Australia produces the largest amount of alumina because she has a large body of bauxite. Jamica, South Africa and some other countries also have a good reserve.

Alcan is an international company in Canada, that produces aluminum products, including aluminum foils. You might have used it to wrap your burgers. Alcan is associated with industries in Australia, Jamica, Brazil, UK, etc. Canada and the United States produces the most amount of aluminum from alumina imported from Austria, but North America does not have a lot of viable alumina mines.

Aluminum oxides often coexist with silicates. Natural aluminum oxide minerals include

Corundum

The structure of corundum can be viewed as a hexagonal close packed array of oxygen atoms with ²/₃ of the octahedral sites occupied by Al³⁺ ions. Thus, the Al³⁺ ions are bonded to 6 oxygen in a distorted octahedron. Each such octahedron share a face with one on the upper and one on the lower layers. The distortion is caused by repulsion between Al³⁺ ions in octahedra sharing the faces.

Corundum is a dense (specific gravity of 3.97), hard (9 on the Mohs' scale, next only to diamond), high melting (melting point 2288 K), and insoluble in water. Crystals of corundum are usually prismatic or barrel-shaped bounded by steep pyramids. A massive grey granular corundum powder is called emery.

Colored corundum are called ruby (deep red due to presence of Cr³⁺ ions) and sapphire (blue, pink, yellow or green due to various degrees of Fe^{2+ or 3+}, and Ti⁴⁺). The color may be modified by heating or irradiation. Some ruby crystals are shown here exposed in a piece of bauxite ore.

Grey corundum or emery are used as abrasive, for example, emery paper (sand paper) and ruby and sapphire are for gemstones. They do have technical applications. For example, the first LASER was produced using a ruby crystal.

The picture shown here are ruby balls of various size ranging from 0.5 to 6 mm. The picture is from High Precision Components for industrial applications in Ceramics, Ruby, Sapphire, and Tungstencarbide, and they are commercial products. This link shows some interesting applications of alumina related materials.

Australia produces about $3 billion worth of alumina a year from six Australian refineries. These refineries use the Bayer Process to extract aluminum hydroxide from the bauxite using hot caustic liquor. Aluminum oxide, Al₂O₃, is a typical amphoteric oxide, which dissolves in a strong acid and a strong base.

The hydroxide ions of gibbsite form two layrs similar to layers of closest packed spheres with Al³⁺ ions filling in some of the octahedral sites. The crystal structure of gibbsite consists of stacked double layers. It is expected that the hydroxide ions form extensive intra- and inter-layer hydrogen bonds.

Further dehydration converts Al(OH)₃ into diaspore and boehmite, both of which have the stoichiometry AlO(OH). Gibbsite is is converted to alumina, Al₂O₃ by calcination. Alumina is marketed as the feed stock to smelters for the production of aluminium metal, ceramics, catalyst supports and other applications.

Jamica also produces alumina by the Bayer process. This Jamica link describes this process very well, including flow chart of operation. For those who are interested in the mining, chemistry, and economics of alumina production, the Australia companies also have nice web sites to describe their operations.

Aluminas are basic materials for ceramics, and they are useful for lining containers and mass transferring pipes, especially if heat resistance is required. Intricate tools such as the 95 % alumina ceramic rotor for 20 cm rotary valve have been made of these materials.

Ceramics are related to many technologies. A list of resources related to ceramics gives many companies, whose main products are made of ceramic materials. For example, aluminas are used for paint, ink, coating and filling paper, adhesives, rubber, pharmaceuticals, tiles, bricks, cooking utilities, table wares, electronic components, porcelain, pottery, dental restoration, and plastics.

Technological changes demand materials with new specific properties. Since changes take place all the time, new materials are also developed all the time. Additions of specific amounts of other oxides to aluminas produce composite materials whose properties differ from both parent materials. This type of blending is a new frontier of material engineering. This type of research is carried out in companies such as Precision Engineered Ceramics, The KEIR Manufacturing, Inc., and Intertec Southwest LLC.

Another important fact is that Al²⁺ ions will not form, and the aluminum oxide is an inert substance.

Solution
The question requires the densities of aluminum and aluminum oxides. The CRC Handbook give their densities as 2.702 and 3.97 g/cc respectively. Thus, molar volumes of Al and aluminum oxides are

Discussion
By applying the Pilling and Bedworth model, aluminum oxide formed has a larger molar volume per Al than the metal itself. Thus, the Pilling and Bedworth model also apply to aluminum and its oxide.

Furthermore, aluminum oxide and some hydrates have different densities,

Solution

Discussion