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In Situ Electric-Field Study of Surface Effects in Domain Engineered Pb(In_{1/2}Nb_{1/2})O_{3}-Pb(Mg_{1/3}Nb_{2/3})O_{3}-PbTiO_{3} Relaxor Crystals by Grazing Incidence Diffraction

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

_{1/2}Nb

_{1/2})O

_{3}-Pb(Mg

_{1/3}Nb

_{2/3})O

_{3}-PbTiO

_{3}(PIN-PMN-PT) [011] poled rhombohedral single crystal. The near surface microstructure (the top several tens to hundreds of unit cells) was measured in situ under an applied electric field. The strains calculated from the change in lattice parameters have been compared to the macroscopic strain measured with a strain gauge affixed to the sample surface. The depth dependence of the electrostrain at the crystal surface was investigated as a function of temperature. The analysis revealed hidden sweet spots featuring unusually high strains that were observed as a function of depth, temperature and orientation of the lattice planes.

## 1. Introduction

_{ij}several times larger than those of commercial lead Pb[Zr

_{x}Ti

_{1−x}]O

_{3}(PZT) ceramics. Recently, significant attention and resources have been put into the development of novel compositions to find better candidates based on solid solution Pb(Mg

_{1/3}Nb

_{2/3})O

_{3}-PbTiO

_{3}(PMN-xPT) and PbZn

_{1/3}Nb

_{2/3}O

_{3}-PbTiO

_{3}(PZN-PT), which are currently being used in medical ultrasound transducers and numerous SONAR transducer and sensors applications [1,2,3,4]. Two specific properties make these crystals ideal for applications: an extraordinarily high piezoelectric coefficient (d

_{33}> 2000 pV/m) combined with an extraordinary coupling coefficient (>0.9) achieved by “domain engineering;” i.e., cutting and poling the crystals along certain planes [3,5,6,7,8,9,10]. In order to extend the linear voltage regime with higher temperature stability to greater than that of binary relaxors, the ternary single crystal system Pb(In

_{1/2}Nb

_{1/2})O

_{3}-Pb(Mg

_{1/3}Nb

_{2/3})O

_{3}-PbTiO

_{3}(PIN-PMN-PT) has recently been developed. This next-generation material overcomes the need for dc electrical bias to achieving high power drive, a requirement for naval projector applications.

_{R}) phase. Additionally, a low-energy X-ray source probed the surface to some extent, and it was believed that the rhombohedral phase existed within a skin layer, caused by an imperfect poling condition at the surface of the crystal [21], somewhat contradicting their neutron results. Furthermore, neutron residual stress measurements on single crystals of PMN show the cubic lattice parameter varied with the depth normal to the crystal surface, and displayed a corresponding large surface strain [18]. That work also demonstrated how the depth dependence of strain was strongly affected by temperature, leading to incorrect phase diagrams for many of the relaxor materials. Crystal chemistry is also important and the later work of Phelan et al. [20], showed that the relaxor skin effect in PMN-xPT vanishes on the Ti-rich side of the MPB. An investigation of 33PIN-35PMN-32PT crystals [22] showed that the full width half maximum of the diffraction intensity, often an indication of inhomogeneous strain within a crystal, increased on cooling from the high-temperature cubic phase to the room-temperature bulk rhombohedral phase, which was presumed to be related to the skin effect in these relaxors. Those results indicated the presence of a surface monoclinic M

_{B}state, which had a small but non-zero piezoelectric coefficient from X-ray diffraction measurements. After annealing the crystal in zero field, the bulk F

_{R}phase was unpoled and showed no piezoelectric response, but the polarization vector of the surface M

_{B}phase could be rotated easily by stress gradients, yielding non-zero piezoelectric coefficients. These results show that the skin effect, phase co-existence, and stress gradients are interrelated and impact the macroscopic properties of single crystals.

## 2. Results and Discussion

#### 2.1. Results

_{32}∼ 1327 pm/V, which closely matches that of both the manufacturer’s data sheet and an independent direct piezoelectric measurement of d

_{32}.

#### 2.2. Discussion

_{31}coefficient and those planes parallel to the long axis of the sample [100] direction representing the d

_{32}coefficient have an inherently different response. In these experiments, none of the grazing incidence planes are aligned to those primary directions, so a direct piezoelectric coefficient calculation was not possible. However, the specular reflection (01$\overline{1}$) corresponds with the out of plane d

_{31}coefficient, which, coupled to the strain gauge data, means a value of the piezoelectric d

_{32}coefficient can be calculated from the appropriate Poisson ratio. The strain associated with the (110) planes closely matches that measured with the strain gauge data. The (110) planes are inclined at an angle of 60° to the electric field direction ([011] X3) and 30° to the [100] X2 axis, and so the resolved strain within that set of planes with respect to the sample surface is expected to most closely match d

_{32}of the crystal, which is ∼ (1600 μϵ)/(cos60° sin60°) ∼ 3700 μϵ, close to the value of ∼ 4000 μϵ, measured by the strain gauge along X1 direction. We note that the analysis here is highly simplified and resolving strains into different directions from known lattice parameter changes is non-trivial, but this serves as a good first approximation.

## 3. Experimental Section

^{3}was supplied by CTS Corporation, USA. For sample details see Table S1 in Supplementary Information. The specular surface in the chosen coordinate system of the sample was X1 [01$\overline{1}$] oriented, with the long direction of the sample along the X2 [100] axis and

**E**along the X3 [011] axis (Supplementary Information Figure S1).The macroscopic strain was recorded along [100] with a strain gauge attached to the sample surface (Supplementary Information Figure S3).

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) Sample geometry and conventionally used crystallographic axes for [011] poled Pb(In

_{1/2}Nb

_{1/2})O

_{3}-Pb(Mg

_{1/3}Nb

_{2/3})O

_{3}-PbTiO

_{3}(PIN-PMN-PT). Note that in this work, the X-ray diffraction data utilised a pseudo cubic orientation axis. (

**b**) Crystallography of X1 (01.1) specular surface of PIN-PMN-PT showing long sample X2 [100] direction, and electroded E-field direction X3 [011], with crystal planes accessible to this experiment: (010)-brown, (11$\overline{1}$)—pink, (32$\overline{2}$)—red and (110)—teal green. The crystal unit cell is also shown. (Atoms are colored as indicated and only O, Pb and Nb are shown in this cross section). CrystalMakerX v10.5.1, Begbroke, Oxfordshire, UK.

**Figure 2.**Schematic of the experimental methodology. The sample is clamped at approximately zero uniaxial stress into the fixture with high-voltage cabling attached as described. The bipolar voltage was cycled with a triangular waveform to yield a constant rate of voltage with time (for accurate PE loop analysis), for each set of planes at each condition of grazing incidence and temperatures.

**Figure 3.**Macroscopic strain—field response of PIN-PMN-PT sample, showing characteristic butterfly loop response. The calculated value of d

_{32}~ 1327 pm/V. Note this measurement was carried out after the grazing incidence experiment with an increased electric field amplitude of 6.5 kV/cm in order to observe the coercive field.

**Figure 4.**Raw data taken from Maxipix camera in pixel coordinates, of the (010) reflection as a function of α at 40 °C at E = 0 and ±4 kV/cm, highlighting the complex diffraction pattern obtained as a result of domain and/or twinning in the crystal. All analyses are based upon the centroid of each reflection, denoted by the small circle. As an average, the centroid should most closely resemble the macroscopic behavior.

**Figure 5.**Electrostrain [Equation (1)] of (010) lattice plane at 40 °C as a function of E for 4 different α values. The complex depth dependent behavior shows evidence of both hysteretic ferroelectric behavior and electrostrictive quadratic field response. The two minor loops observed in the plots for positive and negative fields represents piezoelectric energy loss hysteresis as ferroelectric domains are switched in polarization with applied electric field.

**Figure 6.**Lattice spacings (d spacing) for the grazing incidence angle reflections chosen for this study. The parameters have been calculated based on the measured HKL peak position, assuming pseudo cubic structure. The important features to note are the relative changes in d spacing for the reflections as a function of α and temperature. It is clear that at depths up to and exceeding the maximum accessed here, the d spacings are still changing and have not reached the ‘average’ bulk values, apart from the data shown for the (32$\overline{2}$) planes, which do show a degree of convergence. Each d spacing point has an associated error of ~ ±0.1% with an error in penetration depth of ±2 nm [Supplementary Materials, Equation (2)].

**Figure 7.**Contour maps of the electrostrain [Equation (1)] for different lattice planes as a function of temperature and depth from the surface of the sample (∼2 nm) into its bulk. The contours have been linearly interpolated from the data taken at three specific temperatures and five values of α. These specific temperatures were chosen as representing a range commonly used in real life applications for this class of material.

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**MDPI and ACS Style**

Cain, M.G.; Staruch, M.; Thompson, P.; Lucas, C.; Wermeille, D.; Kayser, Y.; Beckhoff, B.; Lofland, S.E.; Finkel, P.
In Situ Electric-Field Study of Surface Effects in Domain Engineered Pb(In_{1/2}Nb_{1/2})O_{3}-Pb(Mg_{1/3}Nb_{2/3})O_{3}-PbTiO_{3} Relaxor Crystals by Grazing Incidence Diffraction. *Crystals* **2020**, *10*, 728.
https://doi.org/10.3390/cryst10090728

**AMA Style**

Cain MG, Staruch M, Thompson P, Lucas C, Wermeille D, Kayser Y, Beckhoff B, Lofland SE, Finkel P.
In Situ Electric-Field Study of Surface Effects in Domain Engineered Pb(In_{1/2}Nb_{1/2})O_{3}-Pb(Mg_{1/3}Nb_{2/3})O_{3}-PbTiO_{3} Relaxor Crystals by Grazing Incidence Diffraction. *Crystals*. 2020; 10(9):728.
https://doi.org/10.3390/cryst10090728

**Chicago/Turabian Style**

Cain, Markys G., Margo Staruch, Paul Thompson, Christopher Lucas, Didier Wermeille, Yves Kayser, Burkhard Beckhoff, Sam E. Lofland, and Peter Finkel.
2020. "In Situ Electric-Field Study of Surface Effects in Domain Engineered Pb(In_{1/2}Nb_{1/2})O_{3}-Pb(Mg_{1/3}Nb_{2/3})O_{3}-PbTiO_{3} Relaxor Crystals by Grazing Incidence Diffraction" *Crystals* 10, no. 9: 728.
https://doi.org/10.3390/cryst10090728