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Fig. 9--Dark-field image from a fivefold selected area diffraction region. The dark field is formed with a spot from the third ring of reflections. The image contrast features are similar to twinned regions in crystalline specimens.

REFERENCES 1. R. Perez, J.A. Juarez-Islas, L. Martinez, B. Campillo, and J.L. Albarran: unpublished research. 2. D.A. Lilienfeld, M. Nastasi, H.H. Johnson, D.G. Ast, and J.W. Mayer: Phys. Rev. Lett., 1985, vol. 55 (15), p. 1587. 3. K. Urban, N. Moser, and H. Kronsmuller: Phys. Stat. Sol. (a), 1985, vol. 91, p. 411. 4. K.F. Kelton and T.W. Wu: Appl. Phys. Lett., 1985, vol. 46 (11), p. 1059. 5. R. Luck, H. Haas, F. Sommer, and B. Predel: Scripta Metall., 1986, vol. 20, p. 677. 6. Y. Calvayrac, J. Devaud-Rzepski, M. Bessiere, S. Lefebvre, A. Quivy, and D. Gratias: Phil. Mag. B, 1989, vol. 59 (4), p. 439. 7. C.A. Guryan, A.I. Goldman, P.W. Stephens, K. Hiraga, A.P. Tsai, A. Inoue, and T. Masumoto: Phys. Rev. Lett., 1989, vol. 62 (20), p. 2409. 8. A.P. Tsai, A. Inoue, T. Masumoto, and N. Kataoka: Jpn. J. Appl. Phys., 1988, vol. 27 (12), p. L2252. 9. D.H. Kim, J.L. Hutchison, and B. Cantor: Phil. Mag. A, 1990, vol. 61 (2), p. 167. 10. J.E.S. Socolar and P.J. Steinhardt: Phys. Rev., 1986, vol. B34, p. 61"). 11. P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley, and M.J. Whelan: Electron Microscopy of Thin Crystals, R.E. Krieger Publishing Co., New York, NY, 1977.

Effect of Strain Rate on Cell Size Refinement and Strengthening in Nickel and Aluminum DEEPAK SIL, JYOTHI G. RAO, and S.K. VARMA The strengthening achieved by cell size refinement in metals and alloys of moderate to high stacking fault energy (SFE) has been of interest to researchers for the past DEEPAK SIL and JYOTHI G. RAO, Graduate Students, and S.K. VARMA, Professor, are with the Department of Metallurgical and Materials Engineering, The University of Texas at El Paso, E1 Paso, TX 79968-0520. Manuscript submitted May 27, 1992. 3166--VOLUME 23A, NOVEMBER 1992

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where o'0 and K are material constants. This equation has been sometimes referred to as the modified Hall-Petch (MHP) equation for cell size strengthening in the literature tlJ and has been used extensively in describing the cell size strengthening in metals and alloys in spite of its empirical nature. Hansen has recently reviewed the mechanisms of cell formation during cold deformation of face-centered cubic metals, t2] The initial view of the mechanisms involving the cell formation had the following steps: (a) dislocation generation during deformation, (b) minimization of energy by the rearrangement of dislocations in the tangled form, and (c) connection of dislocation tangles in three dimensions to form cells. Hansen TM has suggested that the activation of several slip systems within a grain can result in the formation of substructures giving rise to dense dislocation walls, cell blocks, microbands, and small pancake-shaped cell concepts. One conclusion that can be readily drawn from his observations is that the substructural developments must be grain size and st