J. Phys. Chem. 1990, 94, 1127-1 134
1127
Pressure Tuning of Interatomic Interactions in Solids: Glassy Properties of Ferroelectrics and Dielectricst G.A. Samara Sandia National Laboratories, Albuquerque, New Mexico 871 85 (Received: June 13, 1989)
Frustration-induced disorder and impurity-induced disorder can lead to the formation of a glassy state in ferroelectric (FE) and antiferroelectric (AFE) crystals. This paper compares the glassy properties of a mixed hydrogen-bonded FE and AFE crystal [Rb1-,(NH4),H2PO4]which exhibits frustration-induced disorder with those of a perovskite with dilute substitutional impurities (KTal,Nb,03 for x 5 0.02). The emphasis is on the important role of pressure in delicately tuning interatomic interactions and in understanding the short-range interactions and correlations responsible for the glassy state. It will be shown that modest pressures can suppress this state in both systems and that the manner in which the dynamic glass transition temperature vanishes with increasing pressure is indicative of the nonequilibrium nature of the glass transition. The properties of these novel glassy systems are contrasted with those of more conventional orientational glasses in, e.g., inorganic crystalline solids [KBr,,(CN),] and organic polymers (poly(viny1idenefluoride)), and it is shown that the pressure effects on the two classes are qualitatively different. A novel pressure-induced crossover from long-range FE order to glassy behavior is also discussed.
I. Introduction There has been much recent interest in the dynamic and static properties of systems in which randomly competing interactions cause the formation of a glassy state at low temperatures. Indeed the study of such systems has been one of the more active areas of statistical physics and physical chemistry for the past two decades. Much of this work has dealt with disordered magnetic systems, e.g., systems containing mixtures of competing ferromagnetic/antiferromagnetic interactions which lead to the formation of spin glass state.' A large body of work has also dealt with structural glass systems. In discussing the properties of structural glass systems, we need to distinguish between amorphous solids-the so-called topological glasses which have no crystallographic long-range order, e.g., amorphous silica and many polymersand structurally site-disordered crystalline solids (or orientational glasses). Our interest in this paper is in the latter class and, specifically, with electric dipolar and quadrupolar glasses such as Rbl-,(NH4),H2P04, KBrl-,(CN),, and KTal-,Nb,03. On cooling, these systems exhibit a slowing down of the relaxation of their orientational degrees of freedom, ultimately resulting in a collectively frozen-in, frustrated multipole state with no long-range orientational order. A universal signature of such disordered solids is a relatively sharp, frequency-dependent peak in the temperature-dependent susceptibility. The peak defines a dynamic freezing, or glass transition, temperature. Despite the fairly general character of the phenomena associated with the orientational freezing process, many rather fundamental questions have arisen about the physics involved.' Among these questions are the following: What is the nature of the transition? What are the consequences of the failure of the system to reach thermal equilibrium? Detailed theoretical understanding of these and other questions has proven difficult because of the random and, often, frustrated nature of the interactions. Earlier high-pressure studies have led us to a much better understanding of the nature of the competing inter- and intramolecular interactions that are responsible for the establishment of long-range order and the onset of many structural phase transitions in solids.24 These transitions include displacive, order-disorder, cooperative Jahn-Teller, and coupled orderdisorder/displacive transitions. Pressure turns out to be an excellent, and often the only, variable for continuously tuning the This paper is dedicated to Prof. Harry G. Drickamer on the occasion of his 70th birthday. His leadership, dedication, and counsel have been inspirational. He introduced the concept of pressure tuning in the study of competing interactions in solids. This work represents but one example of the power of this concept.
0022-3654/90/2094-1121$02.50/0
delicate balance between the competing interactions involved. In a broadly similar fashion, we expect pressure to also modify the interactions responsible for the short-range order and correlations in orientational glasses and to thereby provide new insights into the formation and properties of the glassy state. This consideration was the primary motivation for the work to be discussed in this paper. We have investigated the effects of hydrostatic pressure on the glassy behavior of a number of ferroelectrics and dielectrics. In what follows we compare and contrast the results on different materials. Included are the following: (1) Glassy properties resulting from frustration-induced disorder in mixed ferroelectric (FE)-antiferroelectric (AFE) crystals. The prototypical example here is the proton glass Rb1,(NH4),H2PO4 and its deuterated analogue. (2) Glassy properties resulting from impurity-induced disorder in ferroelectrics. Our example in this case is the oxide glass KTal-,Nb,03 in the dilute ( x I0.02) limit. The behavior of this system appears to have provided the first experimental manifestation of a novel pressure-induced crossover from FE order to dipolar glass behavior. As will become evident, several features of the pressure results on the above two classes of glassy behavior are qualitatively similar. However, we emphasize that the physics of the two cases are quite different. To further emphasize this point and highlight the unique features of these two classes, we shall discuss the effects of pressure on two other systems, namely, (3) the glassy properties of orientational disorder in crystalline KBrl,(CN), and (4) the glassy properties of orientational disorder in the amorphous phase of the semicrystalline polymer poly(vinylidene fluoride) (PVDF). It will be shown that the effects of pressure on these two latter systems are qualitatively different from those on the first two. The paper will conclude by a brief assessment and remarks. 11. Glassy Properties of Ferroelectric/Antiferroelectric
Systems A . Frustration-Induced Disorder: Proton Glass Rb,_,(N&),H2Po4. The Rbl,(NH4),H2P04 (or RADP) system has become the most thoroughly investigated and, perhaps, the most understood system among the multipolar g l a s ~ e s . ~Its. ~dynamical (1) See, e.g.: Binder, K.; Young, A. P. Reu. Mod. Phys. 1987, 58, 801, and references therein. (2) Samara, G. A.; Peercy, P. S. In Solid State Physics; Ehrenreich, H., Seitz, F., Turnbull, D., Eds.; Academic Press: New York, 1981; Vol. 36, p 1, and references therein. (3) Samara, G. A. In Physics of Solids under High Pressure; Schilling, J. S., Shelton, R. N., Eds.; North-Holland Publishing Co.: New York, 1981; p 91. (4) Samara, G. A. Ferroelectrics 1987, 71, 161.
0 1990 American Chemical Society
Samara
I128 The Journal of Physical Chemistry, Vol. 94, No. 3, 1990 I
I Rb1.X ( N H 4 ) % H z P O 4
:Q
W
i !
\
Vogel-Fulcher Temp
---J----
I
i 0
8 16 TEMPERATURE
24
(K) Figure 2. Temperature dependences of the imaginary (e/) part of the a-axis dielectric constant of RADP ( x = 0.5) measured at different frequencies and hydrostatic pressures. The 1, 2, 3, and 4 designators on the curves correspond to the frequencies 5 X IO4, 1 X lo5,5 X lo5,and 1 X lo6 Hz, respectively. response has revealed the full evolution of the freezing dynamics over an extremely large range (- 17 order of magnitude) of f r e q u e n ~ y . ~This is a much broader range than is possible for metallic spin glasses, and, consequently, the evolution of the glassy state in RADP is now better established than in any glassy system. The phase diagram for RADP is shown in Figure 1. The system combines a number of very attractive features that make it ideal for studying frustration-induced disorder and the freezing of this disorder. Important among these features are the following. The pure end members, RbH2P04(RDP) and NH4H2P04(ADP), are well-investigated and understood.* They transform on cooling to ordered FE and AFE phases, respectively. A dominant feature of the crystal structure of each compound is the 0-H-0 hydrogen bond which connects adjacent tetrahedral PO4groups which are the main building blocks. The phase transitions are driven by the ordering of protons in double-well potentials along the 0-H-0 bonds. In the high-temperature phases the protons are thermally disordered, but they order in a preferential way in the low-temperature phases leading to a FE state in RDP and to an AFE state in ADP. Both RDP and ADP have the same room-temperature crystal structure with nearly the same lattice parameters. This good lattice match makes it possible to grow high-quality, strain-free mixed RADP single crystals over the whole composition range. These crystals appear to be random mixtures of the two constituents. For RADP compositions with 0 Ix 5 0.2, ferroelectric order is obtained, whereas for 0.8 5 x I1.O, the crystals are antiferr~electric.~ For in-between compositions, i.e, 0.2 5 x 5 0.8, there is no evidence for long-range order but convincing evidence exists for low-temperature short-range correlations and the formation of a proton glass states,6associated with the freezing of protonic motion in the 0-H--0 hydrogen bonds. The suppression of long-range order in this composition range is a consequence of the frustration of the system caused by the random substitutions of NH4 ions for Rb ions (or vice versa) and the resulting competition between two kinds of order-disorder configurations of the protons in their bonds. Specifically, the Rb ion tries to achieve FE order while the NH4 ion tries to achieve AFE order. The first evidence of glassy behavior in RADP came from Courtens’ dielectric constant measurements5 which revealed temperature-induced anomalies and strong frequency dispersion in the real (e’) and imaginary (e”) parts of the dielectric function. Some of our atmospheric-pressure ( 1 -bar) results on an RADP crystal with x = 0.5 (Figure 2 ) are typical of the response.’ As (5) Courtens, E.A. Jpn. J . Appl. Phys. 1985,24 (Suppl. 24-2), 70. and references therein. Courtens, E. A. J . Phys. (Paris), Lett. 1982, 43, L199; Phys. Reo. Lett. 1984, 52, 69. Courtens, E.A,; Rosenbaum, T. F.; Nagler, S. E.; Horn,P.M . Phys. Rev. 1984, 829, 515. (6) Terauchi, H.Jpn. J . Appl. Phys. 1985, 24 (Suppl. 24-2). 75, and references therein. Iida, A,; Terauchi, H. J . Phys. Soc. Jpn. 1983, 52,4044. Terauchi, H . Ferroelectrics 1985, 64, 87.
I x IO6 Hz
5 x lo5 HZ Ix IO~HZ
0
1
2
3
5
1 0 ~ ~ 2
4
5
6
PRESSURE (kbar)
Figure 3. Temperature-pressure phase diagram for an RADP crystal showing the pressure dependence of the dynamic glass transition temperature, Tg,and the expected vanishing of the glass phase above - 5 kbar.
a function of temperature (T), E” exhibits a well-defined peak which shifts to higher 7”s with increasing frequency. These features are characteristic of glassy behavior. Analysis of such results at 1 bar reveals that the peak temperature, Tmax,which defines the dynamic glass transition temperature, Tg,increases nearly linearly with the logarithm of the measuring frequency, and there is a broad distribution of relaxation times, 7. The dielectric data thus show that there is a large slowing down of the relaxation with decreasing T. However, these and similar dielectric data extend over a relatively small range of frequency, and the question had remained as to whether or not the system exhibits glassy behavior over a broad frequency range and a finite ‘static” freezing temperature. Fortunately, this question has been answered in the affirmative for RADP. The key is the fact that the dielectric polarization is the fundamental excitation mode in RADP, and this mode is active in Raman and Brillouin scattering, in addition to dielectric susceptibility. This important feature has made it possible to use all three techniques to follow the full evolution of the freezing dynamics over 17 decades of frequency.
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(7) Samara, G. A,; Terauchi, H. Phys. Reu. Lett. 1987, 59, 347, and references therein.
The Journal of Physical Chemistry, Vol. 94, No. 3, 1990 1129
Glassy Properties of Ferroelectrics and Dielectrics Results at 1 bar show5 that the T dependence of the cutoff (or lowest) frequency, v,, of the distribution of relaxation times is very well represented over this large frequency range by the phenomenological Vogel-Fulcher equation vc
- To)]
= 1 / ~ , = uo exp[-EJ(T
180
I
I
l
I6 0
l
I
i
where R is the tunneling frequency which describes the intrabond proton motion and Jij is the dipolar proton-proton interaction term whose sign determines whether a FE or AFE state is achieved on ordering. Solution of this Hamiltonian for the transition temperature, T,, yields
4 R / J = tanh (R/kTc) (3) This equation has a real solution for T, only if ( 4 R l J ) < 1. It is thus seen that T, is determined by the competition between an ordering dipolar field represented by J and a disordering transverse tunneling field represented by R. At 1 bar the dipolar field dominates, the ratio ( 4 R l J ) < 1, and there is a finite T,. The decrease of T, with pressure can be understood in terms of an increase in tunneling frequency R and/or a decrease in the dipolar interaction J . Both effects are expected on physical grounds2v4 and are observed. On this model, it is seen that at sufficiently high pressure the condition ( 4 R / J ) L 1 should obtain and the FE (or AFE) state should vanish. This prediction is in agreement with the experimental o b ~ e r v a t i o n . ~A*random-bond ~ version of the above king model (eq 2) has been used to describe the glass transition in RADP."l0 In this case the dipolar interaction terms (8) Blinc, R.; Ailion, D. C.; Gunther, B.; Zumer, S . Phys. Rev. Lerr. 1986, 57, 2826, and references therein. (9) Tadic, B.; Pirc, R.; Blinc, R. Phys. Rev. 1988, 837, 679.
I
Rbl-x(NH4)x HZP04
i
I-X.I.0 2-x=o
(1)
Here vo is an attempt frequency, E, is an activation energy in units of temperature, and To is the Vogel-Fulcher temperature where all relaxation times diverge, Le., the "static" glass freezing temperature. Fit of the I-bar data to this expression yield5 vo = 3.5 X 10l2 Hz, E, = 268 K, and To = 8.7 K for an x = 0.35 sample. The strong influence of pressure on the dielectric response of RADP2 is clearly seen in Figure 2. With increasing pressure there is a large displacement of the t/(7') anomaly to lower T, and ultimately this anomaly vanishes.' Figure 3 shows T,, from the e"( r ) data at different frequencies as a function of pressure. At each frequency the decrease of T,,, with pressure is linear, and the dispersion of T,,, with frequency decreases markedly with pressure. We take T,,, as a measure of Tg. Extrapolating the linear T,,,(P) responses to higher pressures suggests that the proton glass phase should vanish by -5 kbar. In support of this suggestion, the 6.0-kbar dielectric data show no anomaly in either t(II(T) or e / ( r ) down to -4 K and no hint of any impending anomalies at lower T (Figure 2). In fact, at 6 kbar the dielectric loss, and thereby e / , becomes extremely small and frequency independent, as shown in Figure 2. We take these results to strongly indicate that the proton glass phase has completely vanished at this pressure. RADP is analogous to magnetic spin systems in that the elementary excitation involves the motion of the proton between two equilibrium sites (S' = f l ) along the 0-H-0 hydrogen bond under ice-rule-like constraints.8 This motion and its freezing dynamics are determined to a large extent by the details of the double-well potential which describes the two equilibrium sites along the O-He-0 bond. Pressure can be expected to significantly modify this potential and thereby the glassy behavior of the system. At the local level, the situation here is quite analogous to that for the end members RDP and ADP whose transitions are also determined by the nature of the double-well potential along the O-H.-O bond.2 Recognizing that the proton can tunnel between the two potential minima, the essential physics of the phase transitions in RDP and ADP can be described in terms of an Ising system in a transverse tunneling field.2v4 The Hamiltonian for such a system is
I
/
3 - x= 0.80
4-Xx0.48 (72%0) 5 - X.0.50
e . ~I . W-81
\-
0 0
4
8
\ I
I
I
12 16 20 24 PRESSURE (kber)
I
28
\ I \
32
36
Figure 4. Comparison of the pressure dependences of the dynamic glass ( Tg), ferroelectric ( Tc),and antiferroelectric (T,) transition temperatures for several members of the RADP family.
Ji/ are taken as random variables with, e.g., a Gaussian probability distribution. A further comment on the results will be given later. Our high-pressure dielectric data do not extend over a broad enough frequency range to allow a meaningful fit to the VogelFulcher equation. Nevertheless, it is possible to make some qualitative remarks about the pressure dependences of E, and T,. In the high-T phase the protons are disordered in their potential wells, leading to an effectively symmetric 0-H-0 bond. On cooling at 1 bar, there is slowing down of protonic motion, and ultimately the proton freezes in one or the other of the potential minima leading to an elongated asymmetric 0-H-0 bond. To support this picture, we note that there is an expansion of the unit-cell volume of RADP on proton f r e e ~ i n g . ~More , ~ generally, it is known that in crystals of the KH2P04 (KDP) family, asymmetric H bonds are longer than symmetric ones, and there is lattice expansion on proton ordering." The energy barrier between the two potential minima relates to the activation energy E,. Pressure opposes the expansion of the unit-cell volume and should thereby suppress proton freezing, Le., lower Tg and To. Alternatively, pressure can be expected to reduce the H-bond length and favor a more symmetric bond. The shorter the bond, the lower the energy barrier and thereby E,. The consequence of this barrier lowering is a lower Tgand To. For sufficiently high pressure we expect that the H bond will become sufficiently short and effectively symmetric, even at the lowest temperatures. In such a circumstance the energy barrier becomes vanishingly small, and there will be no proton freezing; Le., the glassy state vanishes. This is of course what is observed experimentally (Figure 2). It should be emphasized that while the above qualitative picture contains the essential physics of the triggering mechanism for the transition, it is certainly not complete, since it ignores protonproton correlations and the coupling of the proton motion to the lattice. The cited expansion of the lattice observed on proton freezing illustrates the strength of the latter coupling. Coupling and correlations, whether long or short range, are known to be essential for a detailed understanding of the properties of H-bonded systems,2 including the RADP g l a ~ s e s . ~ ~ , ' ~ Figure 4 compares the pressure-induced suppression of the glassy state in RADP with the suppression of the FE state in RbH2PO4l4and the AFE state in NH4H2PO4.I5Also shown are results for an x = 0.8 RADP crystal which exhibits an AFE transition.' The data show an important difference between the (10) Dobrosavljevic, V.;Stratt, R. M. Phys. Rev. 1987, E36, 8484. (11) Cook, W.R.,Jr. J . Appl. Phys. 1967, 38, 1637. (12) Matsushita, E.;Matsubara, T. J . Phys. SOC.Jpn. 1985, 54, 1161. (13) Prelovsek, P.; Blinc, R. J . Phys. 1982, CIS,L985. (14) Peercy, P. S.;Samara, G. A. Phys. Rev. 1973, E8, 2033. (15) Samara, G.A. Phys. Rev. Lerr. 1971, 27, 103.
1130 The Journal of Physical Chemistry, Vol. 94, No. 3, 1990
glassy “transitions” and the FE and AFE transitions which we now discuss. For RDP and ADP (curves 2 and 1 in Figure 4), the magnitude of the slope dT,,N/dP increases with pressure at high pressure with strong indication that the FE transition temperature (T,) and the AFE transition temperature (TN) vanish with infinite slope, Le., dT,,,/dP -a as T,,? 0 K. This behavior, which is in agreement with the prediction of certain models,2 is also dictated by the third law of thermodynamics for an equilibrium first- or second-order phase transition.’ The results on the x = 0.8 RADP sample possibly suggest a similar behavior, but additional data near 8 kbar are needed to confirm this feature. The response of the x = 0.5 RADP sample, on the other hand, is qualitatively different. In this case T , which is frequency dependent, decreases linearly with pressure cfown to -5 K (Figure 4) with no hint of any impending increase in the magnitude of dTg/dP at lower 7%. We cannot of course rule out the possibility of such an increase below 5 K, but experience with other RADP crystals ( x = 0,0.8, and 1.0 in Figure 4) and other crystal^^,^ suggests that this is unlikely. We believe that the different response of the x = 0.5 RADP sample is most likely evidence for the nonequilibrium nature of the transition in this material. Finally, we note that there is a large hydrogen isotope effect not only on TBbut also on its pressure derivative. Here we wish to compare the responses of an x = 0.5 RADP sample with one having x = 0.48 and in which 72% of the protons are replaced by deuterons. These x = 0.5 and x = 0.48 (72%D) samples afford a particularly good comparison. The onset of proton (or deuteron) freezing in the glass-forming range of RADP is weakly dependent of composition (see Figure l ) , so that the small difference in composition between the x = 0.5 and x = 0.48 samples is essentially insignificant. Figure 4 shows the pressure dependence of Tg for both samples. The differences in Tgand dT,/dP between the x = 0.5 and x = 0.48 (72% D) samples, namely, the increase in Tg at lo5 Hz from 17.4 to 56.5 K and the decrease in the magnitude of dT,/dP from -3.6 to -2.0 K/kbar on deuteration, are thus manifestations of hydrogen isotope effects. These effects can be qualitatively understood in terms of proton tunneling in the same way as similar effects for FE and AFE transition^.^*^ Specifically, the higher T, and smaller dT,/dP for the deuterated glass are due to the fact that the deuteron sits deeper in its potential wells than does the proton (lower zero-point energy) and has a much lower probability for tunneling between the two potential wells along the 0-D--0 bond. The RADP results thus again emphasize the important role of the hydrogen-bond potential in triggering the ordering process in KDP-type materials regardless of whether the ordering is long or short range. These results also emphasize the unique role of pressure in delicately and continuously tuning the strength of the intermolecular interactions that are responsible for the ordering process. In summary, our pressure studies of the proton-glass state in RADP have led to the following conclusions: (1) The dynamic glass transition temperature, Tg, decreases with pressure. (2) There is complete suppression of the glassy phase at a modest pressure. (3) The results indicate that Tg 0 K with a finite slope dT,/dP. (4) There is a large hydrogen isotope effect on both Tg and its pressure derivative. Conclusions 1, 2, and 4 are qualitatively similar to earlier results on RDP and ADP and can be understood in terms of the physics of the tunneling model. These results emphasize the point that it is the nature of the hydrogen-bond potential which determines the ordering in these materials regardless of whether the ordering is long or short range. Conclusion 3 is qualitatively different from observations on RDP and ADP where it is found that dTF,N/dP -m as Tc,N 0 K. We believe that the different behavior of RADP emphasizes the nonequilibrium nature of the glass transition. The above results on RADP have stimulated a recent theoretical study by Tadic et al.9 These authors use a random-bond version of the Ising model in a transverse field. The Hamiltonian is that in eq 2 but with one difference: the coupling constants Jij.are now taken to be random variables with a Gaussian probability distribution. The results are in general agreement with our exper-
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-
-
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Samara iments. Earlier, Dobrosavljevic and Stratt’O employed the same transverse Ising spin glass model as used by Tadic et al., but they included more explicitly the influence of quantum fluctuations (or tunneling), Their results show that quantum fluctuations suppress the glass transition as they do the FE and AFE transitions of the end members. The results also reveal that the glass phase is more susceptible to destruction by tunneling (or pressure) than are the ordered phases. These results are in general accord with our experimental findings. B. Impurity-Induced Disorder: Oxide Glass KTa,-,Nb,03. There has been much theoretical and experimental interest in the study of the behavior of isolated impurities in crystals with soft phonon modes.16-19 Of interest have been such issues as the influence of impurities on critical phenomena, the existence of local modes, and the possibility that coupling between the impurities and the soft mode may be responsible for the quasi-elastic central peak observed in scattering experiments. Another important issue is whether such impurities, in the dilute limit, can induce FE phase transitions in soft mode systems which do not undergo phase transitions (e.g., the incipient ferroelectric KTaO, and SrTi0,) and the mechanism by which such transitions are induced. In this latter regard, there has been continuing interest in the low-temperature properties of KTa03 with the random site substitutional impurities Li, Nb, and NaS2O Pure KTaO, has a soft ferroelectric mode which is stabilized at low temperatures by quantum fluctuations; consequently, the crystal does not undergo a phase transition down to the lowest temperatures.2 The substitition of Li or Na for K, or N b for Ta, yields mixed crystals which exhibit dielectric and other anomalies which have long been attributed to ferroelectric phase transitions. However, a strong debate2*has centered on the question of whether the low-temperature polar phase in these materials (particularly in the dilute impurity limit) arises from the spontaneous displacements of the ions below the transition temperature (T,) leading to a static structural phase transition or from the freezing of impurity-induced dipolar motion leading to a dielectric (dipolar) analogue of a spin glass phase. Our high-pressure studies on the system KTal,Nb,03 have provided new insights into the physics and resolved some of the issues in this debate. In what follows in this section, we summarize and discuss the high points of this work. The broad features of the temperature-composition phase diagram of the KTal,Nb,03 (or KTN) system have been known for quite sometime.22 Over most of the composition range (0.1 5 x I1) the system exhibits, on cooling, a sequence of three structural phase transitions from paraelectric cubic to FE tetragonal to FE orthorhombic to FE rhombohedral phases. These are equilibrium first- or second-order phase transitions for which the transition temperatures are independent of measuring frequency below microwave frequencies. For compositions x < 0.1 (and specially x I0.04) the situation has been less clear. There is some evidence for a single phase transition from cubic to trigonal symmetry between x = 0.04 and x = 0.008, at which point the transition vanishes, and the system remains in the high-temperature cubic phase. However, the evidence was not convincing in the dilute limit x C 0.02 and, as we shall see, the system is found to exhibit glasslike properties in this region. We have investigated2’ single-crystal KTN samples with x I 0.02. The results have shed new light on the nature of the “transition” in these low N b concentration samples. A brief summary of some of the results follows. Figure 5 shows some (16) Hijck, K. H.;Thomas, H. 2.Phys. 1977, 827, 267; 1978, 30, 36; 1979, 36, 151. (17) Halperin, B. I.; Varma, C. M . Phys. Reo. 1976, B l 4 , 4030. (18) Bruce, A. D.; Cowley, R. A. Adu. Phys. 1981, 29, 219. (19) Vugmeister, B. E.; Glinchuk, M . D. Sou. Phys.-JETP (Engl. Transl.) 1980, 52, 482. (20) See, e.g.: Proceedings of the 6th International Meeting on Ferroelectricity, Kobe; Jpn. J. Appl. Phys. 1985, 24 (Suppl. 24-2). (21) Samara, G. A. Jpn. J. Appl. Phys. 1985, 24 (Suppl. 24-2). 80, and references therein; Phys. Reu. Lett. 1984, 53, 298. (22) Jona, F.; Shirane, G.Ferroelectric Crystals; The Macmillan Co.: N e w York, 1962; p 225.
Glassy Properties of Ferroelectrics and Dielectrics 6
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The Journal of Physical Chemistry, Vol. 94, No. 3, 1990 1131 I
KTa.98 Nb,0203
P=3.6 kbar
KTa l.x Nbx03
5
x 0.009
n
ir
0 -
0
8
16
24
32
40
48
TEMPERATURE (K)
Figure 5. Isobars of the temperature dependence of the real part of the dielectric constant (c’) at different frequencies for a dilute KTN crystal. Note the pressure-induced frequency dispersion and the suppression of the d ( T ) anomaly at high pressure (9.2 kbar).
lOO/(T-To) (K“) Figure 6. Temperature dependence of the cutoff frequency of the distribution of relaxators of KTN ( x = 0.009) plotted according to the Vogel-Fulcher equation (see text). The data (taken from ref 21 and 24) show the evolution of the dipolar freezing dynamics over 9 decades of frequency.
t vs T isobars for the x = 0.02 crystal measured at different frequencies in the range 102-106Hz. At 1 bar the response is essentially frequency independent in this range. This response is consistent with the existence of a static displacive structural phase transition, as has long been thought to be the case. The x-0.012 roundedness of the e’( T ) peak is not believed to be due to compositional fluctuations (and thereby a distribution in T,‘s) but rather is due to quantum fluctuations, which can suppress T, below its classical limit.23 At high pressure, the peak shifts to lower T, as expected;2but, unexpectedly, a dramatic frequency dispersion 4.3K/kbar is induced in both d ( T ) and t”(T). This dispersion is seen in the 3.6- and 5.6-kbar d ( T ) data in the figure. Additional results show that the c ’ ( T ) and t”(T) peaks and the dispersion vanish at pressures of >8 kbar, and for these pressures the dielectric response 10 resembles that of pure KTa03 which is a quantum p a r a e l e c t r i ~ . ~ . ~ ~ This is, e&, the case for the 9.2-kbar isobar in Figure 5. Results on a sample with 0.9% N b (x = 0.009) exhibited frequency-dependent peaks in both the t’(T) and the t”(T) responses even at atmospheric pressure (1 bar).*’ A modest pressure 0 2 4 6 8 (20.5 kbar) causes the t’(T) and t”(T) peaks and the dispersion PRESSURE (kbar) to vanish. Figure 7. Pressure dependence of the dynamic “glass transition” temThe above results clearly show that the dielectric responses of perature for dilute KTN crystals at lo4 Hz. Similar responses are obthe x = 0.02 KTN crystal at high pressure and the x = 0.009 KTN tained at other frequencies. crystal at I bar are not associated with a static phenomenon (Le., an equilibrium displacive phase transition) but rather are char1-bar data for this sample to eq 1 yieldsz4 vo = 300 cm-I, E, = acteristic of glassy behavior. This behavior is not seen in con70 K, and To = 3.0 K. centrated KTN crystals.z’ On this basis and with other supporting To get a meaningful fit to eq 1 requires data over a broad range e v i d e n ~ e , ~ we ’ J ~argued that these dilute KTN samples do not of frequencies. Becuase the dielectric data cover a relatively undergo bulk equilibrium phase transitions; rather, their glasslike narrow range of frequencies, we did not attempt to fit the highdielectric response can be explained in terms of the freezing of pressure data to obtain the pressure dependences of the various thermally activated dipolar motion. parameters in eq 1. However, a simple fit of the high-pressure The dielectric dispersion data, which show a large slowing down data to an Arrhenius expression of the formz1v, = vd exp(-E,‘/n of the dipolar relaxation with decreasing T, extend over a relatively reveals a large decrease of E,‘ with pressure. We expect a fit to small range of frequency (4 orders of magnitude); however, as eq 1 to yield a similarly large decrease in E, with pressure. This in the case of RADP, the dielectric polarization is the fundamental decrease, which can be interpreted in terms of a pressure-induced excitation mode in KTN, and this mode is active in light (Raman decrease in off-center N b distance in the lattice,21provides an and Brillouin) scattering, in addition to dielectric susceptibility. explanation for the complete suppression of the glassy state at This important feature has made it possible to use the different high pressure (see Figure 5). The activation energy E, relates techniques to follow the full evolution of the freezing dynamics to the average energy barrier between different orientations of over -9 decades of frequency.24 Our dielectric results for the the dipoles. When this barrier vanishes, or, more precisely, when x = 0.009 sample at 1 bar2’ have been combined with Brillouin it becomes sufficiently small to allow the dipoles to reorient or scattering resultsz4to show that the T dependence of the cutoff tunnel freely between different orientations at the lowest tem(or lowest) frequency, v,, of the distribution of relaxators is very peratures, then there is no short-range dipolar or glassy state. This well represented over this large frequency range by the Vogelis what is observed above 8 kbar for the x = 0.02 sample. Fulcher equation, eq 1. This is shown in Figure 6. Fit of the Figure 7 shows the pressure dependence of the glass transition temperature, T8,for two KTN crystals at lo4 Hz. Qualitatively similar results are obtained at other frequencies. The most striking (23) Samara, G . A. Physica 1988, BISO, 179. (24) Lyons, K. B.; Fleury. P. A.; Rytz, D. Phys. Rev. Lert. 1986,57, 2207. feature of the results in Figure 7 for each crystal is the lack of
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1132 The Journal of Physical Chemistry, Vol. 94, No. 3, 1990
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any evidence for an impending increase in slope leading to (dT,/dP) --m as TE 0 K as seen for equilibrium phase transitions. As in the case RADP glasses (see section ILA), we believe that this behavior is indicative of the nonequilibrium nature of the glass transition in Nb-dilute KTN crystals. Finally, one of the more interesting features of thecesults in Figure 5 is the observation that there is no frequency dispersion ) c " ( T ) peaks at 1 bar, but strong dispersion is in the ~ ' ( 7 'and induced by pressure. We have suggested2I that this feature may be a manifestation of a novel, pressure-induced crossover phenomenon from normal ferroelectric ordering to dipolar glass behavior. We have discussed the likelihood of such a crossover phenomenon in terms of the collective properties of electric dipole impurities in highly polarizable, soft ferroelectric mode host crystals.21,23In such hosts the correlation radius, rc, for ferroelectric interaction between dipoles is proportional to the polarizability (or c) of the host, which is very large. Two limiting cases are of interest. In the low-concentration limit, the separation of dipoles is >rc, and spatially inhomogeneous fluctuations of the polarization suppress ferroelectric ordering of the dipolar impurities resulting in the formation of a dipolar glass at low T . In the high-concentration limit, on the other hand, the separation between impurities is 400 at 4 K compared to yc = 1-2 for normal dielectric crystals.* Thus, for soft mode crystals rc3should have a much stronger pressure dependence than V and, consequently, nr: (where n is the concentration of impurities which is proportional to VI)should become much smaller with increasing pressure. This means that, for a given n, pressure should favor the dipolar glass phase, and a pressure-induced normal ferroelectric to dipolar glass phase transition is predictedS2l It is interesting to speculate that the observed behavior of KTN ( x = 0.02) under pressure may be a manifestation of such a transition. As already noted, at atmospheric pressure the c'(T,w) response of this sample is characteristic of a normal ferroelectric transition. However, at high pressure, strong pressure-induced frequency dispersion is observed and the response becomes that characteristic of a dipolar glass. Our x = 0.009 KTN sample, on the other hand, exhibits glasslike behavior already at 1 bar,21 so that no pressure-induced transition is expected in this case. These observations suggest that at atmospheric pressure the crossover from normal ferroelectric ordering to glasslike behavior occurs in KTN at an x value somewhere between 0.02 and 0.009. 111. Glassy Properties of Other Systems A. Orientational Disorder in Crystalline KBr,-,( Crv),. The mixed potassium bromide (KBr)-potassium cyanide (KCN) system has become a model orientational glass system because of the high symmetry of the lattice (NaCI type) and the simple dumbbell shape of the CN- ion which is the orientable entity in the glass.25 A schematic temperature-composition phase diagram for this system is shown in Figure 8. Several important features in the ordered phase are left out for simplicity because they are not relevant to our present considerations. Despite the compositional disorder, at high temperatures mixed crystals have the cubic NaCI-type structure, the high symmetry being established by a very rapid reorientational motion of the CN- ions. For compositions with >60 atom % KCN, cooling results in the formation of an ordered ferroelastic phase in which the CN- ions aligned along various former cubic axes. Below -60 atom % KCN, random strain fields suppress the phase transition to the ordered phase and at sufficiently low temperature (which is a function of composition) a quadrupolar/dipolar orientational glass is formed.25 The process results (25) Loidl, A. Annu. Rev. Phys. Chem. 1989, 40, and references therein.
A
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Disorder (Na CI -type) 100
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s W
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Order 50
Glass State
o r 0
1
1
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04
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CONCENTRATION (x)
Figure 8. Temperature-composition phase diagram for KBr,,(CN),. The glassy state is observed at low temperatures for x < 0.6.
h
Y, 0
t
P (kbar)
Figure 9. Pressure dependence of the dynamic freezing temperature of CN- dipolar motion in KBr,-,(CN),.
in the freezing of two types of orientational degrees of freedom: (1) the freezing of the CN- ions which leads to a cusp in the quadrupolar susceptibility which is reflected in a peak and frequency dispersion in the Cd4(T)elastic constant and (2) the freezing of the head-to-tail arrangement of the CN- dipoles which is reflected in anomalies and dispersion in the dielectric (or dipolar) susceptibility. Interestingly, the freezing of the dipoles and quadrupoles occurs at different temperatures.2s We have begun an investigation of the effects of pressure on the dipolar freezing in this system.26 The dynamic freezing of the CN- dipoles is manifested by peaks in both temperature, Tg, the real and imaginary parts of the dielectric constant t( T,w). Unlike the behavior of RADP and KTN described in section 11, in the present case the peaks (or TE)shift to higher temperatures with increasing pressure. This behavior is shown in Figure 9 where it is seen that Tgincreases with pressure, and the rate of increase increases with increasing pressure. The qualitative explanation is simple. The reorientation process involves activation over an energy barrier, and this barrier gets higher as the ions in the lattice are squeezed closer together. It simply becomes increasingly difficult for the reorientation process to take place as the pressure is increased. The physics here is clearly qualitatively different from that observed for RADP and dilute KTN (see section 11). B . Glassy Behavior in Poly(vinylidenej7uoride). The semicrystalline polar polymer poly(viny1idene fluoride) (PVDF or PVF,) is a linear polymer with a carbon backbone in which each monomer [-CH2-CF2-] unit has two dipole moments, one associated with CF2 and the other with CH2. The material exhibits a variety of scientifically interesting and technologically important (26) Samara, G. A,; Loidl, A.; Bohmer, R. To be published
Glassy Properties of Ferroelectrics and Dielectrics ‘
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The Journal of Physical Chemistry, Vol. 94, No. 3, 1990 1133 ’
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180
220
260
300
340
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TEMPERATURE ( K )
Figure 10. Temperature dependence of the imaginary part of the dielectric constant (6’’) of PVDF at 1 bar showing the strong frequency dispersion of the g relaxation peak.
properties which have made it the most widely investigated piezoelectric polymer.27 It possesses relatively large dielectric constants and piezoelectric and pyroelectric coefficients and was the first known ferroelectric polymer. In the crystalline phase, PVDF exhibits a variety of molecular conformations and crystal structures depending on the method of p r e p a r a t i ~ n .The ~ ~ most common and most studied of these forms are the (Y and (3 phases. (The (3 phase should not be confused with the (3 molecular relaxation process to be discussed below.) Melt-cast films have the helical a form in which the molecular conformation is transgauche (TGTG), and the chains are packed in an antipolar unit cell. By mechanical rolling or stretching, the a phase in the films transforms to the (3 phase in which the molecular conformation is the all-trans (TT) planar zigzag with the dipole moments perpendicular to the chain axis. In this form the crystal structure is polar (orthorhombic C m 2 m ) with two parallel chains per unit cell. It is this (3 form which exhibits reversible spontaneous polarization and is therefore the ferroelectric and strongly piezoelectric phase, which is the most useful phase. Biaxially stretched PVDF film containing the (3 phase was used in our work.2* We have been studying the frequency, temperature, and pressure dependences of the dielectric properties, molecular relaxations, and phase transitions (including melting) of PVDF and its copolymers with trifluoroethylene. The results are providing new insights into the physics of the molecular motions and energy barriers which determine these properties, and they are also relevant to the unique application of these polymers as time-resolved dynamic stress gauges and sensors.28 Here we restrict our attention to the (3 molecular relaxation process in PVDF. This process, which strongly influences the electrical and mechanical responses of PVDF, is attributed to micro-Brownian motions of dipolar molecular segments in the noncrystalline (or amorphous) regions29 and is closely related to the glass transition process. The (3 relaxation exhibits a characteristic glasslike response in its dielectric properties. Figure 10 shows the temperature dependence of e‘‘ at different frequencies. The strong influence of pressure on the (3 relaxation process is seen in Figure 11 where we show the results for only one frequency. The behavior at other frequencies is qualitatively similar. With increasing pressure there is a large displacement of the e”( T ) and e’( T ) responses to higher temperatures. This effect is seen more explicitly in Figure 12 where we have plotted the pressure dependence of the e”( T ) peak, (27) Lovinger, A. J . Jpn. J . Appl. Phys. 1985,24 (Suppl. 24-2), 18, and references therein. See also: Ohigashi, H. Ibid. 1985, 23, and references therein. (28) Samara, G. A. J . Polym. Sci., in press. (29) Yano, S.J . P d y m . Sci. Part A-2 1970, 8, 1057.
0.5
0.0
200
300
500
400
TEMPERATURE (K)
Figure 11. Pressure dependence of the real and imaginary parts of the dielectric constant of PVDF in the region of the @ relaxation peak at 1 X IO6 Hz. Similar behavior is observed at other frequencies.
L 0
I
4
8
12
16
20
PRESSURE (kbar)
Figure 12. Pressure dependence of the dynamic freezing temperature for dipolar motion associated with the @ relaxation in PVDF.
T,,, at different frequencies. The initial slope (dT-/dP)
= 10.0
f 0.3 K/kbar at l o 2 H z and increases slightly to 10.5 f 0.3
K/kbar at lo6 Hz. The increase of T,,, with pressure can be qualitatively understood in terms of closer packing of polymer chains and chain segments, and this closer packing hinders the motion and reorientation of the dipolar groups in the amorphous phase. Thus, a higher temperature (and thereby a higher T,,,) is required to induce this motion. The e ” ( T j plots such as in Figure 10 define relaxation frequencies w (=2.rrf, where f is the measurement frequency) or relaxation times T (=d) corresponding to the peak temperatures, T,,,. Plots of log w vs T 1at different pressures do not obey a simple Arrhenius law even over the limited frequency range covered, but they can be well represented by the Vogel-Fulcher equation, eq 1, as seen in Figure 13. Fits of the data in Figure 13 to this equation yield the pressure dependences of E and TO shown in Figure 14. These results show that To= 190 f 10 K at 1 bar and increases with pressure at an initial rate of dTo/dP = 6.8 K/kbar. At the same time, E (=96 meV, or 2.2 kcal/mol, at 1 bar) increases at an initial rate of dE/dP = 5.2 meV/kbar.
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temperature (and hence higher T,,, and To)to overcome this higher barrier. The physics for this system is thus qualitatively similar to that for dipolar freezing in KBr,,(CN),, and both are qualitatively different from RADP and KTN.
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IV. Concluding Remarks In this paper we have discussed and compared the effects of hydrostatic pressure on the glasslike behavior in crystalline ferroelectric/antiferroelectric systems brought about by (1) frustration-induced disorder and ( 2 ) impurity-induced disorder. In the first case, our example was the proton glass Rb,+ (NH4),H2P0, (or RADP). It was found that the decrease of the dynamic glass transition temperature, Tg,and ultimate vanishing of the glassy phase with pressure and the large hydrogen isotope effects in RADP can be understood in terms of an Ising model with a transverse tunneling field. The situation is qualitatively akin to that for the pure ferroelectric and antiferroelectric end members, RbH2P04and NH4H2P04,respectively, except that in the case of RADP the dipolar interaction coupling constants, J,,, are taken to be random variables. The RADP results also emphasize the importance of the hydrogen-bond potential in triggering the ordering process in these materials, regardless of whether the ordering is long (FE or AFE) or short (glass) range. In the second case of impurity-induced disorder, our example was KTaI-,Nb,O3 (KTN). In the dilute limit (x C 0.02), this system exhibits on cooling a glass transition and not an equilibrium phase transition to a ferroelectric state as has been thought. The glassy state is easily suppressed by pressure, and the manner in which this state vanishes in both KTN and RADP, specifically 0 K with a finite slope dT,/dP, is believed to the fact that T be indicative ofthe nonequilibrium nature of the glass transition. A novel pressure-induced crossover from ferroelectric order to dipolar glass behavior in soft optic mode systems was briefly discussed, and it was suggested that the KTN ( x = 0.02) results provide a manifestation of such a crossover phenomenon. Although there are some qualitative similarities in the pressure results on RADP and KTN, the physics of the glassy state in the two systems are quite different. The physics of these novel systems as well as the pressure effects are also qualitatively different from those of more conventional dipolar glasses such as KBr,-,(CN), and the /3 relaxation in poly(viny1idene fluoride). In these latter glasses, as well as in the majority of orientational glasses, pressure causes closer packing of the molecular species in the solid and thereby hinders the motion of the orientable entities. This hindrance results in a shift of the glass transition to higher temperatures. Finally, the work summarized in this paper emphasizes the important role of pressure in studying orientational glasses. It is the only variable which allows continuous and delicate tuning of the interatomic interaction and short-range correlations which are responsible for the glassy state. This tunability was beautifully illustrated, for example, in RADP, where pressures controls the shape and energy barrier of the double-well potential experienced by the proton (or deuteron) as it moves along the 0-H-0 bond, and in KTN, where pressure tunes the polarizability of the host lattice leading to a pressure-induced crossover from ferroelectric to glassy behavior.
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0
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I
4
'
I
E
'
'
12
'
I
16
'
1
20
1
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PRESSURE (kbar)
Figure 14. Pressure dependence of the energy barrier E and reference temperature To in the Vogel-Fulcher equation for the fl relaxation of
PVDF. This value of E is of the expected order of magnitude (a few kcal/mol) for the hindrance energies of internal rotations in polymers.30 The above results appear to be the first evaluation of the pressure dependences of Toand E for PVDF or, as far as we can determine, for any polymer. These results can be qualitatively understood in that pressure, by reducing the sample volume and available free volume, causes closer packing of PVDF chains and chain segments and hinders the motion of the dipolar groups responsible for the (3 relaxation. This hindrance is reflected by a higher energy barrier E and thereby by the need to go to higher (30)Adam, G.; Gibbs, J . H.J . Chem. Phys. 1965, 43, 139.
Acknowledgment. The expert technical assistance of L. V . Hansen is greatly appreciated. This work performed at Sandia National Laboratories was supported by the U.S. Department of Energy under Contract No. DE-AC04-76DP00789.
