Isotopic mixed crystals

The gap to the perfect random distribution is evaluated, in the case of the isotopic mixed crystal, by comparing the entropy term related to the permutation of the molecules, of the order of kfT, with the elastic energy Ve] introduced by the substitution of one hydrogenated cell by one deuterated cell. Then at the temperature formation, we find kTf 102 Vcl, which is consistent with a random distribution. 

A W The sites A and B are practically equivalent we have a mean crystal whose properties are weighted averages of those of A and B. The singlet excitons of the anthracene isotopically mixed crystal are nice examples of this situation.129... 

In the intermediate domain of values for the parameters, an exact solution requires the specific inspection of each configuration of the system. It is obvious that such an exact theoretical analysis is impossible, and that it is necessary to dispose of credible procedures for numerical simulation as probes to test the validity of the various inevitable approximations. We summarize, in Section IV.B.l below, the mean-field theories currently used for random binary alloys, and we establish the formalism for them in order to discuss better approximations to the experimental observations. In Section IV.B.2, we apply these theories to the physical systems of our interest 2D excitons in layered crystals, with examples of triplet excitons in the well-known binary system of an isotopically mixed crystal of naphthalene, currently denoted as Nds-Nha. After discussing the drawbacks of treating short-range coulombic excitons in the mean-field scheme at all concentrations (in contrast with the retarded interactions discussed in Section IV.A, which are perfectly adapted to the mean-field treatment), we propose a theory for treating all concentrations, in the scheme of the molecular CPA (MCPA) method using a cell... 

In the case of electronic spectroscopy in molecular crystals, the first singlet state of the isotopic mixed crystal of anthracene has been investigated in reflectivity and shown to be of amalgamation type.129 Actually, while the gap of resonances A = va — vg) is about 70 cm-1, the excitonic bandwidth is estimated at 500 cm-1. Very few mixed crystals have been investigated in the whole range of concentrations,120 whereas examples of low concentrations (of impurities, for instance) are very numerous The anthracene crystal contains j8-methylanthracene naturally and shows an impurity level below the excitonic band.120 (This does not suffice, however, to predict that a mixed anthracene-j8-methylanthracene crystal will be of the persistence type.)... 

See, for instance, M. Lax, in Multiple Scattering and Waves in Random Media, P. L. Chow, W. E. Kohler, and G. C. Papanicolaou, Eds., North Holland, 1981, and references therein J. Klafter and M. S. Schlesinger, Proc. Nat. Acad. Sci. U.S.A. 83, 848 (February 1986), and references therein R. Brown, Thesis, University of Bordeaux 1,1987 R. Brown et al. J. Phys. C20, L649 (1987) 21 (1988) in press. (This last work thoroughly discusses the applicability of fractal theory to isotopically mixed crystals as disordered system. Serious criticism is presented both of the analysis of the experimental data and of the fundementals of their description in the present theory of fractals. For this reason we omit all works treated there. 

Isotopically Mixed Crystals Excitons in LiH Crystals Exciton-Phonon Interaction Isotopic Effect in the Emission Spectrum of Polaritons Isotopic Disordering of Crystal Lattices Future Developments and Applications Conclusions... 

NH stretching frequencies observed in the spectrum of an isotopically mixed crystal containing 3% of HD4N2 (24). 

There are multiple rNH bands in the infrared and Raman (Fig. 5) spectra of crystalline pyrrole. Only one band persists in the infrared spectrum of an isotopically mixed crystal and its frequency (3362 cm-1) is very close to the average frequency (3360 cm-1) of three infrared and two Raman bands. Incidentally, this shows that all pyrrole molecules in the crystal are symmetry equivalent and that there is only one N—H distance. 

The infrared spectrum of an isotopically mixed crystal of MgSC>4-6H2O, on the other hand, shows seven rOH bands in the 3500—3200 cm-1 range (39) which correspond (Table 2) to seven R(0.. 0) distances between 2.90 and 2.70 A (38). 

The vAH stretching bands of isotopically mixed crystals at low temperature are usually quite narrow (5 to 15 cm-1) and their frequencies can be determined with an accuracy of 2 cm-1 ( 0.03 to... 

Finally, note that both for pure crystals and for isotopically mixed crystals (for which —> M"p, av uj) —> a(w)) the solution of the system of equa-... 

An interesting special case is exhibited by the the isotopic mixed crystals, e.g. perdeuteronaphthalene (GioDg) and naphthalene (GioHg), or perdeutero-anthracene (GuDio) and anthracene (CuHio). Here, the miscibility is nearly complete. When these crystals are grown from the melt, no noticeable separation of the... 

Splitting of energy levels through aggregation, also exdton dimensionality Individual interaction matrix elements hi hi S, T Pair spectroscopy, high-resolution excitation spectroscopy, isotopic mixed crystals... 

Sensitised emission in isotopic mixed crystals at higher (> 1%) concentrations Exdton transfer in dilute exdton systems kfjG D in dilute exdton systems S,T Intensity of the guest emission with varying trap depth in isotopic mixed crystals as... 

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