Quantitative Correlation between Electrical Resistivity and Microhardness of Cu-Ni-Mo Alloys via a Short-Range Order Cluster Model

Strength and electrical resistivity are coupled in metal alloys as both are based upon a similar microstructure mechanism, but the quantitative relationship between them is not known due to the complex microstructures involved. The present work analyzes the dependence of hardness and electrical resistivity on solute contents for ternary [Mo y /( y +12) Ni 12/( y +12) ] x Cu 100− x alloys (at.%), where x = 0.3–15.0 is the total solute content and y = 0.5–6.0 the ratio between Mo and Ni. The alloys are designed following the cluster-plus-glue-atom model to reach three distinct structural states, i.e., cluster solution state ( y = 1), where Mo is dissolved via a chemical short-range order characterized by Mo-centered and Ni-nearest-neighbored [Mo 1 -Ni 12 ] cluster, cluster solution state plus extra Ni solution ( y < 1), and a cluster solution state plus extra Mo in precipitation ( y > 1). The measured electrical resistivity and microhardness data are correlated with these three structural states to reveal the property dependencies on solute contents. The cluster solution enhances the strength, without causing much increase in the electrical resistivity, as the solutes are organized into cluster-type local atomic aggregates that decrease dislocation mobility more strongly than electron scattering. Analogous to residual resistivity ρ R , which indicates the change of resistivity with reference to pure Cu, residual microhardness H R and residual lattice constant a R are also defined. For the ideal cluster solution state ( y = 1, Mo/Ni = 1/12), the mentioned three parameters are correlated with the total solute content x by ρ R = 1.08· x (10 −8 Ω m), H R = 1.50· x (Kgf mm −2 ), and a R = − 1.08· x (10 −4 nm). From these, ρ R = 0.72 H R = − a R . Such simple relationships indicate that resistivity and strength are dependent on the same cluster-type solution mechanism and can be a good reference for evaluating strength and resistivity performance of Cu alloys.