The Precipitate-Nucleation in the Vicinity of Solubility Limit

The critical minimum size of stable precipitate in the vicinity of edge of miscibility gap is experimentally determined for the Ni3Si precipitate particle in Ni-Si, Ni3Al in Ni-Al, Cu4Ti in Cu-Ti and Co in Cu-Co binary alloy systems by utilizing the macroscopic composition gradient method recently proposed. The results obtained are as follows: The critical nucleus size shows a rapid increase to several tens of nm in a very narrow composition region less than 0.3at% from the phase boundary. Such a big critical size of nucleus is statistically rationalized by the conventional nucleation theories.

Polishing process effect on the image of dispersed precipitates

One important problem in determination of precipitate particle size is the effect of preferential thinning during TEM specimen preparation. Figure 1a schematically represents the original polydispersed Ni3Al precipitates in the Ni rich matrix. The three possible type surface profiles of TEM specimens, which result after electrolytic thinning process are illustrated in Figure 1b. c. & d. These various surface profiles could be produced by using different polishing electrolytes and conditions (i.e. temperature and electric current). The matrix-preferential-etching process causes the matrix material to be attacked much more rapidly than the second phase particles. Figure 1b indicated the result. The nonpreferential and precipitate-preferential-etching results are shown in Figures 1c and 1d respectively.

The effect of particle solubility and inhomogeneities on the kinetics of precipitation in crystals

The dependence of the solubility of a precipitate particle in a matrix on its radius considerably modifies the solute currents to the particle and hence the kinetics of its rate of growth. The effect of particle size on the solubility is large if the interfacial energy is large and the radius R of the particles is small. This effect has been included in the theory of precipitation from a supersaturation of solute. In the extensively used formula, describing the time dependence of W, the fraction of solute precipitated, the effect increases the value of r but leaves n practically unaltered. I t does not therefore solve the problem that although Ham ’s theory of precipitation on a periodic array of dislocations gives n — 1 , the experimentally observed values are n = o §. It is shown that the use of the = 1 equation for non-periodic arrays is invalid in most cases of practical interest and is responsible for the discrepancy. The effective interdislocation distance, Ax, which determines r, is the average of interdislocation distances of only a few dislocations surrounding the dislocation line, more distant dislocations have no strong influence. In view of this and the fact that even small percentage changes in Ax cause appreciable changes in r, inhomogeneities in the distribution of Ax cause different groups of particles to grow with different relaxation times r , and 1 — IF is given by the sum of more than one exponential term. The effect of closely spaced particles or unequally sized particles is similar. Numerically these effects mean that 1 — IF can be represented by (1) but with n reduced to a value less than 1. When inhomogeneities observed by electron microscope studies are taken into account, values of £-§ for n are obtained and experiments on precipitation of iron carbide in a iron (or steel) and in other systems are satisfactorily explained.

The Effect of Stress Upon the Precipitation of Coherent, Tetpagonally-Distorted Particles

The change in energy as a result of interaction between an applied stress and the transformation strain associated with a precipitate particle or inclusion of volume V has been given by Eshelby as where summation over repeated indices is implied. The example that we turn our attention to is the precipitation in a nickel alloy of coherent, tetragonally-distorted DO22 particles of composition Ni3Nb. This precipitate is coplanar with the fcc matrix and its crystallographic coordinates are the coordinates of principle strain, and . The particles form as discs on the ﹛100﹜ fcc planes normal to their axis of major strain, thus three variants are possible. As shown in Fig. 1, under normal aging conditions nearly equivalent amounts of the three variants are observed. The diffraction pattern included in Fig. 1 has been indexed with respect to the fcc matrix.