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Diffuse phase transition in Pb(Fe0.5Nb0.5)O3-based solid solutions
J. Phys. Chem. Solids Vol. 54, No. 4, pp. 491498, Printed in Great Britain.
1993
oozz.3697/93 $6.00 + 0.00 Pcr~mon Press Ltd
DIFFUSE PHASE TRANSITION IN Pb(Fe,,Nbo,,)O,-BASED SOLID SOLUTIONS A. A. BOKOV, L.
A. SHPAK and I. P. RAYEVSKY
Institute of Physics, Rostov State University, Rostov-on-Don, 344104, Russia (Received
1 April 1992; accepted in revised form 18 September
1992)
Abstrati-Temperature dependence of permittivity in ceramic (1 - x)Pb(Fq,,Nb,,,)O, -xABO,, where A = Ca, Sr, Pb, Ba; B = (Fe,.,Nb,,), Ti, Sn, Hf, Zr, Ge, Ce, x G 0.09 were studied. The correlation between the phase transition diffuseness and the rate of Curie temperature variation with composition predicted by the composition fluctuations model was absent. The diffuseness at certain x grows with the increase of difference between substituting B ion radius and the radius of Nb ion, but is practically independent of the type of substituting A-ion. These facts are consistently explained in the frame of the new model [Bokov A.A., Ferroelectrics, (1992) 131,491. Keywords:
Ferroelectric, diffuse phase transitions, dielectric properties, perovskite.
INTRODUCTION
The investigation of ferroelectrics possessing diffuse phase transitions (DPT) is of great interest because they have unique physical properties and wide practical applications [l]. In contrast to normal ferroelectrics, they do not show a sharp change of structure and properties at the Curie point but the transition is smeared over a large temperature range. In spite of numerous attempts to understand the reasons of this smearing there is no agreed-upon viewpoint concerning this problem [4]. The most widely accepted model [l-3] takes into account the fact that the structure of crystals with diffuse ferroelectric phase transitions is characterized by differenttype of ions randomly occupying the equivalent lattice sites. DPT behaviour is considered to result from composition fluctuations on a microscopic scale caused by disordering of the ions. If the Curie temperature depends on composition, the phase transition in different microregions takes place at different temperatures, i.e. the transition becomes diffused. For example, ABOS type ferroelectric oxides of the perovskite family possess sharp phase transitions. They have a cubic structure (in the paraelectric phase) formed by a framework of oxygen octahedra sharing comers. B-cations are lobated in the centers of octahedra and the interstitial sites are occupied by A-cations [S]. In solid solutions A(B:B;_JO, of two different perovskite end members, AB’03 and AB”O,, the octahedral lattice sites are occupied by different ions in disorder. Random excess or deficiency of B’ (or B”) ions in a certain microregion in comparison with
the average concentration x exerts an influence on the Curie temperature (Tc) of this microregion. The greater the dT,-/dx, the greater the influence. The same conclusion is true for (As;_,)BO, solid solutions. So correlation between dTc/dx and the degree of smearing in various solid solutions may be one of the criteria for the validity of the composition fluctuations model. Another recently suggested model [4] puts forward a new reason for the local Curie temperature fluctuations. It was noticed that the positions that are equivalent in ordered structures (e.g. octahedral sites) become nonequivalent in the disordered state. To witness this, let us consider the A(B:BT_,)O, perovskite solid solution, where B’ cations are ferroactive. The size of a certain oxygen octahedron depends on the type of cations (B’ or B”) located in the neighboring octahedra. As a result the microscopic parameters (primarily polarizability) of ferroactive cations B’ differ from each other and this difference grows with the difference in radii between B’ and B”. The DPT behaviour is considered to be caused by concentration fluctuations of ferroactive ions with polarizabilities differing greatly from the average one. The concentration of such ions is comparatively small and thus their relative number may differ greatly in various microregions. On the other hand, the influence of their concentration on Tc is vep;.great. The relative concentration fluctuations of other ferroactive ions are small and they do not make a contribution to the smearing, but their concentration defines the mean Curie temperature. The disorder in the A-sublattice ((Aa;_,)BO, solid solutions) causes the deformation of oxygen 495
A. A. Boxov et al.
4%
octahedra which does not lead to considerable variation of the distance between ferroactive B-cations and oxygen ions and hence to the variation of polarizability. Thus, according to this model, the degree of phase transition smearing in A(B!B;_,)O, compounds where B’ cations are ferroactive should depend on the difference in ionic radii AR = 1Rw - RBe1but not on dTc/dx. The doping in the A-sublattice should not change the degree of smearing signi&ntly. The purpose of the present work was to verify the validity of the predictions of the two models mentioned above when studying the ferroelectric phase transitions in Pb(Fe,,sNbO.s)G,-based solid solutions. Lead iron niobate Pb(Fe0,,Nb,,5)0, (hereafter designated PFN) is a complex oxide with the perovskite structure with a slightly diffuse phase transition from the paraelectric to the ferroelectric phase in the range of llO-120°C [l, 61. We studied the changes in DPT behaviour in ceramic solid solutions (1 -n)PFN-xA2+B4+Oj, where A=Ca, Sr, Pb, Ba; B = (Fe,,Nb,,,), Ti, Sn, Hf, Zr, Ge, Ce; x < 0.09. Temperature dependencies of dielectric permittivity in the vicinity of the transition were used for this purpose.
EXPERIMENTAL
Ceramic samples were prepared by the mixed oxide method. Reagent grade oxide or carbonate powders were used as starting raw materials. The powders were batched in stoichiometric proportions, and then, in addition, 1 wt% L&CO3 powder was added to the batch. This addition leads to a higher quality of the ceramics but slightly reduces the phase transition temperature. The mixed oxides after milling were pressed into disks 10 mm in diameter and about 1 mm thick. These samples were sintered at lOSO-1150°C for 2 h in a closed alumina crucible using a controlled PbG atmosphere to prevent PbG loss at high temperatures. X-ray diffraction patterns from most of the sintered compositions indicated the presence of a single phase of the perovskite structure. Traces (less than 5%) of a pyrochlore phase were observed in some compositions. Silver paste was fired on the samples as electrodes. Low-field permittivity c vs temperature measurements were taken at 1 kHz with a capacitance bridge during slow heating at a rate of l”Cmin-I.
RESULTS AND DISCUSSION
Since an exhaustive presentation of the experimental measurements of all compositions studied
25 -
20 -
-40
0
40
80
120
T (“C) Fig. 1. Pennittivity at 1 kHz vs temperature in three selected compositions: (1) Pb(Fe,,Nb&O~; (2) O.!MPb(Fe,,Nb,,)o, - 0.06 PbGeO,; (3) 0.94 Pb(FeO.,W,,,)O, 0.06 CaTiO,.
would require too much space, the temperature dependence of L of only three compositions is shown in Fig. 1. AU the compounds have a diffuse maximum of c at the temperature T,,,, corresponding to the ferroelectri-paraelectric phase transition. In tmdoped PFN ceramic (x = 0), T, = 95°C. The values of T, of the other compounds studied are shown in Table 1. Table 1. The temperatures of permittivity maximum (T,) for (1 - x)PWFen,Nb,, ,K), - xAB0, solid solutions A Ca Ca Ca Ca ca ca Ca Sr
Dopants B
Sn Hf Ee Ce
Feo.Ph5
Sr
Ti
Sr Sr Sr
Sn Hf Zr
Sr Sr
Pb E Pb Pb Pb Ba Ba Ba Ba Ba Ba Ba
Ti Sn Hf Zr Ge ce
Fe,,Nbo.,
Ti
Sn Hf Zr Ge ce
x = 0.03 52 68 42 17 64 56 42 53
61 46 18 50 51 48 110 75 105
106 82 77 53 70 47 60 64 54 51
T,(“C) x=0.06
25 53 21 17 8 13 29 -5 8 30 9 4 125 54 114 115 72 73 12 53 28 23 35 15 13
x=0.09
15
-8
7 24
72 21
Diffuse phase transition in Pb(Fq,Nb&O,-based
solid solutions
491
To evaluate the degree of phase transition smearing we used the diffuseness e which is known as an effective comparative parameter for ferroelectrics [l, 7981:
where E,,,is the value of e at T,,,. a parameters were determined from the slope of l/c as a function of (T - T,)* at T 2 T,,, which appeared to be straight lines at T - T,,, < (5-2O)“C. These plots for selected compounds are shown in Fig. 2. In most cases the diffuseness grows with increasing ABO, concentration x (see for example Fig. 3) which is in agreement with the composition fluctuation model [l-3] as well as the new model [4]. The compositions in which substitutions in the A-sublattice alone were made (A(Fe,,,Nb,,)O, additions) are an exception, here the diffuseness is practically independent of x. To verify the composition fluctuations model, the influence of the rate of change of the phase transition temperature with composition (dTc/dx) on the diffuseness was studied (see Fig. 4). According to this model, the c(T) maximum is observed at the mean Curie temperature [3] so we may consider that T,(x) = T,,,(x). As in most solid solutions the T,(x) dependences were almost linear (see Table I), and to calculate dTc/dx we used the formula dTc dx=
T,(x,) - T,(x,) x,-x* ’
where x, = 0.06 and x, = 0.03. In other cases, we had to prepare the compositions with x = 0.09 to draw the phase diagram and to estimate dTc/dx = dT,/dx.
0.03
0
Fig. 3. Typical plots of diffuseness vs composition x for (1 - x)Pb(Fe,,Nb,,,)O, - xAB0, solid solutions.
As mentioned in the introduction, the composition fluctuations model predicts a correlation between CJ and dT,/dx. But this correlation is absent in the solid solutions studied (see Fig. 4). Figure 5 shows the relation of diffuseness and the type of A and B dopants introduced. It was found that: (i) for a given substitution level (x) on the B-sublattice, diffuseness grows with the difference in radii between the substituting B4+ cation and Nb cation AR = 1R, - RN,1 (the radii used for the AR calculation are listed in Table 2); (ii) substitutions in the Pb-sublattice do not change c significantly. These results are in agreement with the conclusions of the new model [4] if we assume that in the solid solutions studied Nb cations are ferroactive. It was found [lo] that these cations were really ferroactive in undoped Pb(B&Nb,,,)O, perovskites independent of the type of B’ ion. Perhaps Nb cations remain the sole ferroactive ones also in compositions with small x. The diffuseness of Ge-containing solutions is slightly lower than expected from the general a(AR) dependence. Perhaps this is due to the radius of the 0.94
Pb(FeO.SNb,
A ions:
0 Ca
,)O,-0.06 A Sr
10 01 0
(“C)2
Fig. 2. Typical plots of (l/c - l/r,) vs (T - 7’,,,)2. ( x ) for PbO%NbO.,)O,; (0) for 0.94 Pb(F%.,NbO.,)O, 0.06 PbGeOl; (0) for 0.94 Pb(Fe,,Nb,,,)O, - 0.06 CaTiO,.
0 Pb
ABOj A Ba
45 (Fe Nb)
t
(T-T,)*
0.09
0.06 X
I
I
I
500
1000
1500
dTJdx (‘C) Fig. 4. Plot of diffuseness (u) vs rate of change of phase transition temperature with composition (dTc/dx) for 0.94 Pb(F~.,Nb,&O, - 0.06 ABO, solid solutions.
498
A. A. B Ti
Sn
I
I
BOKOV
et
ions
Hf Zr
Table 2. The ionic radii by Shannon [9] Gc
II
CC
I
0.94 Pb(Fe0~5Nbo~S)03-0.06
I
] 1
ABO,
0
A ions 0 Ca A
Sr
0
Pb Ba
.
0.05
al.
0.10
0.15
AR (A>
Fig. 5. Plot of diffuseness vs ionic radius (by Shannon) difference AR = 1R, - R,,I for 0.94 WFeO,~~O.~)o~ 0.06 ABOj solid solutions.
ferroactive Nb ion being larger than that of Ge (as well as Ti) but smaller than the other B’+ ions (see Table 2). According to the new model, the DPT behaviour is attributed to the variation of the polarizabilities of ferroactive ions caused by the different “squeeze” of them in the oxygen octahedra [4]. Because of the nonlinearity of the repulsive forces determining the polarizability, the increase of Nbcontaining octahedron size (due to the appearance in the neighboring octahedra of B4+ ions with RB < R,,) should lead to a smaller variation of Nb ions polarizability than the same magnitude decrease in size (due to the appearance in the neighboring octahedra of B4+ ions with RB > R,,). Thus the diffuseness in the former case should be smaller than in the latter. This effect is likely to take place in Ge-containing solutions. In Ti-containing solutions it is not noticeable because of the small AR value. It should be emphasized that the lack of a(dTc/dx) correlation alone is insufficient to reject the composition fluctuations model because the spread in values of cr could be explained by the contributions arising from other factors such as incomplete formation of solution, discrepancy in the ceramic grain size, content of parasitic phases and so on. But the distinct regularities in Q vs AR plot strongly indicate that all these factors were insignificant for the ceramics prepared in this work. Reduced value of u in PFN-PbCeO, compounds (compared with the other Ge-containing solutions) is probably connected with one of these factors.
Ion
R(A)
Ge Ti Nb Sn Hf Zr Ce
0.54 0.605 0.64 0.69 0.71 0.72 0.80
CONCLUSIONS The study described in this paper shows that in PFN-A2 + B4+ O3 solid solutions the concentration fluctuations of substituting A’+ and B4+ ions do not contribute to the DPT behaviour and the well-known composition fluctuations model cannot be applied to these compounds. These conclusions are based on three experimental facts: (i) the correlation between diffuseness (a) and the rate of Tc varying with composition (dTc/dx) is absent; (ii) substitutions of any of the ions on Pb-sublattice do not change CT and (iii) substitution on the octahedral sublattice regularly increases 0 as the ditTerence in radius AR = 1R, - R,,I between substituting B4+ ion and Nb ion increases. On the other hand, these facts are a strong confirmation for the new model [4] considering the diffusion to be. caused by the concentration fluctuations of ferroactive ions with microscopic parameters (primarily polarizability) deffering greatly from the average ones. We think that investigations designed to find analogous behaviour in other solid solutions and complex compounds might be very helpful in the verification of the theoretical models as well as for the control of properties in technologically important materials. REFERENCES 1.
2. 3. 4. 5. 6. 7. 8. 9. 10.
Smolensky G. A., Bokov V. A., Isupov V. A., Krainak N. N., Pasynkov R. E., Sokolov A. I. and Yushin N. K. Ferroelectrics and Related Materials. Gordon and Breach, New York (1984). Smolensky G. A. and Isupov V. A., Sov. Phys. Tech. Phys. 24, 1375 (1954) (in Russian). Isupov V. A., Ferroelectrics 90, 113 (1989). Bokov A. A., Ferroelectrics 131, 49 (1992). Galasso F. S., Structure, Properties and Preparation of Perovskite-type Compounds. Pergamon Press, Oxford (1969). Mabud S. A., Phase Transit. 4, 183 (1984). Isupov V. A., Fiz. Tverd. Tela 25, 2235 (1986) (in Russian). Pilgrim S. M., Sutherland A. E. and Winzer S. R., J. Am. Ceram. Sot. 73, 3122 (1990). Shannon R. D., Acta Cryst. A32, 751 (1976). Bokov A. A. Khasabov A. G. and Rayevsky I. P., Izu. AN SSSR Ser. Fiz. 54, 854 (1990) (in Russian).
1993
oozz.3697/93 $6.00 + 0.00 Pcr~mon Press Ltd
DIFFUSE PHASE TRANSITION IN Pb(Fe,,Nbo,,)O,-BASED SOLID SOLUTIONS A. A. BOKOV, L.
A. SHPAK and I. P. RAYEVSKY
Institute of Physics, Rostov State University, Rostov-on-Don, 344104, Russia (Received
1 April 1992; accepted in revised form 18 September
1992)
Abstrati-Temperature dependence of permittivity in ceramic (1 - x)Pb(Fq,,Nb,,,)O, -xABO,, where A = Ca, Sr, Pb, Ba; B = (Fe,.,Nb,,), Ti, Sn, Hf, Zr, Ge, Ce, x G 0.09 were studied. The correlation between the phase transition diffuseness and the rate of Curie temperature variation with composition predicted by the composition fluctuations model was absent. The diffuseness at certain x grows with the increase of difference between substituting B ion radius and the radius of Nb ion, but is practically independent of the type of substituting A-ion. These facts are consistently explained in the frame of the new model [Bokov A.A., Ferroelectrics, (1992) 131,491. Keywords:
Ferroelectric, diffuse phase transitions, dielectric properties, perovskite.
INTRODUCTION
The investigation of ferroelectrics possessing diffuse phase transitions (DPT) is of great interest because they have unique physical properties and wide practical applications [l]. In contrast to normal ferroelectrics, they do not show a sharp change of structure and properties at the Curie point but the transition is smeared over a large temperature range. In spite of numerous attempts to understand the reasons of this smearing there is no agreed-upon viewpoint concerning this problem [4]. The most widely accepted model [l-3] takes into account the fact that the structure of crystals with diffuse ferroelectric phase transitions is characterized by differenttype of ions randomly occupying the equivalent lattice sites. DPT behaviour is considered to result from composition fluctuations on a microscopic scale caused by disordering of the ions. If the Curie temperature depends on composition, the phase transition in different microregions takes place at different temperatures, i.e. the transition becomes diffused. For example, ABOS type ferroelectric oxides of the perovskite family possess sharp phase transitions. They have a cubic structure (in the paraelectric phase) formed by a framework of oxygen octahedra sharing comers. B-cations are lobated in the centers of octahedra and the interstitial sites are occupied by A-cations [S]. In solid solutions A(B:B;_JO, of two different perovskite end members, AB’03 and AB”O,, the octahedral lattice sites are occupied by different ions in disorder. Random excess or deficiency of B’ (or B”) ions in a certain microregion in comparison with
the average concentration x exerts an influence on the Curie temperature (Tc) of this microregion. The greater the dT,-/dx, the greater the influence. The same conclusion is true for (As;_,)BO, solid solutions. So correlation between dTc/dx and the degree of smearing in various solid solutions may be one of the criteria for the validity of the composition fluctuations model. Another recently suggested model [4] puts forward a new reason for the local Curie temperature fluctuations. It was noticed that the positions that are equivalent in ordered structures (e.g. octahedral sites) become nonequivalent in the disordered state. To witness this, let us consider the A(B:BT_,)O, perovskite solid solution, where B’ cations are ferroactive. The size of a certain oxygen octahedron depends on the type of cations (B’ or B”) located in the neighboring octahedra. As a result the microscopic parameters (primarily polarizability) of ferroactive cations B’ differ from each other and this difference grows with the difference in radii between B’ and B”. The DPT behaviour is considered to be caused by concentration fluctuations of ferroactive ions with polarizabilities differing greatly from the average one. The concentration of such ions is comparatively small and thus their relative number may differ greatly in various microregions. On the other hand, the influence of their concentration on Tc is vep;.great. The relative concentration fluctuations of other ferroactive ions are small and they do not make a contribution to the smearing, but their concentration defines the mean Curie temperature. The disorder in the A-sublattice ((Aa;_,)BO, solid solutions) causes the deformation of oxygen 495
A. A. Boxov et al.
4%
octahedra which does not lead to considerable variation of the distance between ferroactive B-cations and oxygen ions and hence to the variation of polarizability. Thus, according to this model, the degree of phase transition smearing in A(B!B;_,)O, compounds where B’ cations are ferroactive should depend on the difference in ionic radii AR = 1Rw - RBe1but not on dTc/dx. The doping in the A-sublattice should not change the degree of smearing signi&ntly. The purpose of the present work was to verify the validity of the predictions of the two models mentioned above when studying the ferroelectric phase transitions in Pb(Fe,,sNbO.s)G,-based solid solutions. Lead iron niobate Pb(Fe0,,Nb,,5)0, (hereafter designated PFN) is a complex oxide with the perovskite structure with a slightly diffuse phase transition from the paraelectric to the ferroelectric phase in the range of llO-120°C [l, 61. We studied the changes in DPT behaviour in ceramic solid solutions (1 -n)PFN-xA2+B4+Oj, where A=Ca, Sr, Pb, Ba; B = (Fe,,Nb,,,), Ti, Sn, Hf, Zr, Ge, Ce; x < 0.09. Temperature dependencies of dielectric permittivity in the vicinity of the transition were used for this purpose.
EXPERIMENTAL
Ceramic samples were prepared by the mixed oxide method. Reagent grade oxide or carbonate powders were used as starting raw materials. The powders were batched in stoichiometric proportions, and then, in addition, 1 wt% L&CO3 powder was added to the batch. This addition leads to a higher quality of the ceramics but slightly reduces the phase transition temperature. The mixed oxides after milling were pressed into disks 10 mm in diameter and about 1 mm thick. These samples were sintered at lOSO-1150°C for 2 h in a closed alumina crucible using a controlled PbG atmosphere to prevent PbG loss at high temperatures. X-ray diffraction patterns from most of the sintered compositions indicated the presence of a single phase of the perovskite structure. Traces (less than 5%) of a pyrochlore phase were observed in some compositions. Silver paste was fired on the samples as electrodes. Low-field permittivity c vs temperature measurements were taken at 1 kHz with a capacitance bridge during slow heating at a rate of l”Cmin-I.
RESULTS AND DISCUSSION
Since an exhaustive presentation of the experimental measurements of all compositions studied
25 -
20 -
-40
0
40
80
120
T (“C) Fig. 1. Pennittivity at 1 kHz vs temperature in three selected compositions: (1) Pb(Fe,,Nb&O~; (2) O.!MPb(Fe,,Nb,,)o, - 0.06 PbGeO,; (3) 0.94 Pb(FeO.,W,,,)O, 0.06 CaTiO,.
would require too much space, the temperature dependence of L of only three compositions is shown in Fig. 1. AU the compounds have a diffuse maximum of c at the temperature T,,,, corresponding to the ferroelectri-paraelectric phase transition. In tmdoped PFN ceramic (x = 0), T, = 95°C. The values of T, of the other compounds studied are shown in Table 1. Table 1. The temperatures of permittivity maximum (T,) for (1 - x)PWFen,Nb,, ,K), - xAB0, solid solutions A Ca Ca Ca Ca ca ca Ca Sr
Dopants B
Sn Hf Ee Ce
Feo.Ph5
Sr
Ti
Sr Sr Sr
Sn Hf Zr
Sr Sr
Pb E Pb Pb Pb Ba Ba Ba Ba Ba Ba Ba
Ti Sn Hf Zr Ge ce
Fe,,Nbo.,
Ti
Sn Hf Zr Ge ce
x = 0.03 52 68 42 17 64 56 42 53
61 46 18 50 51 48 110 75 105
106 82 77 53 70 47 60 64 54 51
T,(“C) x=0.06
25 53 21 17 8 13 29 -5 8 30 9 4 125 54 114 115 72 73 12 53 28 23 35 15 13
x=0.09
15
-8
7 24
72 21
Diffuse phase transition in Pb(Fq,Nb&O,-based
solid solutions
491
To evaluate the degree of phase transition smearing we used the diffuseness e which is known as an effective comparative parameter for ferroelectrics [l, 7981:
where E,,,is the value of e at T,,,. a parameters were determined from the slope of l/c as a function of (T - T,)* at T 2 T,,, which appeared to be straight lines at T - T,,, < (5-2O)“C. These plots for selected compounds are shown in Fig. 2. In most cases the diffuseness grows with increasing ABO, concentration x (see for example Fig. 3) which is in agreement with the composition fluctuation model [l-3] as well as the new model [4]. The compositions in which substitutions in the A-sublattice alone were made (A(Fe,,,Nb,,)O, additions) are an exception, here the diffuseness is practically independent of x. To verify the composition fluctuations model, the influence of the rate of change of the phase transition temperature with composition (dTc/dx) on the diffuseness was studied (see Fig. 4). According to this model, the c(T) maximum is observed at the mean Curie temperature [3] so we may consider that T,(x) = T,,,(x). As in most solid solutions the T,(x) dependences were almost linear (see Table I), and to calculate dTc/dx we used the formula dTc dx=
T,(x,) - T,(x,) x,-x* ’
where x, = 0.06 and x, = 0.03. In other cases, we had to prepare the compositions with x = 0.09 to draw the phase diagram and to estimate dTc/dx = dT,/dx.
0.03
0
Fig. 3. Typical plots of diffuseness vs composition x for (1 - x)Pb(Fe,,Nb,,,)O, - xAB0, solid solutions.
As mentioned in the introduction, the composition fluctuations model predicts a correlation between CJ and dT,/dx. But this correlation is absent in the solid solutions studied (see Fig. 4). Figure 5 shows the relation of diffuseness and the type of A and B dopants introduced. It was found that: (i) for a given substitution level (x) on the B-sublattice, diffuseness grows with the difference in radii between the substituting B4+ cation and Nb cation AR = 1R, - RN,1 (the radii used for the AR calculation are listed in Table 2); (ii) substitutions in the Pb-sublattice do not change c significantly. These results are in agreement with the conclusions of the new model [4] if we assume that in the solid solutions studied Nb cations are ferroactive. It was found [lo] that these cations were really ferroactive in undoped Pb(B&Nb,,,)O, perovskites independent of the type of B’ ion. Perhaps Nb cations remain the sole ferroactive ones also in compositions with small x. The diffuseness of Ge-containing solutions is slightly lower than expected from the general a(AR) dependence. Perhaps this is due to the radius of the 0.94
Pb(FeO.SNb,
A ions:
0 Ca
,)O,-0.06 A Sr
10 01 0
(“C)2
Fig. 2. Typical plots of (l/c - l/r,) vs (T - 7’,,,)2. ( x ) for PbO%NbO.,)O,; (0) for 0.94 Pb(F%.,NbO.,)O, 0.06 PbGeOl; (0) for 0.94 Pb(Fe,,Nb,,,)O, - 0.06 CaTiO,.
0 Pb
ABOj A Ba
45 (Fe Nb)
t
(T-T,)*
0.09
0.06 X
I
I
I
500
1000
1500
dTJdx (‘C) Fig. 4. Plot of diffuseness (u) vs rate of change of phase transition temperature with composition (dTc/dx) for 0.94 Pb(F~.,Nb,&O, - 0.06 ABO, solid solutions.
498
A. A. B Ti
Sn
I
I
BOKOV
et
ions
Hf Zr
Table 2. The ionic radii by Shannon [9] Gc
II
CC
I
0.94 Pb(Fe0~5Nbo~S)03-0.06
I
] 1
ABO,
0
A ions 0 Ca A
Sr
0
Pb Ba
.
0.05
al.
0.10
0.15
AR (A>
Fig. 5. Plot of diffuseness vs ionic radius (by Shannon) difference AR = 1R, - R,,I for 0.94 WFeO,~~O.~)o~ 0.06 ABOj solid solutions.
ferroactive Nb ion being larger than that of Ge (as well as Ti) but smaller than the other B’+ ions (see Table 2). According to the new model, the DPT behaviour is attributed to the variation of the polarizabilities of ferroactive ions caused by the different “squeeze” of them in the oxygen octahedra [4]. Because of the nonlinearity of the repulsive forces determining the polarizability, the increase of Nbcontaining octahedron size (due to the appearance in the neighboring octahedra of B4+ ions with RB < R,,) should lead to a smaller variation of Nb ions polarizability than the same magnitude decrease in size (due to the appearance in the neighboring octahedra of B4+ ions with RB > R,,). Thus the diffuseness in the former case should be smaller than in the latter. This effect is likely to take place in Ge-containing solutions. In Ti-containing solutions it is not noticeable because of the small AR value. It should be emphasized that the lack of a(dTc/dx) correlation alone is insufficient to reject the composition fluctuations model because the spread in values of cr could be explained by the contributions arising from other factors such as incomplete formation of solution, discrepancy in the ceramic grain size, content of parasitic phases and so on. But the distinct regularities in Q vs AR plot strongly indicate that all these factors were insignificant for the ceramics prepared in this work. Reduced value of u in PFN-PbCeO, compounds (compared with the other Ge-containing solutions) is probably connected with one of these factors.
Ion
R(A)
Ge Ti Nb Sn Hf Zr Ce
0.54 0.605 0.64 0.69 0.71 0.72 0.80
CONCLUSIONS The study described in this paper shows that in PFN-A2 + B4+ O3 solid solutions the concentration fluctuations of substituting A’+ and B4+ ions do not contribute to the DPT behaviour and the well-known composition fluctuations model cannot be applied to these compounds. These conclusions are based on three experimental facts: (i) the correlation between diffuseness (a) and the rate of Tc varying with composition (dTc/dx) is absent; (ii) substitutions of any of the ions on Pb-sublattice do not change CT and (iii) substitution on the octahedral sublattice regularly increases 0 as the ditTerence in radius AR = 1R, - R,,I between substituting B4+ ion and Nb ion increases. On the other hand, these facts are a strong confirmation for the new model [4] considering the diffusion to be. caused by the concentration fluctuations of ferroactive ions with microscopic parameters (primarily polarizability) deffering greatly from the average ones. We think that investigations designed to find analogous behaviour in other solid solutions and complex compounds might be very helpful in the verification of the theoretical models as well as for the control of properties in technologically important materials. REFERENCES 1.
2. 3. 4. 5. 6. 7. 8. 9. 10.
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