The Electrocaloric Effect in Ferroelectrics

Many research was done on ceramic and polymer pyroelectric systems with respect to the ECE. The research spans from bulk materials to thick and thin films, as well as multilayer structures (see Figure 1.1.1). For bulk materials different structures were investigated, like perovskites, pyrochlores, aurivillius phases, tungsten bronzes or salts.[1] _{The focus is set to the perovskite structure, which is of main interest}

in ferroelectric investigations and applications. Some characteristics important for the EC performance are described.

As stated in Section 1.2.8. the paraelectric to ferroelectric phase transition can be of first or second order nature. In the case of first order nature the entropy will change discontinuously and in the case of a second order nature the change will be gradually.[113] _{Therefore, a latent heat will contribute to the}

temperature change in FEs with first order phase transition.[53, 62, 114] _{A drawback is that the operational}

temperature range of the first order phase transition is rather narrow.[30, 115, 116] _{In addition the initial}

nature of the phase transition can be altered by the application of strong electric fields (towards second order nature).[117] _{A second order phase transition provides wider operational ranges, but there is no}

contribution to the temperature change from a latent heat.[118] _{For relaxor ferroelectrics the electric field}

induced phase transition plays a crucial role.[110] _{In the thermally annealed state, the transition from}

relaxor phase to ferroelectric phase is typically of first order, accompanied by released latent heat.[119, 120]

This holds for temperatures below the liquid vapor type of critical end point of the relaxor system.[121]

The released latent heat can account for a major part of the adiabatic temperature change.[122] _{It should}

be noted, that in the nonergodic relaxor phase temperature range the electric field induced phase transition is irreversible upon electric field removal[123] _{and therefore cannot add to the cooling of the}

material. Above the temperature induced ferroelectric to relaxor transition, i.e. in the ergodic relaxor phase, the electric field induced phase transition is reversible[123] _{and therefore additional cooling is}

is increased towards the critical end point, which is of second order nature.[121] _{The effect of the electric}

field induced phase transition is crucial in the enhancement of relaxor EC performance over broad temperature ranges. Nevertheless, the largest ECE responsivity, i.e. temperature change over electric field change, can be found at the critical end point.[111] _{Here, the energy required for electric field}

induced polarization rotations is largely reduced, giving rise for large ECE.[121] _{The concept of energy}

minimization between different phases can be observed as well at morphotropic phase boundaries.[124-126] _{These phase boundaries in the temperature composition diagram can be found in}

numerous solid solutions and often feature enhanced electromechanical properties.[127-132]

To achieve substantial EC temperature changes, very large electric fields are required. Intrinsic and extrinsic properties will limit the electric field strength. In single crystals micro-cracks will occur due to the large electromechanical strain.[133] _{Some materials cannot withstand large electric fields, because of}

their limited dielectric strength or grain boundary conductance.[134-136] _{A high ionic or electronic}

conductivity will result in a large leakage current, leading to Joule heating. The Joule heating will decrease the cooling and will increase the heating effect in the material.[137, 138] _{Therefore, materials with}

large electric breakdown fields are desired.

1.3.3. Measures of Electrocaloric Materials

Using the EC material as a coolant awareness has to be given that the temperature change effect only occurs during an electric field change and therefore, after a cooling step a heating step follows. To utilize now the ECE in a cooling device a thermodynamic cycle must be installed with a heat sink and a heat load between which the heat is transferred by the EC element. A possible Carnot-like cycle[18, 46, 49] _for

electrocaloric refrigeration is shown in Figure 1.3.3. Starting at state A, the material undergoes a temperature change. This is due to the compensation of the decrease in entropy of the dipolar subsystem by the lattice subsystem. The total entropy of the state A and the state B are the same under adiabatic conditions. The step A to B can be also described by an isothermal process, at which the dipolar entropy decreases due to the ordering of the dipolar entities in an electric field and an isofield process, at which the temperature increases due to the increase in the lattice vibration entropy. At state B the material is brought into contact with a heat sink and thus allowed to release heat until it reaches state C. From state B to C the electric field is held constant. Step C to D and back to state A is the reversal of the previous processes. At the adiabatic depolarization the increase of dipolar entropy is compensated by the decrease of lattice entropy, hence the temperature of the material decreases. From state D to A the material absorbs heat from the load.

Fig. 1.3.3: Schematic presentation of the entropy and temperature change during an electrocaloric cycle: The path from A to B and C to D represent adiabatic processes and the path from B to C and D to A represent isoelectric heat exchange. E1 and E2 denote constant electric fields.

From the above considerations three quantities, i.e. temperature change, entropy change and absorbed heat, can be deduced that are important measures of potential candidates for EC cooling. Those properties can be transferred into each other if the specific heat capacity is known:

∆𝑇 = 𝑄

𝑐𝑝, (1.3.17)

and

∆𝑇 = ∆𝑆_𝑐𝑇

𝑝. (1.3.18)

Comparison between EC materials are often done by those three quantities but they are not sufficient to find suitable EC materials. Moreover, other performance parameters must be included like the work (𝑊_𝐸) done to drive the ECE. This can be connected to the heat (𝑄_𝐶) absorbed by the EC material towards the materials efficiency[139]_:

𝜂 = 𝑄𝐶

𝑊𝐸. (1.3.19)

Further performance characteristics, i.e. thermophysical behavior, on the material level should be included to find the most suitable EC coolant. Presently, information on thermophysical behavior of ferroelectric materials is lacking. The thermal conductivity of only some materials are reported.[140-152]

Measurements of the specific heat capacity are sometimes largely deviating from the theoretical Dulong- Petit limit which was confirmed for example in barium titanate.[153, 154] _{For barium titanate a specific}

Petit limit. If equations 1.3.17 and 1.3.18 are used to interconvert the EC properties, those large differences in the specific heat capacity will lead to large differences in those properties. Therefore, knowledge about the thermophysical behavior in ferroelectrics should be expanded and the influence of phase transition characteristics should be understood.