B Site Substitutional Alloying in Sodium Bismuth Titanate Kevin Seymour, Elena Aksel, Jacob Jones Honors Thesis
Background: Dielectrics Overview: Definitions: A dielectric is an electrical insulator that can be polarized by an applied electric field . Charges within the material are shifted from th eir equilibrium position to line up with the electric field, and subsequently lower the overall electric field inside the dielectric. The most commonly known dielectric is the capacitor. A capacitor is a system to store energy, in the form of charge, on tw o oppositely charged surfaces separated by a dielectric A simple capacitor schematic can be found below in figure 1 The higher the dielectric polarization of the separation material, the more ch arge can be stored on the s urface This is measured by the d ielectric constant, or relative permittivity. The relative permittivity of free space is one. Dielectric Polarization: There are four main mechanisms by which polarization of a material can occur. Electronic polarization, which is exhibited by all materials, is the shift in the electron cloud of an atom to counteract the electric field. Ionic polarization arises from the d isplacement of negative and positive ions in a crystal. Dipolar polarization arises from a charge separation produced by the inherent bonding properties of a species. An example of dipolar polarization is the water molecule. Water has a permanent dipole in which a slight negative charge surrounds the oxygen atom, while a slight positive charge develops among the hydrogen. Finally, space charge polarization develops from charge separation underpinned from interfacial phenomena. Schematic examples of each ar e shown below in figure 2. Figure 1: A schematic showing the basic concept of a capacitor. Charge, Q, is stored on plates of area, A, separated by a dielectric material of length d. Subject to an electric field. Figure 2: From left to right, electronic, ionic, dipolar, and space charge schematic representations.
Equations and Examples: An ideal capacitor is characterized by a constant capacitance C defined as the ratio of cha rge Q, on each surface to the voltage V, between them . Electric susceptibility, X e measures how easily a material can be polarized, and is related to the relative permittivity (dielectric constant) , of the material. Where, The larger the ratio of the capacitance of a material to that of free space, the larger the susceptibility, and thus, an increase in polarization density, P exists by, Where, is the permittivity of free space, and E, is the electric field. Below, in fi gure 3, are some examples of dielectric constants for various materials. Table 1 : Dielectric constants for various materials.
Piezoelectricity: What is Piezoelectricity? Piezoelectricity is the buildup of charge resulting from the application of mechanical strain; this is known as the direct effect . The converse effect is a strain resulting in applied electric field. Crystals that do not exhibit inversion symmetry, tho se that are non centrosymetric, have the possibility of exhibiting piezoelectricity. Shown below in figure 3 are schematics of the direct and converse piezoelectric effect. Of the 32 crysta l classes, 21 are non centrosymetric and 20 of these exhibit the piezoelectric effect . The mechanism by which the piezoelectric effect occurs is related to the occurrence of electric dipole moments. The dipole moments can either be induced for ions in a crystal lattice or directly carried by a species The polarization, P for crystals can be calculated by summing the dipole moments per unit cell . Dipoles which are near each other usually align with each other in areas called domains. The applicati on of an electric field can align many domains in the same direction, this is known as poling. Not all piezoelectric materials can be poled . Equations: The strain, S, compliance, s, stress, T, converse piezoelectric coefficient, d t electric field, E, electric charge density displacement, D, direct piezoelectric coefficient, d, permittivity, make up the coupled equations, as shown below. Both equations involve tensors. Figure 3: The direct and converse piezoelectric effect.
Applications and Examples: Piezoelectricity is found in applications such as the production and detection of sound, electronic frequency generation, microbalances, and ultra fine focusing of optical assemblies  Quartz was one of the first materials studied for its piezoelectric behavior by the curie brothers in 1880. The bi ggest advanced in piezoelectric materials was the discovery and development of the pervoskite piezoelectric, such as, barium tita nate in the 1940s Ferro electricity: What is a Ferroelectric? A ferroelectric is like a piezoelectric, but possess a spontaneous electric polarization that can be reversed by the application of an external electric field . Unlike a typical dielectric, a ferroelectric exhibits a hysteresis effect of its polarization, seen below in figure 4. Applications: Ferroelectrics have been used in several applications including high permittivity capacitors, displacement transducers and actuators, infrared detectors, gas igniters, accelerometers, wave filters, color filters, optical switches, and used in the generation of sonic energy . Depending on the specific properties needed for an application, several different ferroelectric systems can be used. Some base systems such as l ead titanate (PT) can be doped with lanthanum, zirconium, magnesium niobium, zinc, or any combination of these to cover a wide variety of properties. Other ferroelectric systems include barium titanate (BT), strontium bismuth titanate (SBT), potassium nio bate/ tantalate, sodium niobate/tantalate, and many others . PZT: One of the most common ferroelectrics, lead zirconate titanate (PZT) has been extensively studied and commercialized. The very high electromechanical coupling factor and very large piezoe lectric coefficient, d 33 around the rhombohedral and tetragonal phase boundaries have made it so widely used . Figure 4: Left, a t ypical dielectric polarization. Right, a ferroelectric hysteresis loop.
Lead free f erroelectrics: Recently many governments, such as the European Union and California, have restricted or limited the amount of hazardous materials that can be used in electronic devices . New ferroelectric systems are now being researched to hopefully replace the toxic materials currently being used (i.e. PZT). Some examples of systems being investigated include sodium potassi um niobate sodium bismuth titanate, and bismuth potassium titanate . Hardening and Softening Behavior in Ferroelectrics: Hard vs. s oft: D onor dopant s create (metal) cation vacancies in the crystal structure Soft ferroelectrics produce larger displacements, relative to hard ceramics, but they exhibit greater hysteresis, and are more susceptible to depolarization  Soft ferroelectrics typically have to be used at lower temperatures, and are used primarily in sensing applicatio ns . A cceptor dopant s, on the other hand, create oxygen (anion) vacancies. Hard ferroelectrics are more stable than soft ferroelectrics, and cannot produce the same large displacements. Hard ceramics are used in applications with high mechanical loads or voltages  Undoped Acceptor doped Undoped Donor Doped Figure 5: Polarization vs. electric field hysteresis loops for donor (left) and acceptor doped (right) materials in reference to the undoped state.
Characteristic Soft Hard Piezoelectric Constants larger smaller Permittivity higher lower Dielectric Constants larger smaller Dielectric Losses higher lower Electromechanical Coupling Factors larger smaller Electrical Resistance very high lower Mechanical Quality Factors low high Coercive Field low higher Linearity poor better Donor Doping in Sodium Bismuth Titanate (Na 0.5 Bi 0.5 TiO 3 ) : Why study sodium bismuth titanate? As discussed previously, the development of lead free materials is becoming of increasing importance. An investigation by Rodel et al. into materials systems to replace lead based materials for ferroelectrics resulted in figures 5 and 6 below. Figure 5 first differentiates elements to be used by their relative cost and toxicity and figure 6 show s which crystallographic site the element would sit on in the ABO 3 pervoskite structure  Table 2: A list relating properties to the type of ferroelectric behavior .
One combination of the elements outlined in figure 5 that can be used as a ferroelectric is sodium bismuth titanate (NBT). NBT, also called BNT, has attracted a wide research interest. A solid solution of NBT with BT was found to form a morphotropic phase boundary (MPB), which results in enhanced piezoelectric properties . Although NBT ma kes a poor stand alone material system, information gathered from donor/acceptor doping research can lead to a better understanding of how doping affects more complex solid solutions. NBT is known as a relaxor ferroelectric, meaning it processes a high rel ative permittivity and electrostrictive coefficient, with a diffuse phase transition from rhombohedral to tetragonal (200 320 C) . B Site substitutions: Many different combinatorial and doping schemes can be envisioned for the NBT material system, such as imbalanced concentrations of A site materials (Na/Bi), the creation of vacancies, and many others. The one which will be focused on here will be the substitution of the B site element (Ti) with those of different valences. Substitution of titanium, which carries a 4+ charge in the ABO 3 system, with one of lesser valence generally results in a hardening behavior and conversely substituting with a higher valence creates a soft material similar to that of PZT  The elemental substitutions of Fe an d Mn on the B site have been shown to give rise to hardened NBT, while when doped with La results in a soft material  see figure 8 below Figure 7 : Possible candidates for A, B, and oxygen sites in pervoskite type structures . Figure 6: Diagram showing relative cost a nd toxicity of the elements of interest . Figure 8: Polarization vs. electric field hysteresis loop of Fe, Mn, and La doped NBT .
Using the co ncepts of forming solid solutions of Hume Rothery combined with b site elements as shown in figure 7, a list of possible candidates for Ti substitution can be developed. Using that list to find those elements of higher valence then limits the number of possible softening elements to just a handful, which include Ta, Nb, Sb, W, Ru, and Cr Previ ous research with these dopants: Doping with Ta in a n NB T6BT system reduced the coercive field and improved the piezoelectric constant. More than 2 mol.% tantalum doping induces antiferroelectric properties, showing a typical double hysteresis loops, accompanied by a large maximum strain  Below in figure 9 the lowering of the coercive field and the onset of antiferroelctric behavior at 2 mol.% Ta dopeing can be differentiated from a sample that is undoped. In a Nb/Ni NBT scheme the piezoelectric constant d 33 was reported to increase reaching a maxim um at 3 mol.%, see figure 10  The atomic radius of Nb 4+ is similar to that of Ti 4+, but has a higher polarizability. This could have lead to the increase in d 33 Figure 9: Piezoelectric vs. hysteresis loop for an (a) undoped sample and (b) 2 mol.% doped Ta . Figure 10: Piezoelectric constant d 33 and planar electromechanical coupling factor k p of (Bi 1/2 Na1/2)Ti1 x (Ni1/3Nb2/3) x O3 ceramics as a function of x 
A Ba Cu W system in NBT exhibit ed a relatively high piezoelectric constant and a relatively low dielectric loss This behavior was attributed to the hindrance of grain growth . Sb has a high polarizability and has a similar ionic radius to Ti. The increase in polarizability and similar size should give rise to an increase in it piezoelectric properties much lik e the Nb substitution for Ti. Ru is relatively unstudied. An x ray diffraction pattern of an NBT Ru system showed an increase in the size of the crystal lattice. This increase in size could lead to a larger displacement, and subsequently polarization of the material would increase. See figure 9 below. Cr can come as either a 3+ or a 6+ species. Studying the behavior between the different charges would be interesting . Experimental: Starting powders of high purity (Na 2 CO 3 TiO 2 Bi 2 O 3 Ta 2 O 5 Nb 2 O 5 Sb 2 O 5 WO 3 ,RuO 2 and Cr 2 O 3 ) were mixed to create a compound with the chemical formula found below, where x=0.01 and B is Ta, Nb, Sb, W, Ru, or Cr. Na 0.5 Bi 0.5 Ti (1 x) B x O 3 The mixed powders were then ball milled in a solution of ethanol for 24 hours sieved, calcined at 800C for 2 hours, and sieved again. XRD was performed to confirm that all the powders fully reacted during calcination. A PVA binder solution was added, an d additional sieving occurred. The calcined powder was then pressed axially at 0.5 metric tons for 1 min, then isostatically for 3 min. Figure 9: XRD data of an NBT Ru (green) vs. an NBT Cr (blue) sample.
The green body was then sintered at 1100C for 1 hour, with a holding step at 400C for 1 hour for binder burnout. The r esulting sintered samples where 10mm in diameter and 1mm in thickness with a cream color. The samples were then polished and electrode d as needed. Experiments using a APCI wide range d 33 meter, a custom built polarization vs. electric field setup, and an e lectromechanical coupling factor instrument were used to gather data. Data was gathered from the polarization vs. electric field setup using a triangular wave function at 1Hz. The duration of each test was 2 cycles with an increasing electric field in incr ements of 0.5kV till breakdown or switching occurred Results and Discussion: Below, table 3 and figures 10/11 are data collected from the various measurement techniques Dielectric Breakdown (before E c reached) d 33 (pC/N) k p Undoped No 73 Ta No 74 0 .17 Nb No 74 Sb No 78 0 .14 W Yes Ru Yes 26* Cr Yes The piezoelectric coefficient among the three samples which did not breakdown before reaching their coercive field did not change by any significant means, table 3. Interestingly enough, the coercive field needed to bring the net polarization back to zero did increase figure 10. By conventional means this would indicate a hardening of the sample took place, contrary to what was expected to happen. Generally, as discussed in a previous section, the substitution of a lower valence ion for that of higher valence on the B site should lower the coercive field this behavior is not exhibited here Table 3: Data resulting from experimentation including; relative breakdown point, piezoelectric coefficient (d 33 ), and the planar electromechanical coupling factor (k p ). *polarization saturation did not occur
The NBT samples which were doped with W, Ru, and Cr were unable to be poled. Using the polarization vs. electric field setup, some data before the breakdown point was measured. As shown in figure 11, the NBT sample doped with Ru was the only one to show any hysteresis behavior while the samples doped with W and Cr failed at very low electric fields. The failure of these systems could be attributed to a chang e in oxidation state which would result in an inc reased amount of charge carriers. One example is the change of Cr from the 3+ oxidation state to one of 6+, by the reaction shown below. Cr Cr + 3e' Other explanations could include the small sample thickness (1mm) or relatively low densities of the samples (~95%) Conclusion: With the increase in the coercive field, t he observed behavior of donor doping in NBT is different than the behavior one would expect from a conventional system such as PZT. Further investigat ion will be needed to determine the reason this behavior occurs. Figures 10 and 11: Polarization vs. electric field hysteresis loops of various dopa nts in NBT. Ta, Nb, Sb are shown left and W, Ru, C r are shown right
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