The Crystal Structures

Ionic compounds include all insulating compounds that form closc-packcd structures, that is, solids in which the constituent atoms have more than four nearest neighbors. Transition-metal compounds arc a special case, which we 

We should also mention another class of ionic solids, the ten-electron solids, such as PbS, PbSe, and PbTe (in which lead contributes four and S, Se, or Te contributes six electrons per molecular unit). These form in the same structure as NaCl and can be thought of, by analogy, as consisting of closed-shell S , Se , or Te ions and Pb ions that have fully-occupied s states and completely empty p states the Pb is closed-shell in almost the sense that He is hence, the same approaches that are developed here for other ionic crystals are appropriate to the ten-electron solids. Another such set of compounds are TlCl, TlBr, and Til, which form in the same structure as CsCl. Still another ionic compound without an inert- 

The principal elements lhal form closed-shell ions with the same electron configurations as the inert gases of column 8. The charge Z associated with the ion is indicated along the bottom of the figure. 

Brillouin Zone is the same for both zincblende and rocksalt, and is as shown in Fig. 3-6. 

It is important to recognize that though the lluorinc ions are tetrahedrally surrounded, each calcium ion has eight lluorinc neighbors this makes an ionic not a covalent -structure. Any attempt to construct a reasonable bonding unit leads to a unit that is the fluorine ion. 

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In certain crystals, e.g. in quartz, there is chirality in the crystal structure. Molecular chirality is possible in compounds which have no chiral carbon atoms and yet possess non-superimposable mirror image structures. Restricted rotation about the C=C = C bonds in an allene abC = C = Cba causes chirality and the existence of two optically active forms (i)... 

The crystal structure determines not only the arrangement of atoms in the lattice but also the external form of the crystal. 

Figure 1. shows the measured phase differenee derived using equation (6). A close match between the three sets of data points can be seen. Small jumps in the phase delay at 5tt, 3tt and most noticeably at tt are the result of the mathematical analysis used. As the cell is rotated such that tlie optical axis of the crystal structure runs parallel to the angle of polarisation, the cell acts as a phase-only modulator, and the voltage induced refractive index change no longer provides rotation of polarisation. This is desirable as ultimately the device is to be introduced to an interferometer, and any differing polarisations induced in the beams of such a device results in lower intensity modulation. 

Calculate the surface energy at 0 K of (100) planes of radon, given that its energy of vaporization is 35 x 10 erg/atom and that the crystal radius of the radon atom is 2.5 A. The crystal structure may be taken to be the same as for other rare gases. You may draw on the results of calculations for other rare gases. 

Knowing the lattice is usually not sufficient to reconstruct the crystal structure. A knowledge of the vectors (a, b, c) does not specify the positions of the atoms within the unit cell. The positions of the atoms withm the unit cell is given by a set of vectors i., = 1, 2, 3... u where n is the number of atoms in the unit cell. The set of vectors, x., is called the basis. For simple elemental structures, the unit cell may contain only one atom. The lattice sites in this case can be chosen to correspond to the atomic sites, and no basis exists. 

The empirical pseiidopotential method can be illustrated by considering a specific semiconductor such as silicon. The crystal structure of Si is diamond. The structure is shown in figure Al.3.4. The lattice vectors and basis for a primitive cell have been defined in the section on crystal structures (ATS.4.1). In Cartesian coordinates, one can write G for the diamond structure as... 

Dulmage W J and Lipscomb W N 1951 The crystal structures of hydrogen cyanide, HON Acta Crystallogr. 4 330... 

Figure Bl.8.4. Two of the crystal structures first solved by W L Bragg. On the left is the stnicture of zincblende, ZnS. Each sulphur atom (large grey spheres) is surrounded by four zinc atoms (small black spheres) at the vertices of a regular tetrahedron, and each zinc atom is surrounded by four sulphur atoms. On the right is tire stnicture of sodium chloride. Each chlorine atom (grey spheres) is sunounded by six sodium atoms (black spheres) at the vertices of a regular octahedron, and each sodium atom is sunounded by six chlorine atoms.

Flarker D 1936 The application of the three-dimensional Patterson method and the crystal structures of proustite, Ag,AsS, and pyrargyrite, Ag,SnS, J. Chem. Phys. 4 381-90... 

Satellite transition MAS NMR provides an alternative method for detennining the interactions. The intensity envelope of the spimiing sidebands are dominated by site A2 (using the crystal structure nomenclature) which has the smallest Cq, resulting in the intensity for the transitions of this site being spread over the smallest... 

Taking advantage of the synnnetry of the crystal structure, one can list the positions of surface atoms within a certain distance from the projectile. The atoms are sorted in ascending order of the scalar product of the interatomic vector from the atom to the projectile with the unit velocity vector of the projectile. If the collision partner has larger impact parameter than a predefined maximum impact parameter discarded. If a... 

The melting and boiling points of the aluminium halides, in contrast to the boron compounds, are irregular. It might reasonably be expected that aluminium, being a more metallic element than boron, would form an ionic fluoride and indeed the fact that it remains solid until 1564 K. when it sublimes, would tend to confirm this, although it should not be concluded that the fluoride is, therefore, wholly ionic. The crystal structure is such that each aluminium has a coordination number of six, being surrounded by six fluoride ions. 

It is stable up to 2000 K and melts under pressure at 2500 K. The crystal structure of aluminium nitride resembles that of boron nitride and diamond, but unlike both of these it is rapidly and exothermically hydrolysed by cold water ... 

As a template for an intermediate conformation of protein kinase, the crystal structure of the binary complex of cAPK with adenosine (Ibkx.pdb in the Protein Data Bank) was used. As templates for open conformations... 

To enable an atomic interpretation of the AFM experiments, we have developed a molecular dynamics technique to simulate these experiments [49], Prom such force simulations rupture models at atomic resolution were derived and checked by comparisons of the computed rupture forces with the experimental ones. In order to facilitate such checks, the simulations have been set up to resemble the AFM experiment in as many details as possible (Fig. 4, bottom) the protein-ligand complex was simulated in atomic detail starting from the crystal structure, water solvent was included within the simulation system to account for solvation effects, the protein was held in place by keeping its center of mass fixed (so that internal motions were not hindered), the cantilever was simulated by use of a harmonic spring potential and, finally, the simulated cantilever was connected to the particular atom of the ligand, to which in the AFM experiment the linker molecule was connected. 

The catalytic subunit then catalyzes the direct transfer of the 7-phosphate of ATP (visible as small beads at the end of ATP) to its peptide substrate. Catalysis takes place in the cleft between the two domains. Mutual orientation and position of these two lobes can be classified as either closed or open, for a review of the structures and function see e.g. [36]. The presented structure shows a closed conformation. Both the apoenzyme and the binary complex of the porcine C-subunit with di-iodinated inhibitor peptide represent the crystal structure in an open conformation [37] resulting from an overall rotation of the small lobe relative to the large lobe. 

Eijck B P, W T M Mooij and J Kroon 1995. Attempted Prediction of the Crystal Structures of Six Monosaccharides. Acta Crystallographica B51 99-103. 

Noble M E M, R K Wierenga, A-M Lambeir, F R Opperdoes, W H Thunnissen, K H Kalk, H Groendijk and W G J Hoi 1991. The Adaptability of the Active Site of Trypanosomal Triosephosphate Isomerase as Observed in the Crystal Structures of Three Different Complexes. Proteins Structure, Function and Genetics 10 50-69. 

For crystalline polymers, the bulk modulus can be obtained from band-structure calculations. Molecular mechanics calculations can also be used, provided that the crystal structure was optimized with the same method. 

An additional problem is encountered when the isolated solid is non-stoichiometric. For example, precipitating Mn + as Mn(OH)2, followed by heating to produce the oxide, frequently produces a solid with a stoichiometry of MnO ) where x varies between 1 and 2. In this case the nonstoichiometric product results from the formation of a mixture of several oxides that differ in the oxidation state of manganese. Other nonstoichiometric compounds form as a result of lattice defects in the crystal structure. ... 

Polyethylene. The crystal structure of this polymer is essentially the same as those of linear alkanes containing 20-40 carbon atoms, and the values of Tjj and AHf j are what would be expected on the basis of an extrapolation from data on the alkanes. Since there are no chain substituents or intermolecular forces other than London forces in polyethylene, we shall compare other polymers to it as a reference substance. 

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