【作者】 周国香；

【导师】 何文辰；

【作者基本信息】 河北工业大学 ， 材料物理与化学， 2004， 博士

【摘要】 本文给出了自由能的完整表达式。指出了自由能展开式中各项的物理意义-吉布斯自由能的一阶偏导数都是热力学变量的共轭变量；其二阶及二阶以上偏导数一律都是物性张量，也就是各个物理效应的效应系数。对自由能求二阶偏导数得到的是线性效应系数；而求三阶及三阶以上偏导数得到的是非线性效应系数。本文讨论了序参量是多变数情况下相变过程中自由能展开式应保留的项数。指出当用Landau理论研究相变时，可根据具体情况，在自由能的序参量展开式中保留相应的项；并直接从自由能展开式中系数的正负来判断所发生的相变是一级相变还是二级相变。和传统的方法一样，可能相的序参量可从自由能的一阶偏导等于零求得；相稳定性条件则由序参量的二阶偏导的Jacobi顺序主子式大于0得到。 对于相变的宏观唯象理论而言，关键是写出正确的自由能表达式，它可以用点群的基函数来构造。自由能表达式一般需保留到六次幂项，为了快捷地写出正确的自由能表达式，本文重新计算了具体的表示矩阵下32点群的所有不可约表示的基函数并将其扩充至三次幂。由给出的基函数表看出有十八个点群具有三次不变量，高温相具有这些对称性的晶体将会发生一级铁电相变。 利用朗道理论研究了方硼盐的铁电相变，求出了所有可能的本征铁电相-铁电正交相、三方相和单斜相。利用序参量是多变数情况下的相稳定性条件，计算出了这三个可能的相存在的温区。针对五种特殊的具有铁电三方相的方硼盐，计算出了其铁电三方相的自发极化强度、居里温度和主倒极化率等，发现自发极化在居里点有跃变；沿极化方向的倒极化率分量是连续的，然而垂直于极化方向的倒极化率分量不连续，这是一个非常有趣的现象。鉴于铁电三方相倒极化率的特殊性，提出了其介电测量的实验方案。 在居里原理的基础上，以PZT晶体、钛酸锶晶体和反铁电的简立方晶格模型为例研究了反铁电相变的序参量。给出了寻找合适的序参量的一种途径：即由晶体相变前后的对称性根据居里原理首先确定出序参量应具有的对称性，再根据晶体的物性张量矩阵表，从最低阶的张量找起，直到找出合适的序参量。按照这一思路找出了反铁畸变即θ相变的序参量Π_ijk，它是三阶全对称的物性张量。利用该序参量研究了典型的反铁畸变晶体-PZT晶体和钛酸锶晶体，发现它能很好铁电相变自由能的系列研究与反铁电相变序参量选取地说明这两种晶体夕相变前后对称性的变化。简立方晶格有两种反铁电模型A、B，它们具有的对称性分别为DZJ和q，。通过计算发现模型A、B的序参量分别为n琳、反，并且用它们作序参量能很好地反映模型A、B在相变前后对称性的变化。从而进一步说明了用反和n必作为反铁电相变序参量的合理性。更多还原

【Abstract】 The full free energy expansion was proposed. The physics significations of every part of the free energy expansion are illuminated. The significations of the coefficient of free energy expansion and that of conjugate variable of the independent variable are indicated. The first order partial differential of Gibbs free energy are thermodynamics variable. The second order and the higher order partial differential of Gibbs free energy are substance property tensors, i.e. they are all the coefficients of the physical effects. The term numbers of free energy expansion are studied during the phase transition process when the order parameter is more than one variable. The corresponding terms are retained in free energy expansion according to the specific conditions when Landau theory is used. Furthermore, the order of the phase transition can be obtained by the coefficients in free energy expansions. Besides, by using the traditional method, the order parameter of the possible phase can be obtained by the first order derivative of free energy and the stability condition of the phase can be reached when the Jacobi ordered-main subdeterminant of the second order derivative of the order parameter is definitely positive.As far as Landau theory is concerned, the key is to write out the correct free energy expansion. The expansion can be constructed by the base functions of point group. Generally speaking, the sixth order terms should be retained in the free energy expansion. In order to obtain the correct free energy expansion rapidly, we recalculate the base functions of the irreducible representations for thirty-two point groups corresponding to the specific representative matrix and supplement the third-order base fuctions. Eighteen kinds of point groups are found having third-order invariant. If the group of the high-temperature crystal structure is one of these point groups, then the ferroelectrics will undertake the first orderphase transition.Landau theory is used to describe the ferroelectric phase transition of Boracites. All the possible proper ferroelectric phases are obtained. They are ferroelectric orthogonal phase, ferroelectric trigonal phase and ferroelectric monoclinic phase. The temperature zones of the three possible phases are calculated respectively by using the stability conditions of more variables. There are only five kinds of boracites that have the ferroelectric trigonal phase. The spontaneous polarization and the Curie temperature as well as the temperature dependence of the principal reciprocal susceptibility are obtained respectively. The calculated result shows that at the Curie temperature Tc, spontaneous polarization jumps. The component of the principal reciprocal susceptibility perpendicular to polarization jumps but the component parallel to polarization does not jump. Considering the speciality of the principal reciprocal susceptibility in trigonal boracite, the experiment scheme on the measurement of the principal reciprocal susceptibility components is presented.On the basis of Curie principle, the order parameter of the antiferroelectric phasetransition is investigated by taking crystal PZT, crystal SrTiO and the antiferroelectricmodels of simple cubic lattice as examples. A method of searching for the suitable order parameter is given. Firstly, according to Curie principle, the symmetry of the order parameter is decided by using the symmetry of the crystal before and after phase transition. Then by using the physical tensor matrix, searching from the first order tensor, we can finally obtain a suitable order parameter. A third-order complete symmetry polarizationtensor ijk is put forward as the order parameter of phase transition. The matrix of ijkhas been calculated for PZT and SrTiO3 respectively. We find that this order parameter can reflect the symmetry changes of the two crystals perfectly. There are two kinds of antiferroelectric models for the simple cubic lattice. We called them model A and model Brespectively. The symmetry of model A is D2d and the symmetr更多还原