Displacive disorder

Note that, displacive disorder being associated with a first-order transition, exhibits a jump at whose magnitude decreases from fully ordered albite (i.e., = 1) to... 

The Cp change at the transition temperature resulting from displacive disorder is, according to the Landau expansion above, ACp = 0.66 cal/(mole X K). The resulting entropy change associated with Al-Si substitutional disorder is —4.97 cal/(mole X K), near the maximum configurational effect expected by the random distribution of 3A1 -I- 1 Si atoms on four tetrahedral sites. 

Figure 5.55 Mutual dependence of Q i and Q d order parameters. In the upper part of the figure is outlined the T dependence of substitutional disorder Qod for different values of Qdi and, in the lower part, the T dependence of the displacive disorder parameter Qdt for different values of The heavy lines on the surface of local curves represent the solution for thermal equilibrium. From E. Salje and B. Kuscholke, Thermodynamics of sodium feldspar II experimental results and numerical calculations. Physics and Chemistry of Minerals, 12, 99-107, figures 5-8, copyright 1985 by Springer Verlag. Reprinted with the permission of Springer-Verlag GmbH Co. KG.

Fig. 16. Representation of the electron density in terms of step functions inside the smectic layer. X-rays being only sensitive to the contrast, the electronic density of the mesogenic cores has been arbitrarily assigned to zero. Since we do not make absolute intensity measurements and since we deal with a purely displacive disorder, the backbones and the spacers have been represented by two different step functions of equal hatched areas. The resulting electron density profile is shown in thick broken line. M, S and B stand for the mesogenic cores, spacers and backbones regions respectively...

Diffuse scattering arising from thermal displacement disorder, in the case of a crystal containing only atoms of one kind which vibrate independently about their average lattice sites, corresponds to a very simple formula, given by Eq. 8 [64,152] ... 

The discussed examples of random rotational and translation displacement disorder of chains around their axes have important implications for the interpretation of the X-ray fiber diffraction patterns of poly(tetrafluoro-ethylene) oriented samples in the mesomorphic forms stable at high temperatures (Sect. 5.7). 

Of course, the presence of non-random substitutional, translational or rotational displacement disorder, and hence the presence of short-range lateral correlations between neighboring chains, noticeably complicates the evaluation of the X-ray diffraction intensity distribution. Diffuse scattering in this case appears more localized for instance, in the case of non-random substitutional disorder, for systems where two different structural motifs tend to alternate in neighboring sites, diffuse scattering appears rather peaked near superstructure positions in the diffraction patterns [112]. In these cases, Eq. 3 should be used instead of Eq. 4 for the calculation of diffuse scattering. Equation 3 is usually presented in the form [61,112] ... 

In between the ideal crystalline and the purely amorphous states, most real crystals contain degrees of disorder. Two types of statistical disorder have to be distinguished chemical disorder and displacive disorder (Fig. 1.3-14). Statistical disorder contributes to the entropy S of the solid and is manifested by diffuse scattering in diffraction experiments. It may occur in both periodic and aperiodic materials. 

Displacement disorder and fractional site occupation arise from steric constraints. High amounts of these types of disorder occur for example in ff-Al Mgz from incompatibilities in the packing of Friauf polyhedra. Split occupation is also caused by geometrical hindrances. In this case, two lattice sites are too close to be occupied simultaneously. Locally, only one site can be occupied, while the other remains empty, which in the average structure corresponds to an occupation factor of 0.5 for both sites. 

Static defects in CVD diamonds such as stacking faults, dislocations, twinning, hydrogen, and other impurity atoms introduce displacement disorder of the carbon atoms. They cause shifts of atoms from the equilibrium positions. Static disturbances of lattice periodicity are the cause of X-ray or electron diffuse scattering. The intensity of diffuse scattering is a direct measure of the departure from the periodic network. The diffuse scattering around the 111 reciprocal lattice point is a very sensitive test for lattice periodicity of a CVD single crystal. 

Neutral vacancies formed during the growth are rarely observed in CVD crystals. Instead, vacancies appear as silicon (or silicon pair)-vacancy complexes. This defect is frequently observed in diamond crystals grown on Si. Growth sector (111) can be doped with Si to levels above 1 at%. This doping level introduces displacement disorder of atoms in the diamond lattice to such an extent that the 1332 cm Raman peak almost disappears. This means that the vibration mode related to the optical phonon becomes weak in such a distorted lattice. 

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