Aluminum from clay
Kaolin clay is composed of aluminum and silicon (Si2Al2O5(OH)4). Reduction of Kaolin would then result in an aluminum/silicon alloy. In practice, carbides (usually SiC) resist further reduction except at very high temperatures (2050°C). Thus, the smelted product is likely some aluminum-rich alloy with various highly refractory simple and complex carbides.
Parent material is reduced carbothermically, that is, it is reduced in the presence of carbon and the absence of oxygen at high temperatures. The carbon is oxidized to produce carbon mon- and di-oxide and the metal oxides are reduced.
The paper carbothermal reduction of alumina by m.halmann (at) weizmann.ac.il describes the carbothermic reduction of alumina rich material in an atmosphere of methane gas at high temperatures. Internal copy of this paper: File:Halman.pdf
Such temperatures could be produced with a point focusing solar collector (see Metal Refining for more)
Page 66 in this online book talks about a plant in the Ukraine that smelts kaolin into an aluminum/silicon alloy: The Handbook of Aluminum by George E Totten, D Scott MacKenzie
At temperatures below 2000°C, I assume aluminum metal may be separated from silicon carbide (SiC).