Apple gold

Twitter user Sumocat got some blowback for this tweet:

@marco_org Apple has a patent that can reduce the gold content of their 18k gold by half.
Sumocat (@SumocatS) Mar 6 2015 1:58 PM

It’s inartfully put (140 characters is a bitch), but as a practical matter he’s correct. Apple’s patent application is for a method that allows them to make 18k gold that has, on a volume basis, less gold than regular 18k gold.

How can this be? It’s because Apple’s gold is a metal matrix composite, not a standard alloy. Instead of mixing the gold with silver, copper, or other metals to make it harder, Apple is mixing it with low-density ceramic particles. The ceramic makes Apple’s gold harder and more scratch-resistant—which Tim Cook touted during the September announcement—and it also makes it less dense overall.

The karat measure of gold is based on the mass fraction. One hundred grams of 18k gold has 75 grams of gold and 25 grams of other material. If that “other material” is a low-density ceramic, it takes up a bigger volume than if it’s a high-density metal. Because the casing of a watch is made to a particular size (i.e. volume), not to a particular weight, the Watch will have less gold in it than an 18k case made of a conventional alloy.

As an example, assume a conventional 18k gold alloy with 75% gold (19.3 g/cc), 15% silver (10.5 g/cc), and 10% copper (8.96 g/cc) by weight. The alloy will have a density of

[\frac{1}{\frac{0.75}{19.3} + \frac{0.15}{10.5} + \frac{0.10}{8.96}} = 15.6\;\mathrm{g/cc}]

A cubic centimeter of this alloy will contain

[0.75 \times 15.6 = 11.7\;\mathrm{g}]

of gold.

Now assume an 18k gold with 75% gold and 25% boron carbide by weight (that’s one of the ceramics mentioned in Apple’s patent). Boron carbide has a density of 2.52 g/cc, so a gold/boron carbide metal matrix composite would have a density of about

[\frac{1}{\frac{0.75}{19.3} + \frac{0.25}{2.52}} = 7.24\;\mathrm{g/cc}]

A cubic centimeter of this material will contain only

[0.75 \times 7.24 = 5.43\;\mathrm{g}]

of gold. Here, the gold takes up

[\frac{5.43\;\mathrm{g}}{19.3\;\mathrm{g/cc}} = 0.28\;\mathrm{cc}]

or 28% of the volume.

Table 1 of Apple’s patent gives other configurations and shows the gold savings.

Gold fraction table from Apple patent

Some of these numbers look flatly wrong to me. For example, changing from a baseline of 25.8 g of gold in a particular part to 12.1 g is not a savings of 43%, it’s a savings of 53%. Maybe I’m reading the table wrong.

In any event, the patent makes it clear that saving gold is one of the goals of the process. I suppose it’s not surprising that Tim didn’t make a big deal out of that in September.