Patent ID: 7739075

Claim:
A method of computing crystal shapes from X-Ray Diffraction Data (XRD) of a substance, the method comprising: a) obtaining input parameters associated with said substance, said parameters comprising: (i) number of XRD peaks (n), (ii) (2·θ), wherein θ represents the angle of incidence on said substance of X-rays, and (iii) the peak-width at half maximum, represented as B, for each of the XRD peaks; b) indexing by assigning the Miller indices (h, k, l) to each of the XRD peaks; c) determining at least one unit cell parameter associated with said substance; d) determining crystal thickness associated with said substance in different directions based at least in part on the data gathered from step (a) and step (b) in Scherrer formula (t hkl =0.9λ/B Cos θ hkl ), wherein λ, represents the wavelength of said X-rays, θ hkl represents angle of incidence of X-rays on the planes having Miller indices (h, k, l), and t hkl represents a thickness of crystal perpendicular to said (h, k, l) planes; e) based at least partly on the data gathered from steps (a) to (d), determining using a processor a set of crystal planes which determine the mathematical envelope for the crystal shape associated with said substance, wherein said crystal planes are associated with crystal faces; f) determining co-ordinates of each point of intersection of said crystal planes; g) determining a set of all real points of intersection; h) for each of said crystal planes, identifying a set of real points of intersection which fall on said plane; i) transforming using the processor coordinates of said real points of intersection from Global to Local frames, wherein said real points of intersection are associated with vertices of said crystal faces; j) determining using the processor a polar co-ordinate [θ i ] of each of the vertices ordered in an ascending series in each of the crystal faces; k) determining using the processor a transformation, represented by T, which reshuffles the indices; l) based at least partly on the transformation T obtained from step (k), ordering using the processor the vertices on each crystal plane and computing the areas and Miller indices of exposed crystal faces; and m) determining using the processor a 3D crystal shape associated with said substance.