Electric-field-, temperature-, and stress-induced phase transitions in relaxor ferroelectric single crystals

Electric-field-induced phase transitions have been evidenced by macroscopic strain measurements at temperatures between $25°\mathrm{C}$ and $100°\mathrm{C}$ in ${\left[001\right]}_C$-poled $(1-x)\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3-x\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3[\left(\mathrm{PMN}\text{−}x\mathrm{PT}\right);x=0.25,0.305,0.31]$ and $(1-x)\mathrm{Pb}\left({\mathrm{Zn}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3-x\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3[\left(\mathrm{PZN}\text{−}x\mathrm{PT}\right);x=0.05,0.065,0.085]$ single crystals. Such measurements provide a convenient way of ascertaining thermal and electrical phase stabilities over a range of compositions and give direct evidence for first-order phase transitions. A pseudorhombohedral $\left(M_A\right)$–pseudo-orthorhombic $\left(M_C\right)$–tetragonal $\left(T\right)$ polarization rotation path is evidenced by two first-order-like, hysteretic discontinuities in strain within the same unipolar electric field cycle for PZN-5PT, PMN-30.5PT, and PMN-31PT whereas, in PMN-25PT, a single first-order-like $M_A\text{−}T$ transition is observed. This agrees well with in situ structural studies reported elsewhere. Electric-field-temperature (E-T) phase diagrams are constructed showing general trends for $M_A$, $M_C$, and $T$ phase stabilities for varying temperatures and electric fields in poled samples over the given range of compositions. The complex question of whether the $M_A$ and $M_C$ states constitute true phases, or rather piezoelectrically distorted versions of their rhombohedral $\left(R\right)$ and orthorhombic $\left(O\right)$ parents, is discussed. Finally, stress-induced phase transitions are evidenced in ${\left[001\right]}_C$-poled PZN-4.5PT by application of a moderate compressive stress $(<100\mathrm{MPa})$ both along and perpendicularly to the poling direction (longitudinal and transverse modes, respectively). The rotation path is likely $R\text{−}{M}_B\text{−}O$, via a first-order, hysteretic rotation within the $M_B$ monoclinic plane. The results are presented alongside a thorough review of previously reported electric-field-induced and stress-induced phase transitions in $\mathrm{PMN}\text{−}x\mathrm{PT}$ and $\mathrm{PZN}\text{−}x\mathrm{PT}$.

Figure 1

(Color online) Schematic drawing of the respective ${\left[111\right]}_C$, ${\left[101\right]}_C$, and ${\left[001\right]}_C$ polarization directions for the rhombohedral, orthorhombic, and tetragonal phases. Also shown are the monoclinic planes ${\left(1\overline{1}0\right)}_C$, ${\left(10\overline{1}\right)}_C$, and ${\left(010\right)}_C$ of the $M_A,M_B,M_C$ phases, respectively. The labels $M_A$ and $M_B$ given here are valid only for rotations between the three limiting directions shown.

Figure 2

(Color online) Schematic drawing of the direct (charge-stress) piezoelectric measurements in longitudinal (a) and transverse (b) modes. The arrows represent the polar vectors in the rhombohedral domain-engineered structure formed by poling along ${\left[001\right]}_C$.

Figure 3

Series of converse piezoelectric (strain-electric field) loops for ${\left[001\right]}_C$-oriented PZN-5PT, at varying temperatures between $30°\mathrm{C}$ and $100°\mathrm{C}$. The measurements were made using an optical probe system at a frequency of $1\mathrm{Hz}$. The threshold fields (upon increasing field) for the two electric-field-induced phase transitions, $E_{T\left(1\right)}$ and $E_{T\left(2\right)}$, are indicated by dotted lines. In each case, they are derived from a tangent-intersection construction as shown explicitly for $T=90°\mathrm{C}$.

Figure 4

Series of converse piezoelectric (strain-electric field) loops for ${\left[001\right]}_C$-oriented PZN-6.5PT, at varying temperatures between $25°\mathrm{C}$ and $85°\mathrm{C}$. The measurements were made using an optical probe system at a frequency of $1\mathrm{Hz}$.

Figure 5

Converse piezoelectric (strain-electric field) loops for ${\left[001\right]}_C$-oriented PZN-8.5PT, at $25°\mathrm{C}$ and $40°\mathrm{C}$. The measurements were made using an optical probe system at a frequency of $1\mathrm{Hz}$.

Figure 6

Series of converse piezoelectric (strain-electric field) loops for ${\left[001\right]}_C$-oriented PMN-25PT, at varying temperatures between $40°\mathrm{C}$ and $85°\mathrm{C}$. The measurements were made using an optical probe system at a frequency of $1\mathrm{Hz}$.

Figure 7

Series of converse piezoelectric (strain-electric field) loops for ${\left[001\right]}_C$-oriented PMN-30.5PT, at varying temperatures between $30°\mathrm{C}$ and $85°\mathrm{C}$. The measurements were made using an optical probe system at a frequency of $1\mathrm{Hz}$.

Figure 8

Series of converse piezoelectric (strain-electric field) loops for ${\left[001\right]}_C$-oriented PMN-31PT, at varying temperatures between $30°\mathrm{C}$ and $75°\mathrm{C}$. The measurements were made using an optical probe system at a frequency of $1\mathrm{Hz}$.

Figure 9

Series of converse piezoelectric (strain-electric field) loops for ${\left[001\right]}_C$-oriented PZN-8.5PT, at varying temperatures between $55°\mathrm{C}$ and $75°\mathrm{C}$, in the high temperature tetragonal phase. The measurements were made using an optical probe system at a frequency of $1\mathrm{Hz}$. The hysteretic response is due to ferroelastic (90° domain) switching.

Figure 10

$d_{33}$ as a function of temperature for ${\left[001\right]}_C$-oriented PZN-6.5PT derived from the strain-field (S-E) measurements shown partially in Fig. 4. $d_{33}$ is taken as the gradient of the S-E loop at the zero field. At high temperatures in the tetragonal phase, $d_{33}$ corresponds to the collinear extension of the polar vector. At lower temperatures, $d_{33}$ corresponds to rotation in either the $M_A$ or $M_C$ monoclinic plane, as marked.

Figure 11

Electric-field-temperature phase diagrams, derived from the strain-field loops shown in Figs. 3, 4, 5, 6, 7, 8, for (a) PMN-25PT, (b) PMN-30.5PT, (c) PMN-31PT, (d) PZN-5PT, (e) PZN-6.5PT, and (f) PZN-8.5PT. The phase fields are marked with the symmetry of the phase under finite field.

Figure 12

(a) Unipolar strain-electric-field loop for a (poled) sample of ${\left[111\right]}_C$-oriented PZN-4.5PT measured using an optical probe system. (b) Subsequent direct piezoelectric (charge-stress) response of the same sample upon application of a uniaxial compressive stress along the ${\left[111\right]}_C$ direction.

Figure 13

Quasistatic, direct piezoelectric (charge-stress) measurements on a sample of ${\left[001\right]}_C$-oriented PZN-4.5PT. In the transverse mode (a), a uniaxial compressive stress ${\sigma }_1$ is applied along ${⟨100⟩}_C$ perpendicular to the poling direction and the charge density along the ${\left[001\right]}_C$-poling direction $D_3$ is measured; the reciprocal gradient is a measure of $d_{31}$. In the longitudinal mode (b), a uniaxial compressive stress ${\sigma }_3$ is applied along the ${\left[001\right]}_C$-poling direction, and the charge density $D_3$ is measured; the reciprocal gradient is a measure of $d_{33}$.

Figure 14

Schematic illustration of a single rhombohedral domain variant with polarization $\mathbf{P}$ along ${\left[111\right]}_C$ under compressive stress. In our model, application of the stress will lead to a $R\text{−}{M}_B\text{−}O$ rotation. In the longitudinal mode (a), the polar vector will rotate away from the $P_3$ poling direction. In the transverse mode (b), the rotation is toward the $P_3$ poling direction.