Ting Li, Hejing Wang, Erping Fan, Ling Wang, Zhao Zhou
August 27, 2012

### Abstract

In this paper, we propose a formula to describe the relationship between the Miller indices h , k and the row-row distance for the monoclinic system, which effectively overcomes the difficulty in indexing defective selected-area electron diffraction (SAED) patterns and Fourier transform of high-resolution transmission electron microscopy (HRTEM) images. Such defective SAED patterns are often found in clay minerals and other beam-sensitive materials. The spot-to-spot indexing is therefore transformed into the row-to-row measurement and calculation. This significantly improves the indexing for electron diffraction patterns. According to this formula proposed here, it is only necessary to measure the distance between rows [00 L ] and [ HKL ] and then the h and k and hence the l can be evaluated. This not only indexes the reflections, but also helps to judge the incident electron beam direction. The reliability and practicality of this row-indexing method were verified by both a simulated SAED pattern of chlorite and HRTEM experiments of illite and palygorskite. Formulae of row-indexing for the orthorhombic, rhombohedral, tetragonal, hexagonal and cubic systems are also presented.