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Ferroelectric materials have a wide range uses in industry, such as materials manufacturing, automotive sensors and control systems, aerospace exploration, and nuclear power[1,2]. All ferroelectric materials are piezoelectric due to the "spontaneous polarization". Some of them are good candidates for electromechanical transducers due to their sensitivity, cost and robustness. Quartz, single crystal SiO2, which can work up to 350 ï‚°C, is one of the most widely used piezoelectric materials. Sensors are needed to work at high temperatures. However, the maximum operating temperature is limited by the "Curie points", the ferroelectric-paraelectric transition temperature. Therefore, ferroelectric materials with a high Curie points are desirable for high temperature piezoelectric applications. Some typical ferroelectric materials with high Curie point have been found, such as LiNbO3 (Tc = 1150 C), lithium tantalate, LiTaO3 (Tc = 720 C)[4-7].
The A2B2O7-type ferroelectrics, such as Sr2Nb2O7, Ca2Nb2O7, La2Ti2O7 and Nd2Ti2O7, have a provskite-like layered structure(PLS)[8, 9], and are known for their super-high Curie points (many are above 1300 oC)[10-13]. Furthermore, most of them have a low dielectric constant, high coercive field. Hence, they could be used as high temperature applications. Due to their unique properties, there is a large amount of research focussed on the A2B2O7-type ferroelectrics to investigate their structure, piezoelectric, dielectric constant and coercive field.
Except the piezoelectric application, ferroelectrics can be used as data storages. Ferroelectric materials have domains, which can be reversed by an external electric field, and the domain wall is much thinner than magnetic domain wall, about 1/10 of it. Hence, it is hopeful to make smaller memories by ferroelectrics.
Chapter II. Ferroelectrics
Ferroelectricity of materials was discovered in 1921. Ferroelectric materials have a spontaneous polarization untill cooling below the Curie point. In the 1950's, a huge wave in the research of ferroelectric materials leads to the widespread use of BaTiO3 as capacitors and piezoelectric transducer devices. From then on, many other ferroelectric materials including PbTiO3, PZT(lead zirconate titanate) and PLZT(lead lanthanum zirconate titanate) have been developed and put into service for a variety of applications. The ferroelectric ceramics have been widely utilized in the areas of capacitors, non volatile memories, medical ultrasound imaging and actuators, data storage and displays.
Most materials can be polarized linearly with external electric field, which is called dielectric polarization. Compared to this, some other materials polarize non-linearly and the dielectric constant is a function of the external electric field. However, ferroelectric materials are have a spontaneous polarization. Fig.2.1 is a standard P-E hysteresis loop of ferroelectric crystal.
Fig.2.1 P-E hysteresis loop for typical ferroelectric materials
The application of an external electric field to the piezoelectric crystal causes the polarization to go up with increasing E(electric field strength) untill electric displacement D reaches point C. The polarization does not changed after this point which indicates polarization is saturated. When E is reduced, polarization does not go back the same way as it went up. The remanent polarization(Pr) is the residual polarization left when the electric field(E) reaches zero. Then, the E reverses and the polarization becomes zero when E arrival at point F. In the Figure, the value of |OF| is Ec which is named the coercive field and it is the opposite electric field needed to make the polarization to zero.
But usually a spontaneous polarization in the crystal or a grain is not uniformly aligned throughout the whole crystal. A region that has an oriented polarization direction is called a ferroelectric domain. The region between two domains is called domain wall. If the direction of the domains is random, it is not possible to see the ferroelectric on macroscopically. This is because the effects of individual domains will cancel each other and the net polarization will be zero. Therefore, we need to pole the crystal under a strong DC field. The process, shown in Fig. 2.2, is called polling.
Fig. 2.2 A polycrystalline ferroelectric with random orientation of grains before and after poling.
Compared to single crystal, it is more difficult to pole the polycrystalline ceramics which is result of the random orientations of the grains. The grains oriented in different directions restrict the movements of domain walls under electrical poling, making the Ec of ceramics much larger than the single crystal[44,45]. On the other hand, the ceramics have more single crystal-like properties when all of the grains are oriented in a well direction. This can decrease Ec.
Valasek found the first ferroelectric(Rochelle Salt) in 1921 and there are now over 500 kinds of ferroelectric materials. It is a huge family, normally, they are classified as followed.
1. Corner Sharing Octahedra Compounds
Corner sharing octahedra structured ferroelectrics are the most important family of ferroelectrics. Perovskite compounds, Lithium niobate, Tungsten bronze type compounds are all included in the group. The standard structure is shown in the picture, Bb+ is in the center of the octahedra while all the O2- sited on the six point, and the position between the octahedra is occupied by Aa+.
Fig.2.3. (a) A cubic perovskite-type unit cell(BaTiO3); (b) Network of O2- ions octahedra in the structure.
2. Compounds Containing Hydrogen Bonded Radicals
3. Organic Polymers
4. Ceramic polymer composites
Chapter III. AnBnO3n+2 compounds
3.1. Structure and ferroelectric properties
AnBnO3n+2 compounds is one series of perovskite-related layer structured compounds(PLS family) which are varieties of the perovskite group.The PLS compounds include three series with the structure which looks like a result from cutting the cubic perovskite structure along the ,,  direction by insertion of additional oxygen. The general forms of the three are A'Ak-1BkO3k+1, AnBnO3n+2 and AmBm-1O3m respectively[9,19].
In the AnBnO3n+2 formula, n represents the number of BO6 octahedra that span one layer, and therefore specifies the thickness of the PL(perovskite-layer). Sometimes, n is non-integral due to the mixture of layers with different thickness and it indicates the average number of octahera per layer. In this structure alkaline earth or lanthanide metals often occupy the A positions while the B cations are usually titanium or niobium[8, 9, 19]. Some typical AnMnO3n+2 structures are shown in Fig. 4.1.
Fig.3.1. skeleton diagram of the non-distorted crystal structure of all the members projected along a-axis.
All of the AnBnM3n+2 compounds space groups are either orthorhombic or monoclinic. Different crystal structure corresponds to different distortions of the layers relative to the ideal cubic perovskite structure. In these systems, we can see that the typical distortions are tilting of the BO6 octahedra and displacement of either or both the A and B cations. Due to this, some of them have a symmetry structure while the others are non-centrosymmetrical.
There are many ferroelectrics in the PLS group. Same integer ratio materials and their ferroelectric properties have been summarized in the Tables followed.
Table.3.1 A2B2O8, n=2
Table.3.2 A3B3O11, n=3
Table.3.3 A4B4O14, n=4[9,19, 25]
Table.3.4 A5B5O17, n=5[9,19]
Table.3.5 A6B6O20, n=6
Group n=3 is different from the other groups, this one can be divided into two smaller groups by the structure. One is made of three layers of perovskites and the other is made by a combination of n=2 and n=4 as shown in Fig. 4.2.
Fig.3.2. Structures of two members in n=3; One is mixed by n=2 and n=4 and another has consistent 3-octahedra-thick layers
In the group n=5, most of the materials are not ferroelectrics, an exception is Sr5Nb5O16 which is special in this group. Though it does not look like AnBnO3n+2 in the formula, it can be considered as an oxygen-deficient n=5 type with ordered oxygen vacancies. Its structure is shown in Fig. 4.3.
Fig.3.3. Skeleton drawing of Sr5Nb5O16
From the picture, we can see there are only four layers of integrated octahedra in the structure and could be included in the n=4 group. However it is in n=5 group in this article because its formula is closer to the n=5 materials.
From the data above, it seems to be a general rule that non-centrosymmetric space groups and ferroelectrics exist in the even types n=2, n=3(II), n=4 and n=6. On the other hand, in the uneven types n=3, n=5 centrosymmetric space groups and antiferroelectrics prefer to occur.
3.2. Lanthanum Titanate (La2Ti2O7)
The ferroelectric properties of La2Ti2O7 were first characterized in the 1970s[21-23]. At room temperature, La2Ti2O7 has been found to have two modifications, one is monoclinic (a=7.800 Å, b=13.011 Å, c=5.546 Å, ï§=98.60ï€ ï¯) with space group P21 and the other is orthorhombic (a=7.810 Å, b=25,745 Å, c=5.547 Å) with space group Pbn21. At 780 oC, the structure transforms into a second orthorhombic system (a=3.954 Å, b=25,952 Å, c=5.607 Å) with space group Cmc21. At 1500 ï¯C, it transforms into paraelectric system with space group Cmcm.
Fig. 4.4 The structure of the Cmc21 modification of La2Ti2O7 at 780 ï¯C projected along the a (upper) and c (lower) axes 
In Fig.4.5 and Fig.4.6, it is clear to see the structural change between the orthorhombic Cmc21 and monoclinic P21 modifications at 780 ï¯C. The change is characterized by displacements of La atoms which takes place within the respective planes perpendicular to the a axis, and by rotations of TiO6 octahedra around axes parallel to the b axis and through the respective Ti atoms.
Fig.4.5 The linkages of TiO6 octahedra in the
P21(solid) and Cmc21 (dotted) modifications.
Fig.4.6 A schematic drawing of structural change from the Cmc21 (upper) to the P21 (lower) modification.
The structure of La2Ti2O7 is similar to other members such as Nd2Ti2O7 which is high Curie point ceramic too, but the d33 of La2Ti2O7 is higher at 2.6pC/N.
Fig.4.4. Ferroelectric properties of textured ceramics. Polarizaiton-electric field(P-E) and current-electrical field(I-E) hysteresis loops at 220Â°C and 10Hz along the perpendicular direction to the pressing for La2Ti2O7
This picture shows the P-E and I-E hysteresis loops of the La2Ti2O7 textured ceramics. It is clear to see current peaks corresponding to ferroelectric switching between 40 and 100 kV/cm. The grains of textured ceramics have a general orientation shown in Fig. 4.5.
Fig. 4.5. Scanning electron microscope micrograph of the textured La2Ti2O7
After texturing, generally, most of the grains are plate-like and oriented. In a textured ceramic, the ferroelectric property is perpendicular the oriented direction. And there is no ferroelectric switching peaks along the direction.
3.3. Strontium Tantalite (Sr2Ta2O7) and Strontium Niobate (Sr2Nb2O7)
Compared to Lanthanum Titanate, Sr2Ta2O7 has a very low ferroelectric phase transition temperature(-107oC). Hence it is a paraelectric phase at room temperature. It has orthorhombic symmetry with space group Cmcm. The space group Cmcm has the highest symmetry of all the PLS A2B2O7 compounds. Therefore, the crystal structure of Sr2Ta2O7 at room temperature is expected to be a prototype for these A2B2O7 compounds. Though Sr2Nb2O7 has a similar structure to Sr2Ta2O7, it has a very high Curie point of 1342 oC. The crystal system is orthorhombic with space group of Cmc21 and lattice parameters a=3.933 Å, b=26.726 Å, c=5.683 Å.
The crystal structure of Sr2Ta2O7 viewed along a and c direction is shown in Fig. 4.6. The structure is centrosymmetric, which explains the paraelectric character of Sr2Ta2O7 at room temperature. And the structure of Sr2Nb2O7 has been shown in Fig.4.8.
Fig.4.6. The crystal structure of Sr2Ta2O7 viewed (a) along a; (b) along c direction.
The D-E hysteresis loop of Sr2Ta2O7 c-plate crystal was measured at -190 oC (see Fig. 4.7). The spontaneous polarization Ps, remanent polarization Pr and coercive field at a maximum applied field E0=6.8kV/cm were: Ps=1.9ÂµC/cm2, Pr=0.69ÂµC/cm2, Ec=0.4kV/cm, respectively.
Fig.4.7. D-E hysteresis loop of Sr2Ta2O7 c-plate crystal at -190 oC and 50Hz.
Fig.4.8. The crystal structure of Sr2Nb2O7 viewed (a) along a and (b) along c
The main difference between Sr2Ta2O7 and Sr2Nb2O7 structure is in the degree of deformation of the perovskite-like layers. Unlike the regular arrangement in Sr2Ta2O7, the arrangement of O atoms in Sr2Nb2O7 is largely distorted from that in the ideal perovskite structure. The displacement of Nb atoms from the centres of NbO6 octahedra has z components as well as y components, as is illustrated in Fig.4.9. Consequently, the crystal becomes non-centrosymmetric in this way. In these structures, B ions can displace easily along the c axis, so, usually, the spontaneous polarisation is also directed along the c axis 
Fig.4.9. (a) The displacements of Ta atoms and (b) Nb atoms from the centres of respective octahedral.
Fig.4.10. D-E hysteresis loop of Sr2Nb2O7 c-plate crystal at room temperature and 50Hz. Ps=9ÂµC/cm2, Pr=7 ÂµC/cm2, Ec=6kV/cm at maximum applied field E0=25 kV/cm.
For Sr2Nb2O7, its ferroelectric property has been found in both single crystal and ceramics. And the Sr2Nb2O7 family film has potential to use as ferroelectric memory due to the low dielectric constant, low coercive field and high heat-resistance. The D-E loop is shown in Fig.4.10.
3.4. Calcium Niobate (Ca2Nb2O7)
The structure of Ca2Nb2O7 is similar to La2Ti2O7 and Nd2Ti2O7. At room temperature, it has two modifications and one is monoclinic with space group P21 while the other is orthorhombic with space group Pbn21. The projections of the structure along the a and c axes are shown in Fig.4.11 and Fig.4.12.
Fig.4.11. The structure of monoclinic Ca2Nb2O7 projected along the a axis .
Fig.4.12. The structure of monoclinic Ca2Nb2O7 projected along the c axis.
Ca2Nb2O7 has a very high Curie point above 1500 ï¯C which is assumed by the fact that no dielectric anomaly was found up tp this temperature and 1MHz. P-E loop is shown in Fig.4.13.
Fig.4.13. D-E hysteresis loop of Ca2Nb2O7 c-plate crystal at room temperature and 50Hz. Ps=7ÂµC/cm2, Ec=65kV/cm at E0=160 kV/cm).
3.5. Neodymium Titanate(Nd2Ti2O7)
Compare to La2Ti2O7, Nd2Ti2O7 has higher Curie Point of about 1755K. The single crystals of Nd2Ti2O7, which were prepared by the floating zone technique, has excellent ferroelectric and piezoelectric properties: Ps=9Î¼C/cm2, Ec=200kV/cm, d22=6.5 pC/N[42,12,13].
At room temperature, Nd2Ti2O7 has space group P21 and a monoclinic structure with lattice parameters a=13.02 Å, b=5.48 Å, c=7.68 Å and Î²=98ï¯28ï‚¢ï›ï€±ï€²ï€¬ï€±ï€³ïï€®
Nd2Ti2O7 ceramics can be prepared by sintering the mixed oxide route (Nd2O3 and TiO2) in air from 1300 oC to 1500 oC. Fig.3.5.1 shows the increase of dielectric constant with the increase of sintering temperature and the twinned domain structures indicating the ferroelectric nature of Nd2Ti2O7 ceramics is shown in Fig.3.5.2.
Fig.3.5.1 Dielectric constant of Nd2Ti2O7 as a function of sintering temperature at 1 kHz
Fig.3.5.2 The domain structure in a single grain of Nd2Ti2O7 sintered at 1450 oC
3.5. Other A2B2O7 compounds
In the A2B2O7 group, there are still many other ferroelectrics, and they have not been properly characterized, such as Cd2Nb2O7, Ce2Ti2O7, Pr2Ti2O7. Actually, most of the A2B2O7 compounds can be divided into PLS(perovskite-related layer structure) and PS(pyrochlore structure) . The structure is dependent on the ratio of r(Aa+)/r(Bb-). Compared to PLS compounds, the pyrochlore structured material tends to be more stable with smaller A-site cations. Lanthanide titanites Ln2Ti2O7 (Ln=Sm-Lu) with radius ratios 1.22 â‰¤ rLn3+/rTi4+ â‰¤ 1.5 crystallize in the pyrochlore structure. On the other hand, Ln2Ti2O7 (Ln=La, Ce, Pr, Nd) with radius ratios of the cations rLn3+/rTi4+ â‰¥1.5) prefer the PLS structure. However, under high pressure conditions, Sm2Ti2O7 and Eu2Ti2O7 crystallize with the PLS structure.
It is difficult to prepare cerium titanate (Ce2Ti2O7) at high temperature, because Ce (III) compounds tend to form the thermodynamically stable Ce(IV) when the temperature is above 400oC. For preparing Ce2Ti2O7 (CTO) compounds, CeO2 and Ti2O3 are preferential to be used as the starting materials. The mixture was placed in an argon atmosphere at 1200 oC. Lichtenberg F.[9,19] has reported that the crystal is ferroelectric , but there is no more details about its Curie point and P-E loop.
From the reports, Praseodymium titanate (Pr2Ti2O7) was synthesized from a stoichiomeric mixtures of Pr6O11 and TiO2. The powder mixture was calcinated at 850 ï¯C for 10 hours followed by 1150oC for 10 hours under static air conditions. Differential thermal analysis (DTA) showed that Tc=1755ï¯C for Pr2Ti2O7.
Eu2Ti2O7 has a Curie point of 1100 ï¯C and the structure can convert from pyrochlore to PLS under 8GPa at 1747ï¯C. In a recent paper, Eu2Ti2O7 with PLS structure was synthesized successfully under ambient-pressure at 800ï¯C by using EuTiO3 as the precurso.
Units parameters of some A2B2O7 have been listed in table.4.6
3.6. ABO4 in AnBnO3n+2
In the AnBnO3n+2 PLS family, though n=4 group attracted so much attention due to their excellent ferroelectric properties, there are some other compounds which have possibility to be ferroelectrics. Such as CeTiO4, LaTaO4 in n=2 group; Pr3Ti2TaO11, La3Ti2TaO11 in n=3(II) group; Nd4Ca2Ti6O20, Sr6Nd4Ti2O20, Ca6Nb4Ti2O20 in n=6 group.
In the n=2 PLS group, CeTiO4, LaTaO4 do not have a center of symmetry. The space group of CeTiO4 is Cmc21 with monoclinic structure. Shinya and Takahisa have reported the CeTiO4 can be prepared by oxidating of the Ce2Ti2O7, and in the process of annealing in air for 10 hours, the reddish-brown Ce2Ti2O7 converted into yellow CeTiO4. It was found to exert a relatively high photocatalytic activity under visible light irradiation(Î»>420nm), but there is no report about its ferroelectric properties.
LaTaO4 has two structures orthorhombic and monoclinic. In the temperature range 423K to 1470K, the orthorhombic form of LaTaO4 is stable and coexists with monoclinic LaTaO4 between 423K and 293 K. The large second-order nonlinear response indicates that orthorhombic LaTaO4 has a noncentrosymmetric structure. The spontaneous polarization in orthorhombic LaTaO4, which is assessed from the second harmonic signal, is equal to 1.6muC/cm. The orthorhombic LaTaO4 was prepared by hydroxide coprecipitation followed by calcination and the monoclinic structure can be made by calcinating powder mixures of La2O3 and Ta2O3 at 1200Â°C for 10 hours. The crystal structure is shown in Fig.4.14.
Fig.4.14. The structure of LaTaO4 along c axis
3.7. A3B3O11 in AnBnO3n+2
In n=3 group, most of the materials that are formed by repeated 3 layers(type I) are non-ferroelectrics. But the mixed-layer perovskite-like compounds which are a mixture of two layers and four layers are possible to be ferroelctric(type II).
Pr3Ti2TaO11, La3Ti2TaO11 are in n=3(II) group, and both of them can be made by heat-treating coprecipitated hydroxides. The crystalline materials obtained by heat-treating precipitates with Ln : Ti : Ta = 3:2:1 (Ln = La, Pr, Nd) at 1190-1370 K were found to consist of Ln2Ti2O7-based layered perovskite-like phases with the general formula A4-xB4-xO14 (x=0.18). And the additional heat treatment of a higher temperature can make well-crystallized Pr3Ti2TaO11 and La3Ti2TaO11. For Pr3Ti2TaO11, the temperature is 1570K while 1670K for La3Ti2TaO11.
Both of Pr3Ti2TaO11 and La3Ti2TaO11 belong to a noncentrosymmetric space group P2cm and Pmc21 with orthorhombic structures. Crystallographic data is been shown in Table.4.7.
Yu.A.Titov and A.M.Sych evaluated the spontaneous polarization Ps for La3Ti2TaO11 and Pr3Ti2TaO11 (1.3 and 0.7 relative to La2Ti2O7) is 6mC/cm2 and 4mC/cm2 respectively, and the Ps in La3Ti2TaO11 is higher than that in La2Ti2O7, because the materials contain the same perovskite layers as are present in the ferroelectric materials La2Ti2O7 and Pr2Ti2O7. But there is no literature to support the evaluation. The structural model has been shown in Fig.4.15.
Fig.4.15. Structure of Ln3Ti2TaO11(Ln=La,Pr):
a. identical layers with n = 3; b. alternating layers with n=2 and 4
the solid and dashed lines delineate BO6 octahedraat x = 0.5 and 0, respectively
3.8. A6B6O20 in AnBnO3n+2
With increasing number of the layers, it is difficult to form long ordering in the structure, so there are more defects and there is less integrated ratio compounds in this group.
Nd4Ca2Ti6O20 is one crystal in the n=6 group. It is non-centrosymmetric monoclinic structure with Pna21 space group. The structure has been shown in Fig.4.16. And the crystallographic data is a=7.664Å, b=36.64Å, c=5.436Å while V=1526Å3; Z=4.
Fig.4.16. The structure of Nd4Ca2Ti6O20
The material can be made by Nd2O3, TiO2 and CaCO3. The three materials are used as starting powder in the ratio Nd2O3:TiO2:CaCO3 = 2:6:2 and heat them at 1000ËšC followed by an1800ËšC sinter.
Chapter IV. Proposed research
My proposed research will focus on the AnBnO3n+2 family to find some high curie point compounds with excellent ferroelectric properties. And the experiment includes several steps which is shown in Fig.4.1
Fig.4.1 Flow chart of experiment
For the research, I began with Ce2Ti2O7 and Pr2Ti2O7 which are reported as ferroelectrics but no details can be found about ferroelectric properties. And further more, in the periodic table of elements the Ce and Pr are between La and Nd which means the four have similar atomic radius and electron structure. Nd2Ti2O7 and La2Ti2O7 have excellent high-temperature ferroelectric properties, so Ce2Ti2O7 and Pr2Ti2O7 are good candidates. Especially Pr2Ti2O7, it has a very high Curie point above 1770K reported by F. Lichtenberg[9.19].
The CeO2, Pr2O3 and TiO2 powder are used as raw materials and mix them in accordance with the stoichiometric proportion followed heating to make the Ce2Ti2O7 and Pr2Ti2O7 powder. After this, the ceramics will be prepared for the properties test .
The second stage is to dope Ce into Nd2Ti2O7 and La2Ti2O7 to find the relationship between the dope elements and ferroelectric properties. I hope to get some general rule between the microstructure and the properties which can explain some phenomenon in this family. The last stage will be to attempt to produce some new ferroelectric materials in the AnBnO3n+2 family mixed by different octahedron layers.
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