Dauphine twin

The occurrence of twinned crystals is a widespread phenomenon. They may consist of individuals that can be depicted macroscopically as in the case of the dovetail twins of gypsum, where the two components are mirror-inverted (Fig. 18.8). There may also be numerous alternating components which sometimes cause a streaky appearance of the crystals (polysynthetic twin). One of the twin components is converted to the other by some symmetry operation (twinning operation), for example by a reflection in the case of the dovetail twins. Another example is the Dauphine twins of quartz which are intercon-verted by a twofold rotation axis (Fig. 18.8). Threefold or fourfold axes can also occur as symmetry elements between the components the domains then have three or four orientations. The twinning operation is not a symmetry operation of the space group of the structure, but it must be compatible with the given structural facts. 

The Dauphine twins of quartz are formed when quartz is transformed from its high-temperature form (p or high quartz, stable above of 573 °C) to the low-temperature form... 

Group-subgroup relations and the emergence of twins in the phase transition /3-quartz — a-quartz (Dauphine twins)... 

The Dauphine twin boundaries in a-quartz, which have been studied in detail by McLaren and Phakey (1969), are particularly interesting because the nature of their diffraction contrast fringes depends critically on the operating reflection g. For certain reflections, these twin boundaries behave as a-boundaries, whereas for other reflections, the fringe patterns originate not from any phase difference a, or any misorientation (change of s), but from the fact that the extinction distances in the two parts are significantly different. 

To determine the nature of the contrast of Dauphine twin boundaries, it is necessary to calculate the amplitudes (I lI and iFxl) and phases ( l and 0t) of the structure factors for L quartz and its Dauphine twin (T) for various reflections g, when the atom positions in the two structures are referred to the same axes ai, 82, 83, and c. The calculated values of Fl, Ft, and a = are given in Table 8.4, together with the ex-... 

Figure 8.17. Projection onto (0001) of the Si04 tetrahedra in left-handed (P3221) quartz and its Dauphine twin. The small circles represent Si and the large circles O. The numbers denote the fractional c-axis coordinates.

Table 8.4. Structure factor amplitudes and phase differences, and extinction distances for L quartz and its Dauphine twin for 100-kV electrons...

For a more detailed discussion of the contrast of Dauphine twin boundaries, the reader should consult the paper by McLaren and Phakey (1969), which illustrates the various types of contrast observed and compares... 

Figure 8.19. BF image of a Dauphine twin boundary in a wedge-shaped crystal at =0 for g = 10Tl. Note the change in spacing of the thickness fringes across the twin boundary.

Dauphine twin boundaries are sometimes parallel to low-index planes, but very often there appears to be no crystallographic control. This was certainly the case for the Dauphine twin boundaries observed between the Brazil twin boundaries in amethyst quartz by McLaren and Riakey (1969). 

Whenever a crystal transforms (usually on cooling) to a lower symmetry structure in which a number of orientational variants are possible, transformation twins are an almost invariable consequence if the new phase is nucleated at several different places in the original structure. The formation of Dauphine twins at the jS-to-a transformation in quartz is a classic example, which has already been mentioned briefly in Section 8.6. We now consider the twins and modulated structures associated with the monoclinic-to-triclinic transformation in the K feldspars, KAlSisOg. 

Diffraction contrast from Dauphine twin boundaries in quartz, phys. stat. sol., 31, 723-37. 

Fig. 7.7 (a) Projection of Si-atoms in a-quartz lattice to the (0001)-plane (simplified), (b) Dauphine twins one twin crystal is left from the twinning interface CD, second twin crystal is right from it and rotated by 60° about the optical c-axis. (c) Lattice structure of j8-quartz... 

Dauphin twins are built by two right-handed (or two left-handed) quartz crystals rotated by 60° about the optical c-axis and grown together (Figs. 7.7 and 7.9). 

Optical c-axes are parallel but the electrical a-axes are exactly antiparallel in both twins. Due to this property, Dauphine twins are also called the electrical twins. 

Fig 7.9 Dauphine twins in quartz X-cut observed in bias light after etching. (Courtesy of Kistler Company)... 

Images made in unsplit reflections do not reveal brightness differences due to orientation differences of the lattice, but they may exhibit domain contrast due to differences in the structure factor. This is the case for Dauphine twins in quartz, which are related by a 180° rotation about... 

Figure 36. Dauphine twin lattice in a-quartz close to the phase transition into the high-temperature /i-phase viewed along the threefold axis...

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