Polar nanoregions engineered relaxor-PbTiO.SUB.3 .ferroelectric crystals

Abstract

A relaxor-PT based piezoelectric crystal is disclosed, comprising the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3, wherein: M is a rare earth cation; M.sub.I is selected from the group consisting of Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, and In.sup.3+; M.sub.II is Nb.sup.5+; M.sub.I′ is selected from the group consisting of Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, In.sup.3+, and Zr.sup.4; M.sub.II′ is Nb.sup.5+ or Zr.sup.4+; 0<x≤0.05; 0.02<y<0.7; and 0≤z≤1, provided that if either M.sub.I′ or M.sub.II′ is Zr.sup.4+, both M.sub.I′ and M.sub.II′ are Zr.sup.4+. A method for forming the relaxor-PT based piezoelectric crystal is disclosed, comprising pre-synthesizing precursor materials by calcining mixed oxides, mixing the precursor materials with single oxides and calcining to form a feeding material, and growing the relaxor-PT based piezoelectric crystal having the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 from the feeding material by a Bridgman method.

Claims

1. A relaxor-PT based piezoelectric crystal comprising the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3, wherein: M is a rare earth cation selected from the group consisting of Pm.sup.3+, Sm.sup.3+, Gd.sup.3+, and combinations thereof; M.sub.I is selected from the group consisting of Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, and In.sup.3+; M.sub.II is Nb.sup.5+; M.sub.I′ is selected from the group consisting of Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, In.sup.3+, and Zr.sup.4+; M.sub.II′ is Nb.sup.5+ or Zr.sup.4+; 0<x≤0.05; 0.02<y<0.7; and 0≤z<1, provided that if either M.sub.I′ or M.sub.II′ is Zr.sup.4+, both M.sub.I′ and M.sub.II′ are Zr.sup.4+, wherein the relaxor-PT based piezoelectric crystal is a single crystal boule, and wherein the relaxor-PT based piezoelectric crystal, relative to a comparative crystal having a comparative formula of Pb{[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with the same selections and values for y, z, M.sub.I, M.sub.II, M.sub.I′, and M.sub.II′ and the same crystal symmetry after poling, has at least one of: less variation of dielectric permittivity and piezoelectric coefficient, along a rhombohedral phase section; higher piezoelectric coefficient; higher free dielectric permittivity; higher clamped dielectric permittivity; or combinations thereof.

2. The crystal of claim 1, wherein z is 0, and the crystal is a binary crystal.

3. The crystal of claim 2, wherein M.sub.I is selected from the group consisting of Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, and In.sup.3+, and M.sub.II is Nb.sup.5+.

4. The crystal of claim 1, wherein 0<z<1, and the crystal is a ternary crystal.

5. The crystal of claim 4, wherein M.sub.I is selected from the group consisting of Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, and In.sup.3+, M.sub.II is Nb.sup.5+, and M.sub.I′ and M.sub.II′ are each Zr.sup.4+.

6. The crystal of claim 4, wherein M.sub.I and M.sub.I′ are each independently selected from the group consisting of Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, and In.sup.3+, and M.sub.II and M.sub.II′ are each Nb.sup.5+.

7. The crystal of claim 1, wherein M is Sm.sup.3+.

8. The crystal of claim 1, wherein the crystal is an M-modified Pb(Mg.sub.1/3Nb.sub.2/3)O.sub.3—PbTiO.sub.3 (“PMNT”).

9. The crystal of claim 1, wherein the crystal is an M-modified Pb(In.sub.1/2Nb.sub.1/2)O.sub.3—Pb(Mg.sub.1/3Nb.sub.2/3)O.sub.3—PbTiO.sub.3 (“PIN-PMN-PT”).

10. The crystal of claim 9, wherein the crystal is 1 mol % Sm: 26PIN-46PMN-28PT.

11. The crystal of claim 9, wherein the crystal is 1 mol % Sm: 26PIN-44PMN-30PT.

12. The crystal of claim 9, wherein the crystal is 0.5 mol % Sm: 26PIN-44PMN-30PT.

13. The crystal of claim 1, wherein the crystal includes a phase selected from the group consisting of rhombohedral, orthorhombic, tetragonal, and combinations thereof.

14. The crystal of claim 1, wherein the crystal exhibits at least 25% less variations of the dielectric permittivity and the piezoelectric coefficient along the rhombohedral phase section relative to the comparative crystal having the comparative formula of Pb{[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with the same selections and values for y, z, M.sub.II, M.sub.I′, and M.sub.II′ and the same crystal symmetry after poling.

15. The crystal of claim 1, wherein the crystal exhibits at least 20% higher of the piezoelectric coefficient relative to the comparative crystal having the comparative formula of Pb{[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with the same selections and values for y, z, M.sub.I, M.sub.II, M.sub.I′, and M.sub.II′ and the same crystal symmetry after poling.

16. The crystal of claim 1, wherein the crystal exhibits at least 20% higher of the free dielectric permittivity relative to the comparative crystal having the comparative formula of Pb{[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with the same selections and values for y, z, M.sub.I, M.sub.II, M.sub.I′, and M.sub.II′ and the same crystal symmetry after poling.

17. The crystal of claim 1, wherein the crystal exhibits at least 20% higher of the clamped dielectric permittivity relative to the comparative crystal having the comparative formula of Pb{[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with the same selections and values for y, z, M.sub.I, M.sub.II, M.sub.I′, and M.sub.II′ and the same crystal symmetry after poling.

18. The crystal of claim 1, wherein 0.0015≤x≤0.025.

19. The crystal of claim 1, wherein 0.25≤y≤0.35.

20. The crystal of claim 1, wherein 0≤z≤0.40.

21. A method for forming a relaxor-PT based piezoelectric crystal, comprising: pre-synthesizing precursor materials by calcining mixed oxides at a first calcination temperature; mixing the precursor materials with single oxides and calcining at a second calcination temperature lower than the first calcination temperature to form a feeding material having the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3; and growing the relaxor-PT based piezoelectric crystal having the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 from the feeding material by a Bridgman method, wherein: M is a rare earth cation selected from the group consisting of Nd.sup.3+, Pm.sup.3+, Sm.sup.3+, Gd.sup.3+, and combinations thereof; M.sub.I is selected from the group consisting of Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, and In.sup.3+; M.sub.II is Nb.sup.5+; M.sub.I′ is selected from the group consisting of Mg.sup.2+, Yb.sup.2+, Sc.sup.3+, In.sup.3+, and Zr.sup.4+; M.sub.II′ is Nb.sup.5+ or Zr.sup.4+; 0<x≤0.05; 0.02<y<0.7; and 0≤z<1, provided that if either M.sub.I′ or M.sub.II′ is Zr.sup.4+, both M.sub.I′ and M.sub.II′ are Zr.sup.4+, and provided that if M is Nd.sup.3+, 0<x<0.02, wherein the relaxor-PT based piezoelectric crystal is a single crystal boule, and wherein the relaxor-PT based piezoelectric crystal, relative to a comparative crystal having a comparative formula of Pb{[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with the same selections and values for y, z, M.sub.I, M.sub.II, M.sub.I′, and M.sub.II′ and the same crystal symmetry after poling, has at least one of: less variation of dielectric permittivity and piezoelectric coefficient, along a rhombohedral phase section; higher piezoelectric coefficient; higher free dielectric permittivity; higher clamped dielectric permittivity; or combinations thereof.

22. The method of claim 21, wherein the feeding material is at least 98% perovskite-phase.

23. The method of claim 21, wherein the feeding material is pure perovskite-phase.

24. The method of claim 21, wherein the precursor materials are selected from the group consisting of wolframite, InNbO.sub.4, and columbite, MgNb.sub.2O.sub.6.

25. The method of claim 21, wherein the single oxides are selected from the group consisting of PbO/Pb.sub.3O.sub.4, TiO.sub.2, and rare-earth oxides.

26. The method of claim 21, wherein the first calcination temperature with the range of 1,000-1,300° C.

27. The method of claim 21, wherein the second calcination temperature with the range of 700-950° C.

28. The method of claim 21, wherein the Bridgman method includes a two heating zone Bridgman furnace having an upper heating zone 20-150° C. higher than a melting point of the feeding material and a lower heating zone 50-300° C. lower than the melting point of the feeding material.

29. The method of claim 28, wherein the Bridgman furnace includes an axial temperature gradient of <50° C./cm between the upper heating zone and the lower heating zone.

30. A relaxor-PT based piezoelectric crystal comprising the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3, wherein: M is a rare earth cation other than La.sup.3+; M.sub.I is selected from the group consisting of Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, and In.sup.3+; M.sub.II is Nb.sup.5+; M.sub.I′ is selected from the group consisting of Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, In.sup.3+, and Zr.sup.4+; M.sub.II′ is Nb.sup.5+ or Zr.sup.4+; 0<x≤0.05; 0.02<y<0.7; and 0≤z<1, provided that if either M.sub.I′ or M.sub.II′ is Zr.sup.4+, both M.sub.I′ and M.sub.II′ are Zr.sup.4+, provided that if M is Nd.sup.3+, 0<x<0.02, provided that if z is 0, M is selected from the group consisting of Ce.sup.3+, Pr.sup.3+, Nd.sup.3+, Pm.sup.3+, Sm.sup.3+, Eu.sup.3+, Gd.sup.3+, Tb.sup.3+, Dy.sup.3+, Ho.sup.3+, Er.sup.3+, Tm.sup.3+, Yb.sup.3+, Lu.sup.3+, and combinations thereof, and provided that if 0<z<1, M is selected from the group consisting of Ce.sup.3+, Pr.sup.3+, Nd.sup.3+, Pm.sup.3+, Sm.sup.3+, Eu.sup.3+, Gd.sup.3+, Tb.sup.3+, Dy.sup.3+, Ho.sup.3+, Er.sup.3+, Tm.sup.3+, Lu.sup.3+, and combinations thereof, and wherein the relaxor-PT based piezoelectric crystal is a single crystal boule.

31. The crystal of claim 9, wherein the crystal is 0.5 mol % Sm: 26PIN-43PMN-31PT.

32. The crystal of claim 1, wherein the single crystal boule of the relaxor-PT based piezoelectric crystal is a <001> poled rhombohedral crystal.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows Sm-modified PMN-PT and PIN-PMN-PT single crystals grown by the vertical Bridgman process, according to an embodiment of the present disclosure.

(2) FIG. 2 shows variations of dielectric permittivity along the length of the unmodified and Sm-modified PMN-PT (a) and PIN-PMN-PT (b) crystals (only the rhombohedral phase section and poled along <001>), according to an embodiment of the present disclosure.

(3) FIG. 3 shows variations of piezoelectric coefficient along the length of the unmodified and Sm-modified PMN-PT (a) and PIN-PMN-PT (b) crystals (only the rhombohedral phase section and poled along <001>), according to an embodiment of the present disclosure.

(4) FIG. 4 shows the as-grow single crystal from a mixture of PMN-32PT and 2 mol % Sm.sub.2O.sub.3, according to an embodiment of the present disclosure.

(5) FIG. 5 shows the as-grow single crystal from a mixture of 26PIN-42PMN-32PT and 2 mol % Sm.sub.2O.sub.3, according to an embodiment of the present disclosure.

(6) FIG. 6 shows (a) polarization and strain hysteresis loops under bipolar electric field, showing coercive field (E.sub.C) and saturated polarization (P.sub.S) (sample 1), and (b) dielectric permittivity variation with elevated temperature, showing the Curie temperature (T.sub.C) (sample 2) in samples cut from the crystal growth from 2 mol % Sm: PMN-32PT mixture, according to an embodiment of the present disclosure.

(7) FIG. 7 shows the (a) polarization loops under bipolar electrical field and (b) dielectric permittivity and loss variation with elevated temperature in samples cut from the crystal growth from 1 mol % Sm: 26PIN-PMN-30PT mixture, according to an embodiment of the present disclosure.

(8) FIG. 8 shows the measured strain under unipolar electrical field of sample 1 (a) and sample 2 (b), according to an embodiment of the present disclosure.

(9) Whenever possible, the same reference numbers will be used throughout the drawings to represent the same parts.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

(10) Provided are piezoelectric crystals and methods for forming piezoelectric crystals. Embodiments of the present disclosure, in comparison to methods not including one or more of the features disclosed herein, include decreased variations of dielectric permittivity and piezoelectric coefficient along a rhombohedral phase section, increased piezoelectric coefficients, increased free dielectric permittivities, increased clamped dielectric permittivities, maintaining electromechanical coupling, or combinations thereof.

(11) The present invention relates to piezoelectric crystals suitable for high performance electromechanical applications, such as actuators, piezoelectric sensors, and medical ultrasonic transducers. As ferroelectric crystals capable of attaining a large piezoelectric coefficient and dielectric permittivity, meanwhile maintaining the high electromechanical coupling being on the order of about 0.9, there have hitherto been known, for example, a binary or ternary system composed of lead titanate (PbTiO.sub.3; PT) and relaxor end members, such as Pb(M.sub.I,M.sub.II)O.sub.3, where M.sub.I may be Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, or In.sup.3+, while M.sub.II may be Nb.sup.5+. Relaxor-PT single crystals have attracted extensive attentions in the last two decades for applications in high performance medical imaging transducers. However, because of the low clamped dielectric permittivity, such crystals have required more complicated designs for the electrical impedance matching.

(12) The present disclosure relates to ferroelectric crystals based on relaxor-PT composition, characterized by high dielectric (both free and clamped dielectric permittivities) and electromechanical properties that may be adopted for different uses by modifying the PNRs volume ratio. The piezoelectric crystals based on the system Pb[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z]O.sub.3-PT are modified in order to obtain a high level of dielectric/piezoelectric activity. The invention provides domain engineered piezoelectric crystals based on relaxor-PTs having the perovskite ABO.sub.3 crystal structure, being furthermore substituted with heterovalent cations.

(13) In this disclosure, the PNRs in relaxor-PT ferroelectric crystal systems were controlled by A-site modifications, demonstrating the impact of PNRs and/or local structure on the significantly improved dielectric and piezoelectric properties. A-site modified Pb[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z]O.sub.3-PT binary/ternary crystals have been found to possess high dielectric and piezoelectric properties compared to those of unmodified counterparts, attributing to the local structure distortion and/or existence of controlled PNRs, and/or local structure with different phases from nearby matrix, where the free/clamped dielectric permittivity and piezoelectric coefficients are greatly increased, while maintaining the high electromechanical coupling factors.

(14) Since Pb[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z]O.sub.3-PT binary/ternary single crystals are complete solid solution systems as shown by high temperature phase diagrams, such crystals exhibit an inhomogeneous composition distribution along crystal boules grown by Bridgman method (Luo H, Xu G, Wang P, Yin Z, Growth and Characterization of Relaxor Ferroelectric PMNT Single Crystals, Ferroelectrics, 1999 231 685-690), resulting in the variation of dielectric and piezoelectric properties along the growth direction. However, as is presently disclosed, by A-site substitution with certain types of rare earth cations, the property variation along the crystal growth direction may be significantly reduced.

(15) In one embodiment, a relaxor-PT based piezoelectric crystal comprises the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3, wherein: M is a rare earth cation; M.sub.I is Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, In.sup.3+, or any other suitable cation; M.sub.II is Nb.sup.5+, or any other suitable cation; M.sub.I′ is Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, In.sup.3+, Zr.sup.4+, or any other suitable cation; M.sub.II′ is Nb.sup.5+, Zr.sup.4+, or any other suitable cation; 0<x≤0.05; 0.02<y<0.7; and 0≤z≤1, provided that if either M.sub.I′ or M.sub.II′ is Zr.sup.4+, both M.sub.I′ and M.sub.II′ are Zr.sup.4+.

(16) In one embodiment, wherein z is 0, the crystal is a binary crystal. The binary crystal may include M.sub.I being Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, In.sup.3+, or any other suitable cation, and M.sub.II being Nb.sup.5+, or any other suitable cation.

(17) In another embodiment, wherein z is greater than 0, the crystal is a ternary crystal. The ternary crystal may include M.sub.I being Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, In.sup.3+, or any other suitable cation, M.sub.II being Nb.sup.5+, or any other suitable cation, and M.sub.I′ and M.sub.II′ each being Zr.sup.4+, or any other suitable cation. Alternatively, the ternary crystal may include M.sub.I and M.sub.I′ each being independently Mg.sup.2+, Zn.sup.2+, Yb.sup.3+, Sc.sup.3+, In.sup.3+, or any other suitable cation and M.sub.II and M.sub.II′ each being Nb.sup.5+, or any other suitable cation.

(18) M may be any suitable rare earth cation, including, but not limited to, La.sup.3+, Ce.sup.3+, Pr.sup.3+, Nd.sup.3+, Pm.sup.3+, Sm.sup.3+, Eu.sup.3+, Gd.sup.3+, Tb.sup.3+, Dy.sup.3+, Ho.sup.3+, Er.sup.3+, Tm.sup.3+, Yb.sup.3+, Lu.sup.3+, or combinations thereof. In one embodiment, M is Sm.sup.3+.

(19) In one embodiment, the crystal is an M-modified Pb(Mg.sub.1/3Nb.sub.2/3)O.sub.3—PbTiO.sub.3 (“PMNT”). In another embodiment, the crystal is an M-modified Pb(In.sub.1/2Nb.sub.1/2)O.sub.3—Pb(Mg.sub.1/3Nb.sub.2/3)O.sub.3—PbTiO.sub.3 (“PIN-PMN-PT”). Suitable compositions for the crystal include, but are not limited to, 1 mol % Sm: 26PIN-PMN-28PT, 1 mol % Sm: 26PIN-PMN-30PT, and 0.5 mol % Sm: 26PIN-PMN-30PT.

(20) The crystal may include any suitable phase, including, but not limited to, rhombohedral, orthorhombic, tetragonal, and combinations thereof.

(21) In one embodiment, the crystal exhibits less variation of dielectric permittivity and piezoelectric coefficient along a rhombohedral phase section relative to a comparative crystal having a comparative formula of Pb{[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with the same selections and values for y, z, M.sub.I, M.sub.II, M.sub.I′, and M.sub.II′ and the same crystal symmetry after poling. In a further embodiment, the crystal exhibits at least 25% less variations of dielectric permittivity and piezoelectric coefficient, alternatively at least 30% less, alternatively at least 35% less, alternatively at least 40% less.

(22) In one embodiment, the crystal exhibits higher piezoelectric coefficient relative to a comparative crystal having a comparative formula of Pb {[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with the same selections and values for y, z, M.sub.I, M.sub.II, M.sub.I′, and M.sub.II′ and the same crystal symmetry after poling. In a further embodiment, the crystal exhibits at least 20% higher piezoelectric coefficient, alternatively at least 25% higher, alternatively at least 30% higher, alternatively at least 35% higher.

(23) In one embodiment, the crystal exhibits higher free dielectric permittivity relative to a comparative crystal having a comparative formula of Pb {[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with the same selections and values for y, z, M.sub.I, M.sub.II, M.sub.I′, and M.sub.II′ and the same crystal symmetry after poling. In a further embodiment, the crystal exhibits at least 20% higher free dielectric permittivity, alternatively at least 25% higher, alternatively at least 30% higher, alternatively at least 35% higher.

(24) In one embodiment, the crystal exhibits higher clamped dielectric permittivity relative to a comparative crystal having a comparative formula of Pb {[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with the same selections and values for y, z, M.sub.I, M.sub.II, M.sub.I′, and M.sub.II′ and the same crystal symmetry after poling. In a further embodiment, the crystal exhibits at least 20% higher clamped dielectric permittivity, alternatively at least 25% higher, alternatively at least 30% higher, alternatively at least 35% higher.

(25) The crystal having the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 may include any suitable value for x, including, but not limited to, 0<x≤0.05, alternatively 0.001≤x≤0.03, alternatively 0.0015≤x≤0.025.

(26) The crystal having the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 may include any suitable value for y, including, but not limited to, 0.02<y<0.7, alternatively 0.20≤y≤0.40, alternatively 0.25≤y≤0.35.

(27) The crystal having the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 may include any suitable value for z, including, but not limited to, 0≤z≤1, alternatively 0≤z≤0.40.

(28) A-site modified relaxor-PT based piezoelectric crystals may be grown from their melt using the vertical Bridgman method or any other suitable method. The crystal may be grown along <001>, <110> or <111> orientations, or any suitable arbitrary orientation. The crystals may be poled in any suitable engineered domain configurations. For rhombohedral crystals, it may include [001] poled crystals with 4R engineered domain configuration and [011] poled crystals with 2R engineered domain configuration; for orthorhombic crystals, it may include [001] poled crystals with 4O engineered domain configuration, [111] poled crystals with 3O engineered domain configuration; and for tetragonal crystals, it may include [011] poled crystals with 2T engineered domain configurations [111] poled crystals with 3T engineered domain configuration.

(29) In one embodiment, a vertical Bridgman method is applied to grow the crystals. To keep the crystal growth interface stable in the crystal growth process, at least 98%, alternatively pure, perovskite-phase raw materials may be pre-synthesized for preventing the pyrochlore phase formation during the raw material batching and spontaneous nucleation/polycrystalline grain growth in crystal growth. As used herein, “pure” indicates at least 99.5%. A precursor method may be adopted to a batching process to prevent the formation of a pyrochlore phase. For preparation, different precursor materials, such as, but not limited to, wolframite, InNbO.sub.4, and columbite, MgNb.sub.2O.sub.6, may be synthesized first, respectively, by calcination of mixed oxides at 1,000-1,300° C. Following mixing single oxides, such as, but not limited to, PbO/Pb.sub.3O.sub.4, TiO.sub.2, and rare-earth oxides with the precursor materials, feeding material having the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 may be synthesized by another calcination process at lower temperature (700-950° C.), and powder x-ray diffraction (XRD) may be used to verify that sufficiently pure perovskite phase is obtained through this precursor method.

(30) The crystals may then be grown from the feeding material having the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 by the Bridgman method without crystal seeds or with crystal seeds of the same kind of crystals. A two heating-zone Bridgman furnace may be used for the crystal growth. The upper zone temperature may be higher than the melting point and lower zone temperature may be below the melting temperature, respectively, of the feeding material. In the Bridgman growth process, the cylindrical Pt crucibles charged with single crystal seeds (if applied) at the bottom and the feeding material in either powder or ceramic form above the seeds may be placed in the two-zone furnace. For growth of small crystals, multiple crucibles may be loaded into the furnace together in a single crystal growth run. By setting temperature of the upper zone 20-150° C. higher than the melting points and the lower zone 50-300° C. lower than the melting point, an axial temperature gradient of <50° C./cm may be formed between two zones. After the charge and part of the crystal seeds (if applied) are melted in the upper-zone, the crucibles may be lowered down slowly through the temperature gradient resulting in a unidirectional crystallization. By this method, crystals having the general formula of (Pb.sub.1-1.5xM.sub.x){[(M.sub.I,M.sub.II).sub.1-z(M.sub.I′,M.sub.II′).sub.z].sub.1-yTi.sub.y}O.sub.3 with different diameter and length may be grown.

EXAMPLES

(31) FIG. 1 shows Sm-modified PMN-PT and PIN-PMN-PT single crystals grown by the process described herein. The crystals were oriented using real-time Laue X-ray or an X-ray diffraction unit and then cut to obtain samples with the aspect ratios following IEEE piezoelectric standards (IEEE Standard on Piezoelectricity, ANSI/IEEE Standard, N Y, 1987-176). All the samples were oriented along <001>, <110> or <111> directions and gold was sputtered on the surfaces as the electrodes. Crystal samples were poled under 5-16 kV/cm at room temperature. High field polarization and strain measurements were performed at room temperature at low frequency using a modified Sawyer-Tower circuit and linear variable differential transducer (LVDT) driven by a lock-in amplifier. Room temperature dielectric, piezoelectric, electromechanical properties were determined according to IEEE standards, by using HP4194A Impedance-phase gain analyzer. The dielectric temperature dependence was measured in the frequency range of 0.1 kHz to 10 kHz using a multi-frequency LCR meter (HP4284A), connected to a computer-controlled temperature chamber. The test results of the <001>-poled, Sm-modified PMN-PT and PIN-PMN-PT crystals are summarized in Table 2 in comparison with the unmodified crystals. Some of the A-site modified PMN-PT and PIN-PMN-PT crystals, such as 1 mol % Sm: PMN-28PT, 1 mol % Sm: PMN-30PT, 1 mol % Sm: 26PIN-PMN-28PT, 1 mol % Sm: 26PIN-PMN-30PT and 0.5 mol % Sm: 26PIN-PMN-30PT, have significantly higher free and clamped dielectric permittivity (ε.sub.r and ε.sub.r clamped), piezoelectric coefficient (d.sub.33) and coupling factor than the non-modified counterparts with compromises on rhombohedral-to-tetragonal phase transition temperature (T.sub.rt) and dielectric loss (tan δ). In order to take advantage of the impact of A-site substitution, the binary/ternary base composition and the substitution level may be optimized. It is seen that 2 mol % of A-site substitution by Sm in PMN-32PT and 26PIN-PMN-32PT shifted the majority of the as-grown crystal boules from rhombohedral phase to tetragonal phase, resulting in lower dielectric permittivity and piezoelectric coefficient. It is also seen that the crystal grown from 26PIN-PMN-28PT with 0.25 mol % Sm substitution on the A-site only possesses moderate dielectric and piezoelectric properties, due to the combination of low substitution level and low PT content. It should be noted that Table 2 only lists the feeding material composition of each crystal; however, each as-grown crystal covers a much broader range of compositions due to the compositional segregation effect, which will be described in further detail below.

(32) TABLE-US-00002 TABLE 2 The properties of Sm: PMN-PT and Sm: PIN-PMN-PT crystals. Feeding d.sub.33 tanδ ε.sub.r v T.sub.rt E.sub.C Material Phase (pC/N) (%) ε.sub.r (clamped) k.sub.33 (m/s) (° C.) (kV/cm) PMN-30PT R 1150-2120 <0.6 4100-5800  700-1000 0.89-0.93 4400-4600 88-96 2.0-3.0 26PIN-PMN- R 1000-1800 <0.6 3000-5000 600-900 0.88-0.93 4300-4550 110-130 4.5-6.0 30PT 1 mol % Sm: R 2100-3200 <1.2  6600-11000 1150-1700 0.89-0.94 4300-4550 59-75 2.0-3.0 PMN-28PT 1 mol % Sm: R 2900-3600 <1.5  7600-13000 1000-1300 0.91-0.94 4150-4600 47-60 2.0-3.0 PMN-30PT 2 mol % Sm: T  740-1200 2  2200-12000 /  0.8-0.85 / ≤−50 2.0-2.6 PMN-32PT 1 mol % Sm: R 1700-2600 <1.2 5600-7000 1000-1300 0.89-0.95 4300-4500 65-87 3.5-6.0 26PIN-PMN- 28PT 1 mol % Sm: R 2000-2500 <1.6 5900-8200  900-1250  0.9-0.95 4300-4450 55-82 3.5-6.0 26PIN-PMN- 30PT 2 mol % T  780-1100 2 2000-3200 /  0.8-0.87 / ≤20 5.6-6.0 Sm: 26PIN- PMN-32PT 0.5 mol % R 1240-2680 <1.2 4600-7800 740-940 0.89-0.95 4200-4400 86-94 4.7-6.1 Sm: 26PIN- PMN-30PT 0.25 mol % R 1000-1500 <0.7 3500-5100 580-810 0.88-0.94 4300-4500  98-116 5.0-6.0 Sm: 26PIN- PMN-28PT *R: Rhombohedral; T: Tetragonal * The samples were poled along <001>

(33) The longitudinal property variations in each crystal were characterized between the unmodified and A-site modified PMN-PT/PIN-PMN-PT crystals by measuring the <001>-poled samples taken from different positions along the length of each crystal. FIGS. 2 and 3 show the variations of dielectric permittivity and piezoelectric coefficient along the length of the unmodified and Sm-modified PMN-PT and PIN-PMN-PT crystals (only the rhombohedral phase section in each of the as-grown crystal). It is clearly seen that Sm may largely suppress the longitudinal property variations in the rhombohedral phase of PMN-PT and PIN-PMN-PT crystals. For example, FIG. 2 in (a) and (b) indicates that the dielectric permittivity totally varied over 45% in the rhombohedral section of a PMN-PT crystal and a PIN-PMN-PT crystal, but only about 19% in Sm-modified crystals of the same types. Similarly, as shown in FIG. 3 in (a) and (b), the piezoelectric coefficient totally varied over 75% in the rhombohedral section of a PMN-PT crystal and a PIN-PMN-PT crystal, but only about 22% in Sm-modified crystals of the same types. It is expected that Sm may reduce the variation of other properties in the crystal. In the same way, some of the other A-site substitutes may have the same impact on the crystals property variations as Sm.

(34) The compositions of some of the as-grown crystals were analyzed by electronic probe microanalysis (EPMA). Due to the compositional segregation in these solid-solution systems, the bottom and top of each crystal boule present different concentrations for most of the main elements. As shown in the Table 3, except for Pb, all other elements in Sm:PMN-PT and Sm:PIN-PMN-PT crystals exhibit compositional segregation during Bridgman growth, exhibiting an effective segregation coefficient either larger than 1 (Nb, Mg, In and Sm) or smaller than 1 (Ti). For In, the composition segregation is quite close to 1 as its concentration is relatively consistent from the bottom to top of the crystal boules.

(35) TABLE-US-00003 TABLE 3 Crystal composition determined by EPMA (at % normalized to Pb). Crystal ID Sample location Mg Ti Nb Sm In Zr BV-56B Bottom 17.16% 25.80% 49.86% 0.31% 13.33% / Top 13.58% 35.17% 43.41% 0.17% 12.67% / BV-56C Bottom 16.80% 28.50% 47.66% 0.62% 13.15% / Top 14.02% 33.80% 45.17% 0.43% 12.63% / BV-55A Bottom 24.61% 29.64% 51.14% 0.89% / / Top 22.76% 32.90% 48.66% 0.36% / / BV-54D Bottom 15.80% 29.56% 46.25% 2.67% 13.16% / Middle 15.37% 31.08% 45.64% 2.45% 13.21% / SB-BIII-16 Bottom 18.89% 22.75% 39.77% / / 10.92% Top 18.89% 34.58% 37.06% / /  0.33%

Example 1

(36) Sm:PMN-PT crystal growth: A typical Bridgman process for Sm-modified PMN-PT (2 mol % Sm.sub.2O.sub.3 in 68 mol % PMN-32 mol % PT) crystal growth is described as follows. According to the stoichiometry of the PMN-PT compound, PbO, MgNb.sub.2O.sub.6, and TiO.sub.2 were mixed with 2 mol % Sm.sub.2O.sub.3. The mixture was milled by zirconia grinding media in a ball mill for 16 hours and then was dried in an oven around 50° C. The dried powder was sieved through an 80-mesh nylon screen, and then was calcined at 850° C. Purity of the perovskite phase was confirmed by XRD. The synthesized powder was pressed into small pellets, and then fired at 1250° C. The ceramic pellets were then charged into a tapered platinum (Pt) crucible. The Pt crucible is 15 mm in diameter and 100 mm long with a 10 mm in diameter and 50 mm long seed well (no single crystal seed was charged into the seed well).

(37) A two heating-zone vertical Bridgman furnace was used for the crystal growth. The maximum temperatures for the upper and lower heating zones were 1390° C. and 1100° C., respectively. The vertical temperature gradient along the Pt crucible was >5° C./cm. After the whole charge was melted, it was soaked for 10 hours, and then the crucible was lowered down at a rate of 0.6 mm/hour to initiate the crystallization process at the bottom of the Pt crucible. After moving the crucible down about 150 mm, the crystallization process driven by the vertical temperature gradient was completed. Then the furnace was cooled down to room temperature in 78 hours. Yielded was a single crystal (except for the very beginning part of the boule) with a diameter of 10-15 mm and about 90 mm long and was grown roughly along the <111>-orientation. FIG. 4 is a photograph of this crystal boule.

Example 2

(38) Sm:PIN-PMN-PT crystal growth: A typical Bridgman process for Sm-modified PIN-PMN-PT (2 mol % Sm.sub.2O.sub.3 in 26 mol % PIN-42 mol % PMN-32 mol % PT) crystal growth is described as follows. According to the stoichiometry of the PIN-PMN-PT compound, PbO, MgNb.sub.2O.sub.6, InNbO.sub.4 and TiO.sub.2 were mixed with 2 mol % Sm.sub.2O.sub.3. The mixture was milled by zirconia grinding media in a ball mill for 16 hours and then was dried in an oven around 50° C. The dried powder was sieved through an 80-mesh nylon screen, and then was calcined at 850° C. Purity of the perovskite phase was confirmed by XRD. The synthesized powder was pressed into small pellets, and then fired at 1250° C. The ceramic pellets were then charged into a tapered platinum (Pt) crucible. The Pt crucible is 15 mm in diameter and 100 mm long with a 10 mm in diameter and 50 mm long seed well (no single crystal seed was charged into the seed well).

(39) A two heating-zone vertical Bridgman furnace was used for the crystal growth. The maximum temperatures for the upper and lower heating zones were 1390° C. and 1100° C., respectively. The vertical temperature gradient along the Pt crucible was >5° C./cm. After the whole charge was melted, it was soaked for 10 hours, and then the crucible was lowered down at a rate of 0.6 mm/hour to initiate the crystallization process at the bottom of the Pt crucible. After moving the crucible down about 150 mm, the crystallization process driven by the vertical temperature gradient was completed. Then the furnace was cooled down to room temperature in 78 hours. Yielded was a single crystal (except for the very beginning part of the boule) with a diameter of 10-15 mm and about 110 mm long and was grown roughly along the <111>-orientation. FIG. 5 is a photograph of this crystal boule.

Example 3

(40) Sm: PMN-PT crystal testing: Piezoelectric and dielectric properties of Sm-modified PMN-PT (2 mol % Sm.sub.2O.sub.3 in 68 mol % PMN-32 mol % PT) crystal grown in Experiment 1 have been measured. First, the single crystal boules were oriented by a real-time Laue X-ray photography system. Then thin plate samples with a width to thickness ratio of about 10:1 were cut from the boules with the pair of large faces of the plates in {001} family. After Au electrodes were sputtered onto the pair of large faces, the hysteresis cycles of the polarization and the strain were measured by using the Sawyer-Tower polarization and LVDT strain measurement system under a 10 kV/cm, 0.1-10 Hz AC field, from which the remnant polarization (P.sub.r), coercive field (E.sub.C) and piezoelectric coefficient (d.sub.33) of the samples were obtained; meanwhile, the samples were poled along <001> (through the thickness). Dielectric permittivity and loss vs. temperature were measured within the temperature range 25-150° C. by a HP4174A LCR meter connected to a temperature chamber. The Curie temperature (T.sub.c) & rhombohedral-to-tetragonal phase transition temperature (T.sub.rt) were then determined by the maximum peaks of the dielectric permittivity. The measured dielectric and piezoelectric properties are shown in FIG. 6.

Example 4

(41) Sm:PIN-PMN-PT crystal testing: Piezoelectric and dielectric properties of Sm-modified crystal grown from 26 mol % PIN-PMN-30 mol % PT (with 1 mol % Sm.sub.2O.sub.3 substitution) have been measured. First, the single crystal boules were oriented by a real-time Laue X-ray photography system. Then thin plate samples with a width to thickness ratio of about 10:1 were cut from the boules with the pair of large faces of the plates in {001} family. After Cr/Au electrodes were sputtered on the pair of large face, the hysteresis cycles of the polarization were measured by using the Sawyer-Tower polarization and LVDT strain measurement system under a 10 kV/cm, 0.1-10 Hz AC field, from which coercive field (E.sub.C) and piezoelectric coefficient (d.sub.33) of the samples were obtained; meanwhile, the samples were poled along <001> (through the thickness). Dielectric permittivity and loss vs. temperature were measured within the temperature range 25-200° C. by a HP4174A LCR meter connected to a temperature chamber. The Curie temperature (T.sub.c) & rhombohedral-to-tetragonal phase transition temperature (T.sub.rt) were then determined by the maximum peaks of the dielectric permittivity. The measured dielectric and piezoelectric properties are shown in Table 4. and FIG. 7.

(42) TABLE-US-00004 TABLE 4 The properties of the <001>-poled samples from a Sm: PIN-PMN-PT crystal. tanδ d.sub.33 E.sub.C Samples ε.sub.r (%) ε.sub.r (clamped) (pC/N) T.sub.rt (T.sub.C) (° C.) (kV/cm) D5-3 7640 0.7 1050 2150 77 (141) 6.0 D7-3 7230 1.2 900 2000 82 (143) 5.6

Example 5

(43) <111>-poled Sm-modified crystal testing: Piezoelectric and dielectric properties of Sm-modified crystal grown from PMN-32 mol % PT and 26 mol % PIN-PMN-32 mol % PT (both with 2 mol % Sm.sub.2O.sub.3 substitution) have been measured. First, the single crystal boules were oriented by a real-time Laue X-ray photography system. Then thin plate samples with a width to thickness ratio of about 10:1 were cut from the boules with the pair of large faces of the plates in {111} family. After Cr/Au electrodes were sputtered on the pair of large faces, the polarization and strain were measured by using the Sawyer-Tower polarization and LVDT strain measurement system under a 10 kV/cm, 0.1-10 Hz AC and DC fields, from which coercive field (E.sub.C) and piezoelectric coefficient (d.sub.33) of the samples were obtained; meanwhile, the samples were poled along <111> (through the thickness). Dielectric permittivity and loss vs. temperature were measured within the temperature range 25-200° C. by a HP4174A LCR meter connected to a temperature chamber. The Curie temperature (T.sub.c) & rhombohedral-to-tetragonal phase transition temperature (T.sub.rt) were then determined by the maximum peaks of the dielectric permittivity. The dielectric and piezoelectric properties measured at room temperature (except for T.sub.rt/T.sub.C) are shown in Table 5. and FIG. 8. At room temperature, Samples 1 and 2 may be in orthorhombic and tetragonal phases, respectively.

(44) TABLE-US-00005 TABLE 5 The properties of the <111>-poled longitudinal mode samples from Sm-modified crystals. tanδ ε.sub.r d.sub.33 T.sub.rt (T.sub.C) E.sub.C Sample Sample from ε.sub.r (%) (clamped) (pC/N) (° C.) (kV/cm) 1 2 mol % Sm: PMN- 17000 <2 5000 1400 −30 (80)  4.0 32PT 2 2 mol % 10500 <2 3600 900 −20 (135) 7.7 Sm: 26PIN-PMN- 32PT

(45) While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.