Abstract
The thermodynamics of the constrained phase transformation is presented with particular reference to size effects introduced by surface phenomena concurrent with the transformation, e.g., the formation of solid-solid surfaces (twins, etc.) and solid-vapour surfaces (microcracks). It is shown that these surface phenomena not only introduce a size-dependent energy term into the total free-energy change, but also reduce the strain energy associated with the transformation, which can result in a transformation at a temperature where ¦ΔGc¦, the chemical free energy change, is less thanU se, the unrelieved strain energy associated with the constrained transformation. The results of this analysis lead to a phase diagram representation that includes the size of the transforming inclusion. This diagram can be used to define the critical inclusion size required to prevent the transformation and/or to obtain the transformation, but avoid one or more of the concurrent surface phenomena.
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References
R. C. Garvie, R. H. Hannick andR. T. Pascoe,Nature 258 (1975) 703.
R. C. Garvie andR. T. Pascoe, in “Processing of Crystalline Ceramics” edited by H. Palmour III, R. F. Davis and T. M. Hare (Plenum Press, New York, 1978) p. 263.
D. L. Porter andA. H. Heuer,J. Amer. Ceram. Soc. 60 (1977) 183.
Idem, ibid. 6 (1977) 280.
T. K. Gupta, J. H. Bechtold, R. C. Kuznichi, L. H. Adoff andB. R. Rossing,J. Mater. Sci. 12 (1977) 2421.
T. K. Gupta, F. F. Lange andJ. H. Bechtold,J. Mater. Sci. 13 (1978) 1464.
E. C. Sabbarao, H. S. Maiti andK. K. Srivastava,Phys. Stat. Sol. 21 (1974) 9.
A. Heuer andG. L. Nord, Jr, in “Electron Microscopy in Minerology” edited by H. R. Weuk (Springer-Verlag, Berlin, Heidelberg and New York, 1976) p. 274.
J. E. Bailey,Proc. Roy. Soc. 279A (1964) 395.
G. K. Bansal andA. H. Heuer,Acta Met. 22 (1974) 409.
S. T. Buljan, H. A. McKinstry andV. S. Stubican,J. Amer. Ceram. Soc. 59 (1976) 351.
R. N. Patil andE. C. Subbarao,J. Appl. Cryst. 2 (1969) 281.
K. K. Srivastava, R. N. Patil, C. B. Chandary, K. V. G. K. Gokhale andE. C. Subbarao,Trans. Brit. Ceram. Soc. 73 (1974) 85.
H. C. Scott,J. Mater. Sci. 10 (1975) 1527.
V. S. Stubican, R. C. Hink andS. P. Ray,J. Amer. Ceram. Soc. 61 (1978) 17.
J. D. Eshelby, in “Progress in Solid Mechanics” Vol. 2, edited by I. N. Sneddon and R. Hill (North-Holland Publishers, Amsterdam, 1961) p. 89.
R. C. Garvie,J. Phys. Chem. 69 (1965) 1238.
Idem, ibid. 82 (1978) 218.
F. F. Lange, in “Fracture Mechanics of Ceramics” edited by R. C. Brandt, D. P. H. Hasselman and F. F. Lange (Plenum Press, New York, 1974) p. 599.
Idem, in “Fracture Mechanics of Ceramics” Vol. 4, edited by R. C. Brandt, D. P. H. Hasselman and F. F. Lange (Plenum Press, New York, 1978) p. 799.
Y. M. Ito, M. Rosenblatt, L. Y. Cheng, F. F. Lange andA. G. Evans,Inter. J. Fracture, to be published.
Y. M. Ito andF. F. Lange, unpublished work.
D. L. Porter, PhD thesis, Case-Western University (1977) (University Microfilms Int. Order No. 77-25185, p. 190).
Y. Matsuo andH. Sasaki,J. Amer. Ceram. Soc. 49 (1966) 229.
W. R. Buessem, L. E. Cross andA. K. Goswanii,J. Amer. Ceram. Soc. 49 (1966) 33.
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Lange, F.F. Transformation toughening. J Mater Sci 17, 225–234 (1982). https://doi.org/10.1007/BF00809057
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DOI: https://doi.org/10.1007/BF00809057