Particle critical-size

Once the precipitates grow beyond a critical size they lose coherency and then, in order for deformation to continue, dislocations must avoid the particles by a process known as Orowan bowing(23). This mechanism appHes also to alloys strengthened by inert dispersoids. In this case a dislocation bends between adjacent particles until the loop becomes unstable, at which point it is released for further plastic deformation, leaving a portion behind, looped around the particles. The smaller the interparticle spacing, the greater the strengthening. 

Below a critical size the particle becomes superparamagnetic in other words the thermal activation energy kTexceeds the particle anisotropy energy barrier. A typical length of such a particle is smaller than 10 nm and is of course strongly dependent on the material and its shape. The reversal of the magnetization in this type of particle is the result of thermal motion. 

For a given particle of size d, from the point M where the equilibrium line meets the line of zero vertical velocity (see Fig. 13.4), the critical path of the particle may be defined. All particles of this size between points D and G are entrained in the downward stream and are collected. The remaining particles of this size join in the upward-moving stream of fluid and penetrate the cyclone. The point D may be obtained by tracking back the particle trajectory from the point M using the equation of the particle trajectory, which is given by... 

The first is diffusion capture. This theory was originally proposed by Fitch and Tsai (13) for the aqueous polymerization of methyl methacrylate. According to this theory, any oligomer which diffuses to an existing particle before it has attained the critical size for nucleation is irreversibly captured. The rate of nucleation is equal to the rate of initiation minus the rate of capture. The rate of capture is proportional to both the surface area and the number of particles. 

When a droplet reaches the peak of its appropriate curve, due to being in a region of RH greater than the RH for that critical size, it will continue to grow in an uncontrolled fashion. As it gets larger, the curvature effect decreases its vapor pressure and it enters a region of increased supersaturation relative to that at the peak of the Kohler curve. A particle that turns into a droplet and passes the critical size is said to be an activated CCN. 

In Equation (1) we assume particles are spherical with radius r. The chemical potentials are and for the particle and the solvated atoms or molecules, respectively, n is the number of moles per unit volume and a is the surface energy (or tension). Since the particle has formed, we can take the bulk term as negative with Ap = p — Ps<0 hence favorable, but formation of the surface costs energy so is positive and unfavorable. These two functionalities yield a maximum in AG. Differentiation of Equation (1) finds this maximum to be at a critical size Vc given by... 

Beyond this critical size, the particles grow at the expense of particles less than the critical size. This can be seen graphically in Figure 3 where AG is plotted versus size r (surface -I- bulk, dot dash curve). 

At large size the cubic bulk term finally dominates and suggests that the system would still grow without bound if particles could pass the modified critical size >(, this is Ostwald ripening. 

Frei, E.H., Shtrikman, S. and Treves, D. (1957) Critical size and nucleation field of ideal ferromagnetic particles. Physical Review, 106 (3), 446-454. 

Nickel and selenium interact with incandescence on gentle heating [1], as do also sodium and potassium, the latter mildly explosively [2], Uranium [3] and zinc [4] also incandesce when their mixtures with selenium are heated, and platinum sponge incandesces vividly [5], The particle size of cadmium and selenium must be below a critical size to prevent explosions during synthesis of cadmium selenide by heating the elements together. Similar considerations also apply to interaction of cadmium or zinc with sulfur, selenium or tellurium [6], Interaction of powdered tin and selenium at 350° C is extremely exothermic [7],... 

Prediction of Critical Sizes. In order to use the above model for actual predictions, it is necessary to assign values to the relative velocity U0 this is, at the present level of knowledge, an extremely difficult task since, due to bubble motion (and perhaps the presence of fixed and moving internals in a fluid bed such as, for example, draft tubes) the particle movement in a fluidized bed is extremely complex. Some crude estimates of the relative velocity between particles have been made (Ennis etal., 1991) and these were expressed as... 

Several additional, non-microstructural, inputs are required for the fracture model (i) Particle critical stress intensity factor, KIc. Here, the value determined in a previous study (Klc = 0.285 MPa in )[3] was adopted for all four graphites studied. This value is significantly less than the bulk Klc of graphites (typically -0.8-1.2 MPa rn). However, as discussed in the previous section, when considering fracture occurring in volumes commensurate in size with the process zone a reduced value of Klc is appropriate (ii) the specimen volume, taken to be the stressed volume of the ASTM tensile test specimens specimen used to determine the tensile strength distributions and (iii) the specimen breadth, b, of a square section specimen. For cylindrical specimens, such as those used here, an equivalent breadth is calculated such that the specimen cross sectional area is identical, i.e.,... 

Standardization problems (L4) arise from the polymorphic nature of apo(a) and from its linkage to apo-B within the Lp(a) lipoprotein. A combination of an anti-apo(a) as capture antibody with an anti-apo-B for detection enables the expression of the Lp(a) concentration as lipoprotein particles. The size of the apo(a) isoforms becomes critical in assays using only apo(a) antibodies, so that the problem of the units of mass for Lp(a) has not been solved yet. 

A subcritical aggregate having fewer subunit components than a nucleus. When this term is applied in the kinetics of precipitation, n refers to the number of subunits in a particle and n defines the number of subunits in a particle of critical size. This definition avoids confusion by distinguishing between subcritical (n < n subunits), critical (n = n subunits), and supercritical (n > n subunits) particle sizes. If a nucleus is defined as containing n n subunits, then an embryo contains n n subunits. Note that in this treatment, we are not using a phase-transition description to describe nucleation, and we are focusing on the smallest step in the process that leads to further aggregation. 

---