High-resolution microscopy and early-stage precipitation kinetics
- PDF / 2,119,034 Bytes
- 14 Pages / 597 x 774 pts Page_size
- 8 Downloads / 174 Views
INTRODUCTION AND METHODS
P H A S E separation in solid alloys often occurs by homogeneous nucleation and growth. The two phases, called matrix and precipitate, then have the same crystal structure (except possibly for internal order) hut different compositions; they may differ up to a few percent in lattice parameter (a). The corresponding strain energy Af8 per unit volume must be provided by the total gain in (chemical) free energy Afv driving the transformation and so must be the interphase energy o- per unit area separating matrix and precipitate (in classical nucleation theory). A stable and able-to-grow nucleus of the latter then has a minimum size (radius) R* -
2o"
[1] Afv - Afa Smaller nuclei will also and more frequently occur by thermal fluctuations, but they are subcritical and will most likely dissolve again unless they grow by diffusion to a size R > R*. This is well known from classical nucleation t h e o r i e s I1,2'3], and these are subject to test in the present study. A quantitative estimate of R* by Eq. [1] indicates the need for high-resolution microscopy in order to observe and count nuclei. For the accessible times and temperatures of decomposition, R* is typically of the order of 1 nm. Such small nuclei can be resolved either by highresolution electron microscopy (HREM), by field ion microscopy (FIM), or by small-angle (neutron or X-ray) scattering (SAS). One can also try to extrapolate from larger, already grown, and visible particles back to their nucleation s t a g e - - if there exists a reliable growth stage and if there is neither Ostwald ripening (diminishing the particle density Nv) nor a decrease in supersaturation (changing Afv) in areas of further nucleation. One of the conclusions of the present work is, however, the need to apply a combined theory ~4,5] of nucleation, growth, and ripening to this type of phase transformation. This will be described in detail in Section IV, where the main
P. HAASEN, Professor, is with the Institut fiir Metallphysik, Universit/4t Grttingen, D-3400 Grttingen, Federal Republic of Germany. R. WAGNER, Adjunct Professor, Institut for Metallphysik, is Director, Institut f'tir Werkstoffe, GKSS, Geesthacht, Federal Republic of Germany. This paper is based on a presentation made in the "G. Marshall Pound Memorial Symposium on the Kinetics of Phase Transformations" presented as part of the 1990 fall meeting of TMS, October 8-12, 1990, in Detroit, MI, under the auspices of the ASM/MSD Phase Transformations Committee. METALLURGICAL TRANSACTIONS A
results of the older theories for the three separate stages, i.e., nucleation, growth, and coarsening, will be cited. Concerning high-resolution methods, the following remarks on applicability and limitations may be useful. High Resolution Transmission Electron Microscopy: Atomic resolution imaging of (ordered) superlattices and of lattice planes is a standard technique today. The lattice parameter of the L12 structure of Ni3A1 is 0.356 nm = d~00; the appropriate foil thickness for 120 kV electrons is 3/4 ~100= 1
Data Loading...
