Ceramic and Glass Materials

16 R.H. Doremus

The electrolysis experiments of Ramirez et al. [40] show that when alumina con-
tains some water (OH groups), the electrical conductivity results from the transport of
hydrogen ions (actually hydronium ions, H 3 O+; see [41] for discussion).
The diffusion coefficient of H 3 O+ ions at 1,300°C calculated [41] from the experi-
ments in [40] is 2.3(10)−9 cm^2 s−1. This value is close to measured values of the diffu-
sion coefficients of water in alumina [42]. Thus the mechanism of the diffusion of
water in alumina is the transport of H 3 O+ 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 / Z^2 F^2 D (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 [34] was 2.29

10 −^7

10 −^8

10 −^9

10 −^10

10 −^11

CONDUCTIVITY [Q

−^3

cm

−^1

]

TEMPERATURE [ 
C]

RECIPROCAL TEMPERATURE (10^4 /T
K)

10 −^12

10 −^13

10 −^14

10 −^15

10 −^16

10 −^17

6

1300 120011001000 900 800 (^700600500400)
789
4.8 eV
0.4 eV
10 11 12 13 14 15
Fig. 3The electrical conductivity of pure, dry sapphire along the c-axis. Points, measured values.
From [34]