Determining the unit cells of unknown crystalline phases is a fundamental requirement for materials characterization and the initial step in ab initio structure determination. Electron diffraction, alongside X-ray and neutron diffraction techniques, has been extensively used in material characterization and crystal structure determination. Lattice parameters obtained from selected-area electron diffraction (SAED) have an accuracy of approximately 5%. A SAED pattern can be viewed as a two-dimensional section of a three-dimensional reciprocal lattice. By using a double tilt holder in a transmission electron microscope (TEM), a series of reciprocal planes can be obtained. Due to the nature of the SAED technique, it is logical to determine the unit cell of an unknown crystalline phase from a tilt series of electron diffraction patterns. This traditional method, documented by Vanishtein (1964) and Zou et al. (2011), is, however, cumbersome when applied to crystalline phases in monoclinic or triclinic systems. A crystalline lattice can be uniquely characterized by a reduced cell, and there are 44 primitive Niggli reduced cells corresponding to 14 Bravais lattices (Niggli, 1928). The Niggli cell is crucial due to its uniqueness and its use in determining the Bravais type of the lattice (Gruber, 1973). The Niggli cell has been widely used in X-ray crystallography and in electron diffraction experiments for unit-cell determination of crystalline phases (Kuo, 1978). A modified cell reduction method was adopted in the early version of this software (Li, 2005) . This program set has been significantly updated for improvement (Li, 2019). The current version, described in this manual, serves as a practical tool for unit-cell determination of crystalline phases in TEM, encompassing: 1). Reciprocal lattice reconstruction approach, 2). Cell reduction approach, and 3). Lattice refinement. |
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