Crystal symmetry detecting

In this section some examples for spontaneous magnetovolume effects in cubic Gd based compounds will be presented. As will be discussed in section 5, in cubic systems also distortions of the crystal symmetry have been observed. In all cases of our knowledge these distortions are, however, very small compared to strains which conserve the crystal symmetry and which will be the main topic of the rest of this chapter. The symmetry breaking effects are so small that they probably can only be observed in the highly symmetric cubic systems, where the detection of such distortions is easier. 

What is not shown in the tables, are spontaneous distortions of the crystal symmetry, which are usually very small (i.e. < 10-4) and have only been observed in cubic systems, where the detection of symmetry distortions is easier. To our knowledge the largest symmetry breaking effect has been observed for cubic GdZn by Rouchy et al. (1981), namely a tetragonal distortion of (A///)ooi -3.7 x 10-4 (see section 5). 

It is generally believed that the EPR-detectable nickel in oxidized hydrogenase represents low-spin Ni(III), d . In support of this view, the EPR signal disappears on reduction, consistent with reduction to Ni(II). The g values of oxidized hydrogenase were interpreted by Lancaster (7) as due to a rhombically distorted octahedron with the unpaired electron in a dx2 orbital. Square-pyramidal geometry is also possible. In practice, the coordination sites in proteins are often so distorted that structural interpretations of EPR spectra based on crystal symmetry may be misleading. 

In modern powder diffraction the measurement delivers a raw-file of some thousand step-scan data of counted X-ray photons per step. This raw file contains all the needed information to carry out a crystallographic analysis, but in a way that requires follow up. More informative is a list of distinguishable reflections that includes the position (mostly in the form of f-values) and intensity of each reflection. This dif-file (d-values and intensities) contains some tens to hundreds of reflections. The number of reflections depends on the complexity of the structure and the crystal symmetry the more atoms per cell and the lower the symmetry the more reflections can be identified. But the number of detectible reflections also depends on the resolving power of the equipment, best documented by the half-width of the reflections (more accurately half-width at half-maximum, FWHM). Reflections nearer together than this half-width (or even two half-widths) cannot be resolved. In a second step, very often the Miller indices of the originating lattice planes are added to the dif-file. For this the knowledge of the unit cell is necessary (though not of the crystal structure itself). The powder diffraction file PDF of the International Centre for Diffraction Data (ICDD) contains over 100000 such dif-files for the identification and discrimination of solid state samples. 

Ferroelectricity can arise in a number of ways other than that described previously, in which dipoles are generated in a crystal structure and combine to give a spontaneous polarisation if the crystal symmetry permits. These alternatives have been called improper ferroelectricity (perhaps better extrinsic ferroelectricity, see Lines and Glass 2001). In essence, improper ferroelectricity is ferroelectricity which is not due to the normal polarisation of the stmcture but arises from other interactions. Improper ferroelectricity has been considered to be rare in bulk materials and is a weak effect, usually rather difficult to detect, but the creation of artificial superlat-fices and studies of layered perovskites have changed this and now improper ferro-electrics are becoming widely studied. 

Balster and Wittig (1975) detected another anomaly of La which is shown in fig. 10.4. A point of inflection occurs in the R-T characteristic of fee La above 40 kbar. It readily shifts to higher temperatures with pressure. The positions of the points of inflection are shown by the circles in fig. 10.5 which is a hypothetical low-temperature phase diagram. The locus of the points of inflection passes through room-temperature around 70 kbar. This resistance anomaly is not associated with a change of crystal symmetry. Syassen and Holzapfel (1975) found that La has the fee structure between 30 and 120 kbar at room-temperature. It was hence concluded that the points of inflection may indicate the existence of another isostructural phase change whose phase boundary runs into the pressure axis at —25 kbar just where a second kink in Tc(P) occurs for metastable fee La (fig. 10.2). 

Two types of species have been detected in the /rSR spectrum of Ceo- One shows an unreacted or meta-stable muonium state which may well correspond to an internal state, muonium is trapped inside the cage Mu Ceo in the current notation [2]. This may be compared with normal muonium (Mu ) in diamond and many other elemental and compound semi-conductors, where the trapping site is in one of the cavities of tetrahedral symmetry. This state of CeoMu is not discussed here, but it does exhibit all the characteristics expected of the internal chemistry of Ceo-The anomalous muonium state. Mu, observed in semi-conductors and generally accepted to arise from muonium being trapped within one of the chemical bonds of the crystal, is unknown in molecules [5,6]. The constraints of the crystal lattice are necessary for the bond-centred state to be stable. 

Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

The molecular structure of the parent compound was investigated in the vapor and in the solid phase using X-ray, XN and GED methods. The reported data are shown in Table 16. In both phases a clear bond length separation could be detected with a localized three-membered ring and its three adjacent double bonds. The symmetry-equivalent cyclopropane bonds are rather long in C3v-symmetric BUL (1.533-1.542 A), which can be explained by the common electron-withdrawing effect of the 7r-systems in a. svM-ciinal conformation. For comparison, the unaffected bonds in unsubstituted cyclopropane are 1.499 A in the crystal and 1.510 A in the gas phase. Therefore, the bond lengths in BUL... 

Finally, reference must be made to the important and interesting chiral crystal structures. There are two classes of symmetry elements those, such as inversion centers and mirror planes, that can interrelate. enantiomeric chiral molecules, and those, like rotation axes, that cannot. If the space group of the crystal is one that has only symmetry elements of the latter type, then the structure is a chiral one and all the constituent molecules are homochiral the dissymmetry of the molecules may be difficult to detect but, in principle, it is present. In general, if one enantiomer of a chiral compound is crystallized, it must form a chiral structure. A racemic mixture may crystallize as a racemic compound, or it may spontaneously resolve to give separate crystals of each enantiomer. The chemical consequences of an achiral substance crystallizing in a homochiral molecular assembly are perhaps the most intriguing of the stereochemical aspects of solid-state chemistry. 

---