摘要
The explicit expression of Helmholtz free energy has been obtained from the equation of state from effiective field approach.From the Helmholtz free energy,four characteristic temperatures describing a first-order ferroelectric phase transitions have been determined.The physical meaning of coe±cients in Landau-type free energy has been revealed by comparison with the expanding Helmholtz function.Temperature dependence of polarization under different bias,and hysteresis loops at different temperatures are presented and discussed.These results provide the basic understandings of the static properties of first-order ferroelectric phase transitions.
基金
The authors gratefully acknowledge to MICINN of Spain for supporting the project FIS2008-00715
National Natural Science Foundation of China under Grant Nos.51172129,51172128 and 51102153.
