Atom distributions in sigma phases. I. Fe and Cr atom distributions in a binary sigma phase equilibrated at 1063, 1013 and 923 K

Abstract

same five-dimensional space group because the electron diffraction patterns are similar to those of the 7a structure except for the difference in the wavevectors and N/M varies continuously with the chemical composition (Hirabayashi et al., 1970). This suggests that the five-dimensional space groups of these two structures are the same and a series of incommensurate structures with 3/7 < N/M < 4/9 have the same space group. These are expected to have similar structures.In order to confirm this, we calculated the Fourier amplitude of the 9a structure given by Hirabayashi et al. (1970) and confirmed that the distribution of Au atoms is well approximated by (2). This shows that their five-dimensional structures are isomorphic with each other. The Fourier amplitudes P0 and P~ of this structure are listed in Table 1. Summary and concluding remarksWe carried out a five-dimensional analysis of the 7a structure based on the theory of modulated structure analysis and obtained essentially the same result as in the more sophisticated analysis based on the usual three-dimensional symmetry. It was shown that the 9a structure has the same five-dimensional space group as the 7a structure and has a similar five-dimensional structure. The present paper demonstrates that the refinement can be carried out by using only observed reflections and parameters mainly contributing to these reflections. This saves much computing time and reduces effort in analyses of commensurate structures without accompanying higher-order harmonics. absence of a center of symmetry was found in any data set, or in any of the results obtained by least-squares refinements of parameters assuming space group P42/mnm. Average site-occupation parameters of limited precision (+5-10%) were derived for the five independent sites occupied in the a structure during the refinement based on each data set. The crystal from the alloy equilibrated at 1013 K was also studied using synchrotron-radiation (SR) Bragg diffraction at photon energies just below the Fe and Cr K absorption edges, where relative differences (Alfl/Ifl)

Ab Initio Study of Lattice Site Occupancies in Binary Sigma Phases Using a Single-Site Mean Field Model

“…The results are shown in Figure 2 and agree quite well with the available experimental data [2,28]. At very high temperatures the configurational entropy drives the system to a highly disordered distribution of the alloy components on the five σ-phase sublattices.…”

“…These atoms are located in five nonequivalent groups of sites or sublattices (A, B, C, D, E) [2,3]. One often uses the following formula A to describe the σ-phase structure, where bottom and top indices denote the site multiplicities and coordination numbers for each sublattice, respectively.…”

Non-Stoichiometry and Calphad Modeling of Frank-Kasper Phases

“…Fe site fraction in σ Cr-Fe, obtained by CWM-CVM at 500K (left) [28], and obtained by BWA at 1,000 K (right) [38]. Experimental points from [45]. Increased computer performance has allowed researchers to investigate more complex problems.…”

Direct Observations of Sigma Phase Formation in Duplex Stainless Steels Using In-Situ Synchrotron X-Ray Diffraction

“…This [26], which gave the best fit to the actual sigma phase diffraction pattern at room temperature. The results show that three austenite peaks, three ferrite peaks, and a multitude of sigma phase peaks should appear in the diffraction window, which covers about 10 deg of 2θ for the experimental conditions used in this study.…”