Calorimetric study of field-induced ferroelectric transition in Pb(Mg1/3Nb2/3)O3 relaxor ferroelectrics

Nikola Novak and Zdravko Kutnjak Condensed Matter Physics Department

Jožef Stefan Institute Ljubljana, Slovenia

Zdravko Kutnjak CoE Namaste

Jožef Stefan Institute Ljubljana, Slovenia

Zdravko Kutnjak International Postgraduate School

Ljubljana, Slovenia

Abstract—The electric field induced ferroelectric transition was studied by heat capacity measurements in relaxor Pb(Mg1/3Nb2/3)O3 (PMN) single crystal oriented in [110] direction. The modified relaxation measurements allow us to study the thermal response of sample at glassy to ferroelectric transition at isothermal condition. The thermal response of sample show a temperature anomaly at field induced transition as a consequence of the released latent heat.

Keywords-relaxor ferroelectric; ferroelectric transition; heat capacity;

I. INTRODUCTION In late 1950s an important new group of perovskite

structured ferroelectric material called relaxor ferroelectrics was discovered [1]. Unlike typical ferroelectrics, relaxors possess some unusual properties like frequency dispersion of the dielectric permittivity, absence of the spontaneous polarization in zero electric field, slowing dynamics, and logarithmic polarization decay [1-4]. Various studies over decades show, that the relaxor like behavior is a result of site and charge disorder as a consequence of chemical substitution and the existence of long living polar nanoregions even at higher temperatures above the dielectric peak temperature [2, 5]. One of the key features of relaxors is the absence of the macroscopic phase transition or change of symmetry due to a long range ferroelectric order. However, the long range ferroelectric order can be induced by applying a sufficiently high electric field, EC [6, 7]. In addition to the electric field induced ferroelectric state (E > EC), relaxors exhibit also an ergodic relaxor state at high and non-ergodic relaxor state at low temperatures (E < EC) similar to dipolar glasses [8, 9].

The nature of relaxor ground state is still a matter of studies and discussion. In general there are two widely accepted proposals of the relaxors ground state: (i) a dipolar glass model according to which the polar nanoregions created at high temperatures are treated as dipolar glass system with random interactions in the presence of random electric fields [2, 5, 7-11], and (ii) a random field model which treats polar nanoregions as a ferroelectric nanodomains broken up under

the constraint of quenched random fields [12-13]. Several earlier experimental results such as slowing down of the characteristic relaxation time according to the Vogel-Fulcher law [8], divergence of the longest relaxation times at freezing transition [9], the observed critical behavior of the dielectric nonlinearity [9, 14] and the electric field temperature phase diagram [7, 15] have favored the interpretation of the relaxor ground state as a glassy like state and dipolar glass model. Contrary to this, some experimental measurements like dielectric response in high ac and dc electric fields have shown that the observed dynamic in ergodic phase may be explained as a domain-wall motion process [13] and the existence of Barkhausen jumps of microdomains controlling the poling process below freezing temperature should exclude the glassines in favor of random field model and ferroelectric nanodomains [12].

Important information about the ferroelectric conversion under the external electric field could be provided by isothermal calorimetry. By measuring enthalpy changes it is possible to distinguish between (i) continuous conversion from the random field ferroelectric state to more ordered ferroelectric state and (ii) sharp transition from the dipolar glass to ferroelectric state. Details of the method can be found in Ref. 16. In addition, the presence of the latent heat at ferroelectric transition would indicate a real first order transition between the relaxor and ferroelectric state [17, 18]. Similar experiments performed at Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) showed that with increasing electric field the latent heat diminishes and finally disappears at critical point [17, 18]. In this paper we show calorimetric results of isothermal heat capacity measurements at ferroelectric transition of relaxor PMN single crystal oriented in [110] direction.

II. SAMPLE PREPARATION AND EXPERIMENTAL PROCEDURE In order to perform high-resolution calorimetric

measurements as a function of the electric field and temperature at the relaxor-to-ferroelectric transition we cut a platelet-shaped sample of PMN single crystal perpendicular to [110] direction. The platelet was brushed and polished to the

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geometry size of 3.85x1.80x0.266 mm3. Gold electrodes were sputtered onto the sample by evaporation technique, and a heater and thermistor were attached with electric non-conducting varnish on the opposite sides of the platelet. In addition, a gold contact wires were attached with electrical conducting two component epoxy adhesive to the electrodes.

High-resolution heat capacity measurements were performed using a computerized calorimeter capable of fully automatic operation in either ac or relaxation mode. In the case of ac mode we apply oscillating heater power and computer record the time and temperature response of sample trough which heat capacity and/or enthalpy are calculated. Besides heat capacity in ac mode, a phase shifts of the oscillating sample temperature can be measured which provide information about the existence of two phase coexistence at first order phase transition. A deficit of the ac measurement is that it is sensitive only to the continuous changes of the enthalpy whereas the relaxation measurement is sensitive to both, continuous and discontinuous changes. In relaxation mode the heater power supplied to the sample is linearly ramped which makes it possible to determinate the total change of enthalpy. A detail description of these two modes of operation can be found elsewhere [19, 20].

To detect and to determine the released latent heat at the ferroelectric transition the relaxation technique was adopted which was modify in such a way that we could apply linearly ramped electric field. The measurements were performed as follows. The sample was annealed at 380 K for 15 min and cooled down to particular stabilized temperature to satisfy the isothermal condition. During the measurement, the electric field was linearly increased in time from 0-10 kV/cm in 250 s and at the peak was linearly reduced back to zero again with the same rate. The same was repeated for negative fields giving the total period of 1000 s for the complete field cycle. Within this period around 1500 sample temperature T(t) data points were recorded with accuracy within 0.1 mK with the bath temperature being stabilized. In the case of ac measurements the bath temperature was changed with heating rate of 2 K/h while the bias field was kept constant at the predefined value. Before each measurement the sample was annealed to avoid the history effect of previous treatment.

III. RESULTS AND DISCUSSION As already mentioned above, according to the random field

models the sharp transition with the heat capacity anomaly should be observed at freezing temperature and at lower temperatures only small and gradual changes of enthalpy should be observed with increasing the electric field [21, 22]. In contrast, transition between the short range ordered dipolar glass state and ferroelectric state can be sharp and even first order [23]. So, detection of the released latent heat and the sharp transition would support the glassy scenario and the opposite would support the first random field scenario. At the first order transition the system exhibit a two coexisting phases which distorts the wave form of oscillating sample temperature within the ac mode and this result in characteristic anomalous increase of the phase shift of the observed temperature oscillations within the coexistence range. Fig. 1 shows the temperature and electric field dependences of the phase shift in

the ac heat capacity data for [110] PMN single crystal at ferroelectric phase transition. The anomalous peak in phase shift observed at electric field of 1.8 kV/cm is indication of two coexisting phases and thus of the first order phase transition. The peak turns over into a deep at higher electrical field indicating a crossover from the first order to the continuous perhaps supercritical nature of ferroelectric transition.

Figure 1. The temperature and the electric field dependences of the phase shift φ in heat capacity measurements for [110] PMN single crystal at the glass to

ferroelectric phase transition.

The ac measurements do not provide quantitative information about the released latent heat. To calculate the value of the latent heat at the glass to ferroelectric transition we employ isothermal relaxation measurement as described previously. Fig. 2 shows the thermal response of the sample temperature in the case where electric field is linearly ramped from 0 to 10 kV/cm (line in Fig. 2).

Figure 2. A sharp anomaly in thermal response of sample temperature was

observed at electric field 4.5 kV/cm at 180 K. The peak in the temperature is due to the released latent heat at the field induced ferroelectric transition.

Anomaly observed in the sample temperature as a function of the time, i.e., as a function of the electric field which is linearly ramped in time is due to the released latent heat at field induced ferroelectric transition. The excess of released heat at the ferroelectric transition exponentially relaxes to the

surrounding bath, which is coupled to the sample via wires and exchange gas. The sharp peak indicates an instantaneous or rather strong first order phase conversion in which the released latent heat represents most of the total enthalpy change. This allows us to use a simple exponential decay ansatz to fit the data in order to determinate the change of the temperature, ΔT(0) as shown in the inset of Fig. 2. From L=cp*ΔT(0) we can estimate the value of the latent heat. Calculation using cp=0.25 J/gK gives latent heat L=61±3 J/kg at temperature 180 K. Another way to analyze the relaxation data and to calculate the latent heat is to use a simple zero-dimensional model of thermal analysis. This model is valid if the internal thermal diffusion time of the sample is small in comparison to the external thermal relaxation time and the temperature gradients within the sample can be neglected. Within such model one can define an effective heat capacity, Ceff, for the first order transition by

Ceff=(P-(T-TB)/R)/Ṫ, (1)

where T is the sample temperature, TB is the bath temperature, R is the thermal resistance, P is the input power and Ṫ=dT/dt. The input power of heater in isothermal measurements is zero and the only input heating source is electro-caloric (EC) heating which consist from the continuous and or discontinuous EC effect due to change in the entropy related to the change in the polarization order parameter [23]. The continuous EC effect can be neglected because of the small electric field which is rather slowly linearly ramped. The only significant heating source is thus the released latent heat and P can be replaced by dL/dt, where dL=L*dm with L being the latent heat per unit mass and dm the mass of the sample already converted to the ferroelectric phase. Taking these into account the Eq. (1) can be rewritten in

dL/dt=Ceff*Ṫ+(T-TB)/R. (2)

From Eq. (2) the released latent heat at the ferroelectric transition can be calculated (see Fig. 3).

Figure 3. Time dependent evolution of released latent heat calculated within

the zero-dimensional model at the glass to ferroelectric transition.

At 180 K the critical point is far away [16] and the glass to ferroelectric transition is strongly first order in which the latent heat represents the most of the total change of enthalpy (Fig. 3). The released latent heat calculated within zero-dimensional model of thermal analysis is 59±3 J/kg at 180 K in a good agreement with 61±3 J/kg of our analysis using the simple exponential decay ansatz. It should be noted that the value of the released latent heat in PMN is rather close to the observed latent heat value for the true structural cubic to tetragonal phase transition in the PMN-PT system [17, 18].

IV. CONCLUSIONS The heat capacity study of the relaxor PMN single crystal

oriented in [110] direction shows the crossover from the anomalous to normal anomaly in the temperature dependence of the phase shift in the ac heat capacity data at different bias fields which indicates the crossover from first order to the supercritical ferroelectric conversion. The modified field driven relaxation calorimetric measurements performed at isothermal conditions show a sharp peak in sample temperature as a consequence of the released latent heat at the critical field. The estimated value of the released latent L=60±3 J/kg in PMN is rather close to the observed latent heat at the structural cubic to tetragonal phase transition in the PMN-PT system [17, 18]. These findings support the dipolar glass scenario rather than random field scenario, in which no symmetry difference between the low field and high field states is predicted below the freezing temperature.

Acknowledgment

This work was supported by the Slovenian Research Agency under programs PR-03086-1, P1-0125, project J1-2015 and by the CoE Namaste.

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