Mass deposition rate crystallizers

Crystal growth rate may be expressed either as a rate of linear inerease of eharaeteristie dimension (i.e. veloeity) or as a mass deposition rate (i.e. mass flux). Expressed as a veloeity, the overall linear erystal growth rate, G (=dL/dt where L is the eharaeteristie dimension that is inereasing). The rate of ehange of... 

As with nucleation, classical theories of crystal growth 3 20 2135 40-421 have not led to working relationships, and rates of crystallisation are usually expressed in terms of the supersaturation by empirical relationships. In essence, overall mass deposition rates, which can be measured in laboratory fluidised beds or agitated vessels, are needed for crystalliser design, and growth rates of individual crystal faces under different conditions are required for the specification of operating conditions. 

Methods used for the measurement of crystal growth rates are either a) direct measurement of the linear growth rate of a chosen crystal face or b) indirect estimation of an overall linear growth rate from mass deposition rates measured on individual crystals or on groups of freely suspended crystals 35,41,47,48). 

Because the rate of growth depends, in a complex way, on temperature, supersaturation, size, habit, system turbulence and so on, there is no simple was of expressing the rate of crystal growth, although, under carefully defined conditions, growth may be expressed as an overall mass deposition rate, RG (kg/m2 s), an overall linear growth rate, Gd(= Ad./At) (m/s) or as a mean linear velocity, // (= Ar/At) (m/s). Here d is some characteristic size of the crystal such as the equivalent aperture size, and r is the radius corresponding to the... 

Garside et al. (1982) developed an elegant technique to evaluate crystal growth kinetics from an integral mode of batch experiments. For size-independent growth, the crystal mass deposition rate (Rq) can be given by... 

There is no simple or generally accepted method of expressing the rate of growth of a crystal, since it has a complex dependence on temperature, supersaturation, size, habit, system turbulence, and so on. However, for carefully defined conditions crystal growth rates may be expressed as a mass deposition rate Rq (kgm s ), a mean linear velocity v(ms ) or an overall linear growth rate G (ms ). The relationships between these quantities are... 

Overall growth rates for potash alum measured in the fluidized bed crystallizer coincide very well with those predicted from face growth rates measured in the single crystal cell Figure 6.22). The alums grow as almost perfect octa-hedra, i.e. eight (111) faces, so it is a simple matter, using the crystal density, pc, to convert linear face velocities to overall mass deposition rates Rq = pcV u ))-... 

Crystal growth rates can be expressed in a number of different ways. For the purpose of characterizing the growth kinetics in a maimer that is relevant to the design of a crystallization process, it is convenient to express growth rates in terms of mass deposition rates or overall growth rates ... 

For the purpose of simplification, the assumption has been made in Figure 11.3 that the time for a recirculation process is sufficient to reduce the supersaturation down to negligible levels. This reduction in supersaturation is, however, a function of the mean mass deposition rate and the growing crystal surface area present [2] ... 

The smaller the active crystal surface available, the slower the mass deposition rate d7w/df, and the larger the supersaturation remaining after each recirculation cycle. The point 0, in Figures 11.3 and 11.4 moves up, if crystal growth does not desupersaturate to Ac —> 0. As this residual supersaturation is added to the newly created supersaturation, it is certainly possible that the metastable zone width will be... 

The mass deposition rate dmidt (Eq. (9.2)) can be described as exponential function with supersaturation AC as exponent basis and the crystal surface A as linear factor. The proportionaUty factor /Cg considers the influence of the temperature. 

The mass deposition rate is also equal to the total flux of solute adding to the crystal surface, i.e. 

Chemical vapor deposition processes are complex. Chemical thermodynamics, mass transfer, reaction kinetics and crystal growth all play important roles. Equilibrium thermodynamic analysis is the first step in understanding any CVD process. Thermodynamic calculations are useful in predicting limiting deposition rates and condensed phases in the systems which can deposit under the limiting equilibrium state. These calculations are made for CVD of titanium - - and tantalum diborides, but in dynamic CVD systems equilibrium is rarely achieved and kinetic factors often govern the deposition rate behavior. 

An alternative scheme, proposed by Garside et al. (16,17), uses the dynamic desupersaturation data from a batch crystallization experiment. After formulating a solute mass balance, where mass deposition due to nucleation was negligible, expressions are derived to calculate g and kg in Equation 3 explicitly. Estimates of the first and second derivatives of the transient desupersaturation curve at time zero are required. The disadvantages of this scheme are that numerical differentiation of experimental data is quite inaccurate due to measurement noise, the nucleation parameters are not estimated, and the analysis is invalid if nucleation rates are significant. Other drawbacks of both methods are that they are limited to specific model formulations, i.e., growth and nucleation rate forms and crystallizer configurations. 

Thickness controllability (Table 9.1, no. 6) and reproducibility in OVPD is achieved by accurate adjustment of the flow of carrier gas by means of mass-flow controllers whereas in VTE quartz crystal monitors are used to control the rate of deposition by adjustment of the evaporation temperature. In VTE small deviations of the evaporation temperature are known to affect the stability of the deposition rate and consequently the layer thickness, which may also affect the roughness and morphology of the VTE-deposited layer. 

The rotatable reactor can also be used for reactions in fluids having suitably low (< 10"3 Torr) vapor pressure. In this mode, metal atoms are evaporated upwards into the cold liquid, which is spun as a thin band on the inner surface of the flask. Reactions with dissolved polymers can then be studied. Specially designed electron gun sources can be operated, without static discharge, under these potentially high organic vapor pressure conditions (6). Run-to-nin reproducibility is obtained by monitoring the metal atom deposition rate with a quartz crystal mass balance (thickness monitor). 

The TSM resonator was originally used in vacuo to measure metal deposition rates [1]. More recently, the TSM resonator has been shown to operate in contact with liquids [2,3], enabling its use as a solution-phase microbalance. The device is typically incorporated in an oscillator circuit, where the oscillation frequency tracks the crystal resonance and indicates mass accumulation on the device surface. This microbalance capability has facilitated a number of gas- and liquid-phase sensor applications that will be discussed in Chapter 5. 

Photon correlation spectroscopy measurements for growth rate, together with a quartz crystal microbalance for mass deposition, have been integrated into a single platform to permit simultaneous in-situ real time measurement at times and temperatures representative to those found in aviation fuel systems [323],... 

Another study carried out by these authors [93] modeled the collapsing motion of a single bubble near an electrode surface, and equations for the motion of a spherical gas bubble were obtained. The jet speed and water hammer pressure during jet flow (liquid jet) were calculated, and when the jet speed was 120 m/s, the water hammer pressure was approximately 200 MPa upon the electrode surface. This pressure played an important part in the fineness of the crystal deposits. Mass transfer during the electrode reaction was by turbulent diffusion. The diffusion layer thickness was reduced to approximately 1/10th its size in the presence of the ultrasonic field. The baths contained the ions Cl-, SO -, and Zn2+. The ultrasonic frequency employed in the experiments was 40 kHz and it was seen that ultrasound considerably increased the deposition rate and current efficiency, as well as the smoothness and hardness of the deposit. Microscopy studies showed that the... 

Mass amplification is another strategy to increase the mass sensitivity of a standard QCM device and crystal. Such approaches commonly involve enzymatic catalysis to greatly increase either the rates of electron transfer processes in EQCM applications or to increase rates of insoluble mass deposition as the product of an enzymatic reaction [157-159]. However, mass amplification can also involve the use of larger mass objects binding to the QCM crystal, such as gold particles. We expect that future studies will continue to adapt these general mass amplification strategies to specific systems. 

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