Modulated crystal structures substitutional modulation

Figure 8.21 Schematic representations of normal and modulated crystal structures and diffraction patterns (a) a normal superlattice, formed by the repetition of an anion substitution (b) part of the diffraction pattern of (a) (c) a crystal showing a displacive modulation of the anion positions (d) a crystal showing a compositional modulation of the anion conditions, (the change in the average chemical nature of the anion is represented by differing circle diameters) (e) part of the diffraction pattern from (c) or (d) (f) a modulation wave at an angle to the unmodulated component (g) part of the diffraction pattern from (f). Metal atoms are represented by shaded circles and non-metal atoms by open circles...

Table 1. Crystallographic data are presented for the new phases which resulted from a 3d-metal substitution at the copper site in the n=l, 2 and 3 Bi-based cuprates. The periodicity of the structural modulation (p) is given by bold numbers when obtained from single crystal x-ray studies, otherwise the values were obtained from TEM studies. 

Impuritiesand the a P-quartz tranition. The a- 3-quartz transition was the basis for one of the earliest systematic investigations of the variation of transition temperatures in response to impurities. Pure a-quartz undergoes a first-order transition to a microtwinned incommensurate structure at 573°C, and this modulated phase transforms to P-quartz at 574.3°C with second-order behavior (Van Tendeloo et al. 1976, Bachheimer 1980, Dolino 1990). Tuttle (1949) and Keith and Tuttle (1952) investigated 250 quartz crystals and observed that Tc for natural samples varied over a 38°C range. In their examination of synthetic specimens, substitution of Ge for Si raised the critical temperature by as much as 40°C, whereas the coupled exchange of Ar +Li o Si depressed Tc by 120°C. They concluded from their analyses that the departure of the a-P-quartz inversion temperature from 573°C could be used to assess the chemical environ-ment and the growth conditions for natural quartz. 

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