Question

Calculate the alloy density, rave, for a 75 wt% Au, 25 wt% Ag alloy known as �18k Gold�. Report your answer in g/cm3. How does this value compare to a standard rule of mixtures calculation? Would this be an interstitial or substitutional alloy?

Answer 1

Atomic radius of Gold is 174 pm and atomic radius of silver is 165 pm. The difference is less than 15%. So 18k Gold is a substitutional alloy.

Density of Au (D_Au) = 19.32 g/cm³

Density of Ag (D_Ag) = 10.49 g/cm³

D_mix = (M_Au + M_Ag)/ (V_Au + V_Ag)

1/D_mix = 1/ (M_Au+ M_Ag)*(M_Au/D_Au + M_Ag/D_Ag) = X_Au/D_Au + X_Ag/D_Ag, where X is weight %

1/D_mix = 0.75/19.32 + 0.25/10.49 = 0.063

D_mix = 15.96 g/cm³

In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material. By standard rule of mixtures calculation:

D_mix = X_Au*D_Au + X_Ag*D_Ag

= 0.75*19.32 + 0.25*10.49 = 17.11 g/cm³

There is 7.2% deviation from actual value.