performance of an electrolyte. The transition from the high-temperature δ- to the intermediate β- is accompanied by a large volume change and consequently, a deterioration of the mechanical properties of the material. This, combined with the very narrow stability range of the δ-phase (727–824 °C), has led to studies on its stabilization to room temperature. easily forms solid solutions with many other metal oxides. These doped systems exhibit a complex array of structures and properties dependent on the type of dopant, the dopant concentration and the thermal history of the sample. The most widely studied systems are those involving rare earth metal oxides, , including yttria, . Rare earth metal cations are generally very stable, have similar chemical properties to one another and are similar in size to , which has a radius of 1.03 Å, making them all excellent dopants. Furthermore, their ionic radii decrease fairly uniformly from (1.032 Å), through (0.983 Å), (0.938 Å), (0.912 Å) and (0.89 Å), to (0.861 Å) (known as the "lanthanide contraction"), making them useful to study the effect of dopant size on the stability of the phases. has also been used as sintering additive in the -doped zirconia system for intermediate temperature SOFC. Preparation The trioxide can be prepared by ignition of bismuth hydroxide. Bismuth trioxide can be also obtained by heating bismuth subcarbonate at approximately 400 °C. Reactions Atmospheric carbon dioxide or dissolved in water readily reacts with to generate bismuth subcarbonate. Bismuth oxide is considered a basic oxide, which explains the high reactivity with . However, when acidic cations such as Si(IV) are introduced within the structure of the bismuth oxide, the reaction with do not occur. Bismuth(III) oxide reacts with a mixture of concentrated aqueous sodium hydroxide and bromine or aqueous potassium hydroxide and bromine to form sodium bismuthate or potassium bismuthate, respectively. Usage Medical devices Bismuth oxide is occasionally used in dental materials to make them more opaque to X-rays than the surrounding tooth structure. In particular, bismuth (III) oxide has been used in hydraulic silicate cements (HSC), originally in "MTA" (a trade name, standing for the chemically-meaningless "mineral trioxide aggregate") from 10 to 20% by mass with a mixture of mainly di- and tri-calcium silicate powders. Such HSC is used for dental treatments such as: apicoectomy, apexification, pulp capping, pulpotomy, pulp regeneration, internal repair of iatrogenic perforations, repair of resorption perforations, root canal sealing and obturation. MTA