Stereological Analysis of Nonspherical Particles in Solid Metal
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INTRODUCTION
REMOVING inclusions in metallurgical processes is critical for producing high-quality products. The main goals of metallurgists are to maximize inclusion removal and to control the nature and distribution of residual inclusions. Stereological analysis of inclusions in a metal system can be used to obtain quantitative information about inclusion particles such as their quantity and size distribution. Many methods are available for measuring the particle size distribution (PSD),[1–7] including microscopy, sedimentation, sieving techniques, laser diffraction, and the electrical sensing zone method (using a Coulter Counter). Of these methods, the electrical sensing zone method[7] is the most common and widely accepted one because of its great advantages: size determination is independent of particle shape, and it gives the actual volume of each particle suspended in an electrolyte. While all the above methods can be used for particle measurements, they cannot directly obtain three-dimensional (3D) information about particles in a solid medium because of the opaqueness and high melting points of such media (particularly metals). Currently, the most popular method for determining the PSD in a metal system involves analyzing two-dimensional (2D) microscopy images of the cross sections of samples after polishing. Schwartz[8] and Saltykov[9] developed a stereological method known as the Schwartz–Saltykov (SS) method based on Scheil’s method[10,11] to estimate 3D TAO LI, PhD Student, SHIN-ICH SHIMASAKI, Assistant Professor, SHOJI TANIGUCHI, Professor, and SHUNSUKE NARITA, Graduate Student, are with the Graduate School of Environmental Studies, Tohoku University, Sendai, Japan. Contact e-mail: [email protected] KENTARO UESUGI, Researcher, is with the Japan Synchrotron Radiation Research Institute (JASRI), Hyogo, Japan. Manuscript submitted November 7, 2012. Article published online March 22, 2013. 750—VOLUME 44B, JUNE 2013
information for spherical particles with circular cross sections. The SS method has been applied to various systems. Takahashi and Suito[12–14] estimated the 3D PSD using a simulation model that contained randomly dispersed spherical particles. Enomoto and Kobayashi[15] analyzed the number and size of ferrite particles in a Fe-CNi alloy per unit volume and compared the results with measured values. Susan et al.[16] performed a stereological analysis of pores in a metal, the results of which were highly dependent on the similarity of these pores to a sphere. Saltykov[17] modified the SS method by introducing the ratio of the CSA of particles to the maximum CSA of the particle system, A/Amax, for nonspherical particles when calculating the probability mass function (PMF), to avoid using the diameter of a circular cross section for spherical particles only. Nevertheless, this method has not been developed beyond a theoretical stage because of the lack of PMFs for nonspherical particles. The current study compares the 2D PSD from a projected area (PSDP) obtained by optical microscopy and the
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