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Synthesis, Characterization, and Dielectric Properties of Pyrochlore Bismuth-Dysprosium Titanate Systems

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Synthesis, Characterization, and Dielectric Properties of Pyrochlore Bismuth-Dysprosium Titanate Systems
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Austin, Wells
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English

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Bismuth ( jstor )
Ceramic materials ( jstor )
Density ( jstor )
Dielectric materials ( jstor )
Dielectric properties ( jstor )
Dysprosium ( jstor )
Furnaces ( jstor )
Lattice parameters ( jstor )
Permittivity ( jstor )
Titanates ( jstor )
Arrhenius equation
Dielectrics
Dysprosium
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Undergraduate Honors Thesis

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Abstract:
The structure and dielectric properties of (BixDy1-x)2Ti2O7 for different doping amounts of dysprosium are investigated. Pyrochlore structures for compounds of x = 0, 0.25, 0.50, 0.75, and 1.00 were synthesized using co-precipitation. Through extensive trials, times and temperatures for both calcination and sintering were determined for powders and pellets of each composition. XRD analysis revealed that stable structures of (BixDy1-x)2Ti2O7 were produced at each tested composition and that the lattice parameters of each compound followed trends predicted by Vegard’s law. Measuring dielectric properties of a BiDy2Ti2O7 revealed that relaxation occurred with all three mechanisms for the phenomenon present. Applying the Arrhenius relationship, activation energy and jump frequency were determined for the system, and dispersion was calculated for a comparison with other pyrochlore and weberite structures. ( en )
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Awarded Bachelor of Science in Materials Science and Engineering; Graduated May 7, 2013 summa cum laude. Major: Materials Science and Engineering, Emphasis/Concentration: Metals
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College/School: College of Engineering
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Legacy honors title: Only abstract available from former Honors Program sponsored database.
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UF Honors Program sponosored database

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University of Florida
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Copyright Wells Austin. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires pe

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UNIVERSITY OF FLORID A Synthesis, Characterization, and Dielectric Properties of Pyrochlore Bismuth Dysprosium Titanate Systems Summa Cum Laude Thesis Austin J. Wells 4/17/2013 Bachelor of Science Materials Science & Engineering Graduating May 2013 Advisor: Dr. Juan C. Nino Abstract The structure and dielectric properties of (Bi x Dy 1 x ) 2 Ti 2 O 7 for different doping amount s of dysprosium are investigated. Pyrochlore structures for compounds of x = 0, 0.25, 0.50, 0.75, and 1.00 were synthesized using co precipitation. Through extensive trials, times and temperatures for both calcination and sintering were determined for po wders and pellets of each composition. XRD analysis revealed that stable structures of (Bi x Dy 1 x ) 2 Ti 2 O 7 were produced at each tested composition and that the lattice parameters of each compound ric properties of a BiDy 2 Ti 2 O 7 revealed that relaxation occurred with all three mechanisms for the phenomenon present. Applying the Arrhenius relationship, activation energy and jump frequency were determined for the system, and dispersion was calculated for a comparison with other pyrochlore and weberite structures.

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2 1. Introduction Pyrochlo re systems with stoichiometry have been studied intensely for their applications in dielectrics, conductors, magnetics and solid oxide fuel cells One example, ( BZN ) has been considered for high frequency microwave applications [ 1]. Titanate systems in particular have received special attention because of their dielectric properties at low temperatures and high frequencies [ 2]. Of these ti tanate pyrochlore s, bismuth titanate has been explored extensively for its use in high permittivity dielectrics [3 12 ]. S ince Knop et al. first discovered in 1969 there has been much debate about its dielectric behavior Many early reports claimed was ferroelectric [ 4,5,7 ] but these have been disputed by more recent studies [ 6,8,12 ], particularly by Esquivel Elizondo e t al. as recently as 2011. Much analysis has been conducted on the metastable pyrochlore phase [ 10,11 ] and it has been determined that spin ice occurs at very low temperatures (T < 2 K) [ 8 ]. Of particular interest is the dielectric relaxation behavior in bismuth pyrochlore systems. Simply stated, relaxation is a phenomenon in which the storage permittivity, decreases with an increase in testing frequency at any given temperature. This i s accompanied by a maximum temperature, at which a peak in the loss permittivity, occurs, both of which increase with increasing frequency. This can be clearly seen in BZN, a plot of which is shown in Figure 1 and presented by J. C. Nino [1 ] H ere, a very visible envelope exists in which the frequencies are contained and then collapse into a seemingly constant perm ittivity at higher temperatures (T > 200 K). Relaxation can be explained by three possible mechanisms, the first being the high polarizability of the bismuth lone pair electrons. Atomic displacements, such as those in the perovksite or pyrochlore structure, and substitutional cations from doping may also cause this behavior [13]. Although the dielectric properties of have already been reported at

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3 Figure 1 : Storage and loss permittivity in BZN at various temperatures, displaying idealized dielectric relaxation over a frequency range of 1 kHz to 2 MHz [1] differing frequencies and low temperatures [ 12 ] the same analysis has not been conducted for dysprosium titanate, Dysprosium titanate was first suggested for use in nuclear reactors by K osenkov et al. in 1976 [14] Since then, it has been found that along with hafnium (Hf), can be used to absorb neutrons in the lining of n uclear fuel rods [ 15 17 ]. Of more recent interest, the pyrochlore phase of dysprosium titanate has been deemed analogous to water ice at extremely low temperatures (T < 1 K) making it an ideal spin ice material [ 18 20 ] superior to and others It has even been suggested that due to its monopole behavior, could provide proof of Dirac strings, the once thought fictitiou s one equations while incorporating these magnetic monopoles [ 20 ]. Dysprosium has an ionic radius of 0.912 making it the second smallest ion to form the titanate pyrochlore structure [21 ] and substantially smaller than bismuth which has a radius of

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4 1.03 Due to their structure, bismuth pyrochlore systems are very effective for transporting charge leading to improved electronics. Experiments are done to investigate dysprosium substituting bismuth in a pyrochlore lattice, and the dielectric properties of different compositions of (Bi x Dy 1 x ) 2 Ti 2 O 7 for which are analyzed in an effort to explore whether or not dielectric relaxation occurs in this sy stem at different values of x. In this particular study only x values of 0, 0.25, 0.50, 0.75, and 1.00 are considered 2. Material s & Methods Due to its thermodynamic instability must be synthesized using co precipitation rather than solid state processing, such as ball milling. As such, and all other compositions of (Bi x Dy 1 x ) 2 Ti 2 O 7 were prepared by co precipitation for the first time in literature to ensure valid result s. Bismuth subnitrate ( Fisher ) and dysprosium nitrate ( Pfaltz & Bauer ) were dissolved in stoichi o m etric quantities (Table 1) in 35 mL of nitric acid ( Ricca ). This mixture was allowed to stir for approximately 10 min utes u ntil all bismuth subnitrate and/ or dysprosium nitrate had dissolved and the solution was clear. During this time, 35 mL of ammonium hydroxide (Acros) was prepared and placed in a freezer throughout the process. When the solution was completely transparent, the s toichiometrically appropriate amount of titanium isopropoxide ( Acros, 98% ), was added directly to the solution (Table 1) This mixture was set to stir for another 10 minutes until the solution was again transparent A mmonium hydroxide was sub sequently added and i mmediately formed a white precipitate. This precipitate was filtered until the pH level was ~7.0 and then set to dry for 24 h at 120C. When dried, the nano powder was ground with a mortar and pestle and placed in to a zirconium oxide c rucible. Calcination was performed at various temperatures and times based on composition (Table 1) in a low temperature box furnace (Lindberg/Blue BF51800 Series) with a heating an d cooling rate of 200C/h. The resultant powder was then analyzed with X ray

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5 diffraction (XRD) after which it was pressed into pellets 7 mm in diameter using a mechanical hydraulic press followed by a cold isostatic press. Pelle ts were placed in either a high temperature CM 1708 box furnace, CM 1706 bottom loading furnace or Thermowave MOD III microwave furnace for different temperatures and times to sinter depending up on the composition (Table 1) After ensuring high relative density, s intered pellets were sputtered on each side with gold atoms to form an electrode [ 22 ]. Dielectric analysis was carried out using a Cyrodyne refrigerator with an Agil ent E4980A Precision LCR Meter, and results were analyzed. Table 1 : Processing information for (Bi x Dy 1 x ) 2 Ti 2 O 7 at various compositions, x. (Bi x Dy 1 x ) 2 Ti 2 O 7 x 0.00 0.25 0.50 0.75 1.00 Mass Bi (g) 0.01 mol 0 0.731 1.461 2.192 2.923 Mass Dy (g) 0.01 mol 3.485 2.614 1.743 0.871 0 Mass Ti Iso (g) 0.01 mol 2.958 2.958 2.958 2.958 2.958 Calcination temperature (C) 1200 850 850 560 560 Calcination time (h) 10 36 36 36 10 Sinter temperature (C) 1500 1400 1300 1200 1164 Sinter time (h) 10 ~ 0.5 ~ 0.5 ~ 0.5 ~ 0.5 Sinter furnace High Temp Bottom Loader Bottom Loader Bottom Loader Microwave 3. Results and Discussion 3.1 Processing and Characterization X ray diffraction (XRD) characterization was performed on both the calcined powders and the sintered pellets of each composition to ensure phase purity. These data for the powders are displayed in Figure 2 with both the experimental and theoretical peaks shown for each composition. Regarding it appears that for the powder a minute peak exists, but

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6 ( a ) (b)

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7 Figure 2 : XRD results of powders with theoretical peaks included for comparison and confirmation of phase purity for different compositions of (Bi x Dy 1 x ) 2 Ti 2 O 7 : (a) x = 0.75 (b) x = 0.50, (c) x = 0.25, (d) x = 1.00 (c) (d)

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8 when the powder was pressed and sintered, this peak disappears, proving that the pellet itself was phase pure. In addition, the plane did not diffract in the compounds containing dysprosium due to the limitations of the equipment used, but this did not hinder the data or its analysis. Pellets were sintered at a particular temperature and time s hown in Table 1 that varied for each composition. Initially, the microwave furnace wa s used for samples containing bismuth to prevent other phases from forming during the ramping of the temperature. In addition, a CM 1706 bottom loading furnace was utilized and s et to the sintering temperature before a pellet was introduc ed. Each composition of pellet con taining bismuth was soaked in the bottom loading furnace for the time shown above in Table 1 and then air cooled to room temperature. This, again, prevented the formation of other phases since dysprosium doping did not stabilize the bismuth pyrochlore sy stem. It also allowed for quick reactions to occur and densify the pellet effectively. A CM 1708 box furnace was used to sinter which generated equally successful results. This process produced pellets with a relative density of 87 90% accordi ng to measurements made based upon ASTM Standard B962 08 which uses the Archimedes method for measuring density shown in Equation 1 below (1) Here, is the density of the solid pellet whereas is the density of the auxiliary liquid, which in this case was water. At 22 C, the density of water is = 1.0033 g/cm 3 Furthermore, is the mass of the pellet in air, and is the mass of the pellet mea sured in water. This buoyancy term, allows for the calculation of the density much more effectively and accurately th an crude geometric measurements following found by measuring the volume, V of the pellet. The Archimedes method takes into account the porosity of the pellets as can be seen in Table 2.

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9 Table 2 : Density measurements using a geometric and Archimedes approach, showing inaccuracy of geometric values. Geometric Method Archimedes Method (Bi x Dy 1 x ) 2 Ti 2 O 7 x Theoretical Density (g/cm 3 ) Measured Density (g/cm 3 ) Relative Density Measured Density (g/cm 3 ) Relative Density 1.00 7.632 0.75 7.423 6.300 85% 6.431 87% 0.50 7.215 6.169 86% 6.381 88% 0.25 7.006 0.00 6.797 5.971 88% 6.139 90% 0.00 6.797 5.775 85% 6.052 89% Further analysis of the X ray diffraction peaks from a curved position sensitive detector (CPS) was law and work done by Pramanick et al. [23] shown in Equation 2 describes the change of the lattice parameter , of a cubic unit cell with differing compositions of constituents. ( 2 ) In order to calculate the experimental lattice parameters, the diffraction angles were determined by applying Voigt profile to each peak and utilizing Equation 3 which is explained below. (3 ) Here, is the apparent lattice parameter, is the actual lattice parameter, is the angle at which a diffraction peak is seen, is the vertical displacement of the sample in its holder, is the distance from the sample to the detector, and is the angle between the X ray beam and the sample surface. It should be noted that is a constant dependent upon the CPS instrument used and was accounted for in the actual XRD measurements For this particular setup, , and due to the difficulty associated with measuring it, was determined mathematically. Because a CPS instrument was not used to collect the XRD data for this analysis could not be done for that composition.

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10 The actual lattice parameter, was found by plotting with respect to and extrapolating the value to The value of was determined by understanding the basics of diffraction (4 ) (5 ) Because only Cu radiation was used known values of and were applied. The spacing between two a djacent diffracting planes each of type is represented by Using the miller indices of each plane and the constants above, the experimental lattice parameters for powders of each composition were calculated, the process of which is shown in Figure 3 : Experimental lattice parameter determination from extrapolation of the linear fit for each line to cos 2

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11 Table 3 : Comparison of experimental and theoretical lattice parameters and displacement for various compositions. (Bi x Dy 1 x ) 2 Ti 2 O 7 x (Nominal) Experimental Lattice Parameter () Theoretical Lattice Parameter () Displacement 0.75 10.250 0.026 10.303 310 0.50 10.197 0.015 10.248 344 0.25 10.130 0.018 10.192 343 0.00 10.076 0.014 10.136 351 Figure 4 : Comparison of experimental and theoretical lattice parameters based on Vegard's law according to Table 3 for various comparisons with error included for 95% confidence Figure 3. Although some planes of each composition diffracted at angles inconsistent with compared to theoretical values for the lattice parameter. This is demonstrated in Figure 4 and Table 3

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12 This analysis proves that the lat tice parameter is increasing with increasing amounts of bismuth in a parallel manner with though there is not a close correlation due to the error associated with the XRD diffraction angles This is a simple yet important discovery since Bi Dy pyrochlore lattices have never been reported in literature. This further proves that dysprosium substitution wil l occur in the metastable structure of the pyrochlore lattice, despite the difficulty involved with the sintering process due to instability 3.2 Dielectric Properties The overarching purpose of this study is to determine the storage and loss permittivity behavio r s of the (Bi x Dy 1 x ) 2 Ti 2 O 7 system and to determine the effects of composition on these dielectric properties. Essentially, does a substitution of dysprosium for bismuth in the pyrochlore lattice lead to relaxation? Due to time and equipment limitations, these results are only included for (x = 0.50) Prior to this project, however, Esquivel E lizondo et al. conducted the same experiment with the end group, [12] and their results are analyze d Di electric relaxation does not occur in the system, shown in Figure 5 when compared with BZN in Figure 1 Although the highest frequenci es have the lowest permittivity, most frequencies do not even exhibit distinguishable loss peaks. In order to understand this behavior in systems with dysprosium, the same analysis was conducted. Preliminary tests using an Agilent E4980A Precision LCR meter were done by measuring relative permittivity, of and a t room temperature by utilizing (6) for which is the capacitance displayed by the instrument, and is the permittivity of free space, is the area of one side of the pellet, and is the thickness of the pellet. These measurements, shown in Table 4 were taken at a low frequency of 1 kHz. Such

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13 Figure 5: Storage and loss permittivity at various temperatures a nd a frequency range of 100 kHz to 2 MHz for showing no relaxation behavior [12] preliminary results suggest the pellets are indeed sufficient for dielectric tests However, these permittivities are determined for pellets with substantial pores in them. Thus, it is nec essary to make use of Equation 7 to determine the actual permittivity when porosity is taken into consideration. (7 ) In this expression, is the measured permittivity and is the adjus ted permittivity, both shown in Table 4 Knowing that the relative permittivity of air in the pores is and using the

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14 relative density, to determine the volume fraction of voids, such that more accurate permittivity values were calculated The trend of increasing permittivity over the range of nominal compositions is shown in Figure 6 below. It can be seen that both m easured and Table 4 : M easured and adjusted permittivity at room temperature and 1 kHz frequency. (Bi x Dy 1 x ) 2 Ti 2 O 7 x Measured Permittivity Adjusted Permittivity 0.75 102.6 125.3 0.50 87.2 104.7 0.00 71.4 83.1 0.00 69.1 81.6 Figure 6 : Permittivity values at room temperature and 1 kHz, both measured and adjusted for porosity of each compostition tested.

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15 adjusted values of permittivity increase with increasing amounts of bismuth in the system. Further testing of the pellet at different temperatures in a Cyrodyne refrigerator with the same LCR meter produced the results shown in Figure 7. From this data, it is evident that displays a relatively constant storage permittivity a nd low loss, as well as dielectric relaxation. This is validated by the increase in peak loss and temperature at which this occurs as frequency increases. It is important to note that data at 1 kHz is excessively noisy since it is only based upon the res ponse of the gold electrode. Figure 5 : Dielectric measurements of storage and loss permittivity of shown with a frequency range of 1 kHz to 2 MHz and exhibiting dielectric relaxation Each peak was modeled with a Gaussian fit to determine its maximum temperature value , This information was then used with the Arrhenius relationship to form a plot in order to

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16 determine the activation energy, of the system according to Equation 8. (8) In this case, is the test frequency, is the pre exponential jump frequency, is the peak temperature for loss at the test frequency. The Arrhenius plot is shown in Figure 8 and further proves the presence of relaxation since the points follow a linear path very closely. Fitting the points yields an activation energy of and a jump frequency of Figure 6 : Arrhenius plot of frequency ranging from 10 kHz to 2 MHz against inverse temperature, showing the relaxation behavior in and yielding results for activation energy and jump frequency.

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17 4. Dispersion Based upon the results for the dielectric storage and loss permittivity for various compositions of (Bi x Dy 1 x ) 2 Ti 2 O 7 o ne can study the dispersion shown in Equation 9 and compare any trends that exist between each composition. (9 ) In this expression, is the purely analytical parameter of dispersion, is the change in peak temperature for the range of frequencies, applied. For these tests, usable f requencies range from 10 kHz to 2 MHz. Plotting a material constant such as activation energy against dispersion Figure 7 : Dispersion plot for different ceramic material systems showing relaxation all of which are pyrochlores except and which are weberites [24 27]

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18 is likely to exhibit interesting results, and a trend could be found. Although no trend between compositions of (Bi x Dy 1 x ) 2 Ti 2 O 7 is shown due to limited information, Figure 9 shows a plot of activation energy against dispersion for different ceramic materials that exhibit relaxation. 5. Conclusions Experiments and characterization of the (Bi x Dy 1 x ) 2 Ti 2 O 7 system have only just begun, but much has been learned from completed work thus far. Perhaps most importantly, dysprosium has been substituted in diffe rent amounts into the bismuth pyrochlore lattice through co precipitation for the first time reported according to literature. Furthermore, calcination and sintering techniques have been empirically deter mined through numerous trials XRD analysis and Ve law calculations indicate that pyrochlore system s of the desired compos itions have been successfully created with slight variations from ideality. Further findings have yet to be obtained Primarily, dielectric measurements must be completed in order to understand the relaxation behavior of compo unds with differing amount s of bismuth and dysprosium as well as in order to determine activation energy and find trends in dispersion. However, the results produced by data from have revealed that relaxation in this system does occur with the presence all three possible mechanisms. In addition to these future tasks, some other projects could be performed to enhance the quality and understanding of this research. Using thermogravimetric analy sis (TGA) and differential scanning calorimetry (DSC) to find the exact temperatures of calcination and sintering as well as an in situ XRD detector to determine how the lattice transformation occurs for these processes would contribute greatly to the unde rstanding of the crystallography of the system. Also, polishing and etching pellets to observe their microstructures with a scanning electron microscope (SEM), should provide evidence of how the grain size affects the dielectric properties of each composi tion. In processing mixing titanium isopropoxide and the nitrates used for co precipitation rarely resulted in a violent exothermic reaction that created a strange orange precipitate. Upon

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19 calcination, however, this powder was as phase pure as in trial s during which this reaction did not occur. Therefore, investigating the cause of this phenomenon and how to avoid it would expand upon knowledge of the co precipitation process. 6. Acknowledgements The help of many associates is greatly appreciated. In particular, Paul Johns and other members of the Nino Research Group guidance was certainly necessary to reach the given results SungW ook Mhin and Dr. Jacob t he CPS instrument and gold sputtering. Bibliography [1] 2 O 3 ZnO Nb 2 O 5 Journal of Applied Physics 89 [8] 4512 16 (2001). [2] electric Properties of Ln 3 NbO 7 (Ln = Nd, Gd, Dy, Journal of the European Ceramic Society 27 [13 15] 3971 76 (2007). [3] O. Knop and F. Brisse, Pyrochlores V. Thermoanalytic X Ray Neutron Infrared and Dielectric Studies of A 2 T i 2 O 7 Titanates Canadian Journal of Chemistry, 47 [6] 971 (1969). [4] S. P. Yordanov, I. Ivanov, and C. P. Carapanov, "Dielectric properties of the ferroelectric Bi2Ti2O7 ceramics," Journal of Physics D Applied Physics, 31 [7] 800 06 (1998). [5] Y. Hou M. Wang, X. H. Xu, D. Wang, H. Wang, and S. X. Shang, "Dielectric and ferroelectric properties of nanocrystalline Bi 2 Ti 2 O 7 prepared by a metallorganic decomposition method," Journal of the American Ceramic Society, 85 [12] 3087 89 (2002). [6] W. F. Su a nd Y. T. Lu, "Synthesis, phase transformation and dielectric properties of sol gel derived Bi 2 Ti 2 O 7 ceramics," Materials Chemistry and Physics, 80 [3] 632 37 (2003). [7] Y. Hou, Z. M. Huang, J. Q. Xue, Y. N. Wu, X. M. Shen, and J. H. Chu, "Study of the ferroelectricity in Bi 2 Ti 2 O 7 by infrared spectroscopic ellipsometry," Applied Physics Letters, 86 [11] (2005). [8] R. Seshadri, "Lone pairs in insulating pyrochlores: Ice rules and high k behavior," Solid State Sciences, 8 [3 4] 259 66 (2006).

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20 [9] J. Cag non, D. S. Boesch, N. H. Finstrom, S. Z. Nergiz, S. P. Keane, and S. Stemmer, "Microstructure and dielectric properties of pyrochlore Bi 2 Ti 2 O 7 thin films," Journal of Applied Physics, 102 [4] (2007). [10] B. B. Hinojosa, J. C. Nino, and A. Asthagiri, "Fir st principles study of cubic Bi pyrochlores," Physical Review B, 77 [10] (2008). [11] C. H. Patterson, "First principles calculation of the structure and dielectric properties of Bi 2 Ti 2 O 7 ," Physical Review B, 82 [15] (2010). [12] J. R. Esquivel Elizondo, 2 Ti 2 O 7 : It is not what you Chemical Materials 23 4965 74 (2011). [13] property relationships towards engineering of an integrated NP0 capacitor for bismuth pyrochlore systems dissertation), Pennsylvania State University, PA (2002). [14] V. M. Kosenkov, T. M. Guseva, S. A. Alekseeva, and V. K. Nevorotin, Structural Changes In Irradaiated Dysprosium Titanate ," Soviet Atomic Energy, 40 [5] 513 15 (1976). [15] V. D. Risovanyi, E. P. Klochkov, and E. E. Varlashova, "Hafnium and dysprosium titanate based control rods for thermal water cooled reactors," Atomic Energy, 81 [5] 764 69 (1996). [16] V. D. Risovany, E. E. Varlashova, and D. N. Suslov, "Dysprosium titanate as an absorber material for control rods," Journal of Nuclear Materials, 281 [1] 84 89 (2000). [17] A. Sinha and B. Sharma, "Development of dysprosium titanate based ceramics," Journal of the American Ceramic Society, 88 [4] 1064 66 (2005). [18] T. Fennell, O. A. Petrenko, G. Balakrishnan, S. T. Bramwell, J. D. M. Champion, B. Fak, M. J. Harris, and D. M. Paul, "Field induced partial order in the spin ice dysprosium titanate," Applied Physics A Materials Science & Processing, 74 S889 S91 (2002). [19] B. S. Shastry, "Spin ice and other frustrated magnets on the pyrochlore lattice," Physica B Condensed Matter, 329 1024 27 (2003). [20] D. J. P. Morris, D. A. Tennant, S. A. Grigera, B. Klemke, C. Castelnovo, R. Moessner, C. Czternasty, M. Meissner, K. C. Rule, J. U. Hoffmann, K. Kiefer, S. Gerischer, D. Slobinsky, and R. S. Perry, "Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7," Science, 326 [5951] 411 14 (2009).

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21 [21] C. Jiang, C. R. Stanek, K. E. Sickafus, and B. P. Uberuaga, "First principles prediction of disordering tendencies in pyrochlore oxides," Physical Review B, 79 [10] (2009). [22] Pd, and Pt on Bil 3 ACS Applied Materials Interfaces, 3 [6] 1910 17 (2011). [23] A. Pramanick S. Omar J. C. Nino, and J. L. Jones, Lattice parameter determination using a curved position sensitive detector in reflection geome try and application to Sm x /2 Nd x /2 Ce 1 x O 2 Journal of Applied Crystallography 42 490 95 (2009). [24] Tulinova Soviet Physics Solid State 14 477 845 (1926). [25] ctric Properties Solid State Communications 100 531 (1995). [26] R.S. Roth, T.A. Vanderah, P. Bordet, I.E. Grey, W.G. Mumme, L. Cai, and J.C. Nino TiO 2 (Nb,Ta) 2 O 5 Journal of Solid State Chemistry 181 [3] 406 14 (2008). [27] D. W. Jung, J. C. Nino K. L. Duncan, S. R. Bishop, and E. D. Wachsman, "Enhanced long term stability of bismuth oxide based electrolytes for operation at 500 A d egrees Ionics 16 [2] 97 103 (2010).