Upon heating, the monoclinic phase in zirconia starts transforming to the tetragonal phase at 1,461 K, peaks at 1,471 K, and finishes at 1,480 K. On cooling, the transformation from the tetragonal to the monoclinic phase starts at 1,326 K, peaks at 1,322 K, and finishes at 1,294 K, exhibiting a hysteresis behavior that is well known for this material [61-65]. This transformation can also be affected by irradiation with heavy ions, such as 300 MeV Ge  and 340 keV Xe .
The tetragonal phase transforms to the cubic fluorite structure at 2584 ± 15 K . This transformation temperature has been found to be dependent on the atmosphere
in which the transformation is taking place . In a reducing atmosphere, the transformation takes place at approximately 2,323 K, and in a neutral atmosphere, it takes place at approximately 2,563 K, which is in proximity to the highly accurate value found by Navrotsky et al. . Continued heating of the material results in melting at a temperature of 2,963 K . The phase stability as a function of pressure for this material in its pure form is shown in Fig. 20 .
The practical use of pure zirconia is restricted by the monoclinic to tetragonal transformation, as this transformation causes cracking and sometimes complete disintegration of the specimen. Depending on the orientation of the particular grain that is undergoing the transformation, there is a maximum strain in the lattice of ~4% , which is quite significant and promotes failure of the specimen when undergoing heating and cooling cycles.
This transformation has many characteristics of martensitic transformations in metals, with definite orientation relationships between the two structures. The orientation relationships conform to the following [69-71]:
(100)J(110)bct and [01°]mllbct ,
and by ^innmg (l00)m|1 (Ш)bct and [omjJ1 [00l]bct
where m and t represent the monoclinic and tetragonal phases, and bct refers to the body-centered tetragonal structure. Possible variants of these twin relationships for small tetragonal particles are shown in Fig. 21. In this figure, the hashed areas represent the transformed monoclinic phase and the unhashed areas represent the
5 10 15 20 25 30 35 40
Fig. 21 The four possible arrangements of twin-related variants together with the range of strain values predicted for the directions indicated (adapted from Kelly )
untransformed tetragonal phase. As the transformation progresses, the entire particle eventually forms the stable monoclinic phase for this material. The transformation progresses in two stages. The first stage involves a displacive transformation with small shifts of the atoms and the second stage involves a martensitic transformation in which both structures remain almost unchanged . It is this latter transformation that has been studied the most thoroughly [73-75].
To avoid this destructive transformation, stabilization of the tetragonal and cubic structures of zirconia can be done at room temperature by the addition of trivalent dopant ions such as Y3+ and Ce3+, divalent dopant ions such as Ca2+, or tetravalent dopant ions. Doping of zirconia has enormous consequences not only for the mechanical properties of this material, but also for the electronic properties. In particular, Y3+ has a large solubility range in zirconia and can be used to stabilize both the tetragonal and cubic phases. To maintain charge neutrality, one oxygen vacancy must be created for each pair of dopant cations that are added to the structure. This results in large increases in ionic conductivity. Stabilization of the tetragonal and cubic structures requires differing amounts of dopants. The tetragonal phase is stabilized at lower dopant concentrations. The cubic phase is stabilized at higher dopant concentrations, as shown in the room temperature region of the ZrO2-Y2O3 phase diagram in Fig. 22
 . At higher Y2O3 doping, the material exhibits an ordered Zr3Y4O12 phase at 40 mol% Y2O3, a eutectoid at a temperature < 400°C at a composition between 20 and 30 mol% Y2O3, a eutectic at 83 ± 1 mol% Y2O3, and a peritectic at 76 ± 1 mol% Y2O3
 . Other zirconia phase diagrams have been developed by Stubican and Ray for ZrO2-CaO , Grain for ZrO2-MgO , Cohen and Schaner for ZrO2-UO2 , Mumpton and Roy for ZrO2-ThO2 , Barker et al  for ZrO2-Sc2O3, and Duwez and Odell for ZrO2-CeO2 , among others.
As mentioned briefly in Sect. 4, another way of stabilizing the tetragonal structure at room temperature is the formation of nanocrystalline powders or nanograined sintered specimens. To obtain powders of dense PSZ compacts at room temperature, the material has to contain crystals or grains below a certain critical size, which
increases as the dopant concentration increases. The critical size is 22.6 (also found to be -18 nm by Chraska et al.  and 15.3 nm by Garvie ), 41.7, 67, and 93.8 nm for yttria doping concentrations of 0, 0.5, 1.0, and 1.5 mol% . 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 , where it can be seen that the transformation temperature decreases with decreasing crystallite size and increasing dopant concentration. The dotted lines represent theoretical curves calculated according to:
DH v0l + J suf
where AH. is the volumetric heat of transformation, Ah f is the surface enthalpy difference, dcritical is the critical crystallite size to stabilize the tetragonal phase at room temperature, AS. is the volumetric entropy of transformation, and As, is the surface
entropy difference. The solid curves are from the standard ZrO2-Y2O3 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 :
where dcritical is the critical crystallite/grain size, AH – is the enthalpy of the tetragonal – to-monoclinic phase transformation in a sample with infinite crystallite/grain size, T is the temperature of transformation, Ag is the difference in surface energy in powder crystallites, AS is the difference in interfacial energy in sintered pellets, Tb is the transformation temperature for an infinitely large-grained sample, and AUse 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, AUse, involved in the transformation, which is present only in the pellets since there is a requirement for geometric compatibility that is not present in the powders.