| Various metastable and stable precipitates produced from oversaturated solid solutions play a crucial role in strengthening crystalline materials;however,microstructure characterization of some fine precipitates is not straightforward because of the presence of equivalent variants,and sometimes high-order reflections,which may lead to rather complicated superimposed selected-area electron diffraction（SAED）patterns of the precipitates and the parent phase,especially,when the crystal structure of the precipitates is unknown.This Paper provides a practicable solution on how to accurately reconstruct unknown Bravais cell,and determine orientation relationship between the precipitate and the parent,as well as correctly identify reflections from different variants and even high-order reflections.An accurate 3D reconstruction method for determining the Bravais lattice of such an unknown precipitate based on only three in situ SAED patterns is described in detail and a rhombohedral phase（termed R′）in a solution-aging-treated titanium alloy（Ti-4.5Al-6.5Mo-2Cr-2Nb-1V-1Sn-1Zr,wt.%）is successfully identified by transmission electron microscopy（TEM）.Its accurate Bravais lattice parameters are a R′=0.5395 nm,αR′=117.04°,which have a relation with the b.c.c.βparent.The orientation relationship between the R′phase and the b.c.c.parent is determined to be（0 0 1）R′//（1 （?）1）βand[1 1 0]R′//[1 1 1]β.As far as we know,this is a new orientation relationship between rhombohedral and b.c.c.structures.In cubic crystal system,there are 48 crystallographically equivalent indices for any<u v w>β;therefore,the R′phase with the OR should also possess 48 variants.It is found that the R′phase shows 48variants,which can be divided into four groups according to their habit planes{1 1 1}β.Each group contains 12 variants,half of which have right-handed basis vectors and the other half left-handed ones.Given above lattice parameters of the R′phase and its orientation relationship with the parent,we systematically analyze a series of in situ SAED patterns taken along both low-and high-indices’zone axes.All weak and strong reflections including high-order ones arising from the R′phase’s 48 variants are properly understood and directly assigned self-consistent Miller indices.More importantly,we also propose some criteria for evaluating indexed results of the complicated SAED patterns.All the findings of the present investigation are of theoretical significance in titanium alloys;furthermore,the method for reconstructing Bravais lattice and the idea of indexing complicated SAED patterns as well as the criteria proposed in this study shed light on the microstructure characterization of fine precipitates in other alloy systems. |
