Ceramic and Glass Materials

192 O.A. Graeve

increases as the dopant concentration increases. The critical size is 22.6 (also found to

be∼18 nm by Chraska et al. [85] and 15.3 nm by Garvie [86]), 41.7, 67, and 93.8 nm

for yttria doping concentrations of 0, 0.5, 1.0, and 1.5 mol% [87]. The values decrease

with increasing dopant concentration, consistent with the fact that yttria is a tetragonal-

phase stabilizer. Changes in the transformation temperature with dopant concentration

and crystallite size are shown in Fig. 23 [87], where it can be seen that the transforma-

tion temperature decreases with decreasing crystallite size and increasing dopant con-

centration. The dotted lines represent theoretical curves calculated according to:

T

H

h

d

S

s

d

transformation

vol

surf

critical

vol

surf

crit

=

+

+

D

D

D

D

10

10

iical

, (10)

where∆Hvol is the volumetric heat of transformation, ∆hsurf is the surface enthalpy dif-
ference,dcritical is the critical crystallite size to stabilize the tetragonal phase at room
temperature,∆Svol is the volumetric entropy of transformation, and ∆ssurf is the surface
entropy difference. The solid curves are from the standard ZrO 2 –Y 2 O 3 phase diagram
(Fig. 22). The solid circles represent experimental data on samples that happened to
have crystallite sizes close to those for which the theoretical curves were calculated.
The stabilization of the tetragonal phase at room temperature due to a decrease in
the crystallite size has been attributed to a surface energy difference and roughly
obeys the relationships [88]:

1

d

=-

HT

6T

+

H

6

(for powders)

critical b

∆

∆γ

∆

∆γ

∞∞

(11)

Fig. 22 Zirconia-rich end of the yttria-zirconia phase equilibrium diagram [77] (reprinted with
permission)