Search for: All records

A systematic analysis was performed on Manning’s vacancy wind factor for diffusion in 13 binary solid solutions for which experimentally measured tracer diffusion coefficient data collected from the literature are reliable and comprehensive. Some straightforward yet interesting observations are reported, including a value of ~ 1.85 for the diamond cubic Ge-Si binary solid solution. It is recommended that the vacancy wind factor not be included in the CALPHAD diffusion coefficient (mobility) assessments since the effects have essentially been included in the fitting parameters. For those who use diffusion coefficients directly (not mobility parameters), the factor may still be ignored for both fcc and bcc solid solutions since the maximum effect is only a 28% and 38% increase in the interdiffusion (chemical diffusion) coefficients, respectively. The factor may be included for low diffusion coefficient systems of diamond cubic phases at low temperatures and especially for those systems whose tracer diffusion coefficients differ by orders of magnitude. 

While anomalous diffusion coefficients with non-Arrhenius-like temperature dependence are observed in a number of metals, a conclusive comprehensive framework of explanation has not been brought forward to date. Here, we use first-principles calculations based on density functional theory to calculate self-diffusion coefficients in the bcc metals Mo and β-Ti by coupling quasiharmonic transition state theory and large-displacement phonon calculations and show that anharmonicity from thermal expansion is the major reason for the anomalous temperature dependence. We use a modified Debye approach to quantify the thermal expansion over the entire temperature range and introduce a method to relax the vacancy structure in a mechanically unstable crystal such as β-Ti. The effect of thermal expansion is found to be crucial for the nonlinear, non-Arrhenius “anomalous” self-diffusion in both bcc systems, with β-Ti showing a 60% larger relative nonlinearity parameter than Mo. Our results point to temperature dependence in the diffusion prefactor from thermal expansion as the major origin of anomalous self-diffusion. The methodology proposed for β-Ti is general and simple enough to be applicable to other mechanically unstable crystals. 

The diffusion behavior and phase equilibria in the Cu-Zn binary system were investigated using solid-solid and solid-liquid diffusion couples. Heat treatments at temperatures ranging from 100 to 750 °C were performed and the samples were examined using optical microscopy, energy dispersive x-ray spectroscopy, and electron probe microanalysis to identify the phases and to obtain composition profiles. Solubility limits of both solid solution and intermetallic phases were then evaluated, and a forward-simulation analysis (FSA) was applied to extract interdiffusion coefficients. The composition profiles from Hoxha et al. were also re-analyzed using FSA to obtain more reliable diffusion coefficient data without the assumption of constant diffusion coefficients for the intermetallic phases. A comprehensive assessment of the interdiffusion coefficients in three intermetallic phases of the Cu-Zn system was performed based on the results from the current study as well as those in the literature. Activation energies and Arrhenius pre-factors were evaluated for each phase as a function of composition. The fitted equations based on the comprehensive assessment have the capabilities of computing the interdiffusion coefficients of each of the phase at a given composition and temperature. Suggested modifications to the Cu-Zn binary phase diagram were presented based on the new experimental information gathered from the present study. A clear explanation is provided for the puzzling low Zn concentrations often observed in the Cu-rich fcc phase of Cu-Zn diffusion couples in comparison with the expected high solubility values based on the equilibrium Cu-Zn phase diagram.