Mackay crystal

Figure 7.3 The structure of the three-dimensional Mackay crystals consists of convex and concave elements, (a) A scheme illustrating the structure of such crystals, while structural fragments of these idealized Cso-polymers are shown in (b) and (c) ( RSC 1995).

For materials which are available not in the form of substantial individual crystals but as powders, the technique pioneered by Debye and Scherrer is employed (Moore, 1972). The powder is placed into a thin-walled glass capillary or deposited as a thin film, and the sample is placed in the X-ray beam. Within the powder there are a very large number of small crystals of the substance under examination, and therefore all possible crystal orientations occur at random. Hence for each value of d some of the crystallites are correctly oriented to fulfil the Bragg condition. The reflections are recorded as lines by means of a film or detector from their positions, the d values are obtained (Mackay Mackay, 1972). 

Other structural analyses of crystals in which the bifluoride is present are listed in Table 7. One compound, p-toluidinium fluoride [C7H,oN ][HF2 ], is worthy of further comment. The first X-ray diffraction study reported a symmetrical anion (Denne and MacKay, 1971), but a later analysis showed that the proton was not centred between the two fluorines and 7 f h values were 102.5 and 123.5 pm (Williams and Schneemeyer, 1973). This can be explained not by a double minimum potential energy well but by asymmetry due to other forces, such as secondary hydrogen bonding between one end of the bifluoride anion and the N—H group of the cation. An alternative explanation attributes the asymmetry of the bifluoride hydrogen bond to an unsymmetrical crystal field caused by the cation (Ostlund and Bellenger, 1975). 

Akaganeite formed by hydrolysis of acid FeCls solutions (OH/Fe = 0) at 25-100 °C precipitates as somatoids between 0.2-0-5 p.m in length and 0.02-0.1 Lim in width (Fig. 4.15 a). The crystals are elongated along the c-axis and are bounded by (001) and (200) planes (Mackay, 1962). Crystals grown at room temperature display a square... 

Rod-like crystals (Eig. 4.15 b) are formed from partly neutralized Fe solutions (0 < OH/Ee < 3) (Mackay, 1962 Atkinson et al., 1977 Paterson Tait, 1977). They are usually monodisperse, around 50 nm long, 6 nm wide and also elongated in the [010] direction. In concentrated suspensions, these rods associate to form tactoids,... 

There is an inherent deficiency in crystal symmetry in that crystals are not really infinite. Alan Mackay argued that the crystal formation is not the insertion of components into a three-dimensional framework of symmetry elements on the contrary, the symmetry elements are the consequence [121], The crystal arises from the local interactions between individual atoms. He furthermore said that a regular structure should mean a structure generated by simple rules, but the list of rules considered to be simple and permissible should be extended. These rules would not necessarily form groups. Furthermore, Mackay found the formalism of the International Tables for X-Ray Crystallography... 

It is perhaps worth pointing out that every crystal is in fact defective, even if its only defect is that it has surfaces. However, if a crystal is only a ten-unit-cell cube, about half of the unit cells lie in the surface and thus have environments very different from those of the other half. The physical observation is that very small aggregates need not be crystalline, although they may nevertheless be perfectly structured. Mackay s proposal is to apply the name crystalloid to them. He offered the following definitions [133] ... 

Steinhardt, like Mackay before (see, Section 9.7), felt the need for redefinition of materials categories [144], His suggestions now included the newly discovered quasicrystals. Steinhardt has succinctly characterized the crystals, glassy materials, and quasicrystals as follows ... 

Figure 9-64 shows some beautiful representatives of quasicrystals and Figure 9-65 depicts another quasicrystal and a modern sculpture that could be taken as an artistic expression of a quasicrystal although the artist was not aware of the existence of such materials. The artistic appearance of quasi crystals, however, predates their scientific entry by centuries [150], The discovery of such cultural monuments has generated lively discussions even in the general press [151], Concluding, we quote again Mackay [155], who stated that... 

A. L. Mackay, Quasi-Crystals and Amorphous Materials. J. Non-Cryst. Solids 1987, 97 98, 55-62. 

Mackay MF, Sadek M (1983) The Crystal and Molecular Structure of Picrotoxinin. Aust J Chem 36 2111... 

Mackay ME, Mathieson AMcL (1965) The Crystal Structure of a-Bromoisotutinone. Acta... 

Day and Williams (1962, 1965) reported photoconductivity peaks for CuPc single crystals in the visible and near infrared where there are no strong absorption bands. The peaks in the photoconductivity spectra were attributed to direct singlet and singlet-triplet absorption. Fielding and Mackay (1964) and Schott (1966) later confirmed the existence of absorption bands in the spectral... 

In 1962 Mackay introduced some amazing structures built with hard spheres as possible models for atomic clusters. Their external shape was that of a regular IC, and their size could be extended from the atomic scale to infinity. Despite the perfect fivefold symmetry of these structures, their internal local order was nearly that of a crystal. 

Donadini R, Liew CW, Kwan AF1, Mackay JP, Fields BA Crystal and solution structures of a superantigen from Yersinia pseudotuberculosis reveal ajelly-roll fold. Structure 2004 12 145-156. 

FIG. 8. Examples of the smallest Mackay icosahedra, from sizes of 13, 55, 147, 309 and 561. The larger clusters show the formation of crystal surfaces [93]. 

The conditional stability constants (log K<.) obtained for copper with humic compounds extracted from soils and natural waters are invariably greater than those for other transition metals (see Table IV). This is expected from the enhanced levels of crystal field stabilisation energy which result fi-om the splitting of the 3d electronic orbitals on Cu by an octahedral field (Mackay and Mackay, 1969). The divei ence in the values of log Kc shown in Table IV, may, in part, have arisen from intrinsic variations in the copper-binding properties of the various humic samples. However, these deviations may also be explained in terms of the different experimental conditions employed (pH, ionic strength, temperature, for example) and the assumptions made in the calculations. For example, an increase in the pH will enhance the availability of dissociated binding sites (see Section 6) which are then free to participate in further complexation of copper and... 

Mackay [9-73, 9-74] called attention to yet another limitation of the 230-space-group system. It covers only those helices that are compatible with the three-dimensional lattices. All other helices that are finite in one or two dimensions are excluded. Some important virus structures with icosahedral symmetry are among them. Also, there are very small particles of gold that do not have the usual face-centered cubic lattice of gold. They are actually icosahedral shells. The most stable configurations contain 55 or 147 atoms of gold. However, icosahedral symmetry is not treated in the International Tables, and crystals are only defined for infinite repetition. 

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