Powder neutron diffraction study of phase transitions in and a phase diagram of $(1-x)\left[\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3\right]\text{−}x\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$

Dielectric, piezoelectric resonance frequency, and powder neutron diffraction studies as a function of temperature have been performed on several compositions of $(1-x)\left[\mathrm{Pb}\left({\mathrm{Mg}}_{1∕3}{\mathrm{Nb}}_{2∕3}\right){\mathrm{O}}_3\right]\text{−}x\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ $\left(PM\mathrm{N}\text{−}x\mathrm{PT}\right)$ ceramics in and outside the morphotropic phase boundary (MPB) region to investigate the phase transitions and phase stabilities in this mixed system. Anomalies in the temperature dependence of piezoelectric resonance frequency and dielectric constant are correlated with structural changes using Rietveld analysis of powder neutron diffraction data. The frequency dependent dielectric studies reveal relaxor ferroelectric behavior for $x<0.35$ and a normal ferroelectric behavior for $x⩾0.35$. The dielectric peak temperature and the Vogel-Fulcher freezing temperature are found to increase linearly with “$x$” while their difference, after decreasing linearly with $x$, vanishes at $x=0.35$ suggesting a crossover form relaxor ferroelectric to normal ferroelectric behavior at this composition. A phase diagram of the $\mathrm{PMN}\text{−}x\mathrm{PT}$ system showing the stability fields of ergodic relaxor, monoclinic $M_B$, monoclinic $M_C$, tetragonal and cubic phases is presented. Our results suggest the presence of a succession of three phase transitions, not reported earlier, corresponding to structural changes from the monoclinic $M_B$ to the monoclinic $M_C$ to the tetragonal to the cubic phases for $0.27⩽x⩽0.30$ on heating above room temperature. In addition, our studies confirm the earlier findings on transitions from the monoclinic $M_C$ to the tetragonal to the cubic phases for $0.31⩽x⩽0.34$ on heating above room temperature and tetragonal to monoclinic $M_C$ phase on cooling below room temperature for $x=0.36$. All these transitions are found to be accompanied with anomalies either in the temperature dependence of dielectric constant or the piezoelectric resonance frequency or both. Rietveld analyses of the powder neutron diffraction data at various temperatures on a pseudorhombohedral composition with $x=0.25$ suggest that the short range $M_B$ type monoclinic order present at room temperature grows to long range monoclinic order on lowering the temperature. The temperature variations of the unit cell parameters and atomic shifts are also presented to throw light on the nature of the various phase transitions in this mixed system.

Figure 1

Variation of the real $\left({\epsilon }^{\prime }\right)$ and imaginary $\left({\epsilon }^{″}\right)$ parts of dielectric constant with temperature for upoled $\mathrm{PMN}\text{−}x\mathrm{PT}$ ceramics measured at $1\mathrm{kHz}$: (a) $x=0.36$, (b) $x=0.32$, (c) $x=0.29$, and (d) $x=0.25$. Insets in (b) and (c) illustrate weak dielectric anomaly corresponding to the monoclinic to tetragonal phase transition and inset in (d) shows shift in $T_m{}^{\prime }$ with increasing measuring frequency. The arrow at the main peak in this inset points to increasing frequencies of measurement (0.1, 0.5, 1, 5, 10, and $50\mathrm{kHz}$). The second arrow shows the abrupt disappearance of the frequency dispersion at the Vogel-Fulcher freezing temperature $\left(T_{\mathrm{VF}}\right)$.

Figure 2

Composition dependence of $T_m{}^{\prime }$, $T_m{}^{″}$ and their difference $(\Delta T=T_m{}^{\prime }-T_m{}^{″})$ for $PM\mathrm{N}\text{−}x\mathrm{PT}$ ceramics as obtained at $1\mathrm{kHz}$.

Figure 3

Composition dependence of the Vogel-Fulcher freezing temperature $\left(T_{\mathrm{VF}}\right)$ and $T_m{}^{\prime }$ for $\mathrm{PMN}\text{−}x\mathrm{PT}$ ceramics as obtained from the frequency dispersion of $T_m{}^{″}$. Data points for pure PMN and PMN-0.10PT were adapted from Refs. 41, 42.

Figure 4

Variation of piezoelectric resonance frequency $\left(f_r\right)$ with temperature below $300\mathrm{K}$ for $\mathrm{PMN}\text{−}x\mathrm{PT}$ ceramics with $x=0.25$, 0.29, 0.32, and 0.36. The anomaly around $235\mathrm{K}$ for $x=0.36$ corresponds to room temperature tetragonal to low temperature monoclinic $M_C$ phase transition.

Figure 5

Variation of piezoelectric resonance frequency $\left(f_r\right)$ with temperature above $300\mathrm{K}$ for PMN-0.32PT ceramics depicting a $M_C$ to tetragonal phase transition around $380\mathrm{K}$.

Figure 6

Evolution of 400, 440, and 620 cubic powder neutron diffraction profiles with temperature for PMN-0.25PT ceramics. The observed data is shown by dots, continuous line shows calculated patterns obtained after Rietveld refinement corresponding to various structural models and the vertical tick marks show the positions of various Bragg reflections.

Figure 7

(a) Evolution of the lattice parameters of the pseudorhombohedral $M_B$ phase with temperature for PMN-0.25PT obtained after Rietveld analysis of neutron powder diffraction data at various temperatures. For easy comparison with the cubic cell parameters, the equivalent perovskite cell parameters $a_m$ and $b_m$ calculated from the monoclinic cell parameters $A_m$ and $B_m$ are plotted ($a_m=A_m∕\sqrt{2}$ and $b_m=B_m∕\sqrt{2}$). (b) Temperature dependence of the unit cell volume. The error bar for each data point is smaller than the size of the symbols.

Figure 8

Variation of the atomic shifts with temperature for PMN-0.25PT as obtained by Rietveld analysis of powder neutron diffraction data. The error bar for each data point is smaller than the size of the symbols.

Figure 9

Evolution of the 400, 440, and 620 cubic powder neutron diffraction profiles as a function of temperature for PMN-0.29PT. The solid dots show the observed diffraction profiles, while the continuous line the calculated patterns obtained by the Rietveld analysis of the neutron powder diffraction data for different structures. The vertical tick marks show the positions of various Bragg reflections.

Figure 10

Evolution of the lattice parameters with temperature for PMN-0.29PT obtained after Rietveld analysis of the neutron powder diffraction data at various temperatures. For easy comparison, the equivalent perovskite cell parameters $a_m$ and $b_m$ calculated from the monoclinic cell parameters $A_m$ and $B_m$, are plotted in the monoclinic region ($a_m=A_m∕\sqrt{2}$, $b_m=B_m∕\sqrt{2}$). The error bar for each data point is smaller than the size of the symbols.

Figure 11

Evolution of the 400, 440, and 620 cubic powder neutron diffraction profiles for $PM\mathrm{N}\text{−}0.32\mathrm{PT}$ as a function of temperature. The solid dots show the observed diffraction profiles, while the continuous line the calculated patterns obtained by the Rietveld analysis of the neutron powder diffraction data for various structures. The vertical tick marks show the positions of various Bragg reflections.

Figure 12

Evolution of the lattice parameters with temperature for PMN-0.32PT obtained after Rietveld refinement of neutron powder diffraction data at various temperatures. The error bar for each data point is smaller than the size of the symbols.

Figure 13

Variation of the atomic shifts with temperature in the monoclinic and tetragonal phase regions for PMN-0.32PT obtained after Rietveld analysis of powder neutron diffraction data. The error bar for each data point is smaller than the size of the symbols.

Figure 14

Evolution of cubic 400, 440, and 620 powder neutron diffraction profiles with temperature for PMN-0.36PT ceramics. The solid dots show the observed diffraction profiles, while the continuous line the calculated patterns obtained by the Rietveld analysis of the neutron powder diffraction data corresponding to various structures. The vertical tick marks show the positions of various Bragg reflections. The scale of the $x$ axis is different for $530\mathrm{K}$ pattern.

Figure 15

Evolution of the lattice parameters with temperature for PMN-0.36PT obtained after Rietveld refinement of neutron powder diffraction data at various temperatures. The error bar for each data point is smaller than the size of the symbols.

Figure 16

Variation of the atomic shifts with temperature in the monoclinic and tetragonal phase regions for PMN-0.36PT ceramics. The error bar for each data point is smaller than the size of the symbols.

Figure 17

Phase diagram of $\mathrm{PMN}\text{−}x\mathrm{PT}$ showing the stability region of the pseudorhombohedral $M_B$, monoclinic $M_B$ and $M_C$, tetragonal and cubic phases. The transition temperatures between ferroelectric and paraelectric cubic phase were determined by dielectric measurements on unpoled samples under heating whereas the second transition from tetragonal to monoclinic phase was determined using dielectric constant and/or piezoelectric resonance frequency measurements.