Abstract
Spherical polymer particles in five different size ranges from ∼2 to 200 µm were measured by optical microscopy/image analysis of polished cross sections. From the two-dimensional (2-D) section-size distributions, two stereological techniques were employed to determine the three-dimensional (3-D) particle-size distributions: the classical Schwartz-Saltykov (SS) method, further developed by Takahashi and Suito, and the technique of Harayama, which was applied by Basak and Sengupta (HBS). The objectives of this study were to assess the viability of image analysis and the SS or HBS techniques as quantitative particle analysis methods and to compare them to laser diffraction (LD) of loose powders. It was found that the image analysis/stereology (IA/S) and LD results agreed within about 15 pct over most of the size range studied. Moreover, the IA/S technique accurately estimates experimental particle-size distributions with nonsymmetric or multimodal characteristics. Stereological parameters were studied, such as the number of size classes (histogram step intervals), and methods of displaying the size distributions were compared to develop best practices. The effect of oversight of small particles, which is an area of concern with stereological techniques, was also investigated in terms of changes to the mean and standard deviations of the 3-D particle-size distributions.
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References
J. Takahashi and H. Suito: Acta Mater., 2001, vol. 49, pp. 711–19.
J. Takahashi and H. Suito: Mater. Sci. Technol., 2002, vol. 18, pp. 103–10.
J. Takahashi and H. Suito: Metall. Mater. Trans. A, 2003, vol. 34A, pp. 171–81.
Y. Harayama: Res. Mech., 1985, vol. 16, p. 263.
C.B. Basak and A.K. Sengupta: Scripta Mater., 2004, vol. 51, pp. 255–60.
D.F. Susan, J.D. Puskar, J.A. Brooks, and C.V. Robino: Proc. 11th Solid Freeform Fabrication Conf., Austin, TX, 2000, pp. 50–57.
J.C. Russ: Practical Stereology, 1st ed., Plenum Press, New York, NY, 1986, pp. 62–69.
J.C. Russ: Image Processing Handbook, 4th ed., CRC Press, Boca Raton, FL, 2002, pp. 469–74.
R.T. DeHoff: Trans. AIME, 1962, vol. 224, pp. 474–77.
L. Karlsson and R. Sandstrom: Metallography, 1986, vol. 19, pp. 143–76.
Y. Liu, R.M. German, and R.G. Iacocca: Acta Mater., 1999, vol. 47, pp. 915–26.
J. Wasen and R. Warren: Metallography, 1987, vol. 20, pp. 431–50.
R.G. Iacocca and R.M. German: Int. J. Powder Metall., 1997, vol. 33 (8), pp. 35–48.
A. Jillavenkatesa, S.J. Dapkunas, and L.-S.H. Lum: Particle Size Characterization, SP 960-1, NIST, Washington, DC., 2001, pp. 82–88.
R. Xu and O. Andreina Di Guida: Powder Technol., 2003, vol. 132, pp. 145–53.
N.G. Stanley-Wood, N. Osborne, and M. Till: Particle Size Analysis, N.G. Stanley-Wood and R.W. Lines, eds., Royal Society of Chemistry, London, 1992, pp. 48–57.
G. Jimbo, J. Tsubaki, and H. Yamamoto: Particle Size Analysis, N.G. Stanley-Wood and R.W. Lines, eds., Royal Society of Chemistry, London, 1992, pp. 67–80.
T. Allen: Particle Size Measurement, 4th ed., Chapman and Hall, London, 1990, pp. 217–48.
A. Karasev and H. Suito: Metall. Mater. Trans. B, 1999, vol. 30B, pp. 259–70.
F.A.L. Dullien, E. Rhodes, and S.R. Schroeter: Powder Technol., 1969/70, vol. 3, pp. 124–35.
F.A.L. Dullien and P.N. Mehta: Powder Technol., 1971–72, vol. 5, pp. 179–93.
R.K. Eckhoff and G. Enstad: Powder Technol., 1975, vol. 11, pp. 1–10.
Y-H Xu and H.C. Pitot: Comp. Methods Progr. Biomed., 2003, vol. 72, pp. 1–20.
B.A. Tuttle, P. Yang, J.H. Gieske, J.A. Voigt, T.W. Scofield, D.H. Zeuch, and W.R. Olson: J. Am. Ceram. Soc., 2001, vol. 84 (6), pp. 1260–64.
J. Zhao and M.P. Harmer: J. Am. Ceram. Soc., 1988, vol. 71 (7), pp. 530–39.
E.E. Underwood: in Quantitative Microscopy, R.T. DeHoff and F.N. Rhines, eds., McGraw-Hill, New York, NY, 1968, pp. 149–200.
H.A. Schwartz: Met. Alloys, 1934, vol. 5, pp. 139–41.
E. Scheil: Z. Anorg. Allgem. Chem., 1931, vol. 201, pp. 259–64.
E. Scheil: Z. Metalkd., 1935, vol. 27, pp. 199–208.
S.A. Saltykov: Stereometric Metallography, 2nd ed., Metallurgizdat, Moscow, 1958, p. 81.
S.A. Saltykov: Proc. 2nd Int. Congr. for Stereology, Springer-Verlag, New York, NY, 1967, pp. 163–73.
M. Schafer: Part. Part. Syst. Characterization, 2002, vol. 19, pp. 158–68.
T. Allen: Powder Sampling and Particle Size Determination, Elsevier, New York, NY, 2003, pp. 197–200.
Z. Fang, B.R. Patterson, and M.E. Turner: Mater. Characterization, 1993, vol. 31, pp. 177–82.
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Susan, D. Stereological analysis of spherical particles: Experimental assessment and comparison to laser diffraction. Metall Mater Trans A 36, 2481–2492 (2005). https://doi.org/10.1007/s11661-005-0122-3
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DOI: https://doi.org/10.1007/s11661-005-0122-3