Short-Range Order and Static Displacements in Polycrystalline Ni-13.1at. %W Alloy

Abstract

A methodology accounting for the contributions of static displacements of atoms to X-ray diffuse scattering by binary solid solutions with a face-centered cubic lattice was proposed. By microscopic accounting of static displacements of the atoms on the particular shell, we identified short- range order parameters on the first eight shells of Ni-13.1at. %W alloy from the intensity of X-ray diffuse scattering. The Fourier transform of static displacement of the atoms on every considered shell was calculated with the De Launay model using expressions of elements of dynamical matrix and Fourier transforms of quasi elastic forces, which are calculated by the pseudopotential method.

The calculation of radial and tangential force constants for nickel using an experimental phonon spectrum

“…In general, good agreement was obtained between our phonon spectrum for nickel with the experimental measurements in [2]. Taking the larger number of spheres than the first four spheres in the equations of the dynamic matrix elements into account, it is impossible to improve the description of the experimental spectrum; the elastic constants that were calculated by equations from [9] vary noticeably from the experi- Table 1. The radial and tangential force constants for nickel (10 -3 The phonon spectrum for nickel at 296 K. The experimental data from [2] are highlighted with squares; the solid lines correspond to the calculated phonon branches with account for radial and tangential force constants in the first four coordination spheres.…”

“…This agrees with the results in [2], where it was possible to estimate the Born-von Karman force constants on the first four coordination spheres using the phonon spectrum for nickel, and it was concluded that the smooth branches of the experimental phonon spectrum indicate the short-term actions of interatomic forces in nickel. Meanwhile, the theoretical calculations of the phonon spectrum and elastic constants for nickel using the pseudopotential method take the force constants on the first ten spheres into account [6,9]. According to the procedure that was described in [9], using the Animalu model potential of transition metals [9] we calculated the radial α i and tangential β i force constants for nickel on the first ten coordination spheres at the lattice constant a = 3.5239 Å, whose values are summarized in Table 1 in comparison with the calculations in [6] and with the values that were obtained using the phonon spectrum in this work.…”

“…Meanwhile, the theoretical calculations of the phonon spectrum and elastic constants for nickel using the pseudopotential method take the force constants on the first ten spheres into account [6,9]. According to the procedure that was described in [9], using the Animalu model potential of transition metals [9] we calculated the radial α i and tangential β i force constants for nickel on the first ten coordination spheres at the lattice constant a = 3.5239 Å, whose values are summarized in Table 1 in comparison with the calculations in [6] and with the values that were obtained using the phonon spectrum in this work. It can be seen in Table 1 that the calculations using the pseudopotential method in [6] and in this work agree and in general do not agree with the results that were obtained by data processing of the experimental phonon spectrum for nickel.…”

“…In accordance with Eq. [9], while using the obtained values of α i and β i , it is possible to estimate the elastic constants C 11 , C 12 , and C 44 for an FCC metal during comparisons with experimental data. Then, again using α i and β i , it is possible to calculate the Born-von Karman force constants by Eq.…”

“…In this work the phonon spectrum for nickel that was experimentally measured at 296 K in [2] was applied to calculations of radial and tangential force constants for nickel by the least-squares method using the equations for a dynamic matrix that we developed in [9]. The obtained values of force constants were compared with the results in [2] and the theoretically calculated values using the pseudopotential method.…”