Mighell Alan D
National Institute of Standards and Technology, Gaithersburg, MD 20899-8520.
J Res Natl Inst Stand Technol. 2004 Dec 1;109(6):569-79. doi: 10.6028/jres.109.043. Print 2004 Nov-Dec.
A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The existence of such singularities, therefore, has a practical and theoretical impact on the indexing of powder patterns. For example, in experimental practice an indexing program may find only the lower symmetry member of a singularity. Obviously, it is important to recognize such cases and know how to proceed. Recently, we described: a binary singularity involving a monoclinic and a rhombohedral lattice in a subcell-supercell relationship anda second type of singularity-a ternary singularity-in which two of the three lattices are in a derivative composite relationship. In this work, we describe a ternary lattice metric singularity involving a cubic P, a tetragonal P, and an orthorhombic C lattice. Furthermore, there is a binary singularity, involving a hexagonal P and orthorhombic P lattice, which is characterized by a set of unique d-spacings very close to that of the ternary singularity. The existence of such singularities is more common than once thought and requires a paradigm shift in experimental practice. In addition singularities provide opportunities in material design as they point to highly specialized lattices that may be associated with unusual physical properties.
当定义两个（或更多）晶格的晶胞产生相同的一组唯一计算d间距时，就会出现晶格度量奇点。因此，这种奇点的存在对粉末衍射图谱的指标化具有实际和理论影响。例如，在实验实践中，一个指标化程序可能只找到奇点的较低对称成员。显然，识别这种情况并知道如何处理很重要。最近，我们描述了：一种二元奇点，涉及单斜晶格和菱面体晶格，它们处于子晶胞-超晶胞关系；以及第二种奇点——三元奇点，其中三个晶格中的两个处于衍生复合关系。在这项工作中，我们描述了一种涉及立方P晶格、四方P晶格和正交C晶格的三元晶格度量奇点。此外，还存在一种涉及六方P晶格和正交P晶格的二元奇点，其特征是一组非常接近三元奇点的唯一d间距。这种奇点的存在比人们曾经认为的更为常见，并且需要在实验实践中进行范式转变。此外，奇点在材料设计中提供了机会，因为它们指向可能与异常物理性质相关的高度特殊的晶格。
