Diffusion of manganese, chromium, and titanium in single crystalline copper

The diffusion of Mn, Cr, and Ti in single crystalline copper was investigated in the temperature range between 582 and 800 K, 639 and 829 It and 621 and 747 K, respectively. Ion beam sputtering in combination with secondary ion mass spectrometry (SIMS) was used to measure concentration depth profiles. The temperature dependence of the diffusion coefficients of Mn, Cr, and Ti in copper can be described by D-Mn = (0.43(-0.20)(+0.37)) x 10(-4) exp(-2.01 +/- 0.035 eV/kT) m(2) s(-1) D-Cr = (0.26(-0.06)(+0.09)) X 10(-4) exp (-1.99 +/- 0.02 eV/kT) m(2) s(-1) and D-Ti = (0.37(-0.03)(+1.60)) x 10(-4) exp (-1.99 +/- 0.10 eV/kT) m(2) s(-1) These results are compatible with earlier high temperature data. The combination of them with the present diffusion coefficients reveals a curvature in the corresponding Arrhenius plots, which is ascribed to the contribution of divacancies at higher temperature. The temperature dependence of the diffusion coefficients of Mn, Cr and Ti in copper can be described with the aid of the modified electrostatic model of impurity diffusion, assuming effective values for the charge difference between host atom and impurity.