A structural study of the alloy Cu₃Au above its critical temperature

Abstract

Absolute measurements of the diffuse intensity in a volume in reciprocal space have been made at six temperatures ranging from 2°C above Tc to 930°C. The Warren short-range order parameters were obtained after correcting for the intensity due to atomic displacements in a more complete manner than in earlier studies. As a result the short-range order parameters are considerably smaller than in these earlier investigations. The (previously disputed)specific heat anomalies in Cu3Au above Tc and the L12 phase have been shown to be associated with unusual changes in diffuse X-ray scattering vs temperature. From studies of the scattering distributions, computer simulation and pair potentials obtained with the Warren short-range order parameters, the anomaly at 600°C appears to be due to the disappearance of DO22-1ike fluctuations, whereas above 850°C, CuPt-like fluctuations develop. There are premonitory effects just above To; there is a large increase in the Debye-Waller factor, in the total intensity due to quadratic terms in atomic displacements, and an apparent change in the sign of average first-neighbor displacement. The long-range oscillations in the interatomic potentials determined from the diffuse-scattering data fit the Friedel potential only approximately. The electron-to-atom ratio in Cu3Au was found to be ~0"97, in agreement with results on Cu alloys by other methods.

Equations for diffuse scattering from disordered alloys with h.c.p. structure

“…According to (7) the experimental diffuse scattering data have to be weighted by the thermal DW factor exp [-tOk(Q)]. Since it is rather difficult to calculate exp [-tOk(Q)] accurately, Bardhan & Cohen (1976) employed the ratio I(100)/I(300) (for f.c.c, crystals) to obtain exp [-2to(Q)]. Their claim, that the DW factor thus obtained contains both static and dynamic contributions, is however not correct.…”

Extinction, polarization and crystal monochromators

“…Lorentzian = secondary extinction only, without diffraction broadening, with mosaic distribution [ 1 + (z~e/r/)2]-L Gaussian = same, except for distribution exp(-zce2/r/2). The vertical arrow shows the range of reported experimental K values (Hope, 1971;Vincent & Flack, 1980;Bardhan & Cohen, 1976), all plotted at a y± value measured in our laboratory for a typical graphite monochromator. The Kato curves also give the dependence of K6 on ~0(x±) in the modified Darwin theory, neglecting primary extinction.…”

The role of Debye–Waller-factor measurement in the analysis of diffuse-scattering data

“…1 where the displacement diffuse intensity along (h~00) in reciprocal space is reconstructed from the Fourier coefficients of Bardhan & Cohen's (1976) analysis of Cu3Au at T c + 2°C (T c = 391.1 °C; Hashimoto, Miyoshi & Ohtsuka, 1976) and the average values given by (1) and (4). The DWF's are from a neutron determination (Tibballs, Towers & Barnea, 1978).…”

“…Fourier coefficient 3if0 o of [Iq(h)]xx is a measure of the mean-square displacement (Bardhan & Cohen, 1976). The average diffuse intensity due to displacements is ]aisp= IAfl2cACB~oo(hZ~ + h~ + h~) ( 1) in the Borie & Sparks (1971) notation.…”