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New Pb(Mg1/3Nb2/3)O3−Pb(In1/2Nb1/2)O3−PbZrO3−PbTiO3 Quaternary Ceramics: Morphotropic Phase Boundary Design and Electrical Properties Nengneng Luo,†,‡ Shujun Zhang,‡ Qiang Li,*,† Chao Xu,† Zhanlue Yang,† Qingfeng Yan,† Yiling Zhang,§ and Thomas R. Shrout‡ †

Department of Chemistry, Tsinghua University, Beijing 100084, China Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, United States § School of Materials Science & Engineering, Tsinghua University, Beijing 100084, China ACS Appl. Mater. Interfaces 2016.8:15506-15517. Downloaded from pubs.acs.org by IOWA STATE UNIV on 01/05/19. For personal use only.

‡

ABSTRACT: Four series of Pb(Mg 1/3 Nb 2/3 )O 3 −Pb(In 1/2 Nb 1/2 )O 3−PbZrO 3 −PbTiO 3 (PMN−PIN−PZ−PT) quaternary ceramics with compositions located at the morphotropic phase boundary (MPB) regions were prepared. The MPBs of the multicomponent system were predicted using a linear combination rule and experimentally confirmed by X-ray powder diffraction and electrical measurement. The positions of MPBs in multicomponent systems were found in linear correlation with the tolerance factor and ionic radii of non-PT end-members. The phase structure, piezoelectric coefficient, electromechanical coupling coefficient, unipolar strains, and dielectric properties of as-prepared ceramics were systematically investigated. The largest d33s were obtained at S36.8, L37.4, M39.6, and N35.8, with the corresponding values of 580, 450, 420, and 530 pC/N, respectively, while the largest kps were found at S34.8, L37.4, M39.6, and N35.8, with the respective values of 0.54, 0.50, 0.47, and 0.53. The largest unipolar strain Smax and high-field piezoelectric strain coefficients d33* were also observed around the respective MPB regions. The rhombohedral-to-tetragonal phase transition temperature Trt increased with increasing PIN and PZ contents. Of particular importance is that high Trt of 140−197 °C was achieved in the M series with PZ and PIN contents being around 0.208 and 0.158, which will broaden the temperature usage range. KEYWORDS: morphotropic phase boundary (MPB), linear combination rule, PMN−PIN−PZ−PT, piezoelectric, tolerant factor relatively low Curie temperature, Tc (∼150−170 °C), and rhombohedral-to-tetragonal phase transition temperature, Trt (∼60−100 °C), which strongly restrict their applications in the areas where thermal stability is required.4−7 Moreover, enormous studies showed that the electromechanical properties of many other MPB-based relaxor−PT binary systems were much lower compared with those of PMN−PT and PZN− PT.8−10 Therefore, it is extremely important to develop new materials with better electromechanical properties and/or higher phase transition temperature. For the purpose of exploring new and high-performance relaxor−PT-based materials, various methods have been adopted, among which introducing other components into the binary systems to form multicomposition systems has been found to be one of the most effective ways. As a result, a large number of materials with multiple components have been developed and some of them exhibited remarkably enhanced dielectric and piezoelectric properties.11−18 Compared with those of binary systems, the multicomponent systems enable

1. INTRODUCTION 1.1. Background. The existence of morphotropic phase boundary (MPB) has made MPB-based ferroelectric solid solutions attract immense interest in the global level, due to their significantly enhanced electromechanical properties compared with non-MPB ferroelectric materials.1,2 Generally, the highest piezoelectric and dielectric responses are found in compositions located at or near MPB, being separated by rhombohedral (R) and tetragonal (T) phases.1 The well-known PbZr1−xTixO3 (PZT) solid solution has become the mainstay materials for various piezoelectric devices, such as actuators, sensors, and transducers, due to its excellent piezoelectric properties at MPB. In addition, a large number of PT-based relaxor ferroelectrics, typed as Pb(B′B″)O3−PbTiO3, has been discovered and found to exhibit high electromechanical performance with compositions located at MPB regions. Among them, Pb(Mg1/3Nb2/3)O3−PbTiO3 (PMN−PT) and Pb(Zn1/3Nb2/3)O3−PbTiO3 (PZN−PT) single crystals are the most promising piezoelectric materials exhibiting ultrahigh electromechanical properties (d33 > 2000pC/N; k33 = 90%− 92%).3 However, to one’s desperations, there are still many shortages existing in the PT-based binary systems. Take some, for example, the two systems mentioned above possess © 2016 American Chemical Society

Received: April 13, 2016 Accepted: May 31, 2016 Published: May 31, 2016 15506

DOI: 10.1021/acsami.6b04432 ACS Appl. Mater. Interfaces 2016, 8, 15506−15517

Research Article

ACS Applied Materials & Interfaces

Figure 1. (a) Schematic MPBs in binary and ternary systems; (b) schematic MPB plane in PMN−PIN−PZ−PT quaternary system; (c) new-built vector coordinate system obtained from (a); and (d) schematic MPB plane and positions of the designed compositions. The points in red are on the plane; the points in yellow and blue are respectively below and above the plane.

more flexibility in adjusting compositions such as the electromechanical properties. The Pb(Mg 1/3 Nb 2/3 )O 3 −Pb(In 1/2 Nb 1/2 )O 3 −PbTiO 3 (PMN−PIN−PT) and Pb(Mg1/3Nb2/3)O3−PbZrO3−PbTiO3 (PMN−PZ−PT) ternary systems were reported to exhibit good piezoelectric and dielectric properties, as well as high phase transition temperatures, of which the as-grown single crystals are considered to be the second generation relaxor−PT ferroelectric crystals.6 It is speculated that the combination of PMN−PIN−PT and PMN−PZ−PT systems to form a new quaternary Pb(Mg1/3Nb2/3)O3−Pb(In1/2Nb1/2)O3−PbZrO3− PbTiO3 (PMN−PIN−PZ−PT) may exhibit a higher phase transition temperature with optimized electrical properties. In this work, a series of Pb(Mg1/3Nb2/3)O3−Pb(In1/2Nb1/2)O3− PbZrO3−PbTiO3 (PMN−PIN−PZ−PT) ceramics were prepared, to give a comprehensive understanding of MPB and its physical property in a quaternary system. 1.2. MPB Design of Multicomponent Systems. In order to take full advantage of MPB, it is of particular importance to determine the MPB in multicomponent systems. However, with increasing end-members, the MPB for a multicomponent system becomes more complicated than those of a binary counterpart, due to the lack of a qualitative guide with which the position of the MPB may be predicted prior to experimental study. Because of the absence of such a guide, enormous experimental work has to be done to locate the position of the MPB. Therefore, it is of great importance to predict the position of MPB in multicomponent systems. A. MPB in Binary and Ternary System. The MPBs of many PT-based binary systems were reported to locate around a certain composition in one-dimensional areas. For example, the MPB is known to be around x = 0.42 and x = 0.33 in (1 x)Pb(Sc1/2Nb1/2)O3−xPT (PSN−PT)19 and (1 − x)Pb-

(Mg1/3Nb2/3)O3−xPbTiO320 systems, respectively. Further investigations on Pb(Sc1/2Nb1/2)O3−Pb(Mg1/3Nb2/3)O3−xPT (PSN−PMN−PT) ceramics by Yamashita et al. revealed that MPBs is more complicated in the ternary system, in which many MPBs can be found with compositions located around the linear region combining the MPB of the PSN−PT and PMN−PT binary systems.11 Schematic MPBs in binary and ternary system are shown in Figure 1a. Later on, Pan and Zhang prepared a series of Pb(Ni1/2Nb1/2)O3−Pb(Zn1/2Nb1/2)O3−PbTiO3 (PNN−PZN−PT) ceramics and verified that the MPBs were located around the linear region between the MPBs of these two relaxor−PT binary systems.12 Furthermore, a universal equation was proposed to predict the MPB composition of a ternary system, named as the linear combination rule: MPBT = j1 MPB1 + j2 MPB2

(1)

where the MPB1 and MPB2 stand for MPBs of the two binary ferroelectrics F1−PT and F2−PT, respectively. j1 and j2 are the proportions of the two MPBs, and j1 + j2 = 1. The linear combination rule was further confirmed in other investigations on designing the MPB of PMN−PFN−PT and PMN−PZ−PT ternary systems.13,21 As it is well-known, any MPB of a ternary system can be written using the following equation: MPBT = (1 − xm)[s1F1 + s2 F2] + xm PT

(2)

where xm is the content of PT when the composition of the ternary system is located at MPB. s1 and s2 are relative ratios of the non-PT end-members F1 and F2, and s1 + s2 = 1. Therefore, when s1 = 1, s2 = 0, the formation of the MPB for F1−PT binary system can be written as MPB1 = (1 − xm1)F1 + xm1PT 15507

(3)


Research Article

ACS Applied Materials & Interfaces Table 1. MPB Compositions Calculated from the Linear Combination Rule and Their Abbreviations series

t1

t2

t3

compositional formulation

abbreviations

S L M N

0.65 0.55 0.35 0.45

0.25 0.25 0.25 0.45

0.10 0.20 0.40 0.10

0.442PMN−0.158PIN−0.052PZ−0.348PT 0.374PMN−0.158PIN−0.104PZ−0.364PT 0.238PMN−0.158PIN−0.208PZ−0.396PT 0.306PMN−0.284PIN−0.052PZ−0.358PT

S34.8 L36.4 M39.6 N35.8

⎯→ ⎯ ⎯⎯⎯→ ⎯→ ⎯ ⎯⎯⎯→ OP = (1 − k1 − k 2)OA + k1OB + k 2OC

When s1 = 0 and s2 = 1, the formation of the MPB for the F2− PT binary system can be expressed as MPB2 = (1 − xm2)F2 + xm2 PT

From the equation above, one can use the three MPBs of binary systems to represent the MPB of the quaternary system, written as

(4)

Herein, xm1 and xm2 are the PT contents of F1−PT and F2−PT systems at their respective MPB compositions. From eqs 1, 3, and 4, one can get another representation of eq 1:

MPBQ = (1 − k1 − k 2)MPB1 + k1MPB2 + k 2 MPB3 (10)

MPBT = j1 [(1 − xm1)F1 + xm1PT] + j2 [(1 − xm2)F2 + xm2 PT] (5)

The MPB of the quaternary system in eq 10 can also be changed into another formation, expressed as

As we know, eqs 1 and 5 are the same expression for the ternary system; the amount of F1, F2, and PT should be equal. Thus, one can get the following equations: ⎧ j (1 − xm1)F1 = (1 − xm)s1F1 1 ⎪ ⎪ ⎨ j2 (1 − xm2)F2 = (1 − xm)s2 F2 ⎪ ⎪ j xm1PT + j xm2 PT = xm PT ⎩1 2

MPBQ = j1 MPB1 + j2 MPB2 + j3 MPB3

1 − xm =

s1 1 − xm1

s2 1 − xm2

(11)

where j1, j2, and j3 are the ratios of the binary systems MPB1, MPB2, and MPB3, respectively, and j1 + j2 + j3 = 1. Thus, it can be concluded that the MPB of a quaternary system also obeys the linear combination rule. The MPB of a quaternary system can also be expressed using the following equation:

(6)

MPBQ = (1 − xm)[s1F1 + s2 F2 + s3F3] + xm PT

Therefore, the relationship among xm, s1, s2, xm1, and xm2 can be written as 1 +

(9)

(12)

where xm is the PT content, s1, s2, and s3 are the ratios of F1, F2, and F3, respectively, among the non-PT end-members, and s1 + s2 + s3 = 1. Similarly to that of the ternary system, the relationship among xm, s1, s2, s3, and the PT content in F1−PT, F2−PT, and F3−PT systems at the respective MPB composition will be

(7)

B. Proposed MPB in Multicomponent Systems. According to the configuration of MPB in binary and ternary systems, it is reasonable to expect that the MPB of a quaternary system may locate around the “plane” composed by the three binary systems. Figure 1b gives a schematic phase diagram of a PMN− PIN−PZ−PT quaternary system. The MPB plane is composed by MPBs of the three binary systems: MPB1 (PMN−PT67/ 33), MPB2 (PIN−PT63/37), and MPB3 (PZT53/47). The point (P, for example) on the plane represents one of the MPBs of the quaternary system. Therefore, if the relationship of P with MPB1, MPB2, and MPB3 is known, one MPB of the quaternary system can be obtained. To get the location of point P, a vector triangle was established. The original point O is located at the position of end-member PT; x, y, and z axes are along the edge of PMN, PIN, and PZ, respectively, as shown in Figure 1c. A(MPB1), B(MPB2), and C(MPB3) are on the x, y, and z axes, respectively. If the coordinates of A, B, C, and P are (a, 0, 0), ⎯→ ⎯ (0, b, 0), (0, 0, c), and (x, y, z), the vectors would be AB = (−a, ⎯→ ⎯ ⎯→ ⎯ b, 0), AC = (−a, 0, c), and AP = (x − a, y, z). ⎯→ ⎯ ⎯→ ⎯ ⎯→ ⎯ Suppose the vector AP composed by AB and AC can be expressed using the following equation: ⎯→ ⎯ ⎯→ ⎯ ⎯→ ⎯ AP = k1AB + k 2 AC (8)

1 − xm =

1 s1 1 − xm1

+

s2 1 − xm2

+

s3 1 − xm3

(13)

Herein, xm1, xm2, and xm3 are PT contents in F1−PT, F2−PT, and F3−PT systems at the respective MPB compositions. If comparing eqs 7 and 13, one can deduce that for a system with components of n, the relationship among xm; s1, s2, ..., sn−1; and xm1, xm2, ..., xm(n−1) at MPB composition obeys the following equation: 1 − xm =

s1 1 − xm1

+

s2 1 − xm2

1 + ... +

sn − 1 1 − xm(n − 1)

(14)

where s1, s2, ..., sn−1 are the ratios of F1, F2, ..., Fn−1 among the non-PT end-members, respectively, and s1 + s2 + ... + sn−1 = 1. xm1, xm2, ..., xm(n−1) are the respective PT contents of each binary system at MPB for F1−PT, F2−PT, ..., Fn−1−PT. Therefore, the MPB composition of a system with endmembers of n can be expressed as follows: MPBn = j1 MPB1 + j2 MPB2 + ... + jn − 1 MPBn − 1

(15)

From the mathematical inference above, one can predicate that MPB composition of a multicomponent system with component of n can be predicted by the linear combining rule of the (n − 1) MPBs of the binary systems.

Then, the coordinate of point P should be (a(1 − k1 − k2), bk1, ck2). ⎯→ ⎯ Therefore, the vector OP can be obtained as follows: 15508


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2. EXPERIMENTAL SECTION 2.1. Designed MPB Composition of Quaternary System. To verify the existence of the MPB plane in a quaternary system, PMN− PIN−PZ−PT ceramics were prepared. In our present investigation, four series of compositions were selected according to eq 11, namely, j1(PMN−PT67/33) + j2(PIN−PT63/37) + j3(PZ−PT53/47). Table 1 lists four MPB compositions calculated from the linear combination rule and their abbreviations. The calculated MPB compositions are S34.8, L36.8, M39.6, and N35.8 in each series, which are located on the MPB plane. To further confirm the exact position of MPB in each series, the compositions below and above the MPB plane were also investigated. The detailed compositions are listed as follows, and the schematic positions of all compositions are given in Figure 1d. S series: [(1 − x)/0.652](0.442PMN−0.158PIN−0.052PZ)−xPT (x = 0.308, 0.328, 0.348, 0.368, or 0.388; hereafter denoted as S30.8− S38.8). L series: [(1 − x)/0.636](0.374PMN−0.158PIN−0.104PZ)−xPT (x = 0.324, 0.344, 0.354, 0.364, 0.374, 0.384, or 0.404; hereafter denoted as L32.4−L40.4). M series: [(1 − x)/0.604](0.238PMN−0.158PIN−0.208PZ)−xPT (x = 0.356, 0.376, 0.396, or 0.416; hereafter denoted as M35.6−S41.6). N series: [(1 − x)/0.642]((0.306PMN−0.284PIN−0.052PZ)−xPT (x = 0.318, 0.338, 0.358, 0.378, or 0.398; hereafter denoted as N31.8− N39.8). 2.2. Experimental Procedure. All ceramics were synthesized by the modified columbite precursor method. High-purity oxide powders of PbO, MgO, Nb2O5, In2O3, ZrO2, andTiO2 were used as starting materials. First, the precursor MgNb2O6 (MN) and InNbO4 (IN) was ball milled and calcined at 1100 and 1200 °C for 4 h, respectively. Then, MN, IN, TiO2, ZrO2, and PbO with 2 mol % excess were weighed and milled according to the nominal compositions. After the drying process, the mixed powders were calcined at 850 °C for 4 h. The calcined powders were ball milled for 4 h to reduce particle size and then pressed into disc-shaped pellets with 10 mm in diameter and about 1 mm in thickness under pressure of 7 MPa. After removal of the binder, the green pellets were sintered from 1150 to 1220 °C in a lead atmosphere by using PbZrO3 powders to prevent lead loss. In order to perform electrical properties characterization, the sintered samples were polished and coated with silver on the large faces to serve as electrodes. X-ray diffractometer (D8 Advance, Brüker, Karlsruhe, Germany) was used to identify the crystal structure. The microstructures of the sintered samples were observed by using scanning electron microscope (Quanta 200 FEG, FEI Company, Eindhoven, The Netherlands). The samples were poled in silicon oil at 120 °C for 15 min under 30 kV/ cm DC fields. Dielectric measurements were carried out on poled samples as a function of temperature by using an Agilent 4294A (Agilent Inc., Bayan, Malaysia) impedance analyzer connected to a Delta 9023 (Delta Design Inc., San Diego, CA, USA) temperature control system. Piezoelectric coefficients (d33) were measured by using a quasi-static piezo-d33 meter (Institute of Acoustics, Chinese Academy of Sciences, ZJ-4A). The electromechanical coupling factors (kp) were measured on disk samples using the resonance method, with an Agilent 4294A impedance analyzer according to IEEE standards. The ferroelectric hysteresis (P−E) and unipolar strains (Suni−E) were measured at 1 Hz frequency using a TF Analyzer (Model 2000, aixACCT, Aachen, Germany).

Figure 2. XRD patterns of the as-prepared PMN−PIN−PZ−PT ceramics: (a) S, (b) L, (c) M, and (d) N series.

sintered ceramics. Obvious evolutions can be observed from the (200)-diffraction peaks. Take the S system for instance; there is only one (200)-diffraction peak for S30.8 with PT content of 0.308; the peak becomes broader with increasing PT content and finally splits into two peaks for S38.8, indicating single rhombohedral phase and tetragonal phase at S30.8 and S38.8, respectively. The coexistence of a rhombohedral phase and tetragonal phase may come across in the composition range of S32.8−S36.8, where the MPB of the S system may be located. Actually, the (200)-diffraction peaks for the ceramics with compositions from S32.8 to S36.8 can be fitted into three peaks (002)T, (200)R and (200)T, using Lorenz function. The (002)Tand (200)T-diffractions are characteristic of the tetragonal phase, while the (200)R-diffraction is the feature of the rhombohedral phase. A similar evolution of the diffractions can also be observed in other series. In ferroelectrics with perovskite structure, the relative ratio of tetragonal and rhombohedral phase (T/R) can be calculated from the following equation:22

3. RESULTS 3.1. Phase Structure Analysis. Figure 2 gives the XRD patterns of the as-sintered ceramics for 2θ ranging from 15° to 70°. All samples are crystallized into a single-phase perovskite structure. XRD also indicates rhombohedral-to-tetragonal phase transition with increasing PT content in each series, according to the gradual broadening and splitting of the peaks. Generally, the (200)-diffraction peaks around 2θ of 45° are more obvious to reflect the phase structure evolutions. Figure 3 shows the (200)-diffraction peaks at 2θ = 44.5°−46.0° for all

T/R = [I(002)T + I(200)T]/I(200)R

(16)

Herein, I(002)T and I(200)T respectively correspond to the intensity of (002)T- and (200)T-diffractions, and I(200)R is the intensity of the (200)R-diffraction. All series demonstrate a similar tendency of T/R value with increase of PT content: at low PT content, T/R is far below 1.0, indicating the rhombohedral phase is in a dominant position; T/R increases with increasing PT content and finally comes into T/R ≫ 1.0 15509


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in very high PT counterpart, while, in the MPB region, T/R values are around 1.0.23 Therefore, the compositions S34.8, L36.4, M37.6, and N35.8 should be located near the center of the MPB region in S, L, M, and N series, respectively. It should be noticed that the actual position of the MPB (PT content) and its width are coaffected by many factors, such as inner strain,24−27 grain size,28,29 and crystallization condition of the solid solution.23 The SEM micrographs of the fractured surfaces of selected PMN−PIN−PZ−PT ceramics are given in Figure 4. All ceramics have well-grown grains, showing clear transgranular behavior; few pores were observed, indicating high density of the as-prepared ceramics. The grain size of the ceramics varies from 3 to 15 μm depending on the components, becoming smaller with increasing PIN and PZ contents. 3.2. Electrical Properties Measurement. The electromechanical properties of the as-prepared PMN−PIN−PZ−PT ceramics were measured and shown in Figure 5. It is not hard to find out that both piezoelectric coefficient (d33) and mechanical coupling coefficient (kp) undergo the trend of increasing first and then decreasing with an increase of PT content in each series, forming a peak at a certain value. The largest d33s were obtained at S36.8, L37.4, M39.6, and N35.8, with the corresponding values of 580, 450, 420, and 530 pC/N, respectively; and the largest kps were found at S34.8, L37.4, M39.6, and N35.8, with the respective values of 0.54, 0.50, 0.47, and 0.53. Generally, the largest d33 could be attained at the MPB compositions, indicating the location of the obtained MPB is approximately consistent with the XRD analysis and the compositions predicted by the linear combination rule. In addition, the peak positions of the electromechanical properties change from composition with low PT content to higher value with increasing PZ content, as shown in S, L, and M series, due to the factor that the PT content is much higher for the MPB of

Figure 3. XRD analysis of the as-prepared PMN−PIN−PZ−PT ceramics at 2θ ≈ 45° with fitted peaks: (a) S, (b) L, (c) M, and (d) N series.

Figure 4. SEM micrographs of the fracture surfaces of selected PMN−PIN−PZ−PT ceramics: (a) S35.8, (b) L36.4, (c) M39.6, and (d) N37.8. 15510


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field.18,30 The competition between easier domain switching around MPB composition and the larger lattice distortion (c/a ratio) in tetragonal phase makes a peak near the MPB region. The largest strain appeared at S36.8, L36.4, M39.6, and N35.8, with the corresponding values of 0.106%, 0.107%, 0.109%, and 0.130% at 20 kV/cm, respectively. The high-field piezoelectric strain coefficient (d33*) can be calculated from the measured unipolar strain, following the equation d33* = Smax /Emax

(17)

where the d33* represents the average strain per unit of electric field over the cycle and has the unit of picometers per volt. Figure 7 gives the calculated d33* as a function of PT content

Figure 5. Electrical properties of the as-prepared PMN−PIN−PZ−PT ceramics: (a) d33; (b) kp.

PZT compared to other binary systems. It should be noted that the d33 and kp decrease from S to M series with increasing PZ content at the MPB region, while a small change is observed when comparing L with N series with increasing PIN content. Figure 6 gives the unipolar strain loops of the as-prepared ceramics at electric field of 20 kV/cm. As shown in Figure 6, a strong compositional dependence of strains was observed in each series, forming a peak around the respective MPB composition. Take S series, for example; the strain is 0.079% for S30.8 and reaches the largest strain of 0.106% for S36.8 with composition around MPB, and then the strain decreases with further increasing PT content. Both intrinsic piezoelectric effect and extrinsic domain switching were considered to contribute to the strain, in which the ferroelastic 90° domain reorientation contributes substantially to the measured strain level at high

Figure 7. Calculated d33* from the unipolar strain for all as-prepared PMN−PIN−PZ−PT ceramics.

for all series. The largest piezoelectric strain coefficients are calculated to be 530, 540, 545, and 640 pm/V at S36.8, L36.4, M39.6, and N35.8, respectively. The evolution of d33* is similar

Figure 6. Unipolar strain of the as-prepared PMN−PIN−PZ−PT ceramics at room temperature: (a) S, (b) L, (c) M, and (d) N series. 15511


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Figure 8. Ferroelectric hysteresis of the as-prepared PMN−PIN−PZ−PT ceramics at room temperature: (a) S, (b) L, (c) M, and (d) N series.

Figure 9. PT content (x) dependence of polarization characteristics of the as-prepared PMN−PIN−PZ−PT ceramics: (a) remnant polarization, Pr; (b) coercive field, Ec.

ferroelectric rhombohedral and tetragonal phases. However, Pr was found to decrease continuously with increasing PT content for L and M series with PZ content of 0.104 and 0.208, showing behavior similar to that observed in PZT ceramics.1,33 This phenomenon may result from the completion between the possible polarization directions/easier polarization rotation in the rhombohedral phase and the clamped domain walls due to the larger lattice distortion (c/a ratio) when PT content is increased. Coercive field, Ec, however, was found to increase monotonously in each series with increasing PT content, as the ceramics changed from rhombohedral-to-tetragonal phase. This can be explained by the larger lattice distortion in tetragonal phase, which makes the domain walls harder to move. Figure 10 gives the temperature dependence of dielectric permittivity of as-prepared PMN−PIN−PZ−PT ceramics. Broad peaks were observed from the low PT content compositions with dielectric anomaly at lower temperature for all series, attributing to the ferroelectric-to-paraelectric and rhombohedral-to-tetragonal phase transition, respectively. The low-temperature peaks disappeared at higher PT content counterparts, showing only the sharp peaks relating to Tc. The evolution of the rhombohedral-to-tetragonal phase

to the piezoelectric coefficient d33 measured using the quasistatic method, indicating the existence of the same MPB in each series. It was reported the unipolar strain and the piezoelectric strain coefficient should be the largest at the phase transition region,21,31,32 which further confirms the linear combination rule is applicable to predict the location of MPBs of the multicomponent system. Ferroelectric hysteresis of the as-prepared PMN−PIN−PZ− PT ceramics is shown in Figure 8. For all of the series, typical ferroelectric hysteresis with saturated shapes are observed in the low PT content part at electric field of 30 kV/cm. Larger electric field is needed to obtain a saturated ferroelectric hysteresis when the PT content is very high, due to the increasing of tetragonal phase and clamping of domain walls. The corresponding remnant polarization (Pr) and coercive field (Ec) as a function of PT are shown in Figure 9. For the low PZ content series (S and N series), Pr was found to increase with increasing PT content for the rhombohedral-rich composition, reaching a maximum at the MPB region, and then decreasing for compositions with tetragonal phase. The highest Pr value is expected to be in the MPB region because of the increased possible polarization directions due to the coexistence of 15512


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Figure 10. Temperature dependence of dielectric permittivity of the as-prepared PMN−PIN−PZ−PT ceramics: (a) S, (b) L, (c) M, and (d) N series.

Table 2. Piezoelectric, Dielectric, and Ferroelectric Properties for As-Prepared PMN−PIN−PZ−PT Ceramics composition

d33 (pC/N)

kp

εr

tan δ (%)

Trt (°C)

Tc (°C)

Pr (μC/cm2)

Ec (kV/cm)

S30.8 S32.8 S34.8 S36.8 S38.8 L32.4 L34.4 L35.4 L36.4 L37.4 L38.4 L40.4 M35.6 M37.6 M39.6 M41.6 N31.8 N33.8 N35.8 N37.8 N39.8

233 261 520 580 345 180 185 230 380 450 360 250 199 250 420 260 240 320 530 402 280

0.43 0.45 0.54 0.53 0.42 0.38 0.43 0.45 0.49 0.50 0.39 0.18 0.41 0.43 0.47 0.35 0.42 0.43 0.53 0.42 0.38

970 1080 2560 3830 2460 780 730 810 1850 2360 1490 1450 910 1180 1830 2480 850 1010 1220 2540 1900

1.9 1.6 1.7 1.5 1.4 1.0 1.8 1.8 1.6 1.2 0.9 1.2 2.9 2.1 2.0 1.8 1.8 1.8 1.3 1.1 1.0

155 140 95

204 217 218 231 249 237 243 243 249 255 261 268 274 282 287 >290 237 248 258 269 279

25.6 26.5 30.6 31.9 25.8 35.2 31.4 35.5 30.7 28.5 19.3 18.1 30.0 27.7 28.1 23.2 29.3 32.7 30.3 22.2 21.1

7.3 7.5 7.9 9.0 13.3 10.1 8.8 11.0 10.9 12.1 15.0 17.4 9.8 9.9 13.9 16.7 8.6 8.9 11.7 12.5 15.8

173 145 141 121

197 140

177 156 120

PZ content of 0.052 and PIN of 0.158, it improves to 140−197 °C for the M series when the PZ content increases to 20.8 with small variation in PIN content, and Trt is 121−177 °C by increasing the PIN content to 0.284 with PZ content of 0.052. The higher phase transition temperature will expand its application in high-temperature field. Therefore, it can be deduced that both PZ and PIN help to enhance Tc and Trt at the MPB composition, which may be related to the relative lower tolerant factor of the PZ and PIN end-members than that of PMN.

transition indicates the existence of the MPB in each series. Table 2 gives some typical properties of the as-prepared PMN− PIN−PZ−PT ceramics. Based on the data gotten from the temperature dependence of dielectric permittivity, a phase diagram of MPB relating to compositions and temperature was plotted and shown in Figure 11. In each series, Tc was enhanced with increasing PT content. For example, the Tc is 204 °C for S30.8 and increases to 249 °C for S38.8. A similar tendency can also be observed in other series. What’s more, the Tc was found to increase with increasing PZ content for the composition at the MPB region. Of particular importance is that Trt was enhanced when PZ and PIN content increased for the MPB compositions. Trt is 95−155 °C for the S series with 15513


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dotted line with a slope of 1.0, indicating the predicted MPB are approximate to that obtained from experiment, with minimal scattering. To give a more clear demonstration of the effect of the tolerant factor on the predicted and experimental MPB, the relationship between the PT content of predicted/experimental MPB and the tolerance factor, t, are drawn in Figure 12b. As shown in Figure 12b, the PT content of both predicted and experimental MPB shows a similar tendency with that of the tolerance factor, demonstrating a nearly linear relationship. By fitting the PT content of experimental MPB with that of t, linear relationships can be obtained as follows:

Figure 11. Mapped phase diagram of MPB, relating to compositions and temperatures for the PMN−PIN−PZ−PT system.

exp x PT = 4.53 − 4.26t

(19)

pre x PT = 5.02 − 4.76t

(20)

xexp PT

xpre PT

Herein, and are the experimental and predicted PT content, respectively. As shown in eqs 19 and 20, the position of MPBs show linear correlation with the tolerance factor of the non-PT end-members, and the PT content decreases with the increasing tolerant factor. Furthermore, limited deviations can be observed when comparing the equations above, indicating good matching between experimental and predicted MPB. According to the definition of the tolerance factor, a low tolerance factor results from a large average ionic radii of B cations. In fact, first principle calculations showed that the PT content at the MPB composition in a binary system is linearly dependent on the ionic radii and the ionic displacements (Dav B) of the B cations, as a result of competition between the local repulsion and A-cation displacement alignment interactions.45 After Taylor series expansion, the relationship among PT content at MPB composition, ionic radii, and ionic displacements of the B cations can be expressed using the equation as follows:

4. DISCUSSION Our experimental data showed good matching with the proposed linear combination rule. To illustrate the phenomenon above, the intrinsic mechanism was investigated here. It was found that the structural stability, formability, and physical property of ABO3-type perovskite compounds are closely related to the tolerance factor (t).34−38 Based on the preferred A−O and B−O bond lengths, t can be expressed using the following equation:39 RA + R O t= 2 (RB + R O) (18) where RO is the ionic radius of O2− ions and RA and RB are the average ionic radii of ions at A and B sites, respectively. When t > 1.0, it favors tetragonal and cubic symmetries; when t < 1.0, the lower symmetries such as rhombohedral, monoclinic, and orthorhombic structure are more preferable. From eq 18, it can be deduced a larger ionic radius at the B site will result in a lower tolerance factor. To further investigate the effect of tolerance factor on the position of MPB in a multicomponent system. Table 3 summarizes the ionic radii at the B site, the average radii at the B site (Rav B ), the calculated tolerance factor, the predicted MPB from the linear combination rule, and experimental MPB of some PT-based ternary and quaternary systems.12,17,18,40−44 Figure 12a shows the correlation between the PT content of predicted and experimental MPB. All data are around the

x PT = a + bRBav + cDBav

(21)

Dav B

where a, b, and c are constants. Generally, the is fairly relatively constant.45 Herein, it is expanded to multicomponent av systems, and only the experimental xexp PT vs RB were plotted in Figure 12c. By fitting the data, one can obtain exp x PT = −0.91 + 1.85RBav

xexp PT

(22)

Rav B

The dependence of on exhibits good linear correlation, even though with some scatter. The deviations may be related to the existence of Dav B.

Table 3. Ionic Radii Data; Calculated Tolerance Factor, t; PT Content at Predicted MPB Using Linear Combination Rule, and PT Content at Experimental MPB Obtained from Literature and This Work for PT-Based Materials12,17,18,40−44 non-PT end-member 0.603PMN−0.05PZ 0.192PMN−0.396PYN 0.30PMN−0.36PIN 0.124PH−0.38PYN 0.56PNN−0.14PZN 0.53PMN−0.10PFN−0.05PZ 0.48PMN−0.10PFN−0.10PZ 0.056PZN−0.303PNN−0.317PMN 0.428PMN−0.153PIN−0.051PZ 0.368PMN−0.156PIN−0.102PZ 0.238PMN−0.158PIN−0.208PZ 0.306PMN−0.284PIN−0.52PZ

B′, B″ size (Å) 0.72, 0.72, 0.72, 0.71, 0.69, 0.72, 0.72, 0.74, 0.72, 0.72, 0.72, 0.72,

0.64; 0.64; 0.64; 0.71; 0.64; 0.64; 0.64; 0.64; 0.64; 0.64; 0.64; 0.64;

av radii at B site (Å)

t

pred MPB

exp MPB

0.6708 0.7263 0.6959 0.7439 0.6600 0.6673 0.6712 0.6629 0.6841 0.6888 0.6991 0.6947

0.987 0.961 0.975 0.953 0.992 0.989 0.987 0.991 0.981 0.978 0.974 0.976

0.34 0.443 0.352 0.50 0.30 0.32 0.33 0.332 0.348 0.364 0.396 0.358

0.347 0.412 0.34 0.496 0.30 0.32 0.32 0.324 0.368 0.374 0.396 0.358

0.72, 0.72 0.87, 0.64 0.80, 0.64 0.87, 0.64 0.74, 0.64 0.645, 0.64; 0.72, 0.72 0.645, 0.64; 0.72, 0.72 0.69, 0.64; 0.72, 0.64 0.80, 0.64; 0.72, 0.72 0.80, 0.64; 0.72, 0.72 0.80, 0.64; 0.72, 0.72 0.80, 0.64; 0.72, 0.72 15514

ref 40 41 42 18 12 17 43 44 this this this this

work work work work


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Therefore, the average ionic radius in a quaternary system is a linear combination of the average ionic radii of the non-PT end-members of the three binary systems. If eqs 22 and 23 are combined, one can further find that the PT content at MPB composition also exhibits a linear correlation to the combination of average ionic radii of the non-PT end-member of the three binary systems, which is similar to that of the linear combination rule proposed. As a result of the linear combination of the average ionic radii of non-PT end-members, thus, the linear combination rule is applicable to predict MPB of PT-based multicomponent systems. This rule may also be suitable for the lead-free systems with such a composition driven phase boundary. It should be noted that, besides the tolerance factor, other factors, such as electronegativity values46−48 and weight ratio of A and B sites,49 should also be considered when designing a MPB-based ferroelectric material with high performance.

5. CONCLUSIONS Four series of PMN−PIN−PZ−PT quaternary ceramics with compositions locating at the MPB region were prepared according to a linear combination rule. The phase structure analysis indicated the experimental MPBs of the as-prepared PMN−PIN−PZ−PT quaternary ceramics were very close to the predicted MPB region, being related to the tolerance factor/ionic radii of non-PT end-member, further verified by the piezoelectric coefficient, electromechanical coupling coefficient, unipolar strains, and dielectric properties. Our result gives a comprehensive idea of designing the MPBs of PT-based and lead-free multicomponent systems. All of the quaternary MPB compositions tested show good electrical properties with enhanced phase transition temperatures. The optimum properties were found for the MPB composition of the S series, with d33, kp, εr, tan δ, S, Pr, and Ec of 580 pC/N, 0.54, 3830, 1.5%, 0.106%, 31.9 μC/cm2, and 9.0 kV/cm. Of particular importance is that high Trt of 140−197 °C was achieved for the M series with PZ and PIN content around 0.208 and 0.158, which will enhance the temperature usage range of the piezoelectric ceramics.

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 10 62781694. Fax: +86 10 62771149. E-mail: [email protected]. Notes

Figure 12. Plot of (a) mole fractions of PT at predicted MPB vs those at experimental MPB; correlation between the predicted and experimental MPB vs (b) non-PT end-member tolerance factor, t, and (c) average radii at the B site.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Basic Rsearch Program of China (Grant No. 2013CB632900) and the National Natural Science Foundation of China (Grant Nos. 50972071 and 51172118). The Tsinghua University Initiative Scientific Research Program and the State Key Laboratory of New Ceramics and Fine Processing, Tsinghua University, Beijing, China are also acknowledged for financial support. N.L. acknowledges the support from the China Scholarship Council.

In a multicomponent system, the Rav B is the average ionic radii of the cations at the B site of non-PT end-members. Taking MPB compositional xPMN−yPIN−zPZ−(1 − x − y − z)PT quaternary system as an example, the non-PT end-member is the combination of PMN, PIN, and PZ, in which the Rav B should be obtained as RBav =

■

x(1/3R Mg 2+ + 2/3R Nb5+) x+y+z +

y(1/2R In3+ + 1/2R Nb5+) zR Zr 4+ + x+y+z x+y+z

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