at room temperature which transforms to n-type conductivity (charge is carried by electrons) between 550 °C and 650 °C, depending on the oxygen partial pressure. The conductivity in the β, γ and δ-phases is predominantly ionic with oxide ions being the main charge carrier. Of these δ- has the highest reported conductivity. At 750 °C the conductivity of δ- is typically about 1 S cm−1, about three orders of magnitude greater than the intermediate phases and four orders greater than the monoclinic phase. δ- has a defective fluorite-type crystal structure in which two of the eight oxygen sites in the unit cell are vacant. These intrinsic vacancies are highly mobile due to the high polarisability of the cation sub-lattice with the 6s2 lone pair electrons of . The Bi–O bonds have covalent bond character and are therefore weaker than purely ionic bonds, so the oxygen ions can jump into vacancies more freely. The arrangement of oxygen atoms within the unit cell of δ- has been the subject of much debate in the past. Three different models have been proposed. Sillén (1937) used powder X-ray diffraction on quenched samples and reported the structure of was a simple cubic phase with oxygen vacancies ordered along <111>, the cube body diagonal. Gattow and Schroder (1962) rejected this model, preferring to describe each oxygen site (8c site) in the unit cell as having 75% occupancy. In other words, the six oxygen atoms are randomly distributed over the eight possible oxygen sites in the unit cell. Currently, most experts seem to favour the latter description as a completely disordered oxygen sub-lattice accounts for the high conductivity in a better way. Willis (1965) used neutron diffraction to study the fluorite () system. He determined that it could not be described by the ideal fluorite crystal structure, rather, the fluorine atoms were displaced from regular 8c positions towards the centres of the interstitial positions. Shuk et al. (1996) and Sammes et al. (1999) suggest that because of the high degree of disorder in δ-, the Willis model could also be used to describe its structure. Use in solid-oxide fuel cells (SOFCs) Interest has centred on δ- as it is principally an ionic conductor. In addition to electrical properties, thermal expansion properties are very important when considering possible applications for solid electrolytes. High thermal expansion coefficients represent large dimensional variations under heating and cooling, which would limit the