There have been a large number of studies of electrical conductivity of alumina, with widely different values being reported. Papers before 1961 are listed in  and those from 1961 to 1992 in .
Anyone interested in the electrical conductivity of alumina should read carefully the papers of Will et al. . These authors measured the electrical conductivity of highly pure and dry sapphire from 400°C to 1,300°C; the elemental analysis of their sapphire samples is given in Table 17, and showed less than 35 ppm total impurities. Particularly significant is the low level of alkali metal impurities, which often provide ionic conduction in oxides.
The measurements in  were made with niobium foil electrodes with a guard ring configuration on disc samples, and in a vacuum of 10-7-10-8 Torr. A nonsteady-state voltage sweep technique was used for the measurements. The results are in Table 18 and Fig. 3 for conductivity along the x-axis. Between 700°C and 1,300°C, the activation energy was about 460 kJ mol-1 (4.8 eV) and between 400 and 700°C it was 39 kJ mol-1 (0.4 eV). The great care taken with these measurements and the high purity of the sapphire make them definitive for the electrical conductivity for pure, dry alumina.
Table 17 Chemical analysis of sapphire for electrical conductivity measurements, from 
Table 18 Electrical conductivity of pure, dry sapphire
After 650 h electrolysis at 1,200°C, the conductivity remained constant, showing it was electronic and nonionic . The authors  interpreted their results in terms of electrical conductivity of a wide-band semiconductor. The high-temperature portion resulted from intrinsic conductivity with equal numbers of holes and electrons as carriers; twice the activation energy gives the band gap of about 920 kJ mol-1, or 9.6 eV, which is close to the band gap of 8.8 eV calculated from the optical absorption edge in the ultra-violet spectral range (see Sect. 9.2 on optical absorption). The low activation energy portion at low temperatures was attributed to extrinsic electronic conductivity from ionization of impurities. The authors suggested that silicon as a donor atom was the most likely impurity resulting in the low temperature conductivity. The interpretation of extrinsic conduction in the low activation range agrees well with the results of several other studies of the electrical conductivity of alumina [35-38], which showed close to the same conductivity and activation energy at high temperatures, but a transition to the low activation energy regime at higher temperatures than 700°C, presumably because of more impurities in the samples in those studies.
The electrical conductivity of alumina parallel to the c-axis was found to be a factor of 3.3 higher than perpendicular to this axis .
Of special interest are some experimental results for the conductivity at temperatures from about 1,800°C to near the melting temperature of 2,054°C of alumina , which fall very close to an extrapolation of the data from  up to 1,300°C, with the same activation energy. Thus the intrinsic electrical conductivity s in/ohm cm from 700°C to the melting point follows the equation:
log s = 7.92 – 24,200 / T (9)
where T is in Kelvin.
TEMPERATURE [ °C]
1300120011001000 900 800 700 600 500 400
Fig. 3 The electrical conductivity of pure, dry sapphire along the c-axis. Points, measured values. From 
The electrolysis experiments of Ramirez et al.  show that when alumina contains some water (OH groups), the electrical conductivity results from the transport of hydrogen ions (actually hydronium ions, H3O+; see  for discussion).
The diffusion coefficient of H3O+ ions at 1,300°C calculated  from the experiments in  is 2.3(10)-9 cm2 s-1. This value is close to measured values of the diffusion coefficients of water in alumina . Thus the mechanism of the diffusion of water in alumina is the transport of H3O+ ions, and these ions control the electrical conductivity when the water concentration is high enough.
To calculate the minimum concentration C of water in alumina that can contribute to the electrical conductivity, one can use the Einstein equation:
C = RTs / Z2F 2D (10)
in which R is the gas constant, Z the ionic charge (valence), F the Faraday, and D the diffusion coefficient. The electrical conductivity at 1,300°C from  was 2.29 x 10-11/ohm cm. Thus with D = 2.29(10)-9 cm2 s -1, a concentration of 1.13(10)-8 mol cm-3 of carriers results if one assumes that the conductivity in the samples in  results from H3O+ transport (which, of course, it does not); this concentration is 1.45(10)-7 carriers per Al atom in alumina. The concentration of H+ in the alumina samples of  can be calculated from their highly sensitive infrared absorption measurements to be about 4.7(10)-7 per Al atom. Thus one can conclude that for H3O+ concentrations above about 10-8 mol cm-3 (3 x 10-7 ions per Al atom), there will be a contribution of these ions to the conductivity, whereas for lower H3O+ concentrations the conductivity will be mainly electronic.
The activation energy for water diffusion in alumina is about 220 kJ mol-1 (2.3 eV) from , so that many of the earlier results on electrical conductivity of alumina, for example, those summarized in , probably result from water transport at lower temperature; at higher temperatures, electronic conductivity will predominate, because of the high activation energy of intrinsic electronic conductivity. If the alumina is “dry” (H3O+ concentration below 10-8 mol cm-3) low activation energy extrinsic electronic conduction will be dominant at lower temperatures, resulting from donor and receptor impurities in the alumina.