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The history of magnesium cements goes back millenia, magnesium phosphate cements made from animal faeces or fermented plant material and magnesia were used in the great wall and in many early buildings around the world. It is also likely that magnesium sulfate or chloride type cements were used before their western invention by Stanislaus Sorel .
The oldest cement are probably magnesium phosphate type wherein insoluble magnesium phosphates are formed from a mixture of a soluble phosphate and magnesium oxide. The early magnesium cements were made with soluble phosphate from animal faeces or fermented plants and magnesia and optionally clays. "These natural cements bind naturally and exceptionally well to all things cellulose (i.e. plant fibers, wood chip, etc.) and are often referred to as “living cements.” This is in sharp contrast to Portland cement, which repels cellulose......Blends of magnesium oxide were used in ancient times in Germany, France, Mexico and Latin America, Switzerland, India, China and New Zealand, among other countries. The Great Wall of China and many of the Stupas in India, still standing today, were all made with magnesium-based cements. Ancient European artisans used a timber frame with magnesium oxide infill in constructing homes. No gaps are visible in these 800 - year - old walls that still remain in use." 
Magnesia reacts with soluble phosphates to precipitate almost totally insoluble magnesium phosphate.
MgO + H2O = Mg(OH)2
3Mg(OH)2 + 2H3PO4 = Mg3((PO)4)2 + 6H2O
If a cheap source of potassium hydrogen phosphate  the active chemical in dung could be found then magnesium phosphate cements could make a valuable contribution to reducing global warming and improving building biology from the point of view of occupant health .
A range of magnesium phosphate cements has been used including magnesium ammonium phosphate which is thought to be formed by an acid-base reaction between magnesia and di hydrogen ammonium phosphate. This results in an initial gel formation followed by crystallisation into an insoluble phosphate, mainly magnesium ammonium phosphate hexahydrate, [NH4MgPO4.6H2O]. The magnesium oxide used in this system is produced by calcining at higher temperatures and is referred to in the industry as being “dead burned” and is not as reactive as magnesia made at lower temperatures. A set retarder, typically either borax or boric acid is also used to give a workable set time.
Magnesium phosphate cements develop considerably greater compressive and tensile strengths compared to Portland cement, and given they could take less energy to produce it is a wonder why they are not more commonly used these days. The promotion and proliferation of Portland cement occurred when energy was cheap and health concerns of the public were simply not an issue.
Another advantage of Magnesium-based cements are that they have a natural affinity for cellulose materials, such as plant fibers or wood chips; Portland cement repels cellulose. So you can actually use wood chips as an aggregate to achieve lighter weight and more insulative products. Magnesium oxide when combined with clay and cellulose creates cements that breathe water vapor; they never rot because they always expel moisture. MgO cements do not conduct electricity, nor heat and cold, and have been used for flooring for radar stations and hospital operating rooms.
MgO + NH4H2PO4 + 5H2O = NH4MgPO4.6H2O
This class of binder has unfortunately been replaced by Portland cement type hydraulic cements and one has to question why.
If a salt such as magnesium chloride or sulfate is added to reactive magnesia and the mixture is allowed to react and hydrate magnesium oxy chlorides and magnesium oxy sulfates are formed that can be very strong but are not sufficiently weatherproof and are corrosive. Although there are many patents describing improvements to overcome these deficiencies such as the use of phosphates or soluble silicates, they are not generally economic.
Magnesium oxy chlorides were first discovered in the west by Stanislaus Sorel in 1867. Magnesium oxy sulfates were discovered by Olmer and Delyon in 1934 .
Magnesium oxy chlorides and oxy sulfates are commonly referred to as Sorel cements. A number of compounds are formed when magnesia reacts with magnesium chloride to form oxy chlorides The main bonding phases so far found in hardened cement pastes are Mg(OH)2, (Mg(OH)2)3 .MgCl2 .8H2O and (Mg(OH)2)5.MgCl2.8H2O. (Mg(OH)2)5.MgCl2.8H2O has superior mechanical properties and is formed using a molar ratio of MgO:MgCl2:H2O = 5:1:13
MgCl2 + 5MgO + 13H2O = (Mg(OH)2)5.MgCl2.8H2O
If magnesium sulfate is used instead four oxy sulfate phases are considered to form at temperatures between 30 and 120oC; (Mg(OH)2)5.MgSO4.3H2O,(Mg(OH)2)3.MgSO4.8H2O, Mg(OH)2.MgSO4.5H2O, and Mg(OH)2.2MgSO4.3H2O. Only (Mg(OH)2)3.MgSO4.8H2O is stable below 35 deg C.
3MgO + MgSO4 +11H2O = (Mg(OH)2)3.MgSO4.8H2O
Zinc, calcium, copper and other elements also form similar compounds.
Magnesium oxy chlorides achieve higher compressive strengths than magnesium oxy sulfates The main problem with Sorel cements is that both magnesium oxy chlorides and magnesium oxy sulfates tend to break down in water and particularly in acids. Corrosion of steel reinforcing also occurs.
The use of soluble silicates such as sodium silicate has been described as a means of improving the water resistance of Sorel type cements. These cements are of little practical use however because of the high cost of soluble silicates.
The use of phosphates has also been advocated as a means of improving the water resistance of Sorel type cements. Such cements, although described in the literature, are expensive due to the shortage of economic deposits of phosphate and as a result widespread use is limited.
Generally a blend of magnesium oxysulfates and chlorides are considered the most waterproof.
High-lime magnesiochrome cement finds use in refractories. The cement is based upon magnesia plus calcium chromate - chromite, a complex mineral produced by the combination of lime with chrome oxide (Cr2O3) in an oxidising environment. Hydration is normally performed with a 30% aqueous solution of magnesium chloride hexahydrate (MgCl2.6H2O) solution at 8 per cent by weight of the cement. The products are complex. As well as hydrates they also consist of carbonates, which are formed by the effects of carbonation. Typical products formed can include brucite [Mg(OH)2], various magnesium oxy chlorides [(Mg(OH)2)X.MgCl2.YH2O.] calcium chromate dihydrate (CaCrO4.2H2O), calcium monochromite (CaCr2O4) portlandite [Ca(OH)2], secondary magnesium carbonate (MgCO3), secondary calcium carbonate (CaCO3) and mixed calcium magnesium carbonates [(Ca,Mg)CO3].
Other known cementitious magnesia compounds include hydroxychlorides and sulfates such as Mg(OH)2.MgCl2.8H2O, hydroxy carbonates [Mg5(OH)2(CO3)4.4H2O] and hydroxy chloro carbonates [e.g. Mg2OHClCO3.3H2O] as well as hydro magnesite and magnesite. Hydroxy chloro carbonates and sulfates are also formed as a result of atmospheric carbonation of magnesium oxy chloride and magnesium oxy sulphate, and these often ultimately revert to magnesite and hydromagnesite.
Brucite [Mg(OH)2] alone has not found much commercial use as a cement previously mainly because the setting rate is too slow. TecEco have used brucite to replace Portlandite in modern cements. In permeable substrates carbonation to nesquehonite occurs. 
 Swanson, George. Building Biology Based New Building Protocol. Magnesium Oxide, Magnesium Chloride, and Phosphate-based Cements. Note that George's evidence is hearsay but most likely as what he says is widely known.
 MKP, Monobasic potassium phosphate or monopotassium phosphate; KH2PO4
 Various sources including Shand, M. A. (2006). The Chemistry and Technology of Magnesia, Wiley Interscience and Hewlett, P. C. (1956). Lea's Chemistry of Cement and Concrete. London, Sydney, Auckland, Arnold.