The thermoelastic behavior and crystallography of th 8mol%Ceo-0 5mol%Y.o-Zro t-m martensitic transformation in Ce-Y-TZP ceramics were investigated by means of in situ TEM observation and Wechsler-Lieberman-Read (W-L-R)phenomenolog ical theory. In situ TEM observations [17] showed that in Ce-Y-TZP the t/m interface can move freely with the change of thermal stress generated by beam illumination shown in Fig. 2, whereas it was not found in thermal 3 T cycles. Based on the features of reversibility of interface 2 motion, large thermal hysteresis and high critical driving -2000 Y-TZP was suggested as a semi-thermoelastic one. the habit plane and the lattice correspondence were determined as( 30)t and ([001]t[O10]m), which is in ,(ca)=832.5K agreement with the calculated results by the phenomeno- M(ca)=2499K logical theory. 200300400500600700 Temperature/K 3. Thermodynamics of tetragonal (t-monoclinic(m) martensitic transformation Fig. 3. Thermodynamic evaluation of Gibbs free energies for tetragonal and monoclinic phases of 8Ce-0.5Y-TZP The change in total Gibbs free energy associated with the athermal martensitic transformation t-+ m can be △G1 AGah+△Gstr+△Gsu-△Gext △G1-m=V(-△G+△Gsm)+S△Gmr, △G-△Gext+△ Gb where subscripts"ch", "str", and"sur"refer to the chem- where Gext is the interaction energy density due to the ical free energy, the strain energy including both shear and external stress; Gbarrier is the sum of the changes in surface dilatational energy, and the surface energy including the and strain free energ Considering the phenomenology of stress induced phase surface free energy, twinning energy and micro-cracking transformation, a critical transformation stress may be energy, respectively. V refers to the volume and S, the area associated with the transformation. The equilibrium tem- defined as perature between the t→ m transformation, To, is the tem.o=(-△G+△ Barrier)/e rature at which AGch =0, and the Ms is defined as the temperature at which AGt-m=0 where g is the resultant dilational transformation strain The chemical energy difference between two phases localized in the transformation zone around the crack tip (AGch) of a multi-element system can be calculated from Application of only the resultant dilational transformation models [22]. The other required parameters in the right the controversy(see Section 5[*8]). It is clear that critical hand side of Eq. (1) can be derived through estima- stress is reduced as the temperature approaches Ms, since tion either from some available data or by experiments. the difference of chemical Gibbs free energy between t Thus the Ms temperature can be calculated accordin and m phases increases and contribute more to the driving Eq.(1) The difference of Gibbs free energy between tetragonal Also, from Eq (3), the total free energy change can be and monoclinic phases in ZrO2-CeOxY2O3 as a function increased and t-ZrO2 is retained by, decreasing the chemi of composition and temperature was thermodynamically cal free energy change by stabilizing with the addition of calculated from the three related binary systems [21]. In dopant oxide(e.g. yttria, ceria) increasing the strain free 8 mol% CeO2-05 mol%Y2O3-TZP, the equilibrium tem- energy change by dispersing the tetragonal phase in a con- perature between tetragonal and monoclinic phases, To, straining elastic matrix (e.g. alumina, cubic zirconia) was evaluated as 832.5K and the Ms temperature of this increasing the surface free energy (e.g. by reducing the alloy with a mean grain size of 0.90 um was calculated as tetragonal grain size)[**ll 249.9 K using the approach, which is in good agreement with the experimental one of 253 K by dilation measure- 4. Kinetics of t-m martensitic transformation in TZP (Fig. 3) Related to the application of external stress in the case Generally, athermal diffusionless t-m martensitic of transformation toughening(see Section 5), the total tree transformation takes place quickly, with the motion of energy change per unit volume required for constrained phase boundary as high as the sound speed [*23]. The over transformation [18] can be expressed as I transformation proceeds in two major stages [24]. FirstThe thermoelastic behavior and crystallography of the t ! m martensitic transformation in Ce–Y–TZP ceramics were investigated by means of in situ TEM observation and Wechsler–Lieberman–Read (W–L–R) phenomenolog￾ical theory. In situ TEM observations [17] showed that in Ce–Y–TZP the t/m interface can move freely with the change of thermal stress generated by beam illumination shown in Fig. 2, whereas it was not found in thermal cycles. Based on the features of reversibility of interface motion, large thermal hysteresis and high critical driving force for Ce–Y–TZP, the t ! m transformation in Ce– Y–TZP was suggested as a semi-thermoelastic one. The habit plane and the lattice correspondence were determined as (1 3 0)t and ([0 0 1]tk[0 1 0]m), which is in agreement with the calculated results by the phenomeno￾logical theory. 3. Thermodynamics of tetragonal (t) ! monoclinic (m) martensitic transformation The change in total Gibbs free energy associated with the athermal martensitic transformation t ! m can be expressed as [18–21] DGt!m ¼ V ðDGch þ DGstrÞ þ SDGsur; ð1Þ where subscripts ‘‘ch’’, ‘‘str’’, and ‘‘sur’’ refer to the chem￾ical free energy, the strain energy including both shear and dilatational energy, and the surface energy including the surface free energy, twinning energy and micro-cracking energy, respectively. V refers to the volume and S, the area associated with the transformation. The equilibrium tem￾perature between the t ! m transformation, T0, is the tem￾perature at which DGch = 0, and the Ms is defined as the temperature at which DGt!m = 0. The chemical energy difference between two phases (DGch) of a multi-element system can be calculated from the related binary systems by means of thermodynamic models [22]. The other required parameters in the right hand side of Eq. (1) can be derived through estima￾tion either from some available data or by experiments. Thus the Ms temperature can be calculated according to Eq. (1). The difference of Gibbs free energy between tetragonal and monoclinic phases in ZrO2–CeO2–Y2O3 as a function of composition and temperature was thermodynamically calculated from the three related binary systems [21]. In 8 mol% CeO2–0.5 mol% Y2O3–TZP, the equilibrium tem￾perature between tetragonal and monoclinic phases, T0, was evaluated as 832.5 K and the Ms temperature of this alloy with a mean grain size of 0.90 lm was calculated as 249.9 K using the approach, which is in good agreement with the experimental one of 253 K by dilation measure￾ment (Fig. 3). Related to the application of external stress in the case of transformation toughening(see Section 5), the total tree energy change per unit volume required for constrained transformation [18] can be expressed as DGt!m ¼ DGch þ DGstr þ S V DGsur DGext ¼ DGch DGext þ DGbarrier; ð2Þ where Gext is the interaction energy density due to the external stress; Gbarrier is the sum of the changes in surface and strain free energy. Considering the phenomenology of stress induced phase transformation, a critical transformation stress may be defined as rc ¼ ðDGch þ DGbarrierÞ=e t ; ð3Þ where e t is the resultant dilational transformation strain, localized in the transformation zone around the crack tip. Application of only the resultant dilational transformation strain in explaining the transformation toughening is still in the controversy (see Section 5 [*8]). It is clear that critical stress is reduced as the temperature approaches Ms, since the difference of chemical Gibbs free energy between t and m phases increases and contribute more to the driving force. Also, from Eq. (3), the total free energy change can be increased and t-ZrO2 is retained by, decreasing the chemi￾cal free energy change by stabilizing with the addition of dopant oxide (e.g. yttria, ceria); increasing the strain free energy change by dispersing the tetragonal phase in a con￾straining elastic matrix (e.g. alumina, cubic zirconia); increasing the surface free energy (e.g. by reducing the tetragonal grain size) [**11]. 4. Kinetics of t ! m martensitic transformation in TZP Generally, athermal diffusionless t ! m martensitic transformation takes place quickly, with the motion of phase boundary as high as the sound speed [*23]. The over￾all transformation proceeds in two major stages [24]. First, Fig. 3. Thermodynamic evaluation of Gibbs free energies for tetragonal and monoclinic phases of 8Ce–0.5Y–TZP. X.-J. Jin / Current Opinion in Solid State and Materials Science 9 (2005) 313–318 315