X-Ray Diffraction and the Bragg Equation

Abstract

Typical derivations of the Bragg equation in introductory texts do not adequately explain why x-rays are reflected as if by a mirror by crystal planes, and often lead to the mistaken idea that lattice points can be identified with the centres of atoms or ions in the structure. The treatment offered here is a little more demanding, but to compensate for this also has the advantage that it can easily be extended to provide a basic understanding of the use of XRD in structure determination. Comparison of the x-ray powder diffraction patterns obtained from K Cl and K Br is used to illustrate how both the angles and the intensities of diffracted beams are determined by the structure of a solid. A brief discussion of the effects of crystal size on the broadening of diffraction lines is included both for its intrinsic interest, and because it emphasizes that the sharp diffracted beams which are often observed result from the cooperative effect of very large numbers of scattering centers.

Effect of tensile rates on thermal and mechanical properties of porous PTFE composites

“…It can be noted that the interplanar spacing of the stretched PTFE is slightly increased. According to Bragg equation, 38 the interplanar spacing is inversely proportional to the diffraction angle; so the increase of the interplanar spacing means that the diffraction angle decreases, which is consistent with the phenomenon observed in Figure 6 (shift toward lower diffraction angle). For crystallite size analysis, we can use XRD line profiles, which is obtained in MDI Jade.…”

Effects of the γ″-Ni3Nb Phase on Mechanical Properties of Inconel 718 Superalloys with Different Heat Treatments

“…In the peak fitting results, three peaks, namely, γ" (220), γ' (022), and γ (022), at the 2θ axis at about 74.5° can be fitted to the data. The lattice parameters and lattice misfits of the three precipitates in all samples were calculated using an extrapolating function method based on the Bragg equation [29] and relevant crystal structure, and the calculated values are listed in Table 1.…”

Polymer/clay nanocomposites based on aliphatic–aromatic polyamide containing thiazole ring and new organomodified nanosilicate layers: Synthesis, characterization, and thermal properties study

“…4. The d-value of clay was 1.149 nm which is corresponded to the characteristic reflection at 2h 5 7.768 calculated using the Bragg equation [39] (Eq. 1).…”