Method for determining 3D primitive reciprocal basis of unknown crystal based on single EBSD pattern

A method for determining a 3D primitive reciprocal basis of an unknown crystal based on an EBSD pattern, comprising steps of:

• 1) collecting an electron backscatter diffraction (EBSD) pattern of a crystalline sample with a scanning electron microscope (SEM), recording the pattern center (PC), the detector distance (DD), and the accelerating voltage used;
• 2) identifying edges at the narrowest width of each visible Kikuchi band on the EBSD pattern, determining central line of the Kikuchi bands on the EBSD pattern;
• 3) geometrically correcting the Kikuchi bands with the pattern center and the detector distance, obtaining reciprocal vectors corresponding to the Kikuchi bands, and determining components of the reciprocal vectors in a 3D reciprocal Cartesian coordinate system;
• 4) selecting all possible three non-coplanar vectors in the reciprocal vectors, calculating the volumes of parallelepipeds defined by the non-coplanar reciprocal vectors, sequencing them from the smallest volume to the largest volume, and simultaneously recording the corresponding three non-coplanar reciprocal vectors forming the parallelepipeds;
• 5) circulating the sequenced volumes;
• 6) assigning the current volume to be variable V, wherein the three corresponding non-coplanar reciprocal vectors are respectively set to be a, b, and c, firstly calculating the parallelepiped volumes Vab formed by the a, b, and another reciprocal vector excluding the a, b, and c, then calculating Vab/V, taking the nearest integers I;
• if one of the integers I equals to 2, jumping into step 7);
• otherwise, circulating to the next volume and repeating the step 6);
• 7) firstly calculating the parallelepiped volumes Vbc formed by b, c, and another reciprocal vector excluding the a, b, and c, then calculating Vbc/V, taking the nearest integers J;
• if one of the integers J equals to 2, jumping into step 8);
• otherwise, circulating to the next volume and repeating the step 6);
• 8) firstly calculating the parallelepiped volumes Vca formed by c, a, and another reciprocal vector excluding the a, b, and c, then calculating Vca/V, taking the nearest integers K;
• if one of the integers K equals to 2, jumping into step 9);
• otherwise, circulating to the next volume and repeating the step 6);
• and
• 9) determining the three non-coplanar reciprocal vectors corresponding to the current volume as a 3D primitive reciprocal basis.