Cation Ordering and Dielectric Properties of PMN-PSN Relaxors
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Cation Ordering and Dielectric Properties of
PMN-PSN Relaxors
P. K. Davies, L. Farber, M. Valant*, and M. A. Akbas**
Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104
*
Dept. of Ceramics, Jozef Stefan Institute, Ljubljana, Slovenia
**
Currently at Vishay/Vitramon Inc., Monroe, CT 0648-1610, USA
Abstract. Extended thermal annealing treatments were used to modify the B-site cation order in
the (1-x)PMN - (x)PSN perovskite system. Extensive 1:1 ordering could be induced in
compositions with x ≥ 0.1. The substitution of PSN into PMN produces a large increase in the
thermal stability of the 1:1 ordered phase, with the maximum disordering temperature of
~1360°C being observed for x = 0.5. The order-disorder transition temperature for pure PMN
was calculated to be 913°C. The changes in stability could be rationalized using the random site
model for the cation order. The well ordered, large chemical domain ceramics exhibited relaxor
behavior up to x ~ 0.6, for higher values normal ferroelectric behavior was observed.
Alterations in the size of the chemical domain size had no significant effect on the properties of
the lower x compositions, but induced a transition to relaxor behavior for x > ~ 0.6.
INTRODUCTION
The chemistry and stability of the B-site ordering and its relevance to the relaxor
ferroelectric behavior of the Pb(Mg1/3Nb2/3)O3 (PMN) family of perovskites has been
the subject of considerable debate. For several years the observation of a two-phase
assemblage of nano-sized 1:1 ordered domains and disordered perovskite matrix in
PMN was interpreted using the “space charge” model.[1] In this model the ordered
doubled perovskite structure was claimed to be charge imbalanced and to contain a 1:1
ratio of Mg and Nb. However, recent experimental and theoretical studies of tantalate
(Pb(Mg1/3Ta2/3)O3 - PMT) and niobate (PMN) members of the PMN family have
provided convincing support for an alternate charge balanced ordering scheme.[2-11]
For this model, the “random site” structure, the β" position in the 1:1 ordered
Pb(β'1/2β"1/2)O3 phase is occupied solely by the "active" ferroelectric B-site cation (Nb
or Ta), and the β' site by a random distribution of Mg and the remaining Nb/Ta
cations. According to this model the ordered structure of PMT, for example, can be
represented as Pb(Mg2/3Ta1/3)1/2(Ta)1/2O3.
The primary experimental support for the random site model has come from new
investigations of the ordered structures [10,11] and from the observation of extensive
increases in the size of the chemical domains and the degree of order in samples
equilibrated at elevated temperature.[2-6] Additional support has been provided by
calculations of the relative stabilities of different possible B-site ordering schemes.[7-9] The preparation of large chemical domain relaxors has also clarified the
relationship between the crystal chemistry of the B-site ordering and the dielectric
response. In contrast to the behavior of the Pb(Sc1/2Ta1/2)O3 (PST) and
Pb(Sc1/2Nb1/2)O3 (PSN) systems, the large domain PMT systems retained their relaxor
behavior.[2,3,6] This result implied that the chemical randomness (and associated
random fields) on the β' sub-lattice, and not the actual ordered domain size, is critical
in mediating the ferroelectric coupling.
These new experimental studies also revealed that small concentrations of solid
solution additives have a large effect on the conditions required to promote chemical
ordering and domain coarsening in PMN and PMT. For example, the addition of 5-10
mole % PbZrO3 to PMT induced an order of magnitude increase in the size of the
chemical domains after appropriate thermal annealing.[2] Although the crystal
chemistry of niobate and tantalate members of the PMN family is quite similar, the
stability of their chemical order was found to be quite different. In PMT the cation
ordering is stable up to ~1375°C; however, the absence of any increase in the order or
domain size in pure PMN at any accessible temperature was proposed to result from a
much lower order-disorder temperature, perhaps below 950°C.[6] This suggestion
was also supported by recent calculations of the stability of the ordering in these and
other related perovskite systems.[8,9]
In this paper we investigate the cation ordering and properties of solid solutions in
the (1-x)Pb(Mg1/3Nb2/3)O3 - (x)Pb(Sc1/2Nb1/2)O3 (PMN-PSN) system. By examining
the thermal stability of the cation order across the system we provide evidence for an
order-disorder temperature in PMN between 900-950°C. We also demonstrate that the
alterations in the chemistry of the random site position induce a crossover from relaxor
to normal ferroelectric behavior between x = 0.5 and 0.7.
RESULTS AND DISCUSSION
Structure and Stability Of The B-site Order In PMN-PSN.
As we have reported previously [6], experiments aimed toward enhancing the
degree of ordering in pure PMN, by annealing samples at temperatures from ~ 900 to
1350°C, met with no success. In all cases the degree of order (~ ≤ 20 volume % in
small 2-3nm domains) was essentially the same as that observed in the as-sintered
(1225°C, 3 hours) specimens. However, for the (1-x)PMN – (x)PSN solid solution
system the cation order was responsive to thermal treatment for compositions with x ≥
0.1. For most compositions the as-sintered samples exhibited very limited cation
order; in all cases longer-term annealing and/or slow-cooling treatments induced
extensive order. The maximum degree of order was typically attained through a 24-
hour heat treatment at 1250°C followed by a slow cool at 10°/hr to 900°C (full details
will appear elsewhere); see figure 1. The thermal stability of the cation order in each
composition was examined by re-annealing and quenching the well-ordered samples at
temperatures up to 1350°C. The degree of order was monitored by scaling the
intensity of the (1/2,1/2,1/2) supercell reflection to the (001) sub-cell reflection.Figure 1 shows an example of the x-ray data (for x = 0.5) collected from a well-
ordered sample after the initial annealing and slow cooling, and after successive
quenching treatments at different temperatures. The intensity and width of the
supercell peaks reflect the high degree of order and large chemical domain size in the
slow-cooled specimen. These peaks show a continuous weakening and broadening
after at heating higher temperatures and it is apparent that the disordering reaction
shows second order character. By conducting similar experiments on compositions
across the system we were able to delineate the order-disorder boundary. This is
shown in figure 2 where the boundary is plotted for ~ 20% residual order, i.e.
I(1/2,1/2,1/2)/(100)T/I(1/2,1/2,1/2)/(100)maximum = 0.2.
1350/2
1400
disordered
1300/6
1200
T (°C)
1250/24
1000
1:1 ordered
ordered (1250 / 3 / -10 oC/h)
15 17 19 21 23 25
800
2-Theta
0 20 40 60 80 100
mole % PSN
FIGURE 1. X-ray scans for x =0.5 FIGURE 2. Experimental order-disorder boundary
with maximum ordering, and after for the PMN-PSN system
subsequent high T treatments.
From the data in figure 2 it is apparent that the introduction of Sc into PMN induces
a large increase in the thermal stability of the cation order; for 10% PSN the order-
disorder boundary is close to 1150°C. The maximum stability of the ordering occurs
at x = 0.5 where the order-disorder temperature is approximately 1360°C; this is
significantly higher than the reported temperature for the PSN end-member (Tdis =
1210°C). Simple extrapolation of the boundary to pure PMN yields a transition close
to 950°C, a temperature that is apparently too low for the cations to retain any
reasonable kinetic activity.The microstructures of the well-ordered samples with x = 0.1, 0.5, 0.7, and 0.9 are
shown in the dark-field TEM images in figure 3. Although all the samples show high
levels of order, the size of the chemically ordered domains is clearly different in each
sample. The largest ordered regions (~200nm) are observed in x = 0.5, which also has
the highest order-disorder temperature, and the variation in the domain size is similar
to the trend in the ordering temperatures.
A B
200 nm
C D
FIGURE 3. Dark field images collected from well-ordered samples of (1-x)PMN - (x)PSN with: (A) x
= 0.1; (B) x = 0.5; (C) x = 0.7; (D) x = 0.9. Scale marker holds for all figures.
Additional information on the stability of the ordering and its relationship to the
domain coarsening was obtained by utilizing simple thermodynamic models to
describe the cation mixing. The enthalpic stability of the 1:1 ordered Pb(β'1/2β"1/2)O3
phases in the PMN-PSN system, and also of all other ordered mixed-metal
perovskites, is derived from the valence difference of the β' and β" sites and the
difference in the average β'-O and β"-O bond lengths. The substitution of PSN into
PMN (where the effective replacement scheme is xSc3+ = (2x/3)Mg2+ + (x/3)Nb5+ on
the β' site) does not change the average valence of the two ordered positions (which
remain +3 and +5 for all values of x); however, the incorporation of the larger Sc
cations onto the β' position (r(Sc3+) = 0.745Å, [2/3r(Mg2+) + 1/3r(Nb5+)] = 0.693Å)
does increase their size difference. The random distribution of metal cations on the β'
sub-lattice also introduces a significant configurational entropic contribution to thefree energy of the random site structure, which we have previously noted can produce
large changes in bulk stability.[2, 12]]
Using a simplified approach in which the ordering reactions are assumed to be first
order transitions (which they are not), the enthalpy of ordering can be calculated using
classical thermodynamic treatments. The composition of the 1:1 ordered (1-x)PMN-
(x)PSN structure is given by Pb[(Mg(2-2x)/3Nb(1-x)/3Scx]1/2[Nb]1/2O3 and the disordered
perovskite by Pb(Mg(1-x)/3Nb(4-x)/6Scx/2)O3. Therefore, the configurational entropy of
the random site structure (SRS) can be calculated from:
SRS = -R/2[{(2-2x)/3}ln{(2-2x)/3} + {(1-x)/3}ln{(1-x)/3} + (x)ln(x)] (1)
and the entropy of a fully disordered perovskite (Sdis) from:
Sdis= -R[{(1-x)/3}ln{(1-x)/3} + {(4-x)/6}ln{(4-x)/6} + (x/2)ln(x/2] (2)
By using this mixing model to calculate the entropy of ordering (∆Sord = SRS - Sdis),
the enthalpy associated with the cation order (∆Hord) can be determined from the
experimental order-disorder transition temperature (Tdis) by equating ∆Hord and
Tdis∆Sord. The resultant enthalpies, plotted as a function of composition in figure 4,
show an almost linear variation across the system and range from an extrapolated
value of –3137 J/mole for pure PMN to –8547 J/mole for PSN. The predicted
enthalpy for PMN yields an ordering temperature of 913°C.
-2000
-3000
-4000
-5000
∆Hord
-6000
-7000
-8000
-9000
0.0 0.2 0.4 0.6 0.8 1.0
x(PSN)
FIGURE 4. Enthalpy of ordering, ∆Hord (J/mole), calculated from the experimental transition
temperatures using the mixing models described in the text.Even though these calculations rely on a classical first order treatment of the
disordering reactions, they provide useful additional information on the crystal
chemical stability of the system. As mentioned above the incorporation of Sc onto the
random site position would be expected to stabilize the cation order by increasing the
difference in the size of the β' and β" sub-lattices. Although this expectation is
supported by the increase in the enthalpy of ordering for increasing x, if the average
size difference is the only factor affecting ∆Hord the magnitude of the increase is
surprisingly large. However, for the random site type of ordering unfavorable
"excess" contributions to ∆Hord must arise from the mixing of ions with different sizes
and charges on the β' position. This excess contribution will be maximized for the
ordered PMN end-member where the β' position would contain a 2:1 mixture of
cations with the largest size and charge difference (r(Mg2+)= 0.72Å, r(Nb5+) = 0.64Å).
When the increase in the size difference of the β' and β" positions and the reduction in
the charge/size mismatch on the β' sub-lattice are considered, the very large
enhancement in ∆Hord with x seems reasonable. The overall change in the free energy
of the ordered 1:1 structure and the variation in the transition temperature, which is
maximized close to x =0.5, is ultimately a compromise between the composition with
the highest enthalpic stability (PSN) and the least negative entropy of ordering (PMN).
Having established the changes in stability of the 1:1 order we return to the issue of
the variations in domain size highlighted in figure 3. Although extensive ordering
could be induced for compositions with 0.1≤x≤1.0, the domain size in the annealed
samples shows a non-linear variation with x. It is evident that the degree of domain
coarsening parallels the trend in the energetics of the system with the maximum
domain size and stability occurring for x =0.5. An increase in the stability of the
cation order necessarily increases the excess energy of boundaries (APB's) separating
different translational variants of the ordered structure and of the interfaces between
ordered and disordered regions of the sample. Therefore, while kinetics clearly play a
very significant role in permitting these systems to approach an equilibrated state, the
effect of Sc on the domain coarsening can be rationalized in terms of the
thermodynamic stability and crystal chemical ideas proposed above.
Dielectric Properties
The response of the dielectric properties to the alteration in chemistry and order
was examined by collecting weak field data from well-ordered and disordered
compositions of (1-x)PMN-(x)PSN with x ≥ 0.1. Data collected from the ordered
ceramics, with the microstructures shown previously in figure 3, appear in figure 5(A).
For x ≤ 0.5 the frequency dependent behavior of the permittivity spectra are
characteristic of a relaxor type response. For x ≥ 0.7 the dielectric properties are
similar to those of pure PSN and PST, and the domain-coarsened samples exhibit a
normal ferroelectric response. It is important to note that the crossover from relaxor to
normal behavior is not associated with differences in the size of the chemical domains
in the ordered samples. The largest domains are observed for x = 0.5 (figure 3), which
is a relaxor, while x = 0.2 and x = 0.9 have similar domain sizes but very different
dielectric responses. We have also confirmed that the behavior is not affected by Pb
vacancies. This suggests that the alterations in the properties are induced by thechanges in the chemistry of the ordered structure, specifically the composition of the
β' site.
14000 0.2
0.5 0.9
12000
10000
8000
0.7
6000
4000
2000
(A)
0
-80 -60 -40 -20 0 20 40 60 80 100120140
Temperature, ºC
14000 0.9
0.2 0.7
12000
10000
8000
6000
4000
2000 (B)
0
-80 -60 -40 -20 0 20 40 60 80 100120140
Temperature, ºC
FIGURE 5. Real part of the dielectric permittivity as a function of temperature for samples of (1-
x)PMN-(x)PSN. (A) ordered ceramics, (B) disordered ceramics.
The dielectric behavior of the disordered PMN-PSN ceramics is shown in figure
5(B). The properties of compositions with x ≤ 0.5, which exhibit relaxor behavior in
their ordered forms, show very little change with the reduction in the degree of order
and domain size (see figure 5(B) and figure 6). However, for x ≥ 0.7 (normalferroelectrics in their ordered forms) the reduction in domain size promotes a
transition to frequency dependent relaxor behavior (figure 5B). This change is
accompanied by an increase in the magnitude of the permittivity and the temperature
of the permittivity maximum (e.g. ~ 35°C for x = 0.9, figure 6). The behavior of these
PSN-rich samples is similar to that reported previously for pure PMN and PST.
x = 0.2
15000
10000
ordered
5000
0
x = 0.9
10000
ordered
5000
0
-50 0 50 100
FIGURE 6. Comparison of the real part of the permittivity for ordered and disordered samples of (1-
x)PMN-(x)PSN with x= 0.2 (upper plot), and x = 0.9 (lower plot).
The alterations in the dielectric response of the ordered samples highlight the
importance of the composition of the random site position in mediating the
ferroelectric transitions. For low values of x the fields associated with the random
distribution of "active" (Nb) and "inactive" (Mg,Sc) cations on the β' sub-lattice are
effective in frustrating long-range ferroelectric coupling. The dilution of active Nb
cations on this site for higher x enhances the long-range coupling and increases the
temperature of the permittivity maxima. At a critical dilution limit, or critical
correlation length, the concentration of Nb is apparently low enough to permit the
barriers to long-range coupling to be overcome. In the PMN-PSN system this occurs
for x between 0.5 and 0.7 under weak field conditions. Because the coupling lengthsin the ordered PMN-rich samples are so short, reductions in the size of the chemical
domains have no significant effect on the dielectric response. The correlation lengths
are much longer in the ordered PSN-rich samples and the size of the chemical domains
now becomes an important factor. In this case the coupling can be frustrated, and
relaxor behavior induced, by disordering the samples and reducing the size of the
chemically domains below the critical correlation length. We are currently exploring
these ideas in more detail using TEM to examine the relationship between the ordered
domain and the polar domain structures, particularly in the region of relaxor to normal
ferroelectric cross-over.
CONCLUSIONS
Relatively low-level substitutions of PSN (10 mole %) are effective in stabilizing
extensive 1:1 B-site chemical ordering in PMN. Large alterations in the
thermodynamic stability of the cation ordering are observed across the system with the
maximum disordering temperature occurring for 50% substitution. Relaxor behavior
is observed in both ordered and disordered forms of samples with ≤ ~ 60 mole % PSN.
At higher levels of substitution the dielectric response is dependent upon the degree of
order and domain size; disordered samples are relaxors and ordered samples exhibit
normal ferroelectric behavior.
ACKNOWLEDGMENTS
This work has been supported by the Office of Naval Research through grant
N00014-98-1-0583, and by the National Science Foundation through grant DMR 98-
09035 and grant INT 98-11609 (MV). The work also made use of the MRSEC shared
experimental facilities supported by the NSF under grant DMR96-32598.
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