Abstract
We demonstrate that a hardening rule exists in cubic solid solutions with various combinations of ionic, covalent and metallic bonding. It is revealed that the hardening stress ∆τFcg is determined by three factors: shear modulus G, the volume fraction of solute atoms fv, and the size misfit degree δb. A simple hardening correlation in KCl-KBr solid-solution is proposed as ∆τFcg = 0.27 G. It is applied to calculate the hardening behavior of the Ag-Au, KCl-KBr, InP-GaP, TiN-TiC, HfN-HfC, TiC-NbC and ZrC-NbC solid-solution systems. The composition dependence of hardness is elucidated quantitatively. The BN-BP solid-solution system is quantitatively predicted. We find a hardening plateau region around the x = 0.55–0.85 in BNxP1−x, where BNxP1−x solid solutions are far harder than cubic BN. Because the prediction is quantitative, it sets the stage for a broad range of applications.
Highlights
We find a hardening plateau region around the x = 0.55–0.85 in BNxP1−x, where BNxP1−x solid solutions are far harder than cubic BN
According to Fleischer’s continuum elasticity scheme[1], when solute and solvent atoms in solid solutions differ in size, local stress fields are formed on a slip plane, and these stress fields interact with those of the dislocations, impeding their motion
Where τcg is the stress required for slip by the movement of lattice planes past one another in the glide region, Θ(ψ, φ) is the orientation factor of a glide plane, φis the angle between a glide-plane spacing vector and the section of indenter along the short edge, and ψis the angle between the projection of a glide-plane spacing vector on the section of indenter along the short edge and the short edge of the indenter, φis the angle between the facet and the crystal surface, Λf is a constant, Nbg is the bond electron density in the glide region, fc is covalency, d is bond length
Summary
We demonstrate that a hardening rule exists in cubic solid solutions with various combinations of ionic, covalent and metallic bonding. Because hardness is the resistance to localized fracture or permanent plastic deformation, it relies strongly on the motion of dislocations in addition to atom bonding[1,5] Both dislocations and solid solutions represent great challenges for the current first-principles calculations. Hugosson et al.[19] proposed a mechanism to enhance hardness in multilayer transition metal carbide/nitride coatings Such type of hardening is attributed to a large number of different glide-systems suppressing the propagation of dislocations, which is consistent with the theory of hardness[10]. The C and N atoms locate in the octahedral holes Their bonding is a combined covalent-metallic-ionic type of chemical bond, which is far more complex than that of alkali halides, Au-Ag and InP-GaP solid solutions. The successful application of this method would contribute to the continuing search for novel hard solid solutions for industrial applications
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