Lattice parameters equilibrium samples

Fig. 25. Lattice parameters of equilibrium CAR samples as a function of oxygen nonstoichiometry, after data of Kruger et al. (1997) and Conder et al. (1999). (a) a-parameter (b) 6-parameter (c) orthorhombic strain (d) c-parameter (e) unit cell volume. Note the steep change at the T — O transition, and the deviations from linearity.

Fig. 109. Schematic illustration of phase relationships, structural transitions and anomalies appearing in the nonstoichiometric range of 123-0,. First row EM investigations of Beyers et al. (1989). Second row XRD and NPD on poly- and single-crystalline samples, after Plakhty et al. (1994, 1995). Third row Hard X-ray single-crystal refinements of superstructures, after von Zimmermann et al. (1999). Fourth and fifth rows under normal and higher pressures, measured in equilibrium samples. Sixth to tenth rows phase relationships deduced from lattice parameters of slowly cooled samples (preparation methods described in sect. 3.1.2.2). Eleventh row EXAFS results after Rohler et al. (1997a,b, 1998).

The above-mentioned phase transitions conform to the Le Chatelier principle, the sample volume decreasing under high pressure. They are not basically different Irom those observed in the static method, under conditions of thermodynamic equilibrium. There is, however, a class of anomalous phase transitions, which occur only in dynamic experiments and in which the shock compression gives rise to lower densities. The first of such phases was obtained in 1965 by shock treatment of the turbostratic BN [224] the new phase differed from both the graphite-Uke (/i-BN) like (c-BN) polymorphs of boron nitride and was named E-BN (E standing for the explosion phase ). Later, it appeared that the lattice parameters of E-BN are nearly identical to one of the phases of fullerene Ceo [225, 226], viz. a = 11.14, ft = 8.06, c = 7.40 A for E-BN, cf. a= 11.16, = 8.17, c = 7.58 A for Qo, with similar densities of 2.50 g/cm. Thus, the BN-fullerene was obtained by explosion (though not recognized as such) some 25 years before the carbon fuUerene was identified. Later on. 

For all of the applications outlined above, and many others besides, it is desirable to use NMR parameters which possess an intrinsic temperature dependence in order to measure directly the sample temperature. These measurements can either be performed as a pre-experiment calibration procedure using identical data acquisition parameters as for the actual experiment, or as an in situ measurement using the actual sample. Temperature-dependent NMR parameters include spin lattice (Ti) and spin-spin T2 relaxation times, chemical shifts, dipolar and scalar couplings, molecular diffusion coefficients and net equilibrium polarization. Dependent upon the particular application, each of these parameters has been utilized as an NMR thermometer . 

Another powerful contrast parameter is spin-lattice, or Tj, relaxation. Spin-lattice relaxation contrast can again be used to differentiate different states of mobility within a sample. It can be encoded in several ways. The simplest is via the repetition time, between the different measurements used to collect the image data. If the repetition time is sufficiently long such that Tj )) Tj for all nuclei in the sample, then all nuclei will recover to thermal equilibrium between measurements and will contribute equally to the image intensity. However, if the repetition time is reduced, then those nuclei for which Tr < Tj will not recover between measurements and so will not contribute to the subsequent measurement. A steady state rapidly builds up in which only those nuclei with Tj contribute in any significant manner. As with -contrast, single images recorded with a carefully selected may be used to select cmdely a short component of a sample. 

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