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Body-centered: H+K+L = 2n (even) H+K+L = 2n+1 (odd) Face-centered: H,K,L all odd or all even: H,K,L mixed odd, even: FCC Diamond: H,K,L all odd H,K,L all even and H+K+L = 4n: H,K,L mixed odd, even H,K,L all even and H+K+L 4n: Hexagonal (HCP) L even H+2K 3n: L odd and H+2K = 3n
In three dimensions, end-centered, body-centered, and face-centered arrangements also produce extinctions. We often describe extinctions using arithmetical rules. For body centering, the rule is that an hkl peak will only be present if h + k + l is an even number.
24 de nov. de 2022 · The 7 Crystal Systems. The Body-Centered Cubic (BCC) unit cell can be imagined as a cube with an atom on each corner, and an atom in the cube’s center. It is one of the most common structures for metals. BCC has 2 atoms per unit cell, lattice constant a = 4R/√3, Coordination number CN = 8, and Atomic Packing Factor APF = 68%.
h + k + l = even number. h + k + l = odd number. FCC. h, k, l all even. h, k, l all odd. h, k, l mixed even and odd. Example: Use the following XRD spectrum to determine the element that was investigated. It is either BCC or FCC. Copper Kα radiation was used, which has a wavelength of 1.54 Angstroms.
In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a critical tool in the interpretation of scattering patterns ( interference patterns) obtained in X-ray, electron and neutron ...
hkl for Face Centered Cubic • Substitute in a few values of hkl and you will find the following: – When h,k,l are unmixed (i.e. all even or all odd), then F hkl = 4f. [NOTE: zero is considered even] – F hkl = 0 for mixed indices (i.e., a combination of odd and even). Ffe e e 1 ih k ih l ik l() ( ) ( ) hkl Selection rules for hkl reflections
Table 1.1 summarizes the selection rules (or extinction conditions as they are also known) for cubic lattices. According to these selection rules, the h2 + J<2 + [2 values for the different cubic lattices follow the sequence Primitive I, 2, 3,4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, ... Body-centered 2,4, 6, 8, 10, 12, 14, 16, ...
