Diffusion of Cu in AlCu alloys of different composition by quasielastic neutron scattering

doi:10.1016/j.jnoncrysol.2007.05.074

Journal of Non-Crystalline Solids

Volume 353, Issues 32–40, 15 October 2007, Pages 3295-3299

https://doi.org/10.1016/j.jnoncrysol.2007.05.074 Get rights and content

Abstract

Quasielastic cold neutron scattering experiments on molten Al_1−xCu_x alloys (x = 0.10, 0.17 and 0.25) have been performed at three different temperatures on the FOCUS time-of-flight spectrometer at the Swiss neutron spallation source SINQ. As the main part of the scattering at small Q is incoherent and originating from Cu, self-diffusion coefficients D for the Cu ions could be determined from the widths of quasielastic peaks. The derived values are considerably larger than those found in capillary tube measurements. Even if the accuracy in the determination of D is better than about 4% it could not be concluded whether the temperature variation of D follows an Arrhenius law or a power law.

Introduction

The study of liquid metals and alloys has drawn considerable attention recently, in particular due to the possibility of carrying out ab initio molecular dynamics simulations for these systems [1]. In ab initio simulations, the atomic and electronic structures are evaluated using density-functional theory and the corresponding forces are used to move the ions according to classical molecular dynamics. Such simulations, in principle, can augment experiments and test models, and provide insight into the behavior of real materials. In recent years, the thermodynamic and transport properties of a variety of liquid metals and alloys have been studied by this method. However, the number of atoms in these simulations is small (about 50–100) and the comparison to accurate experimental data is essential. In order to facilitate this a series of experiments and large scale ab initio calculations on the same liquid metals and alloys and at the same temperatures have been initiated. Al-based liquid alloys have been chosen for this purpose, due to both their practical importance as well as to the fundamental theoretical interest in these compounds.

The most sensitive validation of the calculations are made via comparison to the dynamic scattering function S(Q, E) that is experimentally accessible via two complementary experimental techniques, neutron and high energy X-ray inelastic scattering measurements [2]. However, the only direct determination of the self-diffusion coefficient is via quasielastic neutron scattering. Other direct measurements of this quantity have mostly been made using so-called capillary tube methods. Diffusion coefficients are furthermore often calculated from experimental determinations of the shear viscosity coefficients and the use of the Einstein or Sutherland relations as well as from hard sphere models. Usually the accuracy of these last routes is not satisfactory and published values often differ by a factor 2.

Only a few determinations of the diffusion coefficients in molten alloys by neutron scattering techniques have been made. Neutron quasielastic scattering has recently been used to determine the diffusion of Ni in molten Ni₁₅Ge₈₅ [3] and several different kinds of atoms in viscous multi-component metallic liquids forming so-called bulk metallic glasses [4]. Careful experiments, combined with accurate atomic simulation, can provide more accurate measurements, as well as details of the atomic motions.

In this paper, we present the determination of the self-diffusion coefficient of Cu ions in molten AlCu alloys from the width of quasielastically scattered neutron spectra. Three different alloy compositions at and around the eutectic one have been studied at three different temperatures. A full account of the measurements including the determination of S(Q, E) will be presented in a forthcoming publication.

Section snippets

Theoretical background

The neutron scattering cross section for a multi-component system [or, equivalently, the total dynamic structure factor S(Q, E)], can be written as $σ^{sc} S (Q, E) = 4 π \sum_{i} \sum_{j} b_{i} b_{j} (c_{i} c_{j})^{1 / 2} S_{ij} (Q, E) + \sum_{i} σ_{i}^{inc} c_{i} S_{i}^{inc} (Q, E) .$ The effective scattering cross section σ^sc in Eq. (1) is given by $σ^{sc} = 4 π \sum_{i} b_{i}^{2} c_{i} + \sum_{i} σ_{i}^{inc} c_{i} .$ Q is the wavevector and E is the energy transfer in the neutron scattering process. b_i, c_i, $σ_{i}^{inc}$ and $S_{i}^{inc} (Q, E)$ are the scattering length, the concentration, the incoherent scattering cross section and the

Experimental

The inelastic neutron scattering experiments were performed at two occasions on the FOCUS time-of-flight spectrometer at the neutron spallation source SINQ at the Paul Scherrer Institute in Switzerland. The wavelength of the incident neutrons was 4.40 and 4.46 Å⁻¹, respectively, and spectra were recorded at scattering angles ranging from about 15 to about 130°, which corresponds to the Q range 0.46–2.55 Å⁻¹ for elastically scattered neutrons. The energy resolution was about 0.14 meV as determined

Results

The measured spectra of quasielastically scattered neutrons, corrected for experimental effects, such as container scattering, sample absorption and multiple scattering, were fitted according to Eq. (5) with a scattering function of Lorentzian shape (Eq. (3)). The fits were in all cases excellent.

The full widths at half maximum, FWHM, of the Lorentzians are shown in Fig. 1. For two alloys, Al₈₃Cu₁₇ and Al₇₅Cu₂₅, values obtained from the two sets of measurements at 973 K are shown as squares and

Discussion

The values of diffusion coefficients D_Cu given in Table 2 are plotted in Fig. 3. At all compositions the temperature variation seems to be described by an Arrhenius law. The activation energies vary in the range 19–21 kJ/mol. A Tⁿ temperature variation with n = 2 has been invoked from MD simulations [6] and from space experiments [7], [8] on pure elements. Taking into account the error in the determination of D such a temperature variation can, however, not be excluded for the AlCu alloys studied

Conclusions

The derived values of the self-diffusion coefficients for Cu ions in molten Al are considerably larger than the self-diffusion coefficient in molten Cu at its melting point. The values are also considerably larger than impurity diffusion coefficients measured in capillary tube measurements and in directional solidification studies along the solidus line. Even if the accuracy in the determination of D is better than about 4% it could not be concluded whether the temperature variation of D

Acknowledgments

Ames Laboratory is operated for the US Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. Oak Ridge National Laboratory is operated for the US Department of Energy under contract DE-AC05-00OR-22725 with UT-Battelle, LLC. This work was supported by the Director for Energy Research, Office of Basic Energy Sciences and is based on experiments performed at the Swiss Spallation Neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland. Furthermore, this

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Diffusion of Cu in AlCu alloys of different composition by quasielastic neutron scattering

Abstract

Introduction

Section snippets

Theoretical background

Experimental

Results

Discussion

Conclusions

Acknowledgments

J. Non-Cryst. Solids

J. Non-Cryst. Solids

Mater. Sci. Eng. A

J. Non-Cryst. Solids

J. Non-Cryst. Solids

J. Phys.: Condens. Matter