Dilute crystals

Their system consists of a dilute crystal such that solute-solute interactions are negligible. Interactions between solvent and solute are important only insofar as the lattice vibrations are coupled with the zero-order nonstationary levels of the final state. The initial state is considered to be an equilibrated vibronic state, which implies v = 0 state for temperatures around 77°K. 

Very few aromatic 77-radicals have been studied in the solid state. It has been stressed that magnetically dilute crystals are required, and these are not readily prepared. One very important example is that of a.a-diphenyl-jS-picrylhydrazyl. This was incorporated in small quantities in single crystals of the corresponding hydrazine and the 14N hyperfine and gf-tensors derived in the usual manner (Zeldes e.t al., 1960). This method of studying radicals, whilst normal for transition metal ions, is obviously inapplicable to most organic radicals whether stable or unstable. Fortunately, the method of radiation damage beautifully accomplishes this difficult task. This is discussed in Sections V and IX. 

In the limit of large m (dilute crystals) this can be shown to approach AE = <52/12y5 already at m = 4 the value is within of this limit and at m — 6 within ff. The limiting formula may thus be used for all but the most concentrated crystals but it is valid only for a small compared with the least of the energy denominators, namely 1 — cos (2-npjm), so that it holds for a range of trap depths which narrows as the concentration measured by w-1 diminishes. However, in all situations the initial deviation from the unperturbed band is quadratic in the depth 8, just as has been shown for electron traps by Koster and Slater using a different argument. 

Plasma volume expanders such as dextrans may be incompatible at acidic pH.60,70 Care must be exercised with dilutions. Crystals that are formed upon storage may be redissolved by gentle warming. Care must be exercised when preparing doses of recombinant human erythropoietin solution for neonates to maintain the necessary amount of carrier proteins in the formulation 232... 

Doki, N. Kubota, N. Yokota, M. Kimura, S. Sasaki, S. Production of sodium chloride crystals of uni-modal size distribution by batch dilution crystallization. J. Chem. Eng. Japan 2002, 35 (11), 1099-1104. 

Abstract Contribution of the Jahn-Teller system to the elastic moduli and ultrasonic wave attenuation of the diluted crystals is discussed in the frames of phenomenological approach and on the basis of quantum-mechanical theory. Both, resonant and relaxation processes are considered. The procedure of distinguishing the nature of the anomalies (either resonant or relaxation) in the elastic moduli and attenuation of ultrasound as well as generalized method for reconstruction of the relaxation time temperature dependence are described in detail. Particular attention is paid to the physical parameters of the Jahn-Teller complex that could be determined using the ultrasonic technique, namely, the potential barrier, the type of the vibronic modes and their frequency, the tunnelling splitting, the deformation potential and the energy of inevitable strain. The experimental results obtained in some zinc-blende crystals doped with 3d ions are presented. 

We will consider the effect in diluted crystals (i.e., in crystals with small concentration of the Jahn-Teller impurity so that the complexes are located far enough from each other and can be considered as independent). 

Quantum-Mechanical Description of the Jahn-Teller Effect in Diluted Crystals... 

Now we will overview some experiments that reveal the specificities of the Jahn-Teller effect in diluted crystals. First of all, we will discuss a justification of their relaxation origin. We have mentioned before that the first experiments were done on the crystals of aluminum oxide (corundum), yttrium aluminum garnet, yttrium iron garnet, and lithium gallium spinel doped with a number of 3d ions [10,11]. The main result was the discovery of attenuation maximum which was considered to be observed at cot 1 and reconstruction of the relaxation time temperature dependence. In some experiments reported later both the velocity and attenuation of ultrasound were measured as functions of the temperature. They were done on ZnSe and ZnTe crystals doped with transition metals. These crystals have the zinc-blende structure with the Jahn-Teller ion in tetrahedral coordination. The following... 

The temperature dependence of the wave number obtained in ZnSe Cr + is given in Fig. 7, and it is typical for the mentioned diluted crystals. What do we see We see the peak of ImAk and the step-like variation of Re Ak in the interval of 6-20 K. The signs and the relative magnitudes of the variations correspond completely to what should be when the relaxation-origin anomalies take place. Remind, — K, < 0. The difference of the ReAk (Fig. 7) and ReAc/6 (Fig. 1) is in the high-temperature region corresponding to cor < 1. This difference is due to the temperature dependence of the relaxed modulus oc /T. This dependence is clearly seen in Fig. 8, where the result is shown of reconstruction of c (T) and c (T) with the use of the formulas (67) and (68). 

If the ZPL is weak, then variable temperature studies can identify its location from hot electronic and vibronic structure, with the latter illustrated in Fig. 10. The vibronic structure can be used to identify certain symmetry types of transition, for example Ti-T2 (Table 4). One viewpoint has been put forward that the spectral interpretation is confused by phonon dispersion in the vibronic sidebands of transitions. However, this complexity of the vibronic structure can in fact be utilized to provide a fingerprint to identify the location of the electronic origin. Where possible, it is more certain to compare both emission and absorption (or excitation) spectra for a particular transition in order to locate the electronic origin. Otherwise, transitions from different emissive states (with different state irreps) can be employed to confirm the symmetries and locations of terminal levels. Whereas other neat systems such as PrCl3 show additional features not present in the electronic spectra of the diluted crystal (LaCl3 Pr3+) due to interactions between... 

Antimony Trifluorides.—When metallic antimony is brought into an atmosphere of fluorine, it bums, with the production of a white solid fluoride, probably the trifluoride (Moissan). When antimony trioiide is put into hydrofluoric acid and the solution is gradually diluted, crystals of fluoride are deposited. As an amorphous mass, it can be produced by dry distillation of antimony powder with quicksilver fluoride. 

The experimental measurements include susceptibility, magnetic moment, heat capacity (both calorimetric and AC magnetic methods) of the undiluted compounds, together with optical absorption and EPR on diluted crystals. The R ions form a close-packed hexagonal structure, in chains with two nn along the c-axis at +c, and six nnn on adjacent chains. A detailed study of Gd(OH)3 was carried out by Skjeltorp et al. (1973). At liquid-helium temperatures the inverse of the susceptibility is represented by a series... 

Gao SJ, Zhang DJ, Sun YQ, XiuZL. (2007). Separation of 1,3-propanediol from glycerol-based fermentations of Klebsiella pneumoniae by alcohol precipitation and dilution crystallization. Front Chem Eng China, 1, 202-207. 

Fig. 175. FeSiF 6H,0, single crystal, pure and diluted in ZnSiFt 6H,0 pure Fe crystal (solid lines), diluted crystal, Zn Fe ratio 0.855 1 (dashed lines). Temperature dependence of principal magnetic moments pj and p [67M11].

---