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Onset of local ordering in some copper-based alloys: critical solute concentration vis-a-vis various solutionhardening parameters

The mode of planar distribution of solute atoms in Cu single crystals alloyed with 0.5 to 8.0 at.%Ge has been investigated via the temperature dependence of the critical resolved shear stress of these alloys. It is found that there exists a critical solute concentration cm ≈ 5 at.%Ge below which the distribution of solute atoms in the crystal is random, and above which some local ordering occurs. This together with such data available in the literature for Cu-Zn, Cu-Al and Cu-Mn alloys, i.e. cm ≈7 at. %Zn, 7 at.%Al and 1 at.%Mn, when examined as a function of the size-misfit factor δ = (1/b)(db/dc)of a given binary alloy system, shows that the value of cm strongly depends on δ; the smaller the magnitude of δ, the greater the value of cm and vice versa. Also, the value of cm is found to correlate well with the electron-to-atom ratio (e/a)of the Cu-Zn, Cu-Al, Cu-Ge and Cu-Mn alloys with the solute concentration c = cm. However, no systematic correlation exists between the critical solute concentration cm for the onset of local ordering and the modulus-mismatch parameter η = (1/G)(dG/dc).