Temperature-induced and electric-field-induced phase transitions in rhombohedral ${\mathrm{Pb}(\mathrm{In}}_{1/2}{\mathrm{Nb}}_{1/2}){\mathrm{O}}_3\text{−}{\mathrm{Pb}(\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}{)\mathrm{O}}_3\text{−}{\mathrm{PbTiO}}_3$ ternary single crystals

Temperature and electric field effects on rhombohedral $\left(R\right)$ ternary ${\mathrm{Pb}(\mathrm{In}}_{1/2}{\mathrm{Nb}}_{1/2}){\mathrm{O}}_3\text{−}{\mathrm{Pb}(\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}{)\mathrm{O}}_3\text{−}{\mathrm{PbTiO}}_3$ (PIN-PMN-PT) ferroelectric single crystals were comprehensively studied by x-ray diffraction. We have focused on how the individual phase transitions as well as the phase transition sequences depend on thermal and electrical history. Electric field-temperature phase diagrams have been constructed under [001] field-cooling and field-heating conditions. As happens to the $R$ phase of binary PMN-PT crystals [H. Cao, J. F. Li, D. Viehland, and G. Y. Xu, Phys. Rev. B 73, 184110 (2006)], the $R$ phase of the zero-field-cooled (ZFC) state is replaced by a monoclinic A $(M$) phase in the field-cooled (FC) diagram. In particular, reciprocal-space mesh scans demonstrated that the $M$ phase was stable for crystals poled along the [001] crystallographic direction rather than the initial $R$ phase of the ZFC state. Furthermore, an $E$-field-induced phase transformational sequence of $R\to M$→ tetragonal $\left(T\right)$ was observed at constant temperature, revealing a gradual increase in the $c$ lattice parameter. These findings demonstrate that the ternary PIN-PMN-PT crystals exhibit common phase transition features with binary PMN-PT and ${\mathrm{Pb}(\mathrm{Zn}}_{1/3}{\mathrm{Nb}}_{2/3}{)\mathrm{O}}_3\text{−}{\mathrm{PbTiO}}_3$ (PZN-PT) ones for compositions in the low PT side of the morphotropic phase boundary.

Figure 1

(a) Representation of the monoclinic unit cell with respect to the tetragonal unit cell, adapted from Ref. [3]. The polarization in monoclinic $M$_A (space group $C\mathrm{m}$) lies in the $a$_MA$c$_MA monoclinic plane (polarization $P$ = [xxz] in cubic Cartesian coordinates) and is shown as $p$_MA; the polarization in monoclinic $M$_C (space group $P\mathrm{m}$) lies in the ${\mathrm{a}}_{\mathrm{MC}}{c}_{\mathrm{MC}}$ plane (polarization $P=\left[x0z\right]$) and is shown as $p$_MC. (b) Scheme of two possible paths ($R\to M$_A→$T$ and $R\to M$_A→$M_{\mathrm{C}}\to T$) for the polarization vectors to change from [111] in the rhombohedral phase to [001] in the tetragonal one, as proposed by Fu and Cohen [5]. (c) Schematic representation of reciprocal-space maps of a monoclinic structure, indexed in the monoclinic system.

Figure 2

Field-temperature phase diagram of rhombohedral PIN-PMN-PT, respectively obtained from structural measurement in the (a) FC process and (b) FH process with $E$ = 1 kV/cm. The phase transition under ZFC and ZFH was also present in this figure, labeled with dashed arrows.

Figure 3

Temperature dependence of the dielectric constant at 1 kHz (solid lines) and 10 kHz (dash lines): (a) for ZFC, ZFH, and PH processes; (b) under various $E$ fields of $E$ = 0.5, 1, and 2 kV/cm for FC process; (c) under various $E$ fields of $E$ = 0.5, 1, and 2 kV/cm for FH process.

Figure 4

Temperature evolution of the (a) (002)${}_{\mathrm{C}}$ and (b) (220)${}_{\mathrm{C}}$ reflection peaks for ZFC from cubic to rhombohedral phase and (c) (002)${}_{\mathrm{C}}$ and (d) (220)${}_{\mathrm{C}}$ reflection peaks for ZFH from rhombohedral to cubic phase.

Figure 5

Temperature dependence of FWHM of various diffraction peaks along (002)${}_{\mathrm{C}}$ observed in Fig. 4 for (a) ZFC and (b) ZFH conditions.

Figure 6

Lattice parameters as a function of temperature for (a) ZFC and (b) ZFH processes and (c) the tilt angles for $R$ phase. The phase transition sequences for the two processes were also labeled in this figure. In the cubic region, the solid squares are obtained from the (002)${}_{\mathrm{C}}$ diffraction data, while the open squares are obtained from (220)${}_{\mathrm{C}}$ one. The shadow region indicated the coexistence of adjacent two phases. Solid lines drawn though the data points are for guides to the eyes.

Figure 7

Temperature-dependent lattice parameters under (a) FC, (b) FH with $E$ = 1 kV/cm, and (c) PH process. The tilting angles are presented in (d) of this figure. In the cubic phase region, the solid squares are obtained from the (002)${}_{\mathrm{C}}$ diffraction data, while the open squares are obtained from (200)${}_{\mathrm{C}}$ one. Solid lines drawn though the data points are for guides to the eyes.

Figure 8

Reciprocal-space mesh scan around pseudocubic (200) and (220) zone at different temperature in FC process with $E$ = 1 kV/cm parallel to [001] direction.

Figure 9

Reciprocal-space mesh scan around pseudocubic (200) and (220) zone at different temperature in FH process with $E$ = 1 kV/cm parallel to [001] direction.

Figure 10

Reciprocal-space mesh scan around pseudocubic (200) and (220) zone at different temperature in PH process after specimen being poled along [001] direction.

Figure 11

$E$-field evolution of pseudocubic (002) reflection peaks in an $E$-field circle with initially increasing from $E$ = 0 kV/cm to $E$ = 15 kV/cm or 10 kV/cm and then decreasing to $E$ = 0 kV/cm at fixed temperature of (a) 60 °C and (b) 100 °C. The lattice parameters and the $E$-field-induced phase transition sequence were presented in the bottom panels: (c) at 60 °C and (d) at 100 °C.

Figure 12

Reciprocal-space mesh scan around pseudocubic (200) and (220) zone with increasing $E$ field to $E$ = 2 kV/cm at fixed temperature of 100 °C.