Nature of Long-Range Order in Cu3Au and Cu72Au28

Diffuse x-ray scattering and the intensity of Bragg peaks from single crystals of Cu3Au and Cu72Au28 have been studied for various degrees of long-range order. Equations are developed for the effects of differences in atomic size of the species and zero-order temperature effects on diffraction from an alloy when long-range order is present. A peak due to differences in atomic size is predicted under the superstructure reflections as well as under the fundamentals when order is not perfect; this prediction is experimentally confirmed. If the local order is not large for coordination shells greater than the eighth or ninth, then the Warren short-range order parameters can be accurately determined from data along only two lines in reciprocal space. The results indicate that excess Au atoms, replacing Cu in Cu3Au, distribute themselves at random when Cu72Au28 is heat-treated for maximum long-range order. Thus there is no marked tendency for the Au atoms to avoid each other. Local order develops among misplaced atoms as the long-range order decreases with increasing temperature and just below the critical temperature this local order is similar in both Cu3Au and Cu72Au28. There are about the same number of wrong first bonds just below the critical temperature Tc for both alloys, even though the degree of long-range order indicates that there are more wrongly occupied sites for the nonstoichiometric alloy than for Cu3Au. (The data for Cu3Au are in agreement with Cowley's latest thermodynamic treatment and Peierl's theory.) The results for both ordered alloys can be explained in terms of a large number of small antiphased regions in a well-ordered matrix. These regions are essentially two dimensional except near the critical temperature for the nonstoichiometric alloy where they are three dimensional. They vary in composition from point to point in the structure. The extra Au atoms in Cu72Au28 may play a key role in forming these as the temperature is raised, as they appear in the boundaries of the domains. The atomic volumes of Cu and Au in ordered Cu3Au and Cu72Au28 are the same as in the pure metals; their rms vibrations are similar.