CROSS REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to United States Provisional Patent Application number US 63/350,993, filed June 10, 2022, the entire contents of which are hereby incorporated by reference.

FIELD

[0002] The present disclosure relates generally to ferroelectric materials. In particular, the present disclosure relates to solid solution ferroelectric materials.

BACKGROUND

[0003] Piezoelectric materials convert between mechanical and electrical energy and vice versa so they are used in a plethora of electronic devices for sensor and actuator applications including cell phones, sonar equipment, engine knock sensors, pressure sensors, diesel fuel injectors, medical devices, and many more.

SUMMARY

[0004] In an aspect of the present disclosure, there is provided a solid solution having the formula (1-x)BFTM-(x)PbTiO ₃ , wherein BFTM is bismuth iron magnesium titanate.

[0005] In an embodiment of the present disclosure, there is provided a solid solution wherein x is in the range of 0 to 1 [0006] In an embodiment of the present disclosure, there is provided a solid solution wherein x is in the range of around 0.25 to around 0.40.

[0007] In an embodiment of the present disclosure, there is provided a solid solution wherein x is in the range of around 0.30 to around 0.35.

[0008] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution has an atomic stoichiometric ratio of about

BiiPboFe 2sMg 37sTi 375O3 to BioPb-iFeoMgoTi-iOs.

[0009] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution has an atomic stoichiometric ratio of about Bi 7oPb 3oFe 175Mg 2625Ti 562503tO Bi 65Pb 35Fe 1625Mg 24375Ti 59375O3.

[0010] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution has formula of BiFe ₂ /8Ti3/8Mg3/8O3-PbTiO ₃ [0011] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution has a low field piezoelectric coefficient (d ₃ 3) of about 60 pC/N to about 145 pC/N.

[0012] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution has a high field piezoelectric coefficient (d ₃ 3*) of about 60 pm/N to about 190 pm/N.

[0013] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution has a strain response (%) of around 0.6 to around 0.19. [0014] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution has a Curie Temperature (T _c ) between about 489°C to about 730°C.

[0015] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution has a Curie Temperature (T _c ) between about 620°C to about 650°C.

[0016] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution is a hard ferroelectric.

[0017] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution has a coercive field (Ec) between about 30 to about 60 kV/cm; 40 to about 55 kV/cm; or about 38 to about 54 kV/cm.

[0018] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution comprises <30% Pb; or <20% Pb.

[0019] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution is further comprising a ferroelectrically active dopant in place of Fe, Mg or Ti for increasing the piezoelectric coefficient of the solid solution.

[0020] In an embodiment of the present disclosure, there is provided a solid solution wherein the solid solution comprises 5% or less of the dopant by mass.

[0021] In an embodiment of the present disclosure, there is provided a solid solution wherein the ferroelectrically active dopant is selected from a group consisting of:

Al, Ga, In, Nb, and MnO ₂ .

[0022] In another aspect of the present disclosure, there is provided a use of the solid solution in high temperatures or high power transduction applications.

[0023] In another embodiment of the present disclosure, there is provided a use wherein the high temperature comprises an operating temperature ranging up to about 650°C. [0024] In another embodiment of the present disclosure, there is provided a use wherein the high power transduction application comprises use in an electrical transducer.

[0025] In another embodiment of the present disclosure, there is provided a use wherein the application is in structural health monitoring.

[0026] In another embodiment of the present disclosure, there is provided a use wherein the application is in a pressure sensor.

[0027] In another embodiment of the present disclosure, there is provided a use wherein the application is in fuel modulation for engines.

[0028] In another embodiment of the present disclosure, there is provided a use wherein the application is nuclear reactor monitoring.

[0029] In another embodiment of the present disclosure, there is provided a use wherein the application is in deep oil drilling.

[0030] In another embodiment of the present disclosure, there is provided a use wherein the application is in turbine health monitoring.

BRIEF DESCRIPTION OF THE FIGURES

[0031] Embodiments of the present disclosure will now be described, by way of example only, with reference to the attached Figures.

[0032] Figure 1 depicts a) synchrotron X-ray patterns for BFTM-PT at and around the MPB region showing no impurity phases present and b) (104)+(2-10)/(101)+(110) diffraction peaks showing the progression of phases in the solid solution. The tick marks represent the (T) P4mm phase while the x’s mark the (R) R3c phase.

[0033] Figure 2 depicts a) dielectric permittivity and loss as a function of temperature for three select compositions with different room temperature structures and b) Curie Temperature as a function of composition, laying out the phase diagram.

[0034] Figure 3 depicts a) polarization vs electric field, b) bipolar strain vs electric field and c) unipolar strain vs electric field for six compositions both within and nearby the Morphotropic Phase Boundary.

[0035] Figure 4 depicts high and low field piezoelectric coefficients for BFTM-PT.

[0036] Figure 5 depicts a demonstration of the inverse relationship between piezoelectric effect and Curie Temperature. Figure adapted from Yu Z, Zeng J, Zheng L, et al. (2020)[10],

[0037] Figure 6 shows an example of the BFTM-PT solid solutions as described herein doped with aluminum. [0038] Figure 7 shows an example of the BFTM-PT solid solutions as described herein doped with gallium.

[0039] Figure 8 shows an example of the BFTM-PT solid solutions as described herein doped with indium.

[0040] Figure 9 shows an example of the BFTM-PT solid solutions as described herein doped with niobium.

[0041] Figure 10 shows an example of the BFTM-PT solid solutions as described herein doped with manganese dioxide.

DETAILED DESCRIPTION

[0042] Definitions

[0043] Unless defined otherwise, all technical and scientific terms used herein have the meaning as commonly understood in the art.

[0044] As used in the specification and claims, the singular forms "a", "an" and "the" include plural references unless the context dictates otherwise.

[0045] One of the developing applications for piezoelectric materials is to use them as an energy harvesting device to capture the energy from natural repetitive motions generated by vibrations in machinery, vehicles, or human movement to then power devices such as wireless sensor networks in remote locations, wearable biomedical devices, or mobile electronics. A highly utilized piezoelectric material is the perovskite Pb(Zri. _x Tix)O ₃ , (PZT), due a morphotropic phase boundary (MPB) that causes an enhancement of d ₃₃ , the piezoelectric response at x ~ 0.5 and its ability to be easily doped to tune the material for a wide range of applications. [1] However, PZT contains 60 wt% lead, which is a toxic element and in addition, it has a low operating temperature due to a phase transition at its Curie Temperature (Tc) of 350°C, preventing it’s use in high temperature applications.

[0046] As described herein, the end member PbZrO ₃ (PZ) is replaced with BiFe ₂ /8Ti ₃ / ₈ Mg ₃ / ₈ O ₃ (BFTM) to increase the operating temperature of piezoelectric devices. BFTM is unique in that it is one of three perovskites with only bismuth on the A-site that can be synthesized under ambient conditions. [2] Generally, the Bi-cation is too small to stabilize the perovskite phase when it is the only A-cation and therefore can only be synthesized at high pressures. However, in BFTM, the B-site cations have +3, +4, and +2 oxidation states, creating a flexible O-framework that allows for the Bi-coordination environment to be satisfied. BFTM was chosen to replace PbZrO ₃ (PZ) in the solid solution because BFTM has a high Tc of 730°C and with PbTiO ₃ (PT) having a Tc of 489°C, the Tc of the resulting solid solution is expected to fall somewhere in between its end members. This contrasts with PZ, which has a lower Tc than PT, resulting in a phase transition temperature of ~350°C at the MPB of PZT. Additional benefits of using BFTM as an end member is that it decreases the amount of lead in the material. Bismuth also has a lone pair of electrons, like in lead, which will increase the possibility of maintaining a long range ferroelectric ordering, rather than shifting to a relaxor ferroelectric with short range polar nanodomains, as is often observed when making substitutions with a variety of cations that prefer different coordination environments. [3]

[0047] As described herein, solid solutions of BiFe2/8Ti3/8Mg ₃ /8O3-PbTiO ₃ (BFTM- PT) was synthesized, which has a morphotropic phase boundary, a much lower wt% of lead (22% in BFTM-PT compared to 60% in PZT), a higher phase transition temperature of ~650°C for use in high temperature applications, and high d ₃₃ value compared to most materials with a similar Tc.

[0048] In one or more embodiments or examples of the solid solution as described herein, each of the cations is ferroelectrically active and the oxygen provides a charge balance for the cations in the material. As such, the solid solutions described herein may be more polarizable. The solid solutions described herein may have a higher piezoelectric response due to the extrinsic effects that contribute to d ₃₃ . In one or more embodiments or examples of the solid solution as described herein, both Pb and Bi were included in place of Ba. Preparing solid solutions substantially free of Ba can allow for improved long range ferroelectric ordering in the resultant solid solution, which may create increased domain wall motion - an extrinsic factor in the macroscopic d ₃₃ measured as the piezoelectric response. For example, it was found that BFTM-BaTiO ₃ (rather than PbTiO ₃ ) results in a relatively low d ₃₃ .

[0049] In one or more embodiments or examples, the solid solution as described herein may provide a material that can operate at high temperatures. Piezoelectric materials tend to undergo a structural phase transition at lower temperatures - and at that structural phase transition, lose piezoelectric properties. In one or more embodiments or examples, the solid solution as described herein may be used in high temperature applications or high power transduction applications. In one or more embodiments or examples, the solid solution as described herein may be used for health monitoring in harsh conditions. In one or more embodiments or examples, the solid solution as described herein may be used in pressure sensors for use at elevated temperatures. In one or more embodiments or examples, the solid solution as described herein may be used for fuel modulations in engines, nuclear reactor monitor, deep oil drilling sensing, or turbine health monitoring in aircraft. [0050] Generally, the present disclosure provides solid solutions having the formula (1 -x)BFTM-(x)PbTiO ₃ wherein BFTM is bismuth iron magnesium titanate, and uses thereof. [0051] In one or more embodiments of the present disclosure, there is provided a solid solution having the formula (1-x)BFTM-(x)PbTiO ₃ , wherein BFTM is bismuth iron magnesium titanate.

[0052] In one or more embodiments of the present disclosure, there is provided a solid solution wherein x is in the range of 0 to 1 .

[0053] In one or more embodiments of the present disclosure, there is provided a solid solution wherein x is in the range of around 0.25 to around 0.40.

[0054] In one or more embodiments of the present disclosure, there is provided a solid solution wherein x is in the range of around 0.30 to around 0.35.

[0055] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution has an atomic stoichiometric ratio of about BiiPboFe 2sMg ₃ 7sTi ₃ 7sO ₃ to BioPb-iFeoMgoTi-i0 ₃ .

[0056] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution has an atomic stoichiometric ratio of about Bi 7oPb ₃₃ Fe sMg 262sTi 562s0 ₃ to Bi esPb ₃₃ Fe i62sMg 24 ₃ 7sTi 59 ₃ 7sO ₃ .

[0057] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution has formula of BiFe ₂ / ₈ Ti ₃ / ₈ Mg ₃ / ₈ O ₃ -PbTiO ₃

[0058] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution has a low field piezoelectric coefficient (d ₃₃ ) of about 60 pC/N to about 145 pC/N.

[0059] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution has a high field piezoelectric coefficient (d ₃₃ *) of about 60 pm/N to about 190 pm/N.

[0060] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution has a strain response (%) of around 0.6 to around 0.19.

[0061] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution has a Curie T emperature (T _c ) between about 489°C to about 730°C.

[0062] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution has a Curie T emperature (T _c ) between about 620°C to about 650°C. [0063] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution is a hard ferroelectric.

[0064] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution has a coercive field (Ec) between about 30 to about 60 kV/cm; 40 to about 55 kV/cm; or about 38 to about 54 kV/cm.

[0065] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution comprises <30% Pb; or <20% Pb.

[0066] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution is further comprising a ferroelectrically active dopant in place of Fe, Mg or Ti for increasing the piezoelectric coefficient of the solid solution.

[0067] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the solid solution comprises 5% or less of the dopant by mass.

[0068] In one or more embodiments of the present disclosure, there is provided a solid solution wherein the ferroelectrically active dopant is selected from a group consisting of: Al, Ga, In, Nb, and MnO ₂ .

[0069] In one or more embodiments of the present disclosure, there is provided a use of the solid solution in high temperatures or high power transduction applications.

[0070] In one or more embodiments of the present disclosure, there is provided a use wherein the high temperature comprises an operating temperature ranging up to about 650°C.

[0071] In one or more embodiments of the present disclosure, there is provided a use wherein the high power transduction application comprises use in an electrical transducer.

[0072] In one or more embodiments of the present disclosure, there is provided a use wherein the application is in structural health monitoring.

[0073] In one or more embodiments of the present disclosure, there is provided a use wherein the application is in a pressure sensor.

[0074] In one or more embodiments of the present disclosure, there is provided a use wherein the application is in fuel modulation for engines.

[0075] In one or more embodiments of the present disclosure, there is provided a use wherein the application is nuclear reactor monitoring.

[0076] In another embodiment of the present disclosure, there is provided a use wherein the application is in deep oil drilling. [0077] In one or more embodiments of the present disclosure, there is provided a use wherein the application is in turbine health monitoring.

[0078] To gain a better understanding of the invention described herein, the following examples are set forth. It should be understood that these examples are for illustrative purposes only. Therefore, they should not limit the scope of this invention in anyway.

EXAMPLES

[0079] Example 1 - Synthesis and Characterization of a Ferroelectric with Low Lead Content, an Morphotropic Phase Boundary, and a High Curie Temperature [0080] Experimental

[0081] Synthesis

[0082] Samples of (1-x)BFTM- (x)PbTiO ₃ solid solutions were prepared from x=0.1- 0.5 using standard solid-state methods. The precursors used were Bi ₂ O ₃ (Sigma Aldrich 99%), Fe ₂ O ₃ (Sigma Aldrich 99%), TiO ₂ (Sigma Aldrich 99%), Magnesium carbonate hydroxide hydrate (C ₄ Mg ₄ 0i ₂ ■ H ₂ MgO ₂ ■ xH ₂ O) (Sigma Aldrich 99%), and PbCO ₃ (Sigma Aldrich 99%). The mixed powders were first ball milled for 30 h at 350 rpm (15 min on, five minutes rest, and 15 min in the reverse direction) in a Planetary Ball Mill (Fritsch Pulverisette) with 25 mL of ethanol and eight, 10 mm diameter, yttria-stabilized zirconia balls. The resulting powder was used to sinter dense ceramic pellets. The powder was dried and mixed with a 3 wt % polyvinyl butyral (PVB, Butvar B-98, Sigma Aldrich) binder/ethanol solution. The powder was then pressed in a Carver uniaxial press using a die to form pellets with a diameter of 10 mm and thickness of ~1.5 mm. The pellets were placed inside alumina crucibles with sacrificial powder of the same composition and sintered utilizing a two-step sintering process. This includes heating at 300°C for one hour binder burnout stage with a 10 °C/minute ramp rate continuing to the first holding temperature of 1100°C for 5 minutes and then ramping down also at 10 °C/minute until a second holding temp of 800°C for 6 hours after which the oven ramps down again at 10 °C/minute until room temperature. It was observed that using this two-step sintering appeared to generate fewer defects in the final solid solution, and facilitated obtaining the final, desired properties. It was observed that a convention one-step sintering process appeared to create a number of defects in the in the final solid solution, which impacted the final properties, and so was avoided. All physical properties were measured on pellets with densities greater than 95% oftheir crystallographic value as determined by a Mettler Toledo Archimedes kit. [0083] Ceramic preparation

[0084] Ceramic pellets for physical property measurements were carefully polished to appropriate thicknesses of ~1 mm for dielectric measurements and <0.5 mm for strain (S-E) and polarization (P-E) measurements as a function of electric field. The pellets were polished to a mirror finish using a LaboPol-5 (Struers) with #400, #800, #1200, and #4000 SiC foils (Struers) sequentially. For S-E and P-E measurements, electrodes of silver conductive paint (SPI Supplies) was applied to the parallel faces of each pellet before the pellet was heated to 600 °C for 30 min to cure the silver electrodes. Platinum paint (SPI Supplies) was applied to the pellets used in the dielectric measurements and sintered to the polished pellets at 600°C for 30 minutes.

[0085] Physical properties measurements

[0086] Dielectric permittivity was measured using an HP 4192A LF Impedance Analyzer, a NorECsAS ProbostatTM, and a Carbolite tube furnace. The measurements were performed on unpoled samples during cooling as a function of temperature and frequency from 1 kHz to 1 MHz and from 800 °C down to room temperature. Strain vs. electric field (S-E) and polarization vs. electric field (P-E) measurements were performed on a Radiant Precision Premier II, at a frequency of 1 Hz, with the sample pellet submerged in an insulating silicone oil. The S-E measurements were run using 2 loops with the final average being used as the final data set. The strain measurements utilized an optical displacement sensor (MTI-2100). Poling was performed on the Radiant Precision Premier II by first heating the pellet from room temperature (25 °C) to 150°C and then poling at 80 kV/cm for 30 minutes. The direct piezoelectric effect was measured on a Berlincourt- type d ₃ 3 meter (APC International, Ltd. YE2730A).

[0087] X-ray diffraction

[0088] Phase purity of each sample was verified using X-ray diffraction (XRD) on a Rigaku Miniflex 600 using Cu Ka radiation (A = 1.541862 A) and scanning a 29 range from 10 to 60° at a rate of 5° per minute. Synchrotron powder X-ray diffraction data was also collected at Argonne National Laboratory on the 11 BM beamline using their mail-in program. The 11 BM beamline utilized a .458165 Angstrom wavelength scanning from -6 to 28 degrees (2theta) with a step size of .001 degrees and .01 seconds per step. Pawley refinements to determine lattice parameters were performed using Topas Academic software.

[0089] Results and Discussion

[0090] X-ray diffraction measurements indicate this material to be a solid solution with no impurities at all of the compositions synthesized. The diffraction patterns can be seen in Figure 1a, and show that there are multiple phase transitions present. Figure 1 b shows that from X=0.25-0.30 and 0.35-0.4 that there are two perovskite phases present. The Bi-rich side starts off in Rhombohedral (R) R3c, which is the structure of BFTM, and is indicated by splitting of the (10-4) and (2-10) peaks as well as the (202) and (006) peaks. As more PT is added, a mixture of R3c and monoclinic (M) Cm occurs. Between x=0.30- 0.35, a single phase of Cm can be observed. Then on the Pb-rich side of this structure, two phases are again observed, Cm and tetragonal (T) P4mm, then as PT approached the structure changes to single phase P4mm, which can be observed by the splitting of the (101) and (110) peaks. The polarization direction varies in each of these structures going from the [111] direction in R3c on the Bi-rich side and the [001] direction in P4mm on the Pb-rich side of the MPB. The M structure has a polarization of [110] which provides a bridge between the R and T phases. This structural sequence of phase transitions is somewhat similar to PZT where the PZ end starts in the antiferroelectric, orthorhombic Pbam phase, then changing to R3c before reaching the MPB where monoclinic Cm is observed, and finally transforming to P4mm on the Pb-rich side of the MPB. Because the transition sequence in BFTM-PT and PZT is similar, the structural data of BFTM-PT suggests that the Cm structure found between 0.30-0.35 could be an MPB, and therefore a region of the phase diagram with enhanced piezoelectric and ferroelectric properties. While BFTM-PT and PZT are structurally similar, their dielectric, ferroelectric, and piezoelectric properties are different, especially in terms of the Curie Temperature, which in PZT is low and therefore limits its use in high temperature applications.

[0091] Electrical properties of BFTM-PT were measured on dense ceramic pellets. Figure 2 shows the temperature dependent dielectric permittivity and loss data where a sharp phase transition from a ferroelectric to paraelectric state is observed between 630- 650°C depending on the composition. These Tc values lie in between those of the end members BFTM at 730°C and PT at 489°C. Table 1 shows a summary of the permittivity and loss data for the compositions x=0.25-0.40. There is a trend in the room temperature permittivity at 1 kHz where x=0.25 on the Bi-rich end has a value of 357, which increases to 758 at x=0.35 then decreases to 598 at x=0.40. The loss values at this same temperature and frequency vary from 0.029-0.096 depending on the composition. They show no trend that corresponds to the permittivity data, but these loss values are typical for ferroelectric materials. At higher temperatures near Tc, the loss increases significantly and varies from 0.158-0.295. This large increase indicates that the material could be conductive at high temperatures, which could be due to the volatile A-cations or the tendency for iron to change oxidation state, leading to A-site or oxygen vacancies and therefore increased conductivity. These high Tc values are expected as they fall in between the value for the end members which are 730°C for BFTM and 495°C for PT. These dielectric properties contrast with PZT, which has a Tc of 350°C. PZT however, is easily tailorable and shows a range of Tc values from 300-400°C through doping, but still cannot maintain the polar structure up to the Tc values found for BFTM-PT. The Tc of BFTM-PT can also be compared to other well-known PZT competitors. One well studied lead-free piezoelectric Ko ₅ Nao ₅ Nb03 has a Tc that falls between that of PZT and BFTM-PT and ranges from 350 to 450 °C, depending on the dopant incorporated into the structure. [4], [5] Other ferroelectrics such as bismuth ferrite- barium titanate[6]-[10] and the family of bismuth Aurivillius phases (Bi2O2)(A _n -iBnO ₃ n+i) (where n = the number of perovskite blocks between bismuth oxide layers) have Tc values that range from 550-750°C which is similar to what is observed in BFTM-PT. [11]-[13]

[0092] Table 1 : Summary of dielectric properties for a range of (1-x)BFTM-(x)PT compositions.

[0093] The polarization (P) and strain (S) was also measured as a function of electric field (E) on dense ceramic pellets to determine the ferroelectric and piezoelectric properties, respectively. A summary of the ferroelectric and piezoelectric properties can be found in Table 2. Figure 3a shows the composition in the R region of the phase diagram (Bi rich end) does not have a saturated P-E loop and is similar to what is observed in the parent compound BFTM. This loop is common for ferroelectric materials that have a high Tc and/or high coercive field. As more PT is added to the solid solution, the loops show a change in slope as the voltage increases, where this nonlinearity indicates the presence of domain wall motion. When moving into the 2-phase region of R and M phases and through to the T phase on the Pb-rich side, all those loops became saturated, indicating a complete alignment of the dipoles. Table 2 summarizes the ferroelectric and piezoelectric properties. It shows that both the maximum polarization (polarization at saturation), Pm, and remnant polarization (polarization that remains after the field is removed), Pr increase to x=0.325, then slightly decreases as more PT is added. The values for Pm and Pr at this composition are 39 pC/cm ² and 26 pC/cm ² , which are on par with what is found in PZT. The coercive field (Ec) of BFTM-PT is fairly high, varying between 38-54 kV/cm, making these materials hard ferroelectrics. Hard ferroelectrics more readily retain long range ordering and are more difficult to switch, making these materials suitable for applications that require high levels of electrical excitation and/or mechanical stress such as high voltage or high power generators and transducers. Undoped PZT shows a lower Ec of ~20 kV/cm, which is expected because materials with a lower Tc typically have a lower Ec value as well. Doping can change the Ec of PZT in addition to its Tc where soft dopants, consisting of electron donors decrease the Ec and hard dopants consisting of electron acceptors increase Ec. This easy tunability of PZT has been developed over decades through the use of dopants (hard vs soft) and mechanical synthesis techniques, which implies that these techniques could also be utilized to alter the properties of BFTM-PT and tailor it for specific applications. [14]— [17]

[0094] Table 2: Summary of ferroelectric and piezoelectric properties of BFMT-PT solid solutions.

[0095] Both bipolar and unipolar loops, S-E, were measured to determine the electromechanical strain properties as seen in Figure 3b and 3c. Figure 3b shows bipolar strain vs electric field loops. These loops demonstrate ferroelectric backswitching as well as showing the increased strain percentage seen with the MPB region. The strain response was further studied under unipolar electric field cycling to investigate its potential use for actuator applications (Figure 3c). The highest strain achieved is 0.19% in the x=0.325 composition, which is consistent with the observed excellent dielectric and ferroelectric properties of this composition. This value is a drastic increase compared to the strain in BFTM (.04%) and even displays a slight increase compared to PT (.15%) indicating, along with the dielectric and ferroelectric data, the presence of an MPB in this region of the phase diagram. The strain values are comparable to some compositions of PZT (.15-.3% on average) although due to the vast amount of research on strain engineering and dopants on the properties of PZT it can display a wide variance in values. As for materials that show a Tc similar to BFTM-PT the strain values for most Aurivillius phases have not been measured due to the Aurivillius structure only being a 2 dimensional ferroelectric and thus the traditional method of measuring the piezoelectric response along the c-axis results in order of magnitude lower values.

[0096] The indirect piezoelectric response at high field, d ₃ 3*, was determined by calculating the slope of the unipolar S-E data while the direct piezoelectric response at low field, d ₃ 3, was measured by poling the sample and measuring the response with a Berlincourt meter. As shown in Figure 4, there is an increase in both the high field and low field piezoelectric response around x=0.325. At this composition, the d ₃₃ value is 100 pC/N and the d ₃₃ * value is 190 pm/V. Therefore, this increase in the piezoelectric response, the ferroelectric properties, and the strain properties that all occur around the composition 0.325, show that this region of the phase diagram does correspond to the existence of an MPB in this series of solid solutions. The piezoelectric response is typically inversely proportional to Tc, so materials with T c values around room temperature typically have very high d ₃₃ values - on the order of 60-100 while materials with high Tc (>500°C), typically have a very low piezoelectric response, with d ₃₃ values <50 pC/N. The d ₃₃ values in BFTM- PT are much higher than what is typically seen for materials with a similar Tc as shown in Figure 5. The piezoelectric response in BFTM-PT is relatively on par with high Tc BFO-BT materials , but is notably higher than the well-known piezoelectric Aurivillius phases such as Bi ₄ Ti ₃ 0i2 and PbBi ₄ Ti ₄ 0i ₅ which have d ₃₃ values in the range of 10-30 pC/N. Without wishing to be bound by theory, the reason for the differences in the piezoelectric response between the aurivillius materials and the pervoskites BFTM-PT, BFO-BT, BFO-PT, BYOPT is that the aurvillius materials are not a solid solution, so there is no MPB present which enhances the piezoelectric response as in these bismuth-based perovskite materials. Therefore, an example of maximizing the piezoelectric response in high Tc materials may include designing a solid solution with an MPB such as BFTM-PT.

[0097] Other materials, such as BFTM - BaTiO ₃ (BFTM-BT) were previously investigated. BFTM-BT was found to have R3c and P4mm end members, which represent the structures of PZT on either side of its MPB. While the solid solution of BFTM-BT has end members formed of bismuth, iron, magnesium titanium (BFTM), such as with BFTM- PT, the electromechanical properties are very different from BFTM-PT, as described herein. For example, there are a finite number of crystal structures possible (for example, there are 32 symmetry defined space groups possible and, of those, there are 20 point groups where materials with these structures will have piezoelectricity); as such, properties tend to be dependent on composition. In BFTM-BT, the structure changes from R3c to a pseudocubic R3m structure where the properties move towards those of a relaxor ferroelectric. Relaxors are a subset of ferroelectrics where the long range ferroelectric ordering is disrupted by local disorder and forms regions of electric dipole ordering in polar nano domains (PNRs) where those PNRs are not correlated to each other. This phenomenon results in different properties than traditional ferroelectrics and therefore are used in different applications such as energy storage. One notable difference is that while measuring the polarization under an electric field, both traditional ferroelectrics and relaxor ferroelectrics of materials show hysteresis as well as the ability to achieve saturation of the dipoles and switching of those dipoles, but relaxors are unable to maintain a large remnant polarization when the electric field is removed. In addition, there is no Tc as a phase transition does not necessarily occur at high temperatures. Instead, in relaxors there is a broad frequency and temperature dependent permittivity maximum. The origin of this relaxor behavior in BFTM-BT comes from the different preferred cation environments of bismuth and barium. Bismuth has a lone pair of electrons, resulting in a distorted polyhedral environment where barium prefers a symmetric coordination environment, thus causing strain, which disrupts the long range ferroelectric ordering and the onset of relaxor behavior.

[0098] Ternary solid solutions between BFTM-LaFe0 ₃ -La(Mg0.5Ti0.5)0 ₃ (BFTM- LF-LMT) were also previously investigated. [18] LF tends to be used as it has been known to improve the piezoelectric properties of BiFeO ₃ , however iron often results in a lossy dielectric behavior, so LMT tends to be added to counterbalance an increased loss due to the presence of iron. For the phase diagram of BFTM-LF-LMTs, several compositions displayed a new ferroelectric phase with the Pmc21 structure, which is rarely found as a perovskite. The space group of BFTM-LF-LMT has a complex set of displacements, but overall shows a ferroelectric distortion along the [110] direction. These BFTM-LF-LMT solid solutions did display ferroelectric and piezoelectric properties, but the d ₃₃ values were very small at ~0.25 pC/N. Between the ferroelectric phase of the BFTM end member and the new Pmc21 structure, there is a range of compositions where phase separation occurs and results in a mixed phase perovskite and Aurivillius structure. As such, BFTM-LF-LMTs do not exhibit a MPB with an enhancement of the piezoelectric response. [0099] BFTM-PT as described herein differs from BFTM-BT and BFTM-LF-LMT (also referred to as BFTM-LFO-LMT) in that it has an MPB, which allows for the enhancement of its piezoelectric properties. For example, properties of the morphotropic phase boundary may be related to a combination of piezoelectric strain and domain wall motion. This results in d ₃₃ values within the MPB to be relatively much higher than those found in BFTM-BT and BFTM-LFO-LMT. In both BFTM-BT and BFTM-LFO-LMT only the relative amount of each B-cation changes and no additional cation types are placed on this crystallographic site. However, in each case, a different A-cation is introduced where in BFTM-BT and BFTM-LFO-LMT, the Ba ²⁺ and La ²⁺ , having a differing structure and composition to the BFTM-PT solid solution, prefer different coordination environments than Bi ³⁺ due to both the size and the lack of a lone pair of electrons in the former. These differences in coordination preferences can create strain, which can adversely affect the long-range ferroelectric ordering, which leads to BFTM-BT becoming a relaxor ferroelectric and BFTM-LFO-LMT having weak ferroelectric properties. BFTM-PT as described herein is able to maintain strong, long-range ferroelectric ordering due to both A-cations having a lone pair of electrons, which allows them to distort in similar ways and stabilize in similar bonding environments.

[00100] BFTM-CaTiO ₃ (BFTM-CT) solid solutions were also investigated. [19] The BFTM-CT solid solution, having a differing structure and composition to the BFTM-PT solid solution, showed a structural transition from the parent R3c structure to a wide mixed phase region (x =0.05-0.20) of R3c and orthorhombic Pna2 ₁ in what can be defined as the MPB. On the CT rich side of the MPB, the structure was single phase Pna2i. In this solid solution, there is no bridging polarization direction as in PZT and BFTM-PT and the polarization changes from the [111] direction in the R phase directly to the [001] direction in the O phase. The electromechanical properties show that the mixed phase region can be considered an MPB. The ferroelectric hysteresis loops were able to be fully saturated and show well developed loops with the best recording a maximum and remnant polarization of 49 and 44 pC per cnr ² respectively. This can be compared to BFTM-PT with values of 39 and 26 pC per cnr ² respectively. This region of the phase diagram displays a piezoelectric response with a d ₃₃ value of around 50 pC/N, which is lower than that found in BFTM-PT, but BFTM-CT also has a higher Tc of 840°C, so the lower d ₃₃ is not unexpected. BFTM-PT as described herein ranges from 75 to 100 within the MPB a. The piezoelectric response in BFTM-PT is larger due to the inverse relationship between Tc and d ₃₃ as described above. The Tc values within the BFTM-CT MPB are actually higher than that of BFTM because the other end member CaTiO ₃ stabilizes in the Pnma space group, which is centrosymmetric and therefore does not display ferroelectricity. By replacing nonferroelectric CT, with ferroelectric PT, which also has a lower Tc than BFTM, the piezoelectric response within the MPB of BFTM is larger.

[00101] Overall, it appears that the structure of the non-BFTM end member has little effect on the piezoelectric properties in all these BFTM systems. BFTM-BT and BFTM-PT both have end members with the same space groups as in PZT, but BFTM-BT forms a relaxor ferroelectric because of the strain created by the large size difference and coordination environment differences between Ba ²⁺ and Pb ²⁺ . There is a phase separation between the ferroelectric structures in BFTM-LFO-LMT likely due to the increased amount of Fe ³⁺ , which typically distorts along the [111] direction, perhaps restricting the accessible ferroelectric structures in this solid solution. In BFTM-CT, the CT end member is isostructural to LFO, but Ti ⁴⁺ has been shown to displace locally along multiple directions that aren’t necessarily coordinated to the A-cation, thus increasing the accessible ferroelectric structures, which allowed for the formation of an MPB despite CT having a centrosymmetric structure. BFTM-PT and BFTM-CT both displayed MPBs despite Ca ²⁺ and Pb ²⁺ having different coordination environments. However, the d ₃ 3 value of BFTM-CT is much lower. This is perhaps because of the different coordination environments of Bi ³⁺ and Ca2+ and while they show ferroelectric ordering, on a local scale that might be beginning to break down. BFTM-CT is likely to have weaker long range ferroelectric ordering compared to BFTM-PT. This ordering is important to enhancement of domain wall motion, which is an extrinsic mechanism of piezoelectric strain. With Bi ³⁺ and Pb ²⁺ having similar preferred coordination environments, the strong long range ordering can enable more domain wall motion, therefore increasing the extrinsic effects on the measured piezoelectric strain.

[00102] Example 2 - Synthesis and Characterization of a Ferroelectric with Low Lead Content, an Morphotropic Phase Boundary, and a High Curie Temperature with Dopants

[00103] Pure phase doped materials were synthesized utilizing techniques of Example 1.

[00104] Structures were characterized utilizing X-ray diffraction and were determined to show a 99% pure material with three single phase regions and two mixed phase regions. The R3c to Cm to P4mm phase transition scheme directly mirrors the transitions present in PZT. Electrical property measurements show an interesting ferroelectric material with improved piezoelectric and ferroelectric response in the MPB. Shown therein is a Curie temperature transition at around 650 degrees Celsius completing the last main goal and indicates a competitive material for further research and potential industrial use.

[00105] Figure 6 to 10 show examples of the BFTM-PT solid solution as described herein doped with various dopants. Figure 6 shows an example of the BFTM-PT solid solutions as described herein doped with aluminum. Figure 7 shows an example of the BFTM-PT solid solutions as described herein doped with gallium. Figure 8 shows an example of the BFTM-PT solid solutions as described herein doped with indium. Figure 9 shows an example of the BFTM-PT solid solutions as described herein doped with niobium. Figure 10 shows an example of the BFTM-PT solid solutions as described herein doped with manganese dioxide.

[00106] For Figures having three panes, the top pane shows the current maximum pure material. The middle pane shows a composition above the solubility limit of the dopant forming a secondary impurity phase, denoted by stars in the patterns. The bottom pane shows the pure phase composition the structure is closest to. For Figures having two panes, the solubility limit has not been reached.

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[00108] The embodiments described herein are intended to be examples only. Alterations, modifications, and/or variations can be effected to the particular embodiments by those of skill in the art. The scope of the claims should not be limited by the particular embodiments set forth herein, but should be construed in a manner consistent with the specification as a whole.

[00109] The aspects, embodiments, and/or examples of the present disclosure being thus described, it should be recognized that said aspects, embodiments, and/or examples may be varied in ways that do not depart from the spirit and scope of the present disclosure, and that said variations are intended to be included within the scope of the following claims.

[00110] All publications, patents and patent applications mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication patent, or patent application was specifically and individually indicated to be incorporated by reference.