Indexing zone search method

The reciprocal space indexing can be implemented in several different ways. Two of them are trial-and-error and zone search methods. The first one is more efficient in high symmetry crystal systems (from cubic to orthorhombic) but becomes slow for low symmetry crystal systems (especially triclinic), while the second method works quite effectively and is fast with low symmetries (from triclinic to orthorhombic). 

Zone search method begins with searching for one-dimensional and two-dimensional zones and then builds three-dimensional zones using common rows in two-dimensional lattices. When a three-dimensional zone (lattice) is found, it is used in an attempt to index all observed Bragg reflections. This automatic indexing technique is more sophisticated when compared to a trial-and-error approach, but it is still based on Eq. 5.1. First, the analysis of numerical relationships between the observed Q-values is made to identify zones that are invariant with respect to two indices, for example AOO, h 0, OkO and so on. Second, these are combined to identify zones which are invariant with respect to one index and, finally zones where all three indices... 

The zone search indexing method does not require an assumption about the crystal system and therefore, it results in a primitive lattice in most cases. When the lattice is confirmed by the subsequent indexing of all observed Bragg peaks, it shall be converted to one of the 14 standard Bravais lattices. The latter is achieved in a process known as the reduction of the unit cell. 

This algorithm realizes a zone search indexing method combined with the Delaunay-Ito technique (see section 5.10.1) for the reduction of the most probable unit cell. The most commonly used versions of computer codes are ITO 13 and IT015. The program arrives at a solution by using the following algorithm ... 

Figure 4. show the process of searching data or location. This searching method can choose the data or location by LOT, ZONING or REGION. The QuadR-tree indexing engine selection run in this process. Start from find the data or location until the data will be shown and zoom like in Figure 5. Furthermore, this process measure the speed of using indexing or not over Mobile GIS network.

---