Oscillatory zoning

Oscillatory zoning apparently occurred during crystal growth in response to... 

For a mineral with oscillatory zoning (such as plagioclase), the homogenization time (reduction of initial amplitude by a factor of 100) may be estimated from... 

Allegre C. J., Provost A., and Jaupart C. (1981) Oscillatory zoning a pathological case of crystal growth. Nature 294, 223-228. 

Yang P. and Rivers T. (2001) Chromium and manganese zoning in pelitic garnet and kyanite spiral, overprint, and oscillatory ( ) zoning patterns and the role of growth rate. J. Metamorph. Geol. 19, 455—474. 

Figure 11. Plagioclase crystal approximatively 0.5 mm across displaying oscillatory zoning the concentric layers are alternatively richer (dark) and poorer (light) in anorthi-te. View between crossed polars.

This reaction, widely known as the Belousov-Zhabotinskii reaction, can proceed in an oscillatory fashion [68]. For overall slow conversion, the concentrations of intermediates and the catalyst undergo cyclic changes. By this means, many pulselike reaction zones propagate in a spatially distributed system. Ferroin/ferriin can be applied as an optically detectable catalyst... 

Crystallization remains the primary means of controlling the polymorphic or solva-tomorphic state of a compound, and various groups have examined the influences of processing parameters on the identity and quality of the isolated form. Seeding was used to reduce the size of the metastable zone of eflucimibe, and thereby control the identity of the desired polymorphic identity of the product through a reduction in concomitant crystallization [16], Process improvements have been developed that were found to improve the filterability and enhance the bulk density of ranitidine Form-1 [17], while the variation of process parameters used in an oscillatory baffled crystallizer enabled better selection to be made between the metastable a- and /i-forms of (z.)-glutamic acid [18]. 

Fig. 2. The oscillatory signals in the fourth differences of solar frequencies. Panel (a) the 4th differences as points with the fit to the signal from the Hell ionization zone. Panel (b) the signal from the CZ base once the Hell signal is removed. Panel (c) the fit to the CZ-base signature with the ( -dependence of the signal removed.

Fig. 13.16 Stable, oscillatory, and unstable burning zones for a lead-catalyzed double-base propellant.

Figure 13.3 illustrates a typical control action (below) and the response of a process variable (above) in an on - off control system. As a result of on - off control, the response of a process variable inevitably becomes oscillatory around a set-point (overshoot and hunting). Thus, the precise control of a process variable is difficult to achieve using an on-off control system, and, therefore, the on-off control can be applicable only when the minimum and maximum values of the response are acceptable for successful operation of the bioprocess. To decrease the oscillation around a set-point, a differential gap (or a dead zone) is normally used to determine a threshold value. 

Fig. 9.7. Non-stationary behaviour in the diffusive autocatalysis model showing sustained temporal and spatial oscillations with D = 5.2 x 10 3, / = 0.08, and k2 = 0.05 (a) z = 0 or 465 (the oscillatory period) (b) z = 115 (c) z = 140 (d) z = 160 (e) z = 235. The limit cycle obtained by plotting the concentrations at the centre of the reaction zone, a,s(0) and /J (0), versus each other is shown in (f). The broken curve in (a) is the unstable stationary-state profile about...

---