Crystallization curves

These three systems describe a set of crystallization curves that cross at 6 = 0.5 and t = 10 sec. For the case where m = 2, the time span over which the change occurs is widest (1430 sec from 9 = 0.1-0.9) and the maximum slope is flattest... 

Fig. 4-9. This diagram shows the intensity variation with angle for a rock salt crystal in the region near the Bragg angle, 0q, for an incident monochromatic beam. The area under the mosaic crystal curve could be thirty times greater than the ideal. (After Renninger, Z. Krist. 89, 344.)...

Figure 7. Dynamic shear response (expressed as G, G , J" and tanS) of isotactic polypropyienes of varying crystallinity (torsion pendulum, 1Hz, ref 6). O 65%, O 56%, A 50%, achieved by annealing of quenched specimen ( 45%) + 68%, isothermally crystallized. Curves are calculated from parameterized equation (8).

Figure 4. Typical crystallization curves for A, B and B -type syntheses.

Once such detail is available it is possible to scan in the perpendicular direction in reciprocal space, using a scan, to measure the tilt independently of the strain. This is shown in Figure 7.5(c), in which the analyser was set on the prominent left-hand peak in the triple-crystal curve. The tilt variation in this layer is seen to be about 1500. Similar measurements on other peaks and correlation with crystal growth parameters can provide excellent feedback to the crystal grower. 

Figure 9.9 Double-crystal topographs with Ge reference crystal, asymmetric 206 reflection, glancing angle 1.7° Cu K j radiation. Sample is 2 /an Alg osGag 95AS, 2 /an Alo.ssGao.esAs, 1 /an GaAs on (001) GaAs substrate 206 reflection, (a) Flat reference crystal, (b) Reference crystal curved to 12 m radius of curvature. (Courtesy of Dr R.Kohler)...

Figure 1. Crystallization curves of mordenite from a batch composition 8.5 N avO-AWz-85 SiD2 182 H20 as a function of temperature and NaCl content filled symbols, no NaCl open symbols, 4.5 moles of NaCl/mole Al2Oz)...

Crystallization curves were obtained by analyzing the solid product from a number of identically charged autoclaves kept at the crystalliza-... 

The activation energies of the nucleation and crystal growth can be determined from the crystallization curves at various temperatures with the same batch composition. Assuming that the formation of nuclei of a size stable enough not to redissolve but to grow into a crystal is an energetically activated process, and since the nucleation process is rate-deter-... 

Figure 7. Crystallization curves of zeolite X from a batch composition 4 Na O-Al Os-5 Si02-200 H20 at 90°C (O) no seed crystals (A) 0.5-5 /meter seed crystals, 29% initial conversion ( ) 30-70 /meter seed crystals, 15% initial conversion...

Synthesis of Zeolite X. Zeolite X was crystallized from a batch of overall composition 4 Na20-Al203-5 SiO2-200 H20 at 90° C (8). The crystallization curve is shown in Figure 7. After an induction period of 2.4 hours, zeolite X was formed rapidly as a single phase at a conversion... 

Figure 8. Crystallization curves for zeolite A from a batch composition 2.5 NdzO-AUOs-l. 7 SiOz-150 H%0 (solid curves) no seed crystals, (broken curve) 0.5-5 nmeter seed crystals, 25% initial conversion...

Synthesis of Zeolite A. Zeolite A was crystallized from a batch of overall composition 2.5 Na20-Al203-1.7 SiO2-150 H20 at 60, 75, and 90°C (10). The same system was seeded with zeolite A crystals of 0.5-5 /zmeter size at an initial conversion level of 25% and crystallized at 60°C. As with the crystallization of zeolite X from seeded systems, the data were treated by ignoring the presence of seed crystals. The crystallization curves are shown in Figure 8. During the induction time period in the unseeded system, crystallization was taking place at a slow rate in the seeded system, both at 60°C. After this slow crystallization period the crystallization rate reached 22% per hour at the 50% conversion level... 

Fig. 8. Superheating of polyethylene extended chain crystals. Curves 1) at 421.7 K, 2) at 419.2, 3) at 417.7 K, 4) at416.7K, 5) at 414.7 K. The equilibrium melting temperature is 414.6 K. Drawn after Ref.40). "w is the weight fraction molten, obtained by isothermal calorimetry...

Fig. 12. Equilibrium extent of crystal lization, curve 2( and extent of cold crystallization, curve I. Calculated for equalmolecularweightsofri and B units...

In the NaOMe-Fe(OMe)3-MeOH system no complex formation takes place, the polymeric Fe(OMe)3 MeOH not being transferred into solution at any concentration of NaOMe, and its crystallization curve being situated therefore on the side ofthe triangle [1365] (Fig. 8.1 a). 

Figure 3.4a shows a normal crystallization curve with the spinodal (supersaturation limit) curve (CD) and equilibrium curve (AB). At point P neither nuclei nor crystal growth will occur since the solution is superheated by the amount RP. Once the saturation line (AB) is crossed, either through cooling or increase in concentration, nuclei and crystals may or may not form in the metastable region. Metastable point Q is shown between point R and the crosshatched line CD. 

An increase in hydrophobicity by inserting Ti into the framework is further substantiated by the crystallization curves the crystallinity of silicalite-1 decreased with increasing crystallization time after reaching the maximum. The presence of defect sites would make the material hydrophilic, resulting in an easy attack by adsorbed H20, and thus a collapse of the framework (4.1) ... 

Figure 5. Photorefractive two-beam coupling gain coefficient of undoped and doped BaTi03 crystals. Curves are theoretical fits to the data. Experimental conditions X = 515 nm, I = 3-5 W/cm2, beam ratio > 200, s-polarization, grating wave vector parallel to c-axis Concentrations refer to dopant atoms per BaTi03 formula unit in the melt.

Figure 6.27. The potential curves for sudden (2) and adiabatic (3) hydrogen transfer between the tetrahedral interstitial positions in niobium crystal. Curve 1 is the potential in the unrelaxed lattice. (From Chakraborty et al. [1988].)...

The effect of neutral salts (e.g., NaCl) on the composition of borates precipitated from, or in equilibrium with, aqueous solutions doubtless arises from a reduction in water activity, metal borate complexation, and a shift in polyborate equilibria (Sections IV,A, B). The "indifferent or inert component method has frequently been used for the synthesis of borates. Potassium and sodium chlorides can be used to enhance the precipitation of specific nickel (48), aluminum (51), iron (49), and magnesium (151) borates. In the K20-B203-H20 system at 25°C (248), the presence of potassium chloride results in a reduced boric acid crystallization curve, lower borate solubilities, lower pH, and an extended B203 K20 range over which the pentaborate crystallizes. 

Fig. 6. Evolution of the average forces acting on a cation at a corner, and the anion at the opposite comer of (a) NaF, (b) NaCl, (c) CsF crystals. Curves a and e forces resulting from all co-ions curves b and f forces from all counter-ions curves c and g forces resulting from all water molecules curves d and h The sum of the forces a + b + c and e + f + g, respectively. Forces are positive when pointing away from the center of the box. 

Fig. 7 DSC melting and crystallization curves of isotactic poly(S)-4-methyl-hexene-l. Note the two melting peaks (at 193.5 and 227.4 °C, respectively, AH 2.5 and 1.5cal/gram) and two crystallization peaks (at 201 and 120 °C, respectively same AH), as well as the significant temperature gap ( 74 °C) between the lower crystallization and melting processes. (From [44])...

FIGURE 3.10 Crystallization curves (a) clinoptilolite amorphization curve, (b) faujasite crystallization, and (c) zeolite P, crystallization. 

The hydrothermal transformation process, described with the crystallization curves shown in Figure 3.10, was carried out using zeolite Na-HC (the chemical and phase composition of this sample was given in Tables 4.1 and 4.2 besides, in Figure 3.11, the SEM micrograph corresponding to sample HC [119] is shown) with the following procedure the Na-HC was hydrothermally treated with a 7.5M NaOH and 0.6M NaCl (liquid to solid ratio = 1) solution and statically heated at 373 K in methyl polypropylene bottles [119]. 

During the recrystallization process (see Figure 3.10), first, a clinoptilolite amorphization curve was observed, then, the faujasite crystallization (see Figure 3.12) and, finally, the zeolite 1 crystallization curves [119]. 

Figure 4.7 Comparison of glass formation (curve abef ) and crystallization (curve abed). The point T, is the glass transition temperature and Tm is the melting temperature. (After J. West, Solid State Chemistry and Its Applications. Copyright 1985 John Wiley Sons, Inc. Reproduced with permission.)...

Figure 5. Comparison of the crystallization curves for the synthesis in the presence and absence of DMSO (samples 1-7).

Figure 6. Crystallization curves for the ZSM-5 syntheses from the TEA (- -) and TPA (- -) containing mixtures and the organics-free one (-V-).

Initiation of Zeolite Crystallization. An induction period (tj) is always observed at zeolite crystallization, and is accepted to be the period necessary for the formation of zeolite nuclei (20). The inverse value of induction period, 1/t, is called the rate of nucleation. The crystallization curves were plotted as the degree of crystallization (estimated by the XRD method) versus synthesis time. The values of tj were obtained by extrapolating the time when crystal growth started. 

Figure X. Crystallization curves for zeolite omega at 105°C, A115°C, + 130°C.

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