Nucleation definition

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

When a process is continuous, nucleation frequently occurs in the presence of a seeded solution by the combined effec ts of mechanical stimulus and nucleation caused by supersaturation (heterogeneous nucleation). If such a system is completely and uniformly mixed (i.e., the product stream represents the typical magma circulated within the system) and if the system is operating at steady state, the particle-size distribution has definite hmits which can be predic ted mathematically with a high degree of accuracy, as will be shown later in this section. 

Martensitic phase transformations are discussed for the last hundred years without loss of actuality. A concise definition of these structural phase transformations has been given by G.B. Olson stating that martensite is a diffusionless, lattice distortive, shear dominant transformation by nucleation and growth . In this work we present ab initio zero temperature calculations for two model systems, FeaNi and CuZn close in concentration to the martensitic region. Iron-nickel is a typical representative of the ferrous alloys with fee bet transition whereas the copper-zink alloy undergoes a transformation from the open to close packed structure. ... 

Cavitation occurs in a rapidly moving fluid when there is a decrease in pressure in the fluid below its vapor pressure and the presence of such nucleating sources as minute foreign particles or definite gas bubbles. As a result, vapor bubble forms that continues to grow until it reaches a region of pressure... 

The importance of twinned crystals in demonstrating that nucleation is the relevant growth mechanism has been realized since 1949 [64, 99]6. They were first investigated extensively in polymer crystals by Blundell and Keller [82] and they have recently received increased attention as a means of establishing, or otherwise, the nucleation postulate for lamellar growth [90, 91, 95,100-102]. The diversity of opinion in the literature shows that it is very difficult to draw definite conclusions from the experimental evidence, and the calculations are often founded upon implicit assumptions which may or may not be justified. We therefore restrict our discussion to an introduction to the problem, the complicating features which make any a priori assumptions difficult, and the remaining information which may be fairly confidently deduced. 

Before discussing such theories, it is appropriate to refer to features of the reaction rate coefficient, k. As pointed out in Sect. 3, this may be a compound term containing contributions from both nucleation and growth processes. Furthermore, alternative definitions may be possible, illustrated, for example, by reference to the power law a1/n = kt or a = k tn so that k = A exp(-E/RT) or k = n nAn exp(—nE/RT). Measured magnitudes of A and E will depend, therefore, on the form of rate expression used to find k. However, provided k values are expressed in the same units, the magnitude of the measured value of E is relatively insensitive to the particular rate expression used to determine those rate coefficients. In the integral forms of equations listed in Table 5, units are all (time) 1. Alternative definitions of the type... 

Secondary nucleation can, by definition, take place only if crystals of the species under consideration are already present. Since this is usually the case in industrial crystallisers, secondary nucleation has a profound influence on virtually all industrial crystallisation processes. 

For small-scale experiments, the LNG and liquid refrigerant cases are analyzed using a model which assumes that the volatile liquid (or some part of it) is superheated to a temperature at which homogeneous nuclea-tion occurs. Such nucleation is very rapid and the event resembles an explosion. An attempt is made to employ this same model to explain R s in the water-smelt, water-aluminum, and water-reactive metal cases, but data to make definitive conclusions are lacking. 

The reproducibility of the RPT [(100)(number of spills that ended in an RPT)/(total number of spills)] varied from 100 to 12%. At temperatures less than those necessary for an RPT, there was generally nucleate boiling and sometimes the substrate froze. The temperature of the transition from nucleate boiling to an RPT was quite sharp. At temperatures above the RPT region, film boiling took place. However, the temperature of this transition was not definite. The transition would often take the form of decreased reproducibility and RPT intensity at higher temperatures. 

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. 

A structure formed by the reversible association of am-phiphiles in apolar solvents. In inverted micelles, the polar portion of the amphiphile is concentrated in the interior of the macrostructure. Such association usually occurs with aggregation and is not typically characterized by a definite nucleation stage. Thus, inverted micelles (also referred to as inverse or reverse micelles) often fail to exhibit critical micelle concentration behavior. See Micelle... 

This observation is in accordance with the phenomena of the crystallization in the resolution operation mentioned above in the following points. There are no clear, definite critical supersaturations above which nucleation of D-threonine occurs. Ohtsuki (2), however, reported supersolubility curve for this system, who gave the value of the supersaturation width At=7 C at 50 C. Their definition of the metastablllty was that no nucleation of the enantiomer other than seeded one was observed for two hours of resolution experiments. According to this definition, the supersolubility can be determined to lie somewhere between At=8 and 5 C from the present experimental data, this being in agreement with his result. If the crystallization proceeds further, however, D-threonine crystals may start to crystallize from the solution even if the initial supersaturation is 5 C. In this sense it is no longer the metastablllty limit. 

Note 4 If a mixture is thermodynamically metastable, it will demix if suitably nucleated (see Definition 2.5). If a mixture is thermodynamically unstable, it will demix by spinodal decomposition or by nucleation and growth if suitably nucleated, provided there is minimal kinetic hindrance. 

Note In a metastable region of a phase diagram (see Definition 1.2), phase separation is initiated only by nucleation. 

The problem of burn-out prediction is a difficult one, and one on which a great deal of experimental work is being carried out, particularly in connection with nuclear-reactor development. Much of the earlier literature is rather confused, due to the fact that the mechanics of the burn-out were not carefully defined. Silvestri (S8) has discussed the definitions applicable to burn-out heat flux. It appears possible to define two distinctly different kinds of burn-out, one due to a transition from nucleate to film boiling, and one occurring at the liquid deficient point of the forced-convection region. The present discussion treats only the latter type of burn-out fluxes. The burn-out point in this instance is usually determined by the sudden rise in wall temperature and the corresponding drop in heat flux and heat-transfer coefficient which occur at high qualities. 

We now modify the 2D continuum equations of step motion, Eqs. (7) and (8), in order to study some aspects of the dynamics of faceting. We assume the system is in the nucleation regime where the critical width Wc is much larger than the average step spacing In the simplest approximation discussed here, we incorporate the physics of the two state critical width model into the definition of the effective interaction term V(w) in Eq. (2), which in turn modifies the step chemical potential terms in Eqs. (7) and (8). Again we set V(w) = w/ l/w) as in Eq. (4) but now we use the /from Eq. (10) that takes account of reconstruction if a terrace is sufficiently wide. Note that this use of the two state model to describe an individual terrace with width w is more accurate than is the use of Eq. (10) to describe the properties of a macroscopic surface with average slope s = Mw. 

---