Kopský Vojtech
Institut of Physics, Czech Academy of Sciences, Na Slovance 2, 182 21 Praha 8, Czech Republic.
Acta Crystallogr A. 2006 Mar;62(Pt 2):65-76. doi: 10.1107/S010876730600078X. Epub 2006 Feb 18.
The theory of domain states is reviewed as a prerequisite for consideration of tensorial distinction of domain states. It is then shown that the parameters of the first domain in a ferroic phase transition from a set of isomorphic groups of the same oriented Laue class can be systematically and suitably represented in terms of typical variables. On replacing these variables by actual tensor components according to the previous paper, we can reveal the tensorial parameters associated with each particular symmetry descent. Parameters are distinguished by the ireps to which they belong and this can be used to determine which of them are the principal parameters that distinguish all domain states, in contrast to secondary parameters which are common to several domain states. In general, the parameters are expressed as the covariant components of the tensors. A general procedure is described which is designed to transform the results to Cartesian components. It consists of two parts: the first, called the labelling of covariants, and its inverse, called the conversion equations. Transformation of parameters from the first domain state to other states is now reduced to irreducible subspaces whose maximal dimension is three in contrast with higher dimensions of tensor spaces. With this method, we can explicitly calculate tensor parameters for all domain states. To find the distinction of pairs of domain states, it is suitable to use the concept of the twinning group which is briefly described.
作为考虑畴态张量差异的前提，对畴态理论进行了综述。然后表明，在从同一取向劳厄类的同构群集合发生的铁电相变中，第一畴的参数可以用典型变量系统且适当地表示。根据前文将这些变量替换为实际张量分量后，我们可以揭示与每个特定对称性下降相关的张量参数。参数根据它们所属的不可约表示来区分，这可用于确定哪些是区分所有畴态的主要参数，与几个畴态共有的次要参数形成对比。一般来说，参数表示为张量的协变分量。描述了一种将结果转换为笛卡尔分量的通用程序。它由两部分组成：第一部分称为协变量标记，其逆运算称为转换方程。现在，将参数从第一畴态转换到其他态的过程简化为不可约子空间，其最大维数为3，与张量空间的更高维数形成对比。用这种方法，我们可以明确计算所有畴态的张量参数。为了找出成对畴态的差异，适合使用简要描述的孪晶群概念。
