• PDF / 429,952 Bytes
• 5 Pages / 597.6 x 774 pts Page_size
• 88 Downloads / 256 Views

DOWNLOAD

REPORT

---

I.

INTRODUCTION

GROWTH path envelope (GPE) analysis developed by DeHoff[1] is a valuable but seldom employed technique for obtaining a complete picture of the evolution of particle sizes during processes such as nucleation and growth of precipitates, grain growth, and Ostwald ripening or coarsening. Through GPE analysis, the individual growth paths of size vs time for particles of different initial sizes can be unfolded from the experimentally determined particle size distributions obtained at different times in the process. Figure 1 illustrates the GPE for coarsening of cobalt particles in liquid copper during liquid phase sintering, described later in this paper. In addition to this picture of growth or shrinkage of the different particle size groups, growth velocities can be obtained from the slopes of the curves, and in the case of coarsening, critical radii, r*, are obtained from the zero-slope peaks of the curves. These data are valuable in testing theoretical models of coarsening or other processes. As described by DeHoff,P] the GPE construction is based on the cumulative particle size distribution, given by Nv> (r, t)

= Nv(t)

fffiU fer, t) dr

II. [1]

wheref(r, t) is the size distribution density function, Nv(t) is the total number of particles at time t, and Nv> (r, t) is the number of particles per unit volume that are larger than size r at time t. A basic assumption of the GPE analysis is that the growth paths of individual particles do not cross each other, which should be statistically valid for precipitation or coarsening processes. The particle sizes corresponding to a constant value of N v> on the cumulative distribution curves at each time of observation describe the variation of the radius of a particular group of particles vs time, as illustrated in Figure 2. Constructing the GPE for a precipitation or coarsening process and extracting further information, as mentioned Z. FANG, Graduate Research Assistant, Materials Science and Engineering Department, B.R. PATTERSON, Professor, Materials Science and Engineering Department, and M.E. TURNER, Jr., Professor, Biostatistics and Biomathematics Department, are with the University of Alabama, Birmingham, AL 35294. Manuscript submitted January 2, 1990. METALLURGICAL TRANSACTIONS A

above, is a laborious, time-consuming task. In addition to the tediousness of the graphical construction, human variability and bias occur in fitting the cumulative size distribution curves and the slopes of the r-t plots. Lack of a logical basis for selecting constant N v> values for use in the construction can result in redundant or missing information. The efficiency of the GPE can be optimized, however, with respect to selection of Nv> values, and the majority of the analysis is amenable to computer automation through use of standard statistical analysis packages such as SYSTAT.[2] The objective ofthis study is to optimize and automate the GPE analysis procedure to maximize the useful information obtained and reduce the extensive time and labor involved and human error