In reviewing my "back of the envelope" calculations, there may be a subtle error, and the loss of aluminum to oxidation of a 40nm sphere may be "only" 25% or so. I'll leave it as a classroom exercise to detect the possible error. But the fact remains, that as one goes more and more "nano", oxidation losses become more severe.
Let's see.
The volume of a sphere is 4/3 Pi r
3 = 4/3 Pi d
3/8 = 1/6 Pi d
3
With r, the radius, being half the diameter, d.
A sphere of diameter 40 nm thus has a volume of 33,493.33 nm
3
If the top 5nm are oxidized, the radius of the inner, elemental sphere is less by 5 nm, and its diameter by 10 nm, so the diameter is 30 nm, and the volume 14,130 nm
3, that's 42.2% of the 40 nm sphere. The remainder, 57.8% (by volume
*), is then inert oxide.
For a 40,000 nm sphere with a 5 nm oxide layer, the elemental proportion is 39,990
3/40,000
3 = 99,925 %; conversely, oxide is only 0,075 of such a micro-sphere.
*) ETA: aluminium has a density of 2.70 g/cm
3, alumina approx. 4.0 g/cm
3. Let 1 cm
3 worth of 40-nm-sized Al-spheres consist of Al and Al-oxide in the volume proportions given above, then this sphere has a mass of 2.7g*42.2% + 4.0g*57.8% = 3,4514 g: 1,1394 g Al (33%), 2,312 g Al
2O
3 (67%). Such Al nanospheres of 40 nm diameter have only one-third actual aluminum b weight!
Al
2O
3 is 53% by weight Al and 47% by weight O, so elemental composition of the spheres by weight is 31.5% O, 68.5% Al, and slightly less than half (48%) of the Al is elemental.