Ceramic and Glass Materials

10 Zirconia 193

1

d 66

HT

T

HU

for sintered pellets

critical b

=−∆ ∞ + ∞+ se

∆

∆∆

ΣΣ∆

()(12)

wheredcritical is the critical crystallite/grain size, ∆H∞ is the enthalpy of the tetragonal-
to-monoclinic phase transformation in a sample with infinite crystallite/grain size,
T is the temperature of transformation, ∆g is the difference in surface energy in pow-
der crystallites, ∆S is the difference in interfacial energy in sintered pellets, Tb is the
transformation temperature for an infinitely large-grained sample, and ∆Use is the
strain energy involved in the transformation. From these equations, it can be seen that
the same material in the solid form has a lower transformation temperature than in the
powder form. This difference is due to the strain energy, ∆Use, involved in the trans-
formation, which is present only in the pellets since there is a requirement for geomet-
ric compatibility that is not present in the powders.

References

1. G. Stapper, M. Bernasconi, N. Nicoloso, and M. Parrinello, Ab initio study of structural and elec-
   tronic properties of yttria-stabilized cubic zirconia, Phys. Rev. B, 59 (2), 797–810 (1999).


2. J.K. Dewhurst and J.E. Lowther, Relative stability, structure, and elastic properties of several
   phases of pure zirconia, Phys. Rev. B, 57 (2), 741–747 (1998).


3. P. Li, I.-W. Chen, and J.E. Penner-Hahn, Effect of dopants on zirconia stabilization – An X-ray
   absorption study: I, trivalent dopants, J. Am. Ceram. Soc. 77 (1) 118–128 (1994).


4. D.W. Richerson, Modern Ceramic Engineering Properties, Processing, and Use in Design 3/e,
   Taylor and Francis Group, Boca Raton, 2006, p 30.


5. S.-M. Ho, On the structural chemistry of zirconium oxide, Mater. Sci. Eng. 54 , 23–29
   (1982).

Fig. 23Phase diagram representation of the crystallite size and yttria concentration dependency of

the tetragonal-to-monoclinic transformation temperature [87] (reprinted with permission)