Extended defect intergrowths in Zr1-xTi1+xO4

SOLID STATE

Solid State Ionics 57 (1992) 59-69 North-Holland

IOHICS Extended defect intergrowths in Zrl_xTil +xO4 gr R o y Christoffersen t and Peter K. Davies Department of Materials Science and Engineering, University of Pennsylvania, 3231 Walnut St., Philadelphia, PA 19104-6272, USA Received 19 October 1991 ; accepted for publication 12 November 1991

The low-temperature, Zr/Ti ordered, form of zirconium titanate has been investigated using high-resolution transmission electron microscopy in order to characterize the incommensurate structure of phases with compositions ZrTiO4 to near ZrsTi7024. Electron diffraction reveals that compositions with Zr: Ti between 5 : 7 and 1 : 1 have incommensurate superstructures, and phases close to 1 : 1 are commensurate with an a-axis repeat 2 × that of the disordered structure. The a-doubling in the 1 : 1 phase corresponds to two Zr-rich layers alternated with two Ti-rich octahedral layers. The incommensurate compositions are composed of blocks of the 1 : 1 structure intercalated with blocks of the 3 × commensurate 5 : 7 superstructure. The incommensurate structure can be described based on a quasi-periodic insertion of (100) anti-phase boundaries along a. The boundaries are uniformly distributed in such a way as to produce incommensurate satellite reflections. The main driving force for the ordering transformation appears to be the reduction of the number of nearest-neighbor Zr and Ti within the cation layers. This reduction is accomplished by the formation of domain-like segregations of Zr and Ti within the layers, and by "layer reactions" which prevent the formation of Z r - T i - Z r linkages between layers. The layer reactions assure that the distribution of (100) faults is well-mixed in three dimensions, thereby permitting incommensurate diffraction maxima to occur.

1. Introduction

Dielectric ceramics with low dielectric loss and temperature-stable dielectric constants are important components in microwave detection and communication devices [1,2]. Among the most widely used ceramics for microwave applications are the Zrrich members of the ZrTiO4-ZrsTiTO24 solid solution, which can achieve very desirable dielectric loss properties when "adjusted" with chemical additives such as Sn [ 3 ]. Solely from an empirical standpoint, the effect of these chemical additives on the dielectric properties is now well understood [2,4]. However, another less-studied factor that may significantly affect the dielectric properties of zirconium titanate, particularly the loss, is the set of structural changes associated with site ordering of the Zr and Ti cations below approximately 1200°C. This ordering transformation leads to the development of Paper presented at SSI-8, Lake Louise, Canada, October 2026, 1991. J Author to whom correspondence should be addressed.

commensurate and incommensurate superstructures across the solid solution [ 5,6 ]. These ordered phases have been little studied, either with respect to their detailed structure or their bulk dielectric properties. In particular, the structure of the incommensurate members of the series has gone unsolved, partly because of the small grain size of most samples, and the limitation of powder X-ray or neutron diffraction methods in solving such structures. As a first step to understanding the role of cation ordering in the overall picture of zirconium titanate dielectric performance, we have carried out a structural study of ordered zirconium titanates using highresolution transmission electron microscopy (HRTEM). This method is not limited by grain size, and has in the past proved instrumental in determining the nature of incommensurate structural modulations and related quasi-periodic defects in a variety of systems, including other dielectric ceramics. Our HRTEM observations reveal that, although ordered zirconium titanates show incommensurate diffraction effects, their structures are not modulated in the true sense. Instead they contain

0167-2738/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

R. Christqffersen, P.K. Da vies / D~:[k'ct inletxron'ths in Zr~_, 7)~ +, 04

60

uniformly distributed commensurate structural units or "modules" that produce non-integral diffraction spots by forming an "interface modulated" structure. Although it is well known in metals, this type of incommensurate structures is rare in oxides. Our characterization of this structure in zirconium titanate has given us insight into the details of the atomic rearrangements associated with the Z r / T i ordering, and has led us to the discovery of a commensurate form of ordered ZrTiO4 with a previously unknown oxide structure.

2. Background and previous work

Presently, it is known that all compositions across the ZrTiO4-ZrsTiTO24 solid solution adopt the orthorhombic a-PbO2 structure above 1200°C, with Zr and Ti disordered on a single set of symmetrically equivalent octahedral sites (fig. la) [6,7]. Below 1200°C all compositions undergo a phase transformation characterized by increasing order in the Z r Ti distribution [5,8]. For compositions near Zr-

Ti206 (e.g. ZrsTiTO~4 ), the ordered structure has Zr segregated onto every third octahedral layer along the a-axis, and consequently has an a repeat exactly three times that of the the disordered structure (fig. lb) [ 6 ]. The resulting commensurate, ordered phase has a Z ~ Z vr (Z = Zr, T = Ti ) occupancy sequence along a, with alternating pairs of down-pointing (rT) and up-pointing (TT) Ti-octahedra (fig. lb) [6]. For compositions in the range ZrTiO4 to near ZrsTiT()24 the structure corresponding to partial or complete Zr-Ti order is more problematical, with the nominally-ordered phase exhibiting non-integral satellite reflections [ 5 ]. The satellite positions are consistent with the development of an incommensurate structural modulation along a, but the exact nature of this modulation and its associated Zr-Ti distribution was unknown at the outset of the present study. Because we were interested in attaining a better understanding of how the order-disorder phase transition might affect the dielectric properties of zirconium titanate, an understanding of the structure of this complex phase was seen as an important requirement.

3. Experimental procedures

I f

(

,

a

©:0;

~ aor d @:Zr, Ti; ©: l'i; •:Zr

-,

Fig. 1. [010] projection of zirconium titanate structures: (a) disordered zirconium titanate solid solution with the ct-PbOe structure: (b) the commensurate ordered slructure (a~,,.d=3a,~,~) for composilions close to ZrTi206.

HRTEM observations were carried out on a 1/2 mm-size single crystal and a ceramic powder of zirconium titanate synthesized by McHale and Roth [ 5 ] as part of their phase equilibrium study of the ZrO2TiO2 system. These donated samples were selected in particular because they had thermal histories consistent with the attainment of a m a x i m u m degree of Zr-Ti order. The single crystal was cooled through the order-disorder transition interval (1200l l 0 0 : C ) at 3~C/h during growth from a lithium molybdate molten flux. The ceramic powder was initially synthesized from mixed oxides at 1500°C, slowly cooled through the phase transition at I=C/ h, then subsequently re-annealed at 1100°C for two weeks. Its cell parameters indicate a relatively wellordered state with reference to the data of McHale and Roth [8]. For TEM study the single crystal was crushed between glass slides and the fragments transferred to a holey carbon grid. The crystal was anticipated to have a composition close to ZrTiO4, but quantitative energy-dispersive X-ray analysis of the fragments on

R. Christoffersen, P.K. Davies/Defect intergrowths in Zr t ~Til+.~04

the TEM grid yielded compositions in the approximate range ZrTiO4-Zro.vTil.304, indicating the crystal was strongly zoned. In comparison to the single crystal, the ceramic powder was more homogeneous, with a composition between ZrTiO4 and Zrl.o7Tio.9304, close to the intended ZrYiO4 stoichiometry. It was prepared for TEM study by grinding under acetone and dispersal onto a holey carbon grid. Diffraction and energy-dispersive X-ray analytical work were carried out using a Philips 400T microscope operating at 120 kV. For H R T E M imaging we utilized a JEOL 4000EX 400 kV microscope, combined with multislice image calculation routines developed at Northwestern University.

4. Results The incommensurate form of ordered zirconium titanate is characterized by the presence of satellite reflections at non-integral positions on either side o f the main reflections o f the disordered ct-PbQ-type subcell (fig. 2) [5]. In our samples both first- and second-order satellite were observed, with the second-order satellite being very diffuse or absent in some cases. The positions of any satellite can be given by a reciprocal lattice vector r* according to the relation: r*=hoa*+kob*+loc*+_ maa*,

( 1)

61

where ho, ko and lo are the indices of main reflections from the disordered subcell, and rn is the order of the satellite. The constant a determines a satellite's distance from its corresponding main reflection in terms of a fraction of the length o f a* for the disordered structure. For the commensurate, ordered form with a tripled a-repeat, a = 2 / 3 and the rn= + 1 satellite from the central spot becomes 200ord, and the m = - 1 satellite from 200dis becomes 400orj. (See ref. [9] for a complete discussion of zirconium titanate diffraction patterns.) In the incommensurate ordered structure, a is always less than 2/3 such that satellites move closer to their corresponding main reflection. For the fragments of the flux-grown single crystal in the present study, a was found to be in the approximate range of 0.67 (exactly 3 × commensurate) to 0.61 (fig. 2). The ZrTiO4 powder on the other hand had a = 0 . 5 6 to 0.50. The a = 0 . 5 0 case (exactly 2 × commensurate, fig. 2) was of particular interest in subsequent high-resolution imaging because it represented a commensurate superstructure not previously reported for zirconium titanate. The structure of the samples was imaged down the [010] and [001 ] zones, which are normal to a*, the direction of the incommensurate repeat. Fig. 3 shows an [ 010 ] high-resolution image o f a fragment of the flux-grown single crystal. The diffraction pattern of this fragment exhibits incommensurate satellites along a* with a = 0 . 6 3 . The image contains regions whose overall contrast and sequence of Zr-rich and

Fig. 2. Representative [010] diffraction patterns for ordered zirconium titanates with 3× commensurate (right), incommensurate (middle), and 2 × commensurate (left) structures. Indices correspond to the disordered ~t-PbO2-typesubcell. Arrows indicate satellite spacings equal to 2/3a,]i., 0.61 a~is and 1/2 a,~i~respectively.

62

R ('hristq(fersen. P.K. Davies /De[i, ct intergrowlhs in Zrr _ ,17~+,04

Fig. 3. An [010 ] high-resolution image of a fragment of the flux-grown single crystal taken at Scherzer defocus ( -44 nm ). A calculated image for the commensurale ZrsTiTO24 structure computed for the same defocus and a crystal thickness of 0.5 nm is shown in the inset. Zr-rich ("Z") and Ti-rich ("T") layers are indicated by arrows.

Ti-rich layers show good agreement with the calculated image o f c o m m e n s u r a t e ZrsTiTO24 (fig. 3). There are, however, instances where the c o m m e n surate ZvVZv-r sequence is broken at intervals by extra Zr-rich layers, forming double-layer slabs o f Zr. This produces local regions with a Z Z TT (or ZZv-r) sequence, On the larger scale, regions consisting o f integral n u m b e r s o f Z Z vv (or ZZvT) units are alternated with regions of variable width consisting o f 1/ 2 multiples o f the ZTTZvT repeat unit (fig. 4). Images o f other fragments o f the flux-grown crystal taken in both the [001 ] and [010] orientations c o n f i r m e d that this intercalation of ZTTrZvT and Z Z vv units is representative o f the whole crystal. F u r t h e r details on the arrangement o f the d o u b l e d Zr-layers are visible in [001 ] images (fig. 5). These images show a b r u p t changes in occupancy of cation layers from more Zr-rich to m o r e Ti-rich compositions and vice versa. Typically the switch converts

one Ti layer of a ZZ Tv slab into a Zr layer, and the " n e w " Zr layer is c o m p e n s a t e d for by converting a next-adjacent Zr layer to Ti (figs. 5 and 6a). In this m a n n e r formation of either triple- or single-Ti slabs are prevented and the n u m b e r o f Zr and Ti layers is conserved (fig. 6a). The net effect o f the switch in occupancy is to shift the original Z Z vv unit laterally by 3 / 2 adds. Other more complex occupancy shifts involving inter-conversion o f multiple Z Z vv and ZvVZvT units also occur, and these can produce local changes in c o m p o s i t i o n in a d d i t i o n to simple lateral displacements (fig. 6b). For the ZrTiO4 p o w d e r sample we found the same intercalation of ZTvZvv and Z Z vT structural slabs as for the flux-grown single crystal. However, the proportion o f zTVzvT units was much smaller, with most grain fragments consisting p r e d o m i n a n t l y of ZZ Tv slabs. For the special case where c~=0.5 and the grain is exactly 2 × commensurate, the structures consist

R. Christoffersen, P.K. Davies/Defect intergrowths in Zr ~_xTi l +xO,

63

Fig. 4. An [010 ] high-resolution image showing the extended sequence of single Zr and double Zr layers in a fragment of the flux-grown single crystal. The inset lists the entire structural sequence between points A and B. entirely of ZZ TT units (fig. 7). The 1:1 proportion o f Zr-rich and Ti-rich layers in this structure permits compositions close to ZrTiO4 to attain long-range structural and topochemical order.

5. Discussion 5. I. Structure o f i n c o m m e n s u r a t e ordered Zrl_xTil+x04

We find that ordered zirconium titanates intermediate in composition between ZrTiO4 and ZrsTivO24 are mixtures of two types o f structural regions, one based on 1/2 multiples o f a Z x T Z xx occupancy sequence, and the other based on integer multiples o f a ZZ TT (or ZZxT) sequence. Detailed examination o f the images o f these regions, as well as optical microdiffraction of the T E M negatives, confirm that the regions show no special modulation of their atomic positions or site occupancies. Each region can be described as a commensurate superstructure o f the disordered subcell, the ZZ xv regions corresponding to exact doubling of the disordered cell, and the ZxxZ vx regions to exact tripling.

The fact that intermediate-composition zirconium titanates exhibit incommensurate diffraction phenomena yet consist of mixtures of commensurate structural "modules" is an apparent paradox. However, the two observations can be reconciled based on theories that have been developed to explain similar structures in certain ordered alloy systems [ 10]. These studies have shown that incommensurate diffraction effects can arise when the commensurate units are the result o f periodic or quasi-periodic antiphase boundaries inserted into a parent structure. In the present case, a single unit of ZZVX-type structure can be produced from a z v r z v v - t y p e unit cell by the insertion on (100) of a planar fault boundary with displacement vector R = - l / 3 aord (fig. 8). The boundary is of a non-conservative type, and depending on its position in the cell, it results in the local removal of either two up-pointing or two downpointing Ti-rich octahedral layers (fig. 8). A series of such faults in the appropriate sequence will describe any structure composed of integral numbers of ZZ xT or ZZvx units alternated with 1/2 multiples of the Z x x Z x x unit cell (fig. 8). The concept that periodic or quasi-periodic sequences of structural faults can produce crystals that

64

R. ChristQ[l'ersen, P.K. Davies / D£/'ect inlergrowths in Zr t_ , Ti ~+ ~04

Fig. 5. An [001 ] high-resolution image of a fragment of the flux-grown single crystal. Double Zr layers are indicated. Locations where layers undergo a switch in occupancy are indicated by arrows. display i n c o m m e n s u r a t e satellite reflection was initially d e v e l o p e d in studies o f ordered alloy structures that contained faults with displacements parallel to the boundary (so-called conservative faults) [ 10,1 1 ]. Later the theory was generalized to include structures such as the present one with displacements normal to the b o u n d a r y [12]. In this case, a local change in c o m p o s i t i o n occurs at each fault, and if the faults are periodic, or nearly so, the structure can be described using site occupancies m o d u l a t e d by a square wave with wavelength L [ 13 ]. The m o d u l a tion causes non-integral satellites with spacing 1/L×a~ to occur a r o u n d the main reflections o f the u n m o d u l a t e d ( d i s o r d e r e d ) structure. (The parameter 1 / L is equivalent to c~ in eq. ( 1 ).) It is further possible to relate the m o d u l a t i o n wavelength L to the average spacing between the fault boundaries. Fujiwara [ 10] and Cowley [ 1 1 ] have shown that if an ordered superstructure is periodically faulted, the superlattice reflections caused by

ordering are displaced from their c o m m e n s u r a t e positions. For the present structure the a m o u n t of displacement is given by the relation: d=l/3M,

(2)

where d is the displacement in terms of a fraction of a~,s, M is the average spacing of the faults in multiples o f ad,s, and 3 represents the n u m b e r of faults that must be crossed to regain the same structural position (see fig. 8). F o r the 3 × c o m m e n s u r a t e superstructure o f the ordered 5 : 7 phase, the first-order satellites occur as c o m m e n s u r a t e superstructure reflections with positions given by c~= 1 / L = 2 / 3 . If structural faults with average spacing M are introduced, the satellites' new positions are given by: c~= 1 / L = 2 _ d =

(2M-1)/3M.

(3)

Because each doubled Zr layer occurs at the site of a fault we can count the n u m b e r o f faults in a given high-resolution image and compute an average fault

R. Christoffersen, P.K. Davies/Defect intergrowths in Zr l_ x Ti l +xO# Zr Zr I ]

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-1i 1i Zr 1i "1i Zr Ti 1i

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o G 0 0 ~ id~~ 0 0

Zr 1i 1i Zr Zr

Ti Zr 1i "1i Zr Zr 1~ 1i

a.

b.

Fig. 6. Schematicdiagram of cation layers in zirconiumtitanate projected along the c-axis: (a) typical layer reaction involving lateral shift of double Ti and double Zr slabs but no change in composition; (b) less common formation of new Zr layer and double Zr slab from sequence containingonly single Zr layers. spacing for the imaged region. For the grains in figs. 4 and 5 the values of M determined from the images are 5.1 and 5.7 respectively, with corresponding calculated values for 1 / L ( = o 0 of 0.60 and 0.61. These values show good agreement with the observed values of 0.63 and 0.62 determined from the electron diffraction patterns of these grains. Eqs. (2) and (3) apply in the present case even though the spacing of the doubled Zr layers and the associated structural faults is not particularly periodic. According to Fujiwara [ 10 ], satellites will form at discrete positions determined by the average fault spacing M as long as the range of spacings is relatively narrow. That is, the faults should be "wellmixed" or uniformly distributed throughout the crystal but do not have to be spaced in a perfectly periodic manner. As viewed in [010] high-resolution images the distribution of faults (i.e. of ZZ TT units) is actually quite inhomogenous, but the agreement between the observed and calculated values for ! / L is good nevertheless. We see, however, in [001 ] images (fig. 5) that the faults represented by each ZZ Tx slab undergo a random series of 3/2 adis shifts with depth in the [010] direction. These shifts with rare exceptions do not change the frequency of faults or the average fault spacing, but will serve to assure that the distribution of faults is well-mixed in three

65

dimensions. Because it is a projection of a very thin crystal edge normal to [010], fig. 4 does not reveal the fact that structural shifts homogenize the distribution of faults with depth in the [010] direction and therefore throughout the diffracting volume of the crystal. The ordered superstructure that we observe for ZrTiO4 consists of a commensurate, perfectly periodic ZZ vT sequence of double layers of Zr and Ti. Given that intermediate compositions in the ZrTiO4-ZrsTiTO24 solid solution consists of mixtures of ZZ TT and zTTZTT units, it is logical from a structural and stoichiometric standpoint that ZrTiO4 should consist entirely of ZZ TT. According to the scheme of structural faulting outlined above, the ZrTiO4 ordered phase can be described as a faulted derivative of the zTTZTT structure, with a perfectly regular fault spacing of M = 2. The ordered structure that we have determined for ordered ZrTiO4 has not been previously proposed for zirconium titanate or other compounds to our knowledge. 5.2. Implications f o r Z r - T i ordering m e c h a n i s m

The detailed features we observe in [010] and [001 ] high-resolution images of ordered zirconium titanate can provide some insight into the factors that control the rearrangement of Zr and Ti during the ordering process. We have already noted the fact that in [001 ] images we observe abrupt switches in occupancy of the Zr/Ti cation layers. These features indicate that, rather than consisting entirely of Zr or Ti, the (100) layers of cations in the ordered phase consist of domain-like segregations of Zr and Ti. Such segregations suggest that the driving force for ordering is primarily related to the undesirability of having Zr and Ti coordination polyhedra next to one another in the same cation layer. This intralayer Zr-Ti repulsion makes sense given the fact that Zr is larger and prefers a distorted cubic coordination site, whereas the smaller Ti prefers octahedral coordination. From an analysis of the frequency with which the cation layers switch occupancy in [001 ] images we estimate that the Zr and Ti "domains" within a given layer have widths in the b-axis direction of between 5 to 20 nm. In [010] images, switches are much less common, and layers retain the same occupancy along

66

R. Christo(['ersen P.K. D a v i e s / Defect i n t e r g r o w t h s in Z r l _ ~7"i ~+ , 0 4

Fig. 7. An [010] image of a grain from the ZrTiO4 powder sample. The diffraction pattern (insel) has o~=0.50, corresponding to a doubled a-axis repeat. the c-axis for distances o f a least 50 nm. The dom a i n s are thus not equidimensional, and are longer along c than along b (fig. 9). As shown in fig. 9, a possible structural reason for this shape is that it shortens the d o m a i n ' s b o u n d a r y where it cuts across the octahedral chains p e r p e n d i c u l a r to c, thereby

m i n i m i z i n g the n u m b e r o f shared edges between Zr and Ti c o o r d i n a t i o n polyhedra. Perpendicular to b, the o c t a h e d r a l chains do not share edges with one another within the same layer, so the b o u n d a r y can be longer p e r p e n d i c u l a r to this axis. It is unclear whether the d e v e l o p m e n t of the Z r

67

R. Christoffersen, P.K. D a v i e s / D e f e c t intergrowths in Z r l_ x Ti l +~04

mm'~ .....

' 1/3 aor d

, 1/3 aord

'

I

=

I

i ,

displacement =

~,

0 aor d

M

•

adi s

-1/3 aord

-2/3 aor d

0 aor d

~-

Fig. 8. Schematic [010 ] projection of the 3 × commensurate zirconium titanate structure showing planar anti-phase boundaries (structural faults) with displacement of l/3 aord. A double Zr slab (shaded) formed at a fault boundary is bounded by double Ti slabs that point up (upper left diagrams) or down (upper right diagrams) depending on the boundary's placement in the unfaulted unit cell. The bottom diagram illustrates the sequence of Zr and Ti layers that can result from faults with different spacings. and Ti domains during the ordering transformation proceeded simply by redistributing the existing Zr and Ti cation on each layer, or whether exchange of Zr and Ti between the layers was also involved. It would seem that formation of the domains would not r e q u i r e interlayer cation exchange. Indeed, diffusional anisotropy in the structure may have been a deciding factor in the final cation arrangement by making it easier to attain intralayer Z r - T i avoidance through atomic jumps within the octahedral layers, rather than between them. In addition to strong Z r - T i avoidance within the (100) cation layers. There is evidence for a variety o f interactions and correlations across the cation layers. As we have previously noted, in [001] images we consistently observe that switches in occupancy are strongly correlated between different layers. As illustrated in fig. 6a, the "loss" of a Ti layer in the sequence Z Z T T Z is compensated for by converting the next-adjacent Zr layer to Ti, giving the sequence ZTTZZ. This particular layer-conversion "reaction", involving a Ti double layer with a double layer of Zr on one side and a single layer of Zr on the other, is the most c o m m o n one observed. More rarely, formation of double Zr layers can occur from sequences

containing only single Zr layers (fig. 6b). In this case the formation of a "new" double Zr slab involves the loss of one Ti layer and the net gain of one Zr layer. Such a reaction is not compositionally conservative, and reflects some degree of local inhomogeneity in the crystal. From a crystal chemical standpoint the main controlling factor in the above reactions is the avoidance of single layers of Ti sandwiched between any combination of double or single layers of Zr. This avoidance is again very likely associated with the very different coordination geometries of the Zr and Ti layers. In particular, as ordering proceeds from the disordered ct-PbO2-type structure, a Ti-rich layer must "tolerate" distortion o f one o f its adjacent oxygen layers in order to accommodate the eight-fold coordination of the adjacent Zr layer. The Ti layer is able to do this more easily if the unfavorable oxygen shifts caused by the Zr are compensated for by having a row o f Ti on the layer's other side. This "compensation" is lost, and the overall distortion greatly increased, if Zr layers are present on both sides. The ZTZ sequence is therefore avoided in the ordered structure, including at sites where layer "reactions" occur.

68

R. Christoffersen, P.K. Davies / Defi'et intergrowths in Zr ~ , 17~+,O4

Fig. 9. Projection on (100) of calion layer in zirconium titanate. Chains of edge-sharing octahedra run parallel to the c-axis. The domain of Zr sites (shaded octahedra ) is surrounded by Ti (unshaded octahedra ). 5.3. I m p l i c a t i o n s f o r dielectric p r o p e r t i e s

In efforts to o p t i m i z e the properties o f z i r c o n i u m titanate dielectric ceramics, the role o f Z r / T i ordering has received scant attention in comparison to that o f chemical additives [ 2 - 4 ] . Except for a recent exploratory study [4], the effect of ordering on the dielectric constant Er, and the m i c r o w a v e loss quality Q, r e m a i n s u n d e t e r m i n e d . In m i c r o w a v e applications Q is o f principal concern, because it determines

the quality of the ceramic as a resonator and filter, and it shows much greater sensitivity to changes in microstructure and c o m p o s i t i o n c o m p a r e d to er. By analogy with other systems, and using the structural information o b t a i n e d from our H R T E M observations, we can anticipate some of the possible effects o f ordering on Q in the ZrTiO4-ZrsTiTO24 system. F o r the two e n d - m e m b e r compositions, the ordered phases develop c o m m e n s u r a t e superstructures with a high-degree of long-range cationic order.

R. Christoffersen, P.K. Davies/Defect intergrowths in Zrl _,Ti ~+~04

Similarly, long-range order occurs in compositions between these two extremes, though in this case this leads to incommensurate repeats. Regardless of whether the ordered superstructures are commensurate or incommensurate, the structure permits the cations to order onto their own domains and adopt their "equilibrium" bond lengths and a more suitable site coordination. Because Zr and Ti have significantly different ionic radii, this ordering will lead to a reduction in the lattice strain. An analogous consequence of ordering occurs in the dielectric perovskite Ba(Zn~/3Ta2/3)O3, in which Zn and Ta adopt an ordered configuration with the larger Zn on every third octahedral layer [14]. Considerable data for this system show that Zn/Ta ordering increases Q (reduces loss ) by as much as a factor of 10 [ 15,16 ]. The decrease in loss is considered to be partly the result of the decrease in lattice strain associated with segregating the two cations [ 15 ]. Similarly, we would predict that ordering in the zirconium titanate system will lead to significant reductions in the dielectric loss. Although most previous loss determinations have been conducted on ceramics with disordered cation arrangements, limited data by Hirano [ 4 ] for ZrTiO4 support this prediction and show an increase in Q with at least a partial increase in Zr/Ti order. To further clarify the effects of structural order upon the microwave loss characteristics, dielectric measurements are currently being made on a complete series of fully ordered and disordered ceramics.

6. Conclusions

The ordered structure of ZrTiO4 is related to that of Z r s T i 7 0 2 4 but instead has t w o intervening layers of Zr in eight-fold coordination, separating two Tirich octahedral layers. Intermediate compositions have an ordered structure consisting of slabs of the 1 : 1 and 5:7 structure alternated along the a-axis. Even though the width of these slabs is variable, discrete non-integral diffraction maxima occur in the a* direction. By describing the intermediate compositions as structurally faulted derivatives of the 5 : 7 structure, the non-integral satellites can be explained using the established diffraction theory for structures with quasi-periodic structural faults. Under this theory it is more important that the faults (each

69

equivalent to a single unit cell of l : 1 structure) are well-mixed over the volume of the crystal, rather than having separations that are perfectly ordered. The criterion of uniform distribution is met in the present case due to the "mixing" effect of lateral shifts of the boundary positions with depth along the b-axis.

Acknowledgement

The authors wish to thank R.S. Roth and A. McHale for the samples that were examined in this study; D. Luzzi for help with the NUMIS image calculation routines, and D. Ricketts-Foot for technical support. This work was supported by the National Science Foundation through Grant DMR 88-19027. We also acknowledge the National Science Foundation, MRL program, Grant DMR 88-19885, for support of the Electron Microscopy Facility.

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