Low Temperature Heat Capacity Of Ferroelectric

In the 70s and 80s of the 20th century,American scientist Lawless discovered that the specific heat of a series of ferroelectric materials in the temperature range of 2-35 K was not suitable for the classical Debye T3 law.By combining different theoretical models and fitting the specific heat in the temperature range of 1.9 to 10 K,it is concluded that adding the T3/2 term can greatly improve the effect of fitting the specific heat experimental data of the ferroelectric material.Lawless believes that the T3/2 contribution is caused by the ferroelectricity of the ferroelectric material itself,called "Lawless Law".However,in the 1980s,two German scientists,E.Gmelin and G.Burns,studied a series of high-purity ferroelectric materials.It was found that the ferroelectric material does not have a T3/2 contribution.Therefore,they speculated that the T3/2 contribution may be caused by vacancies or impurities in the material.Since then,more attention has been paid to the phase transition of ferroelectric materials.Therefore,the key issue of whether ferroelectric materials contribute to the existence of T3/2 in the liquid helium temperature zone has been left behind.In view of the above problems,13 kinds of powdered ferroelectric materials,3 kinds of single crystal ferroelectric materials and 2 kinds of doped ferroelectric materials were selected in this paper,ie,Ba1-xMgxTiO3(BTAMg)and BaTi1-xSixO3(BTBSi).The specific heat of the 0-300K temperature range of the ferroelectric material is measured using a comprehensive physical property measurement system(PPMS),and its specific heat is fitted using a three-stage theoretical model to calculate its standard molar transmutation,standard molar entropy change,and other thermodynamics function.By analyzing the specific heat of 13 kinds of powdered ferroelectric materials,it was found that the addition of T3/2 term can better fit the specific heat;in order to investigate the causes of the existence of 73/2 contribution to ferroelectric materials,we chose 3 kinds of high purity.The single crystal ferroelectric material,similarly,was tested for its specific heat and found that the high-purity single crystal ferroelectric material did not have a T3/2 contribution;subsequently,we selected Mg and Si as impurities to be doped in barium titanate,and measured The specific heat found that with the gradual increase of the impurity content,adding the T3/2 term can better fit the specific heat.In general,we conducted a series of specific thermal analysis of powders,single crystals,and doped ferroelectrics.We found that the contribution of ferroelectric T3/2 is not due to its own ferroelectricity,which is an impurity in ferroelectric materials.It is the most important factors causing the contribution of the ferroelectric material T3/2.