Refractories can be classified according to their chemical compositions. They can also be classified according to the method of installation. The large refractory manufacturers tend to organise their websites in terms of applications.

Chemical classification

Alumina 

aluminosilicates

silicates

silica

silicon carbide

Doloma

Calcia

Magnesia 

Chrome magnesia

Chromia 

Zirconia 

Carbon

ALUMINA 

Alumina is aluminium oxide, Al2O3. The mineral name is corundum. The        name is alpha alumina. 

Raw materials:

Corundum is found naturally and in the Northern Cape there was a deposit called Pella sillimanite corundum. It consisted of big boulders buried in the sand. It was too hard to crush and had to be calcined to 1300 degrees to make it brittle.  It didn't make great bricks because it was just too difficult to sinter. The main source of pure alumina is tabular alumina, a synthetic product. Tabular alumina is a porous compound of tabular shaped crystals of alumina. It has good thermal shock resistance.  White fused alumina is the dense form of alumina. Brown fused alumina is bauxite that has been fused. Other variants are made for the abrasive industry.  Bubble alumina is hollow spheres of alumina.  Calcined aluminas are fine powders of alumina. Reactive aluminas are easily sinterable calcined aluminas. Aluminium hydroxide is also used, also known as alumina trihydrate. Cell grade alumina is purified bauxite mainly used as feedstock for aluminium manufacture. Chrome alumina is a by- product; a slag from the thermit reaction to make chrome metal.  Calcium aluminate is a hydraulic binder for castables, and can be bought as a foamed aggregate. 

The melting point of pure alumina is 1713C.  It is free from most of the drawbacks of other oxides. It does not hydrate, has no inversions, no toxicity and no harmful reactions. It is hard; 9 on the Moh scale. 

ALUMINOSILICATES 

Al2O3.SiO2 is the composition of andalusite, kyanite and sillimanite. They are all metamorphic minerals formed under different conditions. Fired to high temperatures they all convert to mullite.  Then there is Chamotte, which is calcined flint clay. It occurs occasionally naturally next to coal seams which have burned out underground.

Clay's are natural aluminosilicates with layers of alternating alumina and silica, with water and ions between layers. They impart plasticity to refractories and are excellent binders. There are many different crystal types, such as kaolinite, illite, sericite, palygorskite, attapulgite, sepiolite, smectite, pyrophyllite, montmorillonite, etc.  Commercially they are called kaolin, ball clay, flint clay, Wonderstone, bentonite, fireclay, veegum,          . Yes, it gets quite confusing.

SILICATES 

Wollastonite is a calcium silicate, used mainly for its long crystals which act as reinforcing.

Zircon is zirconium silicate, ZrOSiO2. It is very dense, very resistant to fluxes, and has very high electrical resistance. It is a by-product of titanium mining in heavy sand beach deposits.

SILICA

Silica, SiO2, is the commonest oxide on Earth. The main form of silica is quartz. Quartz is the main component of sand. 

It is quite hard and abrasive. It has excellent acid resistance. It is only dissolved by hydrofluoric acid.  "Quartz tubes" are made of fused silica.