the same time the strain contribution to the Gaussian broadening was decreased by a factor of 10, presumably due to the essentially single phase nature of the sample.

4. Analysis and discussion The re®nements clearly contradict the ªspace-chargeº models that have been suggested for this and other similar systems. However, for the sake of completeness we did attempt to re®ne the pro®les of the annealed samples using the space-charge model. In this scenario, albeit already contradicted by the TEM patterns, the sample would be comprised of two phases; one chemically ordered with complete occupation of the b 0 and b 00 sites by Mg and

21

Ta, respectively and the other a Pb(Zr1/4Ta3/4)O3 disordered perovskite matrix. To conserve overall charge neutrality, for this model the volume fractions of the ordered and disordered phases would be 0.6 and 0.4, respectively. As might be expected it was possible to obtain a similar ®nal R-factor using a two-phase model, however, the re®ned volume fraction of the ªorderedº phase was only 0.23, which is too small to maintain overall charge neutrality, yields a bulk composition that is completely inconsistent with the overall stoichiometry, and does not agree with the magnitude of the ordering observed in the dark ®eld TEM images. It is also important to note that the temperature factors for lead and oxygen remain large even in the ordered sample; this again indicates local displacements of these atoms from their average crystallographic sites. This type of displacement has been observed in PMN as well [10]. In contrast the temperature factors of the B-site cations in the ordered sample are again quite small, and do not indicate any significant displacements of the octahedral site cations. As discussed above while the degree of 1:1 order and the size of the chemically ordered domains in the as-sintered and annealed samples of PMT±PZ are very different, their frequency-dependent dielectric behavior are essentially identical. Therefore, for this and other related systems the size of the chemically ordered domains does not seem to be critical in producing the relaxor behavior. It is our opinion that the relaxor ferroelectricity of this class of materials is directly attributable to the random distribution of the cations on the b 0 positions of the ordered 1:1 structure. In mixedmetal perovskites such as Pb(Sc1/2Ta1/2)O3, where the Bsites contain a 1:1 mixture of two different cations, complete 1:1 structural order induces complete chemical order and in turn produces a transformation to normal ferroelectric behavior. For the PMT (and by inference the PMN) based systems where the overall B-site chemistry (1:2) is not compatible with the 1:1 structural order, complete positional or structural order does not produce complete chemical order. The residual randomness on the b 0 sites apparently still frustrates the long range ferroelectric coupling, perhaps through the presence of the associated random electric ®elds and electric ®eld gradients (crystal-®eld), and local rotation of the BO6 octahedra (Table 4). While the intrinsic disorder in the random site structure provides the trigger mechanism for the relaxor behavior of the large domain PMT samples, the small B-site cation displacements indicate that the local polarization has to be produced by displacements of Pb and O atoms. The X-ray and neutron Rietveld re®nements provide support for the local atomic displacement of the Pb and O atoms from the average positions through the large temperature factors in both the as-sintered and annealed samples. More insights into the nature of these displacements have been gined by the pair distribution function (PDF) studies of PMT±PZ and other lead-based, relaxor ferroelectric perovskites [11±14]. In particular, it was found that the Pb ion is off-centered in  covalent the cage of 12 O atoms, and forms short …ù 2:4 A†

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W. Dmowski et al. / Journal of Physics and Chemistry of Solids 63 (2002) 15±22

Pb±O bonds in all Pb containing ferroelectric oxides. This distortion of the oxygen cage is associated with the accommodation of the lone-pair electrons of Pb ions. The offcentering of the Pb ion in the O cage produces a sizable local polarization, while its orientation is controlled by the con®guration of the B-site ions nearby. Apparently the disorder on the b 0 site results in the random local orientation of the polarization of Pb ions.

Acknowledgements

5. Conclusions

[1] M.P. Harmer, J. Chen, P. Peng, H.M. Chan, D.M. Smyth, Ferroelectrics 97 (1989) 263. [2] L.D. Hilton, D.J. Barber, A. Randall, T.R. Shrout, J. Mater. Sci. 25 (1990) 3461. [3] C.A. Randall, A.S. Bhalla, Jpn. J. Appl. Phys. 29 (1990) 327. [4] J. Chen, M. Chan, M. Harmer, J. Am. Ceram. Soc. 72 (1989) 593. [5] M.A. Akbas, P.K. Davies, J. Am. Ceram. Soc. 80 (1997) 2933. [6] S.L. Swartz, T.R. Shrout, Mater. Res. Bull. 17 (1982) 1245. [7] M.A. Akbas, P.K. Davies, J. Mater. Res. 12 (1997) 2617. [8] A.C. Larson, Von Dreele, GSAS Program Manual, NM Los Alamos National Laboratory, USA, unpublished 1990. [9] L.W. Finger, D.E. Cox, A.P. Jephcoat, J. Appl. Crystallogr. 27 (1994) 897. [10] H.D. Rosenfeld, T. Egami, A. Bhalla, IEEE Trans, UFFC 38 (1991) 559. [11] I-Wei Chen, P. Li, Y. Wang, J. Phys. Chem. Solids 57 (1996) 1525. [12] S. Teslic, T. Egami, D. Viehland, J. Phys. Chem. Solids 57 (1996) 1537. [13] T. Egami, S. Teslic, W. Dmowski, D. Viehland, S. Vakhrushev, Ferroelectrics 199 (1997) 103. [14] T. Egami, W. Dmowski, M.K. Akbas, P.K. Davies, AIP Conf. Proc., vol. 436, 1998, p. 1.

The structure of the relaxor ferroelectric compound Pb(Mg0.3Ta0.6Zr0.1)O3 (PMT±PZ) was studied in the assintered as well as annealed states using TEM, X-ray and neutron diffraction. Although the degree of 1:1 chemical ordering and the size of the chemically ordered domain was very different in these two states the relaxor behavior was largely unaffected. Rietveld re®nements show that the high temperature annealing induces extensive B-site ordering, with the b 00 site occupied predominantly by the Ta cations and the b 0 site randomly populated by the Mg, Zr and remaining Ta cations. This occupancy is in agreement with the charge-balanced ªrandom siteº model for the PMN relaxor family. The mixed occupancy of the b 0 position appears to be responsible for maintaining the relaxor behavior in the well ordered, annealed samples. The temperature factors for lead and oxygen are large in the as-sintered and annealed samples indicating that these atoms are displaced from their average, crystallographic positions. These displacements can play a crucial role in determining the local polarization.

This work was supported by the Of®ce of Naval Research through grants N00014-98-10584 (WD and TE), N0001498-1-0583 (PKD) and by the MRSEC program of the National Science Foundation, grant DMR 96-32598 (MKA). References