Abstract
The current study uses high-temperature differential scanning calorimetry to document the shift in phase-transformation temperature with particle size throughout a series of alloys in the zirconia–yttria system (0–1.5 mol% yttria). The tetragonal-to-monoclinic (T→M) phase-transformation temperature is seen to vary inversely with particle size. It is shown that a simple thermodynamic approach first proposed by Garvie predicts this inverse linear relationship. Subsequent determination of the key thermodynamic parameters therein (e.g., the surface and volume free energy, enthalpy, and entropy changes involved in the phase transformation) allows a complete predictive equation for the T→M phase transformation in the yttria–zirconia system to be developed as a function of particle size and yttria dopant level. The yttria–zirconia phase diagram is then redrawn with grain size as a third variable. It should be stressed that the current analysis is valid for particulate systems only; a parallel paper tackles the problem for fine-grained yttria–zirconia solids, where the approach is similar, but additional strain energy terms come into play.
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References
Ph. Buffat and J.P. Borel, Phys. Rev. A 13, 2287 (1976).
A.N. Goldstein, C.M. Echer, and A.P. Alivisatos, Science 256, 1425 (1992).
M. Hasegawa, M. Watabe, and K. Hoshino, Surf. Sci. 106, 10 (1981).
R.P. Berman and A.E. Curzon, Can. J. Phys. 52, 923 (1974).
M. Winterer, R. Nitsche, S.A.T. Redfern, W.W. Schmahl, and H. Hahn, Nanostructured Mater. 5, 679 (1995).
R.C. Garvie, J. Phys. Chem. 82, 218 (1978).
R.C. Garvie and M.V. Swain, J. Mater. Sci. 20, 1193 (1985).
R.C. Garvie and M.C. Goss, J. Mater. Sci. 21, 1253 (1986).
T. Chraska, A.H. King, and C.C. Berndt, Mater. Sci. Eng. A 286, 169 (2000).
T. Chraska, A.H. King, C.C. Berndt, and J. Karthikeyan, in Phase Transformations and Systems Driven Far from Equilibrium, edited by E. Ma, P. Bellon, M. Atzmon, and R. Trivedi (Mater. Res. Soc. Symp. Proc. 481, Warrendale, PA, 1998), pp. 613–617.
G. Skandan, H. Hahn, M. Roddy, and W.R. Cannnon, J. Am. Ceram. Soc. 77, 1706 (1994).
R. Nitsche, M. Winterer, and H. Hahn, Nanostructured Mater. 6, 679 (1995).
Z. Ji, J.A. Haynes, M.K. Ferber, and J.M. Rigsbee, Surf. Coat. Technol. 135, 109 (2001).
E.K. Akdogan, W. Mayo, A. Safari, C.J. Rawn, and E.A. Payzant, Ferroelectrics 223, 11 (1999).
M.H. Frey and D.A. Payne, Phys. Rev. B 54, 3158 (1996).
B.D. Begg, E.R. Vance, and J. Nowotny, J. Am. Ceram. Soc. 77, 3186 (1982).
S. Schlag, H-F. Eicke, and W.B. Stern, Ferroelectrics 173, 351 (1995).
G.A. Rossetti, J.P. Cline, and A. Navrotsky, J. Mater. Res. 13, 3197 (1998).
J.M. McHale, A. Auroux, A.J. Perrotta, and A. Navrotsky, Science 277, 788 (1997).
H. Zhang and J.F. Banfield, in Phase Transformations and Systems Driven Far from Equilibrium, edited by E. Ma, P. Bellon, M. Atzmon, and R. Trivedi (Mater Res. Soc. Symp. Proc. 481, Warrendale, PA, 1998), pp. 619–624.
H. Zhang and J.F. Banfield, J. Mater. Chem. 8, 2073 (1998).
H. Zhang and J.F. Banfield, J. Phys. Chem. B 104, 3481 (2000).
A.A. Gribb and J.F. Banfield, Am. Miner. 82, 717 (1997).
H. Hahn, G. Skandan, and J.C. Parker, Scripta Metall. Mater. 25, 2389 (1991).
G. Skandan, C.M. Foster, J. Frase, M.N. Ali, and J.C. Parker, Nanostruct. Mater. 1, 313 (1992).
A.P. Alivasatos, Ber Bunsenges Phys. Chem. 101, 1573 (1997).
C-C. Chen, A.B. Herhold, C.S. Johnson, and A.P. Alivisatos, Science 276, 398 (1997).
S.H. Tolbert and A.P. Alivisatos, Science 265, 273 (1994).
H. Sato, O. Kitakami, T. Sakurai, Y. Shimada, Y. Otani, and K. Fukamichi, J. Appl. Phys. 81, 1858 (1997).
W. Shi, J. Kong, H. Shen, G. Du, W. Yao, and Z. Qi, Vacuum 42, 1070 (1991).
K. Asaka, Y. Hirotsu, and T. Tadaki, Mater. Sci. Eng. A 272–275, 262 (1999).
J.A. Kittle, Q.Z. Hong, H. Yang, N. Yu, S.B. Samavedam, and M.A. Gribelyuk, Thin Solid Films 332, 404 (1998).
P.I. Gouma, P.K. Dutta, and M.J. Mills, Structural Stability of Titania Thin Films. Nanostructured Mater. 11, 1231 (1999).
S. Schlag and H-F. Eicke, Solid State Commun. 91, 883 (1994).
M.J. Mayo, A. Suresh, and W.D. Porter, Thermodynamics for Nanosystems: Grain and Particle Size Dependent Phase Diagrams. Rev. Adv. Mater. Sci. (in press).
M. Çiftçioglu and M.J. Mayo, in Superplasticity in Metals, Ceramics, and Intermetallics, edited by M. Kobayashi, M.J. Mayo, and J. Wadsworth (Mater. Res. Soc. Symp. Proc. 196, Pittsburgh, PA, 1990), pp. 77–86.
H.P. Klug and L.E. Alexander, X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials, (Wiley, New York, 1974).
R.P. Ingel and D. Lewis III, J. Am. Ceram. Soc. 69, 325 (1986).
R.C. Garvie and P.S. Nicholson, J. Am. Ceram. Soc. 55, 303 (1972).
A. Suresh, MS Thesis, Pennsylvania State University, University Park, PA, 2001.
P. Li, I-W. Chen, and J.E. Penner-Hahn, J. Am. Ceram. Soc. 77, 1281 (1994).
W.D. Kingery, H.K. Bowen, and D.R. Uhlman, Introduction to Ceramics (John Wiley & Sons, New York, 1976).
G.S.A.M. Theunissen, A.J.A. Winnubst, and A.J. Burggraaf, J. Eur. Ceram. Soc. 9, 251 (1992).
X. Li and W-H. Shih, J. Am. Ceram. Soc. 80, 2844 (1997).
M. Natarajan, A.R. Dar, and C.N.R. Rao, Trans. Faraday Soc. 65, 3081 (1969).
Y-M. Chiang, I.P. Smyth, C.D. Terwilliger, W.T. Petuskey, and J.A. Eastman, Nanostructured Mater. 1, 235 (1992).
C.D. Terwilliger and Y-M. Chiang, J. Am. Ceram. Soc. 78, 2045 (1995).
H. Holmes, E. Fuller, Jr., and R. Gammage, J. Phys. Chem. 76, 1497 (1972).
H.G. Scott, J. Mater. Sci. 10, 1527 (1975).
D.J. Green, R.J.H. Hannink, and M.V. Swain, Transformation Toughening of Ceramics (CRC Press, Boca Raton, FL, 1988).
R. Srinivasan, L. Rice, and B.H. Davis, J. Am. Ceram. Soc. 73, 3528 (1990).
H.S. Maiti, K.V.G.K. Gokhale, and E.C. Subbarao, J. Am. Ceram. Soc. 55, 317 (1972).
W.Z. Zhu, Ceram. Int. 22, 389 (1996).
K. Fukuda, E. Iizuka, H. Taguchi, and S. Ito, J. Am. Ceram. Soc. 81, 2729 (1998).
R.N. Patil and E.C. Subbarao, Acta Crystallogr. A 26, 535 (1970).
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Suresh, A., Mayo, M.J. & Porter, W.D. Thermodynamics of the tetragonal-to-monoclinic phase transformation in fine and nanocrystalline yttria-stabilized zirconia powders. Journal of Materials Research 18, 2912–2921 (2003). https://doi.org/10.1557/JMR.2003.0406
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DOI: https://doi.org/10.1557/JMR.2003.0406