Hectorite - (Mg,Li)3 Si4O10 (OH)2 Na0.3 (H2O)4 is lithium magnesium sodium montmorillonite (bentonite is largely sodium calcium magnesium montmorillonite). Typically hectorite contains much less iron and titanium than bentonite and contains almost no alumina (being essentally a hydrated silicate). In addition it is very high in magnesia compared to other clays.
While 1-2% iron content in regular bentonite has minimal effect on fired whiteness, tiny amounts of titanium do affect translucency, making otherwise white ware look grey. This is attributed to fibrous rutile crystals in the porcelain matrix. In addition, titanium can react with any iron present to produce Fe/Ti spinel which is intensely black in colour.
The purest kaolins are also the least plastic, plastic ball clays are high in Fe/Ti. This makes hectorite an interesting material for the best white porcelain.
Analysis from Handbook of Mineralogy, 2001.
Clays that are not kaolins, ball clays or bentonites. For example, stoneware clays are mixtures of all of the above plus quartz, feldspar, mica and other minerals. There are also many clays that have high plasticity like bentonite but are much different mineralogically.
Formulating a Porcelain
The principles behind formulating a porcelain are quite simple. You just need to know the purpose of each material, a starting recipe and a testing regimen.