On the Influence of B-Metals on the Elastic Modulus of Copper, Silver and Gold

Abstract

Using old and new measurements, the change of the elastic modulus of copper, silver and gold with the addition of B-metals of the Zn and Cd period is analyzed. It is shown that the elastic modulus E in general decreases with alloying. An exception is the addition of Cd and Mg to gold, which increases the elastic modulus. The modulus change ΔE depends on two terms, one being proportional to the concentration c, while the other is proportional to the product of the concentration and the square of the valency difference between the alloying element and the base metal ΔZ. Thus an empirical relationship of the form
ΔE=−βc−αc(ΔZ)² (1)
is obtained. β and α are constants. The value of β only depends on the base metal and the period, being the same for all metals of one period. α increases with the distance of the period from the base metal in the periodic table. Experiments on poly-and single crystals give the same results.
This empirically determined relationship is compared with the theories of the elastic modulus of pure noble metals and its change caused by solid solution alloying. A good agreement is obtained, if the measured values are corrected to the lattice parameter of the pure metal. Due to this correction, a third term is introduced into equation (1). This term is proportional to the product c·ΔZ. Thus the expression for the corrected modulus change ΔC′_R is given by
ΔC′_R=(Kβ₂−β₁)c+Kα₂cΔZ−α₁c(ΔZ)² (2)
where K, β₂ and α₂ are constants.
The influence of the lattice parameter change (1⁄a) (da⁄dc) on ΔE is further analyzed. It is shown that like many other properties of the noble metals da⁄dc also varies systematically with ΔZ on addition of B-metals. In this case the formal relationship is given by
(1⁄a)(da⁄dc)=β₂+α₂ΔZ. (3)
Because β₂ may be positive or negative depending on the system studied, the lattice parameter may increase or decrease with alloying. Therefore, the change of the lattice parameter cannot be used for a unique explanation of the change of the elastic modulus due to alloying.
Finally the functional dependency of the change of various properties Δp of noble metals due to alloying with B-metals is discussed. It is shown that depending on the property in question, Δp may depend linearly or quadratically on ΔZ, or on a combination of both. These basic formulas may further be complicated by a term, which depends on the concentration alone, or on the product of the concentration and valency difference.