Analytical Expressions for the Composition Dependence of Stacking Fault Energies and Probabilities in Binary Silver Systems

The following straight‐line relationship between the stacking‐fault probability α and alloying concentration has been obtained by fitting published data: $$\ln \mathrm{\alpha =}\ln {\alpha }_0{\mathrm{+K}}_{\alpha }\text{\hspace{0.17em}[C/(1+C)]}$$ . In this expression, C=X/X*, where X is the alloying concentration and X* is the solubility limit (both in atomic percent) at either the peritectic or the eutectic temperature, α₀ is the stacking‐fault probability for pure silver and K_α is an experimental constant. The value of α₀, obtained by extrapolation, is 3.13±0.14×10⁻³; K_α is usually within the range 6.2±0.5, but is lower in those binary systems alloyed with the hcp elements Mg, Zn, and Cd. Similarly, an analytical expression relating stacking‐fault energy γ and alloying concentration may be written as $$\ln \mathrm{\gamma =}\ln {\gamma }_0{\mathrm{+K}}_{\gamma }{\text{\hspace{0.17em}[C/(1+C)]}}^2$$ , where γ₀ is the stacking‐fault energy of silver. The value of K_γ for the Ag–Sn, Ag–In, and Ag–Al systems ranges from −10.0 to −10.5, but is −6.5 in the Ag–Zn system. The relationship between α and γ is discussed on the basis of these equations.