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True-remanent, resistive-leakage and mechanical studies of flux grown 0.64PMN-0.36PT single crystals
⁎Corresponding author. b3kumar69@yahoo.co.in (Binay Kumar)
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Received: ,
Accepted: ,
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.
Peer review under responsibility of King Saud University.
Abstract
Abstract
Ferroelectric single crystals of 0.64Pb(Mg1/3Nb2/3)O3-0.36PbTiO3 (PMN-PT), which have attracted lot of attention because of its excellent ferroelectric and piezoelectric response, has been successfully grown in the vicinity of morphotropic phase boundary, using high temperature solution method with PbO/B2O3 as flux. The crystals were characterized for its dielectric, ferroelectric, piezoelectric and pyroelectric properties along with the investigation of its domain structure. A high Curie temperature (Tc = 190 °C) was observed in the dielectric study. Well-saturated ferroelectric hysteresis loops with high remanent polarization, good switching and fatigue resistant nature indicated the high ferroelectric quality of the crystals. A high value of piezoelectric coefficient (d33∗ = 1398 pm/V) was obtained from the butterfly loops. True-remanent hysteresis study unveiled the practically usable polarization value, which actually serves as memory component in devices and has never been reported for PMN-PT crystals. Time-dependent compensated hysteresis analysis was carried out to study the resistive-leakage nature of the grown crystals which is also a new study for this system. Weibull statistics was used to analyze the distribution of hardness number and to find the values of critical load for the flux grown PMN-PT crystals which helps to critically analyze materials suitability for device fabrication.
Keywords
PMN-PT
Flux growth
True-remanent polarization
Time-dependent compensated hysteresis
Piezoelectricity
Micro-hardness
1 Introduction
The discovery of ferroelectric material has greatly influenced the modern electronic era. Among the ferroelectric systems, Pb(Zr, Ti)O3 (PZT) ceramic has been a dominating material due to its large dielectric and piezoelectric properties, which triggered a revolution that led to the development of various electromechanical devices like actuators, industrial sensors and sonar transducers (Park and Shrout, 1997; Zhang and Shrout, 2010; Ray et al., 2013). To further improve on the properties of PZT ceramics, a new interest was focused on the growth of single crystals of PZT which was believed to have an electromechanical factor and piezoelectric coefficient an order higher than the corresponding ceramics. However, due to the incongruent melting behavior of PZT, it is hard to grow its single crystals (Cao et al., 2010). The breakthrough in piezoelectric performance occurred with the discovery of relaxor-PT single crystals which displayed high values of the electromechanical coefficient (k33) and piezoelectric coefficient (d33) near morphotropic phase boundary (MPB) making them very attractive for electronic devices applications (Masuzawa et al., 1989; Fan et al., 2003; Kelly et al., 2005). Of the many interesting relaxor single crystals discovered, Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) is the most promising single crystal with high dielectric permittivity and excellent piezo/-ferroelectric performance. Although PMN-PT exhibits a lower piezoelectric response than (1 − x)Pb(Zn1/3Nb2/3)O3–xPbTiO3 (PZN-PT), it displays a more stable perovskite phase and a lower probability of formation of unwanted pyrochlore phase and thus it is comparatively easier to grow (Zawilski et al., 2003; Dong and Ye, 2000; Ye et al., 2000).
Myl’nikova and Bokov (1959) reported the use of PbO flux for the synthesis of PMN crystals. Thereafter, works on PMN crystal and its combination with other systems especially PbTiO3 (PT) were reported by many other groups (Dong and Ye, 2000; Setter and Cross, 1980). PMN-PT crystals were first grown using flux method by Shrout et al. where a combination of PbO and B2O3 was used as flux (Shrout et al., 1990). Since then different techniques like modified Bridgman, Top Seeded Solution Growth etc have been used for the growth of PMN-PT single crystals (Yin et al., 1999; Long and Ye, 2007). Various studies like morphology, dielectric and ferroelectric on PMN-PT crystal system has been reported by Dong and Ye (2000), Jiang et al. (2001) and Fan et al. (2003). These crystals found applications especially in memory switching devices, actuators and other sensor based device fabrication.
PMN-PT single crystals display better properties than PMN-PT film and PMN-PT ceramics (Jiang et al., 2001) due to many advantages, such as homogeneity, compositional and microstructural controllability, although the growth of single crystal of a complex compound has always been a challenging endeavor. The main problem in the growth of lead-based single crystals includes high melting point of oxides and volatilization of PbO. This leads to the formation of non-perovskite (pyrochlore) phase which hinders the crystallization process leading to defects and polycrystallization, thus degrading the properties of the material. Also, decomposition of PbO (i.e. into Pb and O2) may lead to platinum degradation which further may affect the homogeneity of the material.
Here, in our work, we have grown 0.64PMN-0.36PT single crystals using flux method. The flux method is not only one of the most economic method for crystal growth compared to other techniques like zone melting, modified Bridgeman method, etc., but also has an added advantage that the flux grown crystals show natural facets which make their preparation for various measurements relatively easy. Various domain features observed on the as grown crystal surface have been analyzed. The true-remanent polarization value (which is the most important parameters when it comes to using the material as a memory component) of the crystal after isolating the non-remanent contributions has been investigated, which revealed the actually usable component of polarization for memory devices. Also, time-dependent compensated hysteresis which probes the frequency dependent components of polarization present in the material was carried out on the PMN-PT crystal. Normally in literature, the mechanical strength of a material is reported as an average value along with its standard deviation, which for a device manufacturing purpose is not completely reliable. Thus, in present work, we have also reported the statistical study of hardness using Weibull statistics and various mechanical parameters such as variation coefficient, correlation coefficient and Weibull modulus were also evaluated.
Along with this, the variation of average indentation length and depth with applied load has also been discussed. Moreover, the values of indentation and volume at the transition point between load dependent and load independent hardness were evaluated for PMN-PT crystal, which is also one of the novelties of the present work.
2 Experimental
Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) ceramic in the ratio 64:36 was synthesized using two-step columbite precursor method (Hussain et al., 2016; Hussain et al., 2017), where PbO, MgO, Nb2O5, TiO2 (all with purity > 99.0%, Sigma Aldrich) were mixed according to the stoichiometry. The synthesized PMN-PT ceramic (charge) was then mixed with the flux PbO and B2O3 (PbO:B2O3 = 49:1) in the ratio 2:1. PbO reduces the possibility of pyrochlore phase formation whereas B2O3 aids crystal growth by breaking large ionic complexes, leading to large sized crystals (Lim et al., 2005). A total of 90 g of mixture (60 g charge + 30 g flux) was put in a platinum crucible which was covered with a lid. The platinum crucible was then placed in alumina crucible which was sealed using alumina cement to avoid evaporation of PbO. The mixture was then heated upto 1300 °C (soaking temperature) where it was kept for 4 h and then subsequently cooled to 1000 °C at a cooling rate of 6 °C/h. Further cooling (from 1000 °C to 550 °C, see Fig. 1) was done at a much faster rate to avoid the formation of pyrochlore phase. Fig. 1 summarizes the temperature profile which was used for crystal growth and Fig. 2 displays sequentially, various steps involved in the growth and extraction of 0.64PMN-O.36PT crystals.
The phase structure of the crystal was analyzed using powder XRD (Rigaku Ultima IV X-ray Diffractometer; using Cu Kα radiation of wavelength λ = 1.5405 Å). The surface morphology of PMN-PT single crystals was observed using field emission scanning electron microscope (Tescan Mira3 FE-SEM). High grade silver paste was used to make electrical contacts on the surface of polished crystals for various electrical measurements. Dielectric measurements were performed using a Novocontrol dielectric/impedance spectrometer in the frequency range 100 Hz–10 MHz. The ferroelectric characterizations of the grown crystal were carried out using Radiant Precision LCII ferroelectric tester. Butterfly loops of PMN-PT crystal were traced using MTI 2100 fotonic sensor in combination with the Radiant ferroelectric tester. Micro-hardness studies on PMN-PT crystal were performed using Vickers micro-hardness tester (MVH-I).
3 Results and discussion
3.1 Crystal quality
A very low weight loss of 1% was observed after the reaction. The low loss may be due to the formation of the B2O3 layer which encloses the solution during the growth process. The crystals were separated by dissolving the flux in hot nitric acid. Most of the crystals found were dark brown in color (found near the bottom of the crucible) with size varying from 4 mm to 9 mm across. Fig. 3(a) shows the grown crystals with residual flux inside the platinum crucible Fig. 3(b) shows one of the lumps obtained from the crucible after washing with nitric acid. Fig. 3(c) displays various as grown crystals after complete removal of flux whereas Fig. 3(d) shows one of the crystals after polishing. The surface of as grown crystals was not flat and smooth. In order to obtain uniformly shining crystal surface, the crystals were polished using 3 M Polishing Papers continuously for 3 h (micron sized aluminum oxide particles on a smooth nonwoven backing) and were further employed for various electrical characterizations. Fig. 3(e) shows the step growth patterns obtained on the surface of as grown PMN-PT crystal and Fig. 3(f) displays the step-size and step-width of these patterns. Also from Fig. 3(f) one can observe the turning of domains across the steps of varying height and width.
3.2 Powder XRD
The structural analysis by powder XRD of the sintered pellets was done in the range 20–80° at a scanning speed of 2°/min. Fig. 4 shows the XRD pattern of the powdered crystals of PMN-PT. The pattern reveals the formation of a pure perovskite phase without any trace of pyrochlore (non-perovskite) phase. The absence of pyrochlore phase indicates good quality of the crystals. The splitting of the peak at 45° confirms the tetragonal structure of the system (Bhandari et al., 2014; Xia and Li, 2007). The inset of Fig. 4 shows the XRD pattern performed on one of the plane of as grown PMN-PT crystal which indicates that the as grown plane is (0 0 1) plane.
3.3 Various interesting features of (0 0 1) oriented PMN-PT crystal
Field emission scanning electron microscopy (FE-SEM) technique was employed to record various characteristics of the (0 0 1) surface of as grown PMN-PT crystal. Fig. 5 shows the SEM micrographs, displaying several interesting features observed on the (0 0 1) face of PMN-PT crystal which we have tried to correlate with the growth conditions. Fig. 5a displays the stripe-like patterned domains observed on (0 0 1) face, which may be related to the tetragonal phase of as grown PMN-PT crystal (Tu et al., 2001). Different widths of the stripes may be associated with the non-uniform distribution of strain and interaction among neighboring domains during the growth stage of the crystal (Karas, 2005; Tsai and Cowley, 1992). The white particles of varying size and shape were observed on various portions of the crystal surface (see Fig. 5b), which could probably be gas inclusions (MgO, PbO, etc.). These inclusions result from the large difference in melting points of various starting oxides (PbO: 888 °C, Nb2O5: 1512 °C and MgO: 2825 °C) leading to melt inhomogeneity (Karas, 2005). Some of the inclusions displayed regular cubic external shape with well defined faces which could be a PMN-PT micro-crystal (Fig. 5c). Owing to faster PbO evaporation rate, during crystal growth a few cavities may have formed on the surface of PMN-PT crystal. On probing one of the cavity on the surface of the crystal using FE-SEM, complex domain walls configuration were observed indicating poor growth conditions inside it (see Fig. 5d). We propose that this complexity of domain configuration is a result of larger strain induced due to larger tetragonality in the poorly grown crystal region (cavity), possibly due to heavy evaporation of PbO. However, simpler domain arrangements (see Fig. 5e) was observed at high-quality crystal surface indicating reduced strain energy and hence, lower tetragonality (Chou et al., 1996). Fig. 5f–h depicts the enlarged views of the stripe-like pattern, which clearly shows the fact that these strips contain further finer structures. An obvious question that arises is: what are these finer band structures inside the stripes and what is their origin? Various researchers have studied these finer structures and have related them with different polarization arrangements in these ferroelectric domains (Chou and Chen, 2000; Shin et al., 2004). For instance, Chou et al. have extensively studied the existence of 90° and 180° domain walls in flux grown PbTiO3 crystal (Chou et al., 1996; Chou and Chen, 2000, 1998). Tsai and Cowley (1992), in their work, have reported the REM images of 90° a-c and 90° a-a domain boundaries on the (0 0 1) surface of the BaTiO3 crystal. Overall we can state that the SEM micrographs presented here will provide an important insight to the researchers for favorably engineering the domain structure of PMN-PT crystal with an aim of increasing its piezo-/ferroelectric response in near future.
3.4 Dielectric studies
The dielectric measurement was carried out as a function of frequency (100 Hz–10 MHz) and temperature (25–230 °C). Measurements were taken every 10 °C for the temperature range 25–100 °C and 200–230 °C. The readings near transition temperature (100–200 °C) were taken at a step size of 2 °C. The entire experimental run took over 8 h. Fig. 6a shows the temperature dependence of real part of dielectric constant (ε′) of 0.64PMN-0.36PT single crystal. The maximum value of ε′ at 1 kHz was found to be ∼2000. The Curie temperature (Tc) i.e. the temperature at which dielectric anomaly occurs was found to be ∼190 °C which is greater than many reported values on different PMN-PT compositions (Zhao et al., 2002; Tian and Han, 2014; Li et al., 2010; Mackeviciute et al., 2015). The transition at Tc does not show any frequency dependence which indicates a normal ferroelectric phase transition in PMN-PT. Similar dielectric response was also observed by Colla et al. for compositions with “x” > 0.3 (Colla et al., 1998). The dielectric loss vs. frequency (at different temperatures) for the PMN-PT crystal exhibits a monotonous decrease in the entire frequency range as is shown in Fig. 6b. High Tc and low dielectric loss validate the feasibility of 0.64PMN-0.36PT crystal as a high temperature ferroelectric candidate for various devices.
3.5 Ferroelectric studies
Ferroelectric measurements on PMN-PT crystals were done using Radiant Precision Tester which uses a virtual ground measuring system which uses the current flowing through the sample for measuring the data rather than the voltage developed across the sample. Ferroelectric characteristic of a single crystal of PMN-PT along (0 0 1) plane is revealed through the P-E loop traced on a crystal with thickness 0.95 mm at 1300 V with a hysteresis period of 700 ms and is shown in Fig. 7. Normally, the defects (such as oxygen vacancies) which are associated with flux grown crystals due to lead volatilization causes leakage current at high electric field, which results in unsaturated P-E hysteresis loops. Secondly, clamping of domains due to defects lead to an internal bias filed causing an asymmetry in the P-E loop of the crystal. However, we obtained excellent saturated loops with symmetric nature for as grown PMN-PT crystals, which indicated good ferroelectric quality of the crystal and the absence of internal field induced by defects with low leakage behavior (Yang et al., 2015). A very high value of remanent polarization (Pr = 42.36 μC/cm2) and low coercive field (Ec = 7.82 kV/cm) was obtained for the PMN-PT single crystal making it a desirable material for memory device application. The maximum of current density (J = dP/dt) vs. field (Fig. 7), where P stands for polarization and t represents time also gives an estimate of Ec. The maximum was found to be at 7.03 kV/cm. Also, the squareness factor of P-E loops was calculated using the expression: Rsq = Pr/Pmax + P1.1Ec/Pr (Singh et al., 2009; Singh and Kumar, 2010; Kumar et al., 2011). The value of Rsq was calculated to be 1.13 indicating good switching characteristics of the crystal. The high value of Pr, low value of Ec coupled with good switching characteristics make PMN-PT crystal a useful material for ferroelectric memory and switching devices.
For a long term operation, a material should be resistant to fatigue i.e. it should be able to withstand variation in its ferroelectric properties (e.g. Pr), when subjected to cyclic loads. The electrical-fatigue nature of the crystals was studied over 107 switching cycles. As can be seen from Fig. 8a, the value of switching polarization and non-switching polarization component did not show a noticeable change in their values for the entire range. This negligible variation in polarization components over 107 cycles strongly suggests the stable polarization retention characteristics of PMN-PT crystal. Fig. 8b shows P-E loops before and after fatigue test from which on can observe negligible variation in the nature of loops after the test. The non-degradation of polarization values indicate that the defects (specially due to lead volatilization) are minimal in PMN-PT crystals. Hence, PMN-PT crystal is a suitable material for long time ferroelectric applications especially in devices where the field is switched at various rates.
3.6 Displacement-voltage loop
Ferroelectric materials also display hysteresis in their displacement-voltage (D-V) curve also known as butterfly loops. The bipolar butterfly loops (on (0 0 1) plane, which has shown to be more sensitive to the converse piezoelectric effect (Davis et al., 2005) is shown in Fig. 9. The slope of D-V curves gives the value of piezoelectric coefficient (d33*). The maximum value of d33* was found to be ∼1398 pm/V (between ∼300–500 V). The large value of piezoelectric coefficient makes PMN-PT crystal a useful material for transducer applications.
3.7 True-remanent study
Ferroelectric memories use the remanence property of the material for information storage as it is related to the amount of charge which can be detected during a ‘read’ operation. Remanent polarization is used as Boolean 1 and 0 in memory devices (Zhao et al., 2015). Hence, a high value of remanent polarization is preferred for memory applications. The remanent polarization obtained from conventional hysteresis loop is not all ‘usable polarization’ for device application since it consists of ‘true-remanent’ and ‘non-remanent’ components. It is the ‘true remanent’ component which maintains its state even after switching and therefore serves as memory characteristic of the sample in memory devices. On the other hand, the ‘non-remanent’ component randomizes after removal of the applied electric field and is the non-usable component of polarization. Hence, to find the value of practically useful polarization component for application in memory devices it is necessary to nullify the contribution of non-remanent components. Here,‘remanent hysteresis task’ was used to eliminate non-remanent contributions to polarization and hence reveal the value of true-remanent polarization.
This task comprises of two logics namely Logic 1 and Logic 0, executed using a bipolar triangular wave as a stimulating voltage. Both the logics comprise of two hysteresis measurements. Logic 1 polarization measurement (measured during S1 and S2 pulse) consists of both remanent (switchable) and non-remanent (non-switchable) components while the Logic 0 (measured during NS1 and NS2 pulse) records only the non-remanent components of polarization (see Fig. 10). Subtracting Logic 0 from Logic 1 eliminates the non-remanent contributions and thus we obtain the value of “true-remanent” polarization (Joseph et al., 2017; Joseph and Kumar, 2018). The value of the true-remanent component was found to be 34.55 μC/cm2 (Fig. 10) which is different (lower) from the Pr value obtained from the standard hysteresis curve (Fig. 7). This is because conventional hysteresis method contains contributions from several other (nonusable) components as mentioned above. Therefore, for application purpose, especially in memory components, it becomes essential to report the true Pr value which is possible by using true-remanent hysteresis or other similar characterization. This characterization is very useful for identifying materials containing a large contribution from non-remanent components (leading to high Pr) which otherwise remains hidden in conventional P-E measurement.
3.8 Time-dependent compensated hysteresis
Various ferroelectric parameters like Pr and Ec are time (frequency) dependent since the switching dynamics of hysteresis is influenced by the frequency of the applied field. Resistive leakage is a parameter which leads to degradation of ferroelectric properties, also depends on the frequency of the applied field. Here, the ‘Time-dependent compensated (TDC)’ task was executed to analyze the resistive leakage behavior of the PMN-PT crystal. In this task, two hysteresis measurements were performed at the same voltage but at two different frequencies. From these measurements, the time-dependent component is extracted and one of the hysteresis measurement is compensated using this time-dependent component. This task uses Meyer et al’s. algorithm (Meyer et al., 2005) according to which the time-dependent and time-independent features of a ferroelectric material can be separated by subtracting their respective hysteresis measurements which are plotted at two different frequencies but at the same voltage. This gives the time-dependent (leakage) compensated plot of the ferroelectric material. Fig. 11a shows the polarization response of a resistor which resembles “ball-like” pattern and hysteresis response of a capacitor. Fig. 11b shows the TDC plot of combined resistor and capacitor where the time-dependent plot clearly resembles the hysteresis response of a resistor (ball-like pattern) and time-compensated (resistive-leakage compensated) plot represents the hysteresis response of a capacitor as expected (Joseph et al., 2017; Joseph and Kumar, 2018). Fig. 11c shows the TDC plot of a resistor combined with a ferroelectric capacitor. Here the time-compensated plot clearly shows a conventional P-E loop. Fig. 11d shows the normalized capacitance (NCv) plot of a resistor which representing alphabet “X”.
Fig. 12a shows the NCv plot of a ferroelectric capacitor which contains peaks indicating domain switching. Fig. 12b shows the NCv plot of PMN-PT crystal which also contains domain switching peaks. Fig. 12c represents the TDC plot of PMN-PT crystal where the hysteresis measurements were performed at two different hysteresis periods (frequencies) 700 ms (measurement 1) and 1400 ms (measurement 2). The non ball-like pattern of the time-dependent component clearly suggests the absence of resistive leakage in the crystal. However, there are other frequency-dependent factors as displayed in Fig. 12c, but clearly these are not related to resistive leakage (non ball- like pattern). Resistive leakage free nature of PMN-PT crystals make them a suitable candidate for devices (e.g. actuators) where the field is constantly flipped at various frequencies.
3.9 Pyroelectric studies
The pyroelectric property i.e. the variation of spontaneous polarization with temperature was studied for PMN-PT crystal and is shown in Fig. 13a. The maximum value of pyroelectric coefficient (p) was evaluated from the slope of spontaneous polarization vs. temperature plot i.e. p = ΔPs/ΔT, where ΔPs is the change in spontaneous polarization due to change in temperature ΔT which came out to be 889 μC m−2 °C−1 in the temperature range of 80–125 °C. The high value of pyroelectric coefficient makes PMN-PT crystal useful for various applications like energy harvesting, infrared detection and thermal imaging.
At higher temperature (beyond 130 °C) it was observed that the P-E loops of PMN-PT crystal started showing leakage behavior. To confirm the nature of this leakage, TDC hysteresis and NCv plots were analyzed at 150 °C. From TDC studies it was found that the time-dependent component plot showed a ball-like pattern (Fig. 13b) resembling the resistive-leakage nature as explained in the TDC section above. Also, the “X” like pattern of NCv further confirmed the resistive-leakage nature of the crystal at high temperature (Fig. 13c). Thus at a higher temperature, PMN-PT crystals show degradation in polarization value which can be attributed to the resistive-leakage behavior of the material.
3.10 Vicker’s micro-hardness analysis
Piezo-/ferro-electric materials find their applications in functional devices such as piezoelectric actuators (Park and Shrout, 1997), mechanical energy harvesters (Qi et al., 2010), ferroelectric memories (Scott and Paz de Araujo, 1989), and microwave devices (Fiebig, 2005). The mechanical deformation can remarkably have an effect on the reliability and performance of these devices. For instance, Furuta et al. in their work reported a decrease in the displacement of multilayer actuator as a result of increase in deformation stress around the edge of internal electrodes (Furuta and Uchino, 1993). On the macro-scale, the electromechanical loading of ferroelectrics has been studied to conduct actuation testing of the PMN-PT and BaTiO3 crystals under unipolar electric fields (Li and Li, 2013).
Vicker’s micro-hardness test was used to analyze the hardness of the flux grown PMN-PT crystal, which is a useful study especially when it comes to the applications of these crystals in device fabrication. In this test, a pyramidal shaped indenter was used to apply a different amount of load (5 g, 10 g, 20 g, 30 g, 40 g, 50 g and 100 g) on the top plane (0 0 1) of as-grown PMN-PT crystal. The images of the indentations at various loads observed using FE-SEM are shown in Fig. 14. Corresponding to each indentation impression (at various applied indenter loads), the value of hardness number was calculated using the expression: Hv = 1.8544P/d2 (Gao et al., 2003; Goel et al., 2020), where Hv (hardness number) is in kg/mm2, P is the applied load (in kg) and d is the diagonal length of the indentation (in mm). Fig. 15 shows the variation of Hv (in GPa) with applied load P (in g). As can be seen from Fig. 15, the value of Hv first increases as applied load increases (reverse indentation size effect or RISE), attains a maximum value at 20 g and decreases rapidly upto 30 g (indentation size effect or ISE). No variation in Hv is observed after 40 g, which is also called the transition point. The Hv value of PMN-PT crystal was found to be close to many other reported Hv values of flux grown crystals. Zeng et al. (2008) has reported the hardness value on (0 0 1) oriented flux grown PZN-PT crystal. Srimathy et al. (2013) studied the variation in Hv with a change in composition (%PT) in PZN-PT single crystal. Babu et al. (2017) reported the Hv value for flux grown crystal NBT crystals. The Hv number for above and various other flux grown crystals have been summarized in Table 1. From Table 1, one can clearly conclude that flux grown PMN-PT crystal is a potential and robust material for various practical device fabrication.
| Crystal name | Hv (GPa) | Reference |
|---|---|---|
| 0.64PMN-0.36PT | 8.32 | Present work |
| PZN-PT | 5.2–6.4 | Zeng et al. (2008) |
| PZN-PT | 3.93–4.02 | Srimathy et al. (2013) |
| NBT | 0.5 | Ramesh Babu et al. (2017) |
| YbFeO3 | 11.44 | Raina et al. (1993) |
| DyFeO3 | 8.71–9.75 | Raina et al. (1993) |
| KNiF3 | 3.5 | Kotru et al. (1985) |
| HoFeO3 | 9.45–10.96 | Bhat et al. (2004) |
| ErFeO3 | 8.8–1.3 | Sharma et al. (1994) |
3.11 Indentation depth vs. load
Fig. 16 shows the variation of average indentation depth ‘h’ and average indentation length ‘d’ with applied load ‘P’. The value of ‘d’ showed a non-linear (increasing) variation with applied load. For the lower value of loads (5–30 g) the rate of increase in the value of ‘d’ is much faster than at higher loads (30–100 g). The rate of increase in the value of ‘h’ which is found using the relation:
h = 21/2 cot (68°) d/4, was also observed to follow the same trend as ‘d’.
3.12 Weibull analysis
Traditionally, the mechanical hardness parameters like indentation depth, elastic modulus and hardness number, etc., are reported only as an average value with standard deviation, which is not complete information from engineer’s perspective. In order to provide a more reliable data, one needs to resort to statistical methods. Towards this aim, a statistical distribution of the hardness values of (0 0 1) plane of PMN-PT crystal over a range of applied indenter loads was studied using Weibull statistics. Weibull statistical distribution has been successfully employed for determining the lifetime and mechanical strength of various brittle materials. The distribution function for Weibull statistics is given by, F(x) = 1 − exp[−(x/x0)]m (Yin et al., 2007; Yadav et al., 2015; Goel et al., 2016).
Where F(x) represents the probability distribution function, x stands for Vickers micro-hardness number Hv, ‘x0’ denotes the value above which only 36.8% of the data is distributed and ‘m’ represents Weibull modulus. A higher value of ‘m’ implies lower variability of mechanical strength across the surface of the material.
After rearranging the Weibull distribution function and taking natural logarithm of the equation obtained twice, we get, ln{ln[1/(1 − F(x))]} = m[ln(x) − ln(xo)]. The value of F(x) is calculated by arranging the micro-hardness data points (in ascending order) and using F(x) = i/(N + 1). Here ‘i’ represents the ith order in the arranged sequence of data and N denotes the total number of data points. For each load, various parameters like standard deviation, variation coefficient (Vc), correlation coefficient (R) etc. were calculated and is summarized in Table 2 shown below. Variation coefficient is the variation in Vickers micro-hardness number (VHN) data, a low value of which indicates lesser scattering of the data points at a given load. The distribution of VHN data (Weibull plots) for all loads on the (0 0 1) plane of PMN-PT crystal is shown in Fig. 17a and b. The linear nature of all the plots suggests that VHN data points follow the Weibull distribution statistically. As can be observed from Table 2 the value of Vc decreases whereas the value of ‘m’ increases with increasing value of indentation load. The increase in the value of Weibull modulus (m) and a decrease in value of variation coefficient (Vc) as load increases can be attributed to the fact that at lower loads the probability of the indent landing on a defective region of the crystal surface is more as compared to that at higher load. Hence, variation in HNV data points is more at lower loads and thus Weibull modulus value is higher at higher loads.
| Indenter load (g) | Average hardness (kg mm−2) | Correlation coefficient, R | Weibull modulus, m | Xo (kg mm−2) | Standard deviation (kg mm−2) | Variation coefficient, Vc | Regression R-squared |
|---|---|---|---|---|---|---|---|
| 5 | 3.20403 | 0.94685 | 2.65186 | 3.67254 | 0.98829 | 0.30845 | 0.89203 |
| 10 | 6.96389 | 0.99676 | 6.47213 | 7.45699 | 0.96252 | 0.13822 | 0.99326 |
| 20 | 8.32525 | 0.98571 | 8.28797 | 8.80239 | 0.92979 | 0.11168 | 0.97039 |
| 30 | 4.57372 | 0.97494 | 10.27328 | 4.79052 | 0.4839 | 0.10580 | 0.94835 |
| 40 | 4.59492 | 0.97937 | 11.77572 | 4.78712 | 0.42383 | 0.09224 | 0.95739 |
| 50 | 4.67103 | 0.94233 | 13.84161 | 4.84023 | 0.35622 | 0.07626 | 0.88311 |
| 100 | 4.36496 | 0.96467 | 23.15570 | 4.46156 | 0.20359 | 0.04664 | 0.92757 |
3.13 Transition point
The indentation area for the diamond indentor with a pyramidal geometry (square base) is given by A = d2/(2sin(68°)) and indentation volume is given by V = d3cot (68°)/(12 × 21/2). The plot of indentation impression area and volume versus Weibull modulus (at various indenter loads 5, 10, 20, 30, 40, 50 and 100 g), is shown in Fig. 18a and b, respectively. Both the plots include two regions, one with a lower slope (data points for 5, 10, 20 g) and the other with a higher slope value (30, 40, 50 and 100 g). The data points with higher slope show there is a large change in indentation area and volume for a small change in ‘m’, suggesting that for the higher loads there is hardly any variation in the area or volume of defects encountered. The transition point is defined as the point after which there is no variation in hardness values due to the applied load. In Fig. 18a and b indentation area greater than ∼64 μm2 and indentation volume greater than 36 μm3 can represent the transition point. The knowledge of indentation area and indentation volume near transition point are important parameters especially for the selection of material for fabrication of device components.
4 Conclusions
Single crystals of 0.64PMN-0.36PT were successfully grown by flux technique. The structural, morphological, dielectric and ferroelectric properties were studied systematically for the grown crystal. Various interesting surface features such as stripe like domain pattern along with different domain arrangements, which were related to the growth conditions and hence the quality of the crystal at that site were observed. High Tc (190 °C) was displayed by the 0.64PMN-0.36PT crystal authenticating its applicability in high temperature ferroelectric applications. Ferroelectric characterization revealed the excellent quality of the crystal and its anti-fatigue nature, making it a prominent material for long-term ferroelectric applications. High piezoelectric coefficient (d33* = 1398 pm/V) indicated the applicability of the crystal in sensors. Value of true-remanent or usable polarization component was found using the remanent hysteresis task which was different from the remanent polarization value obtained using traditional P-E loop analysis. Resistive-leakage nature of the crystal was analyzed using the time-dependent compensated task which revealed the time-dependent polarization components present in the material. Hardness study on the PMN-PT crystal using Weibull statistical analysis showed that at low indentation loads there is large variability in VHN data distribution and this variability reduced as indentation load increased. The load independent hardness value was found to be ∼4.5 GPa. The value of transition load is 30 g with critical area of ∼64 μm2 and critical volume of 36 μm3. In conclusion, high Tc, fatigue and resistive-leakage free nature of the material along with excellent ferro-/piezoelectric characteristics makes 0.64PMN-0.36PT crystal an excellent candidate for memory devices and high temperature ferroelectric applications.
Acknowledgements
We are thankful for the financial support received through the DRDO Project (ARMREB/MAA/2015/163) and DST project (EMR/2015/000385). Abhilash J. Joseph, Sahil Goel and Abid Hussain would like to thank DRDO and CSIR for providing the Senior Research Fellowship (SRF). Dr. Nidhi Sinha expresses her gratitude to the Principal, SGTB Khalsa College for encouragement and support for research work.
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