Scaling for the refrigeration effects in lead-free barium titanate based ferroelectric ceramics

The refrigeration effect (ΔQ) or temperature change (ΔT) resulting from electro-caloric (EC) effect in BaTiO3multilayered structures and Ba1-xSrxTiO3ceramics are directly measured using differential scanning calorimetry (DSC). At high electric field and near the Curie temperature, the relation between ΔQ and the applied field E is found to follow a power-law relation ΔQmax~ Eb, which is explained by the critical scaling near the Curie temperature. The exponent b is found to decrease with increasing disorder in the barium titanate based EC materials. Furthermore it is found that under the same electric field the maximum ΔQ of Ba1-xSrxTiO3ceramics which occurs around the Curie temperature first increases and then decreases with the increasing content of disorder x. A random-field ferroelectric transition model is used to investigate the effect of disorder on ΔQ and the scaling exponent b. The results from numerical solutions of this model are consistent with those from experiments. The scaling for the refrigeration effect in barium titanate based ferroelectrics is useful in the development of multilayered ferroelectrics with large cooling capacity for the practical application of lead-free barium titanate based ferroelectrics.