Question

# Calculate the alloy density, rave, for a 75 wt% Au, 25 wt% Ag alloy known as...

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?

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 (DAu) = 19.32 g/cm3

Density of Ag (DAg) = 10.49 g/cm3

Dmix = (MAu + MAg)/ (VAu + VAg)

1/Dmix = 1/ (MAu+ MAg)*(MAu/DAu + MAg/DAg) = XAu/DAu + XAg/DAg, where X is weight %

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

Dmix = 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:

Dmix = XAu*DAu + XAg*DAg

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

There is 7.2% deviation from actual value.

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