Energy conversion from heat to electricity by highly reversible phase-transforming ferroelectrics

A series of Ba_0.95Ca_0.05Ti_1-x-yZr_xCe_yO₃ oxides were synthesized by solid-state reaction and densification process to obtain homogeneous polycrystalline rods of high density. The powders of CaCO₃(Alfa Aesar, 99.5%), CeO₂(Alfa Aesar, 99.9%), ZrO₂(Sigma Aldrich, 99%), BaCO₃ (Alfa Aesar, 99.8%) and TiO₂(Alfa Aesar, 99.8%) were weighed and well mixed according to the stoichiometric formulation Ba_0.95Ca_0.05Ti_1-x-yZr_xCe_yO₃, for ($x$,$y$) = (0.001, 0.005), (0.005, 0.005), (0.01, 0.005), (0.01, 0.01), and (0.01, 0.001). Then, the powder mixture was dissolved in the ethanol solvent, which was milled by zirconia balls in a planetary ball miller at 630rpm for 24hrs. The ball-milled solution was dried and calcined at 1000^∘C for 10 hours to obtain the tridoped barium titanate powder through solid state reaction. Under a 30MPa hydrostatic pressure at room temperature, the powder was hot-pressed for 30 minutes to form a rod-shape green body with size $10$mm $\times\phi 6$mm. The sintering process is divided into two steps by four-mirror Infrared furnace (Quantum Design IRF11-001-00): 1) densification of feed and seed rods [40]; 2) grain-coarsening by floating-zone method [44, 45]. The densification was conducted as a pre-sintering process by passing through the focal point of the four mirrors slowly with the axial speed 3mm/hr and the angular speed 3rpm. With much less sintering time, all pre-sintered rods show high densities ($5.4\sim 5.6$g/cm³) that is $>90$% of theoretical density of BaTiO₃. The compositions of tridoped BT samples are characterized by the Energy-dispersive X-ray Spectroscopy analysis by JEOL 6390. The variation of the normalized intensity was characterized for elements Ba, Ti, O, Ca, Zr and Ce along a 1.2 mm line on surface for all samples. The atomic weight percentages were analyzed based by the spectra of the polycrystalline tridoped BT samples. The compositions are consistent with the nominal compositions, and the variations are sufficiently small with respective to their mean values.

The temperature dependent ferroic properties were characterized by the aix ACCT TF2000E ferroelectric analyzer at a temperature step 0.5^∘C. Figure 1 (a) and (b) show the temperature dependent spontaneous polarization and corresponding $|dP/dT|$ of five compositions, labeled as “Zr$x$ Ce$y$” for $(x,y)=(0.005,0.005)$, $(0.001,0.005)$, $(0.01,0.005)$, $(0.01,0.01)$ and $(0.01,0.001)$.

All of the tridoped BT show large $[\![P]\!]$ and steep $dP/dT$ slope within 100 to 120^∘C, among which the Zr0.005 Ce0.005 specimen gives the largest $[\![P]\!]=7.58\mu$C/cm² and $\kappa=1.31\mu$C/cm²K. The thermal analysis was conducted by differential scanning calorimetry (DSC) using TA Instruments DSC-250 in Figure 1(c). The result reaffirms that they all undergo first-order phase transformations as big peaks of the heat flow are detected during heating and cooling through the transformation temperatures. Table 1 summarizes the ferroelectric properties and FOM defined in Eq. (1) for these five samples compared with typical ferroelectric poly/single crystals reported in literature. Among them, Zr0.005 Ce0.005 gives the largest FOM, that is 1.52 $\mu$C²/JcmK in polycrystal and 3.55 $\mu$C²/JcmK in single crystal.

The lattice parameters were measured by neutron diffraction at the general purpose powder diffractometer beamline (GPPD) at China Spallation Neutron Source, suitable for structural characterization of large bulk samples.[47] We conducted the temperature varying diffraction experiments for densified polycrystalline rods ($\phi 5\times 50$mm³) from 40^∘C to $140^{\circ}$C at a step of 10^∘C per scan. Before each of the $\theta-2\theta$ scans, the bulk sample was set in an isothermal environment until the temperature reading was stable. The cubic (high temperature phase) and tetragonal (low temperature phase) lattice parameters were refined by $Pm\bar{3}m$ and $P4mm$ space groups by the Rietveld refinement using GSAS suite with EXPGUI [48]. Same procedure was conducted for rest four bulk samples in different compositions. The tetragonality defined as the $c/a$ ratio is presented in Figure 1(d) where the lattice parameters were refined based on the diffraction patterns at different temperatures (e.g. Figure 2).

Stark discontinuity of tetragonality exists in all compositions (Figure 1d), which evidences the first-order structural phase transformation in consistent with the abrupt jump of polarization (Figure 1a), the singularity of pyroelectric coefficient (Figure 1b) and the big heat flow peaks in DSC measurements (Figure 1c).

The transformation stretch tensor between tetragonal and cubic phases is calculated as

where $a_{0}$ is the lattice parameter of cubic phase, $a$, $c$ are the lattice parameters of tetragonal ferroelectric phase. The primary compatibility indexer $\lambda_{2}$ is calculated as the middle eigenvalue of $\mathbf{U}$, directly computed as $\lambda_{2}=\frac{a}{a_{0}}$. It has been theorized that the distance of $\lambda_{2}$ to 1 underlies the height of energy barrier of a symmetry-breaking transformation [49]. It has been shown in many phase-transforming systems that the thermal hysteresis and reversibility of a solid phase transformation strongly relies on the compatibility condition.[26, 28, 29, 30]

The thermal hysteresis was calculated as $\Delta T=(A_{s}+A_{f}-M_{s}-M_{f})/2$, in which the austenite start/finish $A_{s}$/$A_{f}$ and martensite start/finish $M_{s}$/$M_{f}$ temperatures were determined as the onsets of the heat emission/absorption peaks in Figure 1(c). In our material system, the composition Zr0.005 Ce0.005 shows the smallest thermal hysteresis, 2.5^∘C corresponding to the largest FOM among all tested compositions in Figure 3(a) and (b), meanwhile it satisfies closely the compatibility condition as indicated in Figure 3(c) corresponding to the structural parameters and compatibility indexers listed in Table 2. Our observation in tridoped BT system implies a strong correlation between the compatibility indexer $\lambda_{2}$ and the change of polarization across the first-order phase transformation. The maximum FOM resonates with the minimum of hysteresis corresponding to the most compatible first-order phase transformation. The large FOM given by the composition Zr0.005 Ce0.005 makes it an ideal material candidate for the heat-to-electricity conversion demonstration.

For demonstration, it is critical to fabricate a high quality capacitor with the capacitance sensitive to temperature variation within the thermal fluctuation range. A previous energy conversion attempt [18] by first-order phase transformation evidently suggests that the single BaTiO₃ crystal can magnificently enhance the performance of the device. We adopted the floating zone method, an economic way to grow single crystals, to coarsen the grains in two fine-grained polycrystals: Zr0.01 Ce0.001 and Zr0.005 Ce0.005. We selected two of the polycrystalline rods as the seed and feed aligned vertically for the crystal growth by floating zone method at a growth speed 10mm/hr and relative angular speed 25rpm at an increasing lamp power. The molten zone was created and monitored throughout the entire growth period. Finally, the as-grown rod was solidified as the furnace cools down. The rod was sliced along the growth direction followed by mechanical polish. The size of the ceramic slices is about $19.5\times 5.5\times 0.4$ mm³. After mechanical polishing, both Zr0.01 Ce0.001 and Zr0.005 Ce0.005 slices are semi-transparent in the insets of Figure 4(a) and (b).

Since we used polycrystal seeds for the floating zone process, the cutting process of the as-grown rod was done without acknowledgment of orientation information. Figure 4 shows the post-cut orientation maps characterized by synchrotron X-ray Laue microdiffraction at Advanced Light Source, Beamline 12.3.2 at Lawrence Berkeley National Lab. Clearly, the Zr0.005 Ce0.005 plate is a single crystal of millimeter size, while the Zr0.01 Ce0.001 plate is a coarse-grained crystal having multiple millimeter grains. The surface normal of Zr0.005 Ce0.005 is measured as [0.9, 1.5, 1.8] written in the crystal basis. Although it is not perfectly aligned with the polar axis [001], its $[\![P]\!]$ reaches 11.7$\mu$C/cm², corresponding to $\kappa=1.93\mu$C/cm²K, shown in Figure 5(a)-(b).

These values are about twice of the largest reported values in single crystal BaTiO₃ aligned with its polar axis [16]. Since the goal of energy conversion is to harvest low-grade waste heat, we consider 20^∘C temperature difference near 100^∘C to benchmark the ferroelectrics in our work and literature in Table 1. Zr0.005 Ce0.005 single crystal exhibits by far the largest polarization jump and pyroelectric coefficient. The coarsened Zr0.01 Ce0.001 crystal also exhibits some degree of improvement in $[\![P]\!]$ compared with its fine-grained polycrystal counterpart. Figure 5 compares the ferroic properties near the transformation temperature between the single/coarsened crystals and their polycrystalline form. First, we confirmed that both transform at the same temperature despite whether they are single or poly crystals. Second, both polarization jump and pyroelectric coefficient at transition temperature are magnified significantly. The leakage current densities are 0.064 $\mu$A/cm² for Zr0.005 Ce0.005, and 0.337 $\mu$A/cm² for Zr0.01 Ce0.001.

We make planar capacitors using the Zr0.005 Ce0.005 single crystal and the Zr0.01 Ce0.001 coarse-grained slices. The dimensions of the transforming capacitors are 16.5mm${}^{2}\times 0.46$mm for Zr0.005 Ce0.005 single crystal capacitor and 25.28mm${}^{2}\times$0.44mm for Zr0.01 Ce0.001 coarse-grain capacitor. The demonstration apparatus is illustrated in Figure 6, which was analyzed by a thermodynamic model with complete removal of external bias field during energy conversion [25, 40].

A non-transforming capacitor (10$\mu$F) used as charge reservoir is connected to the phase-transforming capacitor. Both are grounded and bridged via a resistor (1 M$\Omega$) to measure the electric signal generated by first-order phase transformation of the active material. The capacitors were initially charged up to hold sufficient initial charges, then detached from the external power source throughout the heating and cooling cycles. The heating/cooling rates mimic the natural thermal fluctuations from waste heat between 95 and 125^∘C. The charges flow back and forth between the transforming and non-transforming capacitors driven by the ferro-to-paraelectric phase transformation. We measured the electric voltage $V$ by Agilent 34970A data acquisition module on the load resistor $R$ in Figure 6(b) to calculate the pyroelectric current as $V/R$, in short pyro-current³³3For simplicity, we still use the terminology pyro-current as the current generated purely by phase transformation.. Note that the voltage signal can be magnified by using a large resistor, but it does not represent a true improvement of energy conversion performance, as the load resistance is given in practical applications. Hence, pyro-current is a more proper meter in our energy conversion setup.

Figure 7(a) demonstrates continuous generation of electricity more than 3 hours by Zr0.005 Ce0.005 capacitor, compared to the Zr0.01 Ce0.001 capacitor over hundreds of transformation cycles. The current is generated when temperature passes the phase-transformation temperatures during both heating and cooling processes, in Figure 7(b)-(c). It verifies that the electric energy is purely converted from temperature differences, not from the discharge of external battery. The pyro-current generated by the Zr0.005 Ce0.005 single crystal capacitor reaches up to 1 $\mu$A stably and continuously lasting over 500 transformation cycles. For the Zr0.01 Ce0.001 coarse-grained capacitor, the pyro-current generated in the first few cycles is 0.5 $\mu$A. In order to benchmark capacitors with different areas, we calculated the current density, i.e. current per area: 6 $\mu$A/cm² for Zr0.005 Ce0.005 and 2 $\mu$A/cm² for Zr0.01 Ce0.001. These results are aligned with our theoretical prediction by figure of merit for material development. This confirms that the FOM in eq. (1) is a good performance indexer of energy conversion by first-order phase transformation.

As the Zr0.01 Ce0.001 capacitor exhibits larger electric leakage, it suffers electric degradation [40] over a period of energy conversion process. Consequently, a recharge is necessary after several thermodynamics cycles. The half-life – number of cycles since a full recharge till the peak signal reduces 50% – shortens considerably after each full recharge. It requires 4 full recharges to maintain a decent power output at the 106th cycle, labeled in the bottom panel of Figure 7(a). In contrast, the Zr0.005 Ce0.005 capacitor has no visible electric degradation during the first 135 cycles. After a recharge, the generation of pyro-current sustains for 365 cycles until the second recharge, corresponding to the top panel of Figure 7(a). An important observation is that the number of cycles in each half-life in the Zr0.01 Ce0.001 capacitor keeps shrinking, which implies a functional degradation of the transforming material.

The Zr0.005 Ce0.005 capacitor with $\lambda_{2}$ much closer to 1 exhibits magnificent reversibility for cyclic phase transformation. The thermal reversibility of these two capacitors were examined by cyclic DSC experiments, shown in Figure 8. The Zr0.005 Ce0.005 capacitor after 1024 thermal cycles shows no migration of transformation temperature (115^∘C), nor the magnification of the hysteresis (2.7^∘C) compared to the hysteresis in the first cycle (2.5^∘C). This coincides with the satisfaction of the compatibility condition $\lambda_{2}=1$ (Figure 3b-c).

We then cut 38 pieces of the similar sizes from several rods of Zr0.005 Ce0.005 synthesized by the same method, and assembled them in parallel in our demonstration setup. The total area of them is 2344.88mm², and the mean thickness is about 0.4mm. In this setting, we used a bigger reference capacitor (140$\mu$F) connected to the same load resistor. All capacitors were initially charged up to have 1.2 kV/cm electric field inside, then completely disconnect to the external power to begin the energy conversion cycles. The grid of energy conversion devices generates stably 15 $\mu$A electric current in consecutive cycles, in Figure 9(a). Thanks to the phase stability, low hysteresis and large pyro-current generated per cycle, the Zr0.005 Ce0.005 capacitor can directly light up a LED during both heating (Figure 9b) and cooling process through phase transformation (see Movie S1).