Alloy

An alloy is a combination of metals or of metals and other elements.

Examples

Crown gold

A 22 karat (kt) (916 ²⁄₃ fine) gold alloy used for English & UK gold coins from 1526 (Henry VIII) to 1914 (as currency), and since then for trade and bullion coins. (‌²²⁄₂₄ gold, ‌²⁄₂₄ copper)

𝜌 = 17.61 g/㎝³

“standard gold” (US)

A 900 fine gold alloy used for US coins. (90% gold, ≤5% silver, 5-10% copper)

𝜌 = 17.43±.12 g/㎝³

Britannia silver

An 11 ℥ 10 ʤ (958 fine) silver alloy required in England for “wrought plate” (non-monetary silversmithing) from 1697–1720 to inhibit coin clipping and melting. (‌²³⁄₂₄ silver, ‌¹⁄₂₄ copper)

𝜌 = 10.42 g/㎝³

Sterling silver

An 11 ℥ 2 ¹⁄₄ ʤ (926 fine) fine silver alloy used for English & UK silver coins from before 1158 (Henry II) to 1919. (92.6% silver, 7.4% copper)

𝜌 = 10.37 g/㎝³

“standard silver” (US)

A 900 fine silver alloy used for US coins from ____ to 1964. (90% silver, 10% copper)

𝜌 = 10.32 g/㎝³

Density

ᴍ = material constituent

𝜌 = density (i.e. g/㎝³)

𝐴ᵣ = atomic weight

𝑤 = mass fraction (i.e. ‌⁹⁄₁₀, .900 or 90%)

𝑎𝑡٪ = atomic percent

Alloy (general)

𝜌Alloy	=	1
		𝑤ᴍ₁ 𝜌ᴍ₁ + 𝑤ᴍ₂ 𝜌ᴍ₂ + 𝑤ᴍ₃ 𝜌ᴍ₃ + ⋯

Au-Ag

𝜌_Au-Ag = 𝜌Au 𝑤Au + 𝜌Ag 𝑤Ag − 4 exp(0.005 𝑤Au) 𝑤Au 𝑤Ag

Au-Cu

𝜌_Au-Cu = 𝜌Au 𝑤Au + 𝜌Cu 𝑤Cu − 5 exp(0.01 𝑤Au) 𝑤Au 𝑤Cu

Ag-Cu

𝜌_Ag-Cu = 𝜌Ag 𝑤Ag + 𝜌Cu 𝑤Cu − 0.12 exp(0.02 𝑤Cu) 𝑤Ag 𝑤Cu

Au-Ag-Cu

𝜌_Au-Ag-Cu = 1.004 𝑎𝑡٪Au 𝜌Au + 1.03 𝑎𝑡٪Ag 𝜌Ag + 0.096 𝑎𝑡٪Cu 𝜌Cu + x − y

x = 0.35 ( cos(45+0.45 𝑎𝑡٪Au) + cos(45+0.45 𝑎𝑡٪Ag) + sin(𝑎𝑡٪Au) )

y = 0.005 (𝑎𝑡٪Au+𝑎𝑡٪Ag) cos(0.9 𝑎𝑡٪Cu) + 0.2 cos(3.2 𝑎𝑡٪Cu)

𝑎𝑡٪ᴍ₁	=	𝑤ᴍ₁ 𝐴ᵣᴍ₁
		𝑤ᴍ₁ 𝐴ᵣᴍ₁ + 𝑤ᴍ₂ 𝐴ᵣᴍ₂ + 𝑤ᴍ₃ 𝐴ᵣᴍ₃ + ⋯

References

• Kraut, J.C.; Stern, W.B. (June 2000) “The Density of Gold-Silver-Copper Alloys and its Calculation from the Chemical Composition”. Gold Bulletin, Vol. 33, Iss. 2, pp. 52–55. Springer-Verlag. doi:https://doi.org/10.1007/BF03216580.