Mössbauer diffraction was used to measure different autocorrelation functions for 57 Fe atoms in different chemical environments. The sample was polycrystalline 57 Fe 3 Al with the ordered DO 3 structure. Diffraction peaks from a fcc structure with a doubled unit cell were detected when the incident radiation was tuned to the Mössbauer resonance of the Wyckoff 4(b) Fe site, but not for tuning to the 8(c) site, thereby distinguishing the spatial arrangements of these two Fe sites.[S0031-9007(96)02020-0] PACS numbers: 76.80.+y, 07.85.Nc, 61.10.Eq Most of what we know about atomic arrangements in materials has been learned from diffraction experiments. Three coherent scattering processes have proved useful: scattering of x rays by atomic electrons, scattering of electrons from Coulombic interactions with the electronic and nuclear charge of the atom, and scattering of neutrons from nuclei or magnetic electrons. Some Mössbauer scattering processes are coherent and may be useful for diffraction experiments on materials. Coherent interference between x-ray and Mössbauer scattering was first identified in Mössbauer energy spectra [1,2]. Later experiments with high quality single crystals measured diffraction peaks directly [3][4][5]. These later studies showed that with strong dynamical diffraction there is a suppression of incoherent decay channels such as internal conversion processes, and a large lifetime broadening of peaks in the Mössbauer energy spectra [6][7][8][9][10][11][12].In this Letter, we show a new feature of Mössbauer diffraction that is useful for studies of atomic arrangements in materials-we show that Mössbauer diffraction can measure the autocorrelation function of 57 Fe atoms as a functional of their chemical environment. By working with polycrystalline materials near the kinematical limit of diffraction, the broadening of nuclear energy levels is not severe, so the spectroscopic capabilities of Mössbauer scattering are preserved. The structure of the bcc-based DO 3 structure is shown in Fig. 1. The two sites for the 57 Fe atoms, the Wyckoff 4(b) and 8(c) sites, differ in both their chemical environment (0 versus 4 Al neighbors) and in their spatial arrangement (face-centered cubic, fcc, with lattice parameter 2a 0 versus simple cubic, sc, with lattice parameter a 0 ). In the present experiment, we tuned the incident beam to the hyperfine magnetic field (HMF) of each chemical environment (0 Al and 4 Al), and detected diffraction peaks characteristic of their spatial arrangements (fcc and sc).Pieces of 57 Fe (95% isotopically enriched) and Al metal were arc melted under an argon atmosphere and remelted several times to ensure homogeneity. The 50 mg ingot was then induction melted and splat quenched in high vacuum to obtain a chemically disordered foil of 35 mm thickness. This foil was cold-rolled to a thickness of 3 mm. To obtain DO 3 chemical order, the samples were annealed in evacuated quartz ampoules at 773 K for 6 days, followed by 723 K for 40 days. Xray diffractometry showed ͑ 1 2 1 2 1 2 ͒...