Crystal three-dimensional arrangement

Figure 7. Crystal structures of (a) hollandite, (b) romanechite (psilomelane), and (c) todorokite. The structures arc shown as three-dimensional arrangements of the MnO() octahedra (the tunnel-tilling cations and water molecules, respectively, are not shown in these plots) and as projections along the short axis. Small, medium, and large circles represenl the manganese atoms, oxygen atoms, and the foreign cations or water molecules, respectively. Open circles, height z. = 0 fdled circles, height z = Vi.

Figure 16. Crystal structure of a-MnOOH. The structure is shown as a three-dimensional arrangement of the Mn(0,0H)6 octahedra with the protons filling the [2 x 1] tunnels, and as a projection along the short crystallographic oaxis. Small circles, manganese atoms large circles, oxygen atoms open circles, height z - 0 filled circles, height z = A The shaded circles represent the hydrogen ions.

The techniques of X-ray diffraction analyses of crystals of compounds of interest can be used to determine, with high precision, the three-dimensional arrangement of atoms, ions and molecules in such crystals (14) in each case the result is referred to as the "crystal structure." X-ray diffraction by crystals was discovered by von Laue, Friedrich and Knipping (15) and the technique was applied by the Braggs to the determination of the structures of... 

Fig. 2.4-9. Different views of the crystal structure of KHgn (a) KHg2o polyhedra, (b) three-dimensional arrangement of single Hg atoms (small white ball) and KHg2o polyhedra, (c) another view of the structure emphasizing...

In summary, while some of the above polymers can form polar crystals, their three-dimensional arrangement in macroscopic specimens results in internal electrical compensation. To overcome this, such specimens must be externally polarized [55]. 

Heteropolyanions and isopolyanions are polymeric oxoanions (polyoxometalates) (2, 3, 5, 6). The structure of a heteropolyanion or polyoxoanion molecule itself is called a primary structure (5, 6, 77). There are various kinds of polyoxoanion structure (Section II.A. 1). In solution, heteropoly anions are present in the unit of the primary structure, being coordinated with solvent molecules and/ or protonated. Most heteropolyanions tend to hydrolyze readily at high pH (Section 1I.C). Protonation and hydrolysis of the primary structure may be major structural concerns in solution catalysis. Heteropoly compounds in the solid state are ionic crystals (sometimes amorphous) consisting of large polyanions, cations, water of crystallization, and other molecules. This three-dimensional arrangement is called the secondary structure. For understanding catalysis by solid heteropoly compounds, it is important to distinguish between the primary structure and the secondary structure (5, 6, 17). Recently, it has been realized that, in addition... 

The long extensions of the -R groups are three-dimensionally arranged around the polymer back-bone chain, and the floppy chains prevent the formation of a lattice and therefore crystallization. Plasticization with materials ester-benzoates would further separate the molecules and provide more flexible hardened cement. 

Both rutile and anatase crystallize in a tetragonal lattice, and their bulk structure can be described basically in terms of a three-dimensional arrangement of TiOe octahedra. The two polymorphs differ by the degree of distortion of each octahedral unit and by the manner in which the TiC>6 building blocks are spatially assembled. The structural differences described previously result in different physicochemical properties, such as density (4.250 g cm 3 for rutile and 3.894 g cm-3 for anatase) and stabihty (rutile is more stable than anatase by about 4.9 kJ mol-1). 

Space Lattice or Crystal Lattice The regular pattern of points which describe the three dimensional arrangement of particles (atoms, molecules, ions) in a crystal structure is called space lattice or crystal lattice. 

X-ray crystallography is a technique determining the three-dimensional arrangement of atoms in a protein from the diffraction pattern of X-rays, passing through a crystal of the protein or an other molecule. 

We have discussed the unit cell, which has imaginary boundaries. For simplification, each unit cell in a crystal can be represented by a single point. The result is called a crystal lattice, which is an imaginary three-dimensional arrangement of points such that the view in a given direction from each point in this lattice is identical to the view in the same direction from any other lattice point. In other words, it is an array of points that... 

The discovery of five-fold symmetry prompted the arf-interim Commission on Aperiodic Crystals of the International Union of Crystallography to change the definition of a crystal as a periodic three-dimensional arrangement of identical unit cells to the following ...by crystal we mean any solid having an essentially discrete diffraction diagram, and by aperiodic crystal we mean any crystal in which three-dimensional lattice periodicity can be considered to be absent . International Union of Crystallography. Report of the Executive Committee for 1991, Acta Cryst. A48,922 - 946 (1992). 

We have discussed some simple structures that are easy to visualize. More complex compounds crystallize in structures with unit cells that can be more difficult to describe. Experimental determination of the crystal structures of such solids is correspondingly more complex. Modern computer-controlled instrumentation can collect and analyze the large amounts of X-ray diffraction data used in such studies. This now allows analysis of structures ranging from simple metals to complex biological molecules such as proteins and nucleic acids. Most of our knowledge about the three-dimensional arrangements of atoms depends on crystal structure studies. 

Chirality is the non-identity of two objects that are related by a mirror symmetry relationship and can be a property common to both molecules and crystals (7). Whereas molecular chirality results from the disymmetric, three-dimensional arrangement of the constituent atoms, crystal chirality can be considered to result from a similar spatial arrangement in which the objects to consider are the molecules in the crystal (7b). It is for this reason that resolyed molecular chirality is a sufficient but not necessary requirement for crystal chirality (7a). 

Solids are most stable in crystalline form. However, if a solid is formed rapidly (for example, when a liquid is cooled quickly), its atoms or molecules do not have time to align themselves and may become locked in positions other than those of a regular crystal. The resulting solid is said to be amorphous. Amorphous solids, such as glass, lack a regular three-dimensional arrangement of atoms. In this section, we will discuss briefly the properties of glass. 

Figure 4. Crystal structure of [Ta6Cli2(EtOH)6][(Mo6Cl8)Cl6]-6EtOH showing the three-dimensional arrangement of cluster cations and cluster anions via oxygen bridges (oxygen atoms from crystalline ethanol molecules). Note Octahedra are constructed of the oxygen (or chlorine) atoms in the X positions Cl, C, and H atoms are omitted for reasons of clarity darker octahedra correspond to the [(Mo6Cl8)Cl6] anions.

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