Crystal structure diagrams

FIGURE 15.5. Beryllium chloride (a) in the gaseous state, and (b) in a crystal. In the gaseous state the coordination number of the beryllium is 2, in the crystal it is 4, giving a continuous series of BeCl tetrahedra that share edges, (c) A stereoview of the coordination in the crystal structure [diagrammed in (b)] (Refs. 44 and 45). 

Readers unfamiliar with crystal-structure diagrams are advised first to read appendix 2. 

Crystal-structure diagram for 5-0-(chloroacetyl)-142 3,4-di-0-isopropylidene-a-D-glucoseptano e (26). (The numbers given along the bonds are the projected dihedral angles between the atoms attached to the bonded atoms,)... 

Figure 5.29 Representations of tetrahedra found in crystal structure diagrams (a) a ball-and-stick diagram of a tetrahedron, with a central silicon atom surrounded by four oxygen atoms and (b) its representation as a polyhedron. The views in parts (c), and (d) are the equivalent to those in parts (a) and (b), along the direction A in part (b), in which one tetrahedral vertex is uppermost. The views in parts (e) and (f) are the equivalent to those in parts (a) and (b), along the direction B in part (b), in which one tetrahedral edge is towards the observer...

One of the most important and useful tools is the existence-crystal-structure diagram which summarizes the known crystallographic data and the existence/non-existence of compounds at all possible compositions in the R—M binary systems for a given M. A typical example is shown in fig. 18. Basically this diagram represents... 

Fig. 18. The existence-crystal-structure diagram for the R-Al alloys. (After Gschneidner and Calderwood 1983a).

Figure A1.12 shows the phase diagram for ice. (The pressures are so large that steam appears only at the extreme upper left.) There are eight different solid phases of ice, each with a different crystal structure. 

Figure 8.4 Cro molecules from bacteriophage lambda form dimers both in solution and in the crystal structure. The main dimer interactions ate between p strands 3 from each subunit. In the diagram one subunit is green and the other is brown. Alpha helices 2 and 3, the helix-turn-helix motifs, are colored blue and red, respectively, in both subunits. (Adapted from D. Ohlendorf et al., /. Mol. Biol. 169 757-769, 1983.)...

Figure 13.15 Schematic diagram of the heterotrimeric Gap complex based on the crystal structure of the transducin molecule. The a suhunit is hlue with some of the a helices and (5 strands outlined. The switch regions of the catalytic domain of Gq are violet. The (5 suhunit is light red and the seven WD repeats are represented as seven orange propeller blades. The 7 subunit is yellow. The switch regions of Gq interact with the p subunit, thereby locking them into an inactive conformation that binds GDP but not GTP.

Figure 17.12 Ribbon diagram of EMPl bound to the extracellular domain of the erythropoietin receptor (EBP). Binding of EMPl causes dimerization of erythropoietin receptor. The x-ray crystal structure of the EMPl-EBP complex shows a nearly symmetrical dimer complex in which both peptide monomers interact with both copies of EBP. Recognition between the EMPl peptides and EBP utilizes more than 60% of the EMPl surface and four of six loops in the erythropoietin-binding pocket of EBP.

Colloidal crystals . At the end of Section 2.1.4, there is a brief account of regular, crystal-like structures formed spontaneously by two differently sized populations of hard (polymeric) spheres, typically near 0.5 nm in diameter, depositing out of a colloidal solution. Binary superlattices of composition AB2 and ABn are found. Experiment has allowed phase diagrams to be constructed, showing the crystal structures formed for a fixed radius ratio of the two populations but for variable volume fractions in solution of the two populations, and a computer simulation (Eldridge et al. 1995) has been used to examine how nearly theory and experiment match up. The agreement is not bad, but there are some unexpected differences from which lessons were learned. 

Fig. 5.8. Crystal structures of bis(cyclopropyl)hydroxymethyl cation and 1-cyclopropyl-1-phenylhy-drox methyi cation. (Stmctural diagrams are rqrroduced from Ref 45 with permission of the American Chemical Society.)...

Fig. 7.3. Crystal structures of some lithium etiolates of ketones. (A) Unsolvated hexameric enolate of methyl t-butyl ketone (B) tetrahydrofuran solvate of tetramer of enolate of methyl r-butyl ketone (C) tetrahydrofuran solvate of tetramer of enolate of cyclopentanone (D) dimeric enolate of 3,3-dimethyl-4-(r-butyldimethylsiloxy)-2-pentanone. (Structural diagrams are reproduced from Refs. 66-69.) by permission of the American Chemical Society and Verlag Helvetica Chimica Acta AG.

The binary oxides and hydroxides of Ga, In and T1 have been much less extensively studied. The Ga system is somewhat similar to the Al system and a diagram summarizing the transformations in the systems is in Fig. 7.13. In general the a- and y-series have the same structure as their Al counterparts. )3-Ga203 is the most stable crystalline modification (mp 1740°) it has a unique crystal structure with the oxide ions in distorted ccp and Ga " in distorted tetrahedral and octahedral sites. The structure appears to owe its stability to these distortions and, because of the lower coordination of half the Ga ", the density is 10% less than for the a-(corundum-type) form. This preference of Ga "... 

Figure 17.4 The phase diagrams of the systems (a) HF/H2O and (b) HCI/H2O. Note that for hydrofluoric acid all the solvates contain >1HF per H2O, whereas for hydrochloric acid they contain <1HC1 per H2O. This is because the H bonds F-H F and F-H O are stronger than O-H O, whereas C1-H---C1 and C1-H---0 are weaker than 0-H---0. Accordingly the solvates in the former system have the crystal structures [HsOJ+F , [H30]+[HF2] and [H30] [H3F4], whereas the latter are [H30]+C1 , [H502]" C1 and [H502]" CP. H2O. The structures of HCI.6H2O and the metastable HCI.4H2O are not known.

Figure 29.1 Crystal structures of ZnS. (a) Zinc blende, consisting of two, interpenetrating, cep lattices of Zn and S atoms displaced with respect to each other so that the atoms of each achieve 4-coordination (Zn-S = 235 pm) by occupying tetrahedral sites of the other lattice. The face-centred cube, characteristic of the cep lattice, can be seen — in this case composed of S atoms, but an extended diagram would reveal the same arrangement of Zn atoms. Note that if all the atoms of this structure were C, the structure would be that of diamond (p. 275). (b) Wurtzite. As with zinc blende, tetrahedral coordination of both Zn and S is achieved (Zn-S = 236 pm) but this time the interpenetrating lattices are hexagonal, rather than cubic, close-packed.

The two most familiar allotropes of sulfur, rhombic and monoclinic, have the same molecular formula, S8. However, they differ in crystal structure. Using the phase diagram shown in Figure C. you can deduce how to convert either of these allotropes to the other. Notice that rhombic sulfur is the stable allotrope at temperatures below about 95°C. If it is heated to that temperature at... 

At high pressures, solid II can be converted (slowly) to solid III. Solid III has a body-centered cubic crystal structure. Line bd is the equilibrium line between solid II and solid III, while line be is the melting line for solid III.P A triple point is present between solid II, solid III, and liquid at point b. Two other triple points are present in this system, but they are at too low a pressure to show on the phase diagram. One involves solid II, liquid, and vapor while the other has solid I, solid II, and vapor in equilibrium. 

Sn2Sl2, was said (385) to exist in an a and a )8 form. The crystal structures of both forms have been elucidated (119, 239, 240, 388). Apart from questions that still remain concerning the true relationship of a-and )8-Sn2Sl2, a publication by Fenner (121) on the synthesis and structure of a new ternary phase, Sn4SIe, contradicts both of the phase diagrams already mentioned. 

Fig. 1 A ribbon diagram of the crystal structure of a substrate complex of the homo-dimer HIV-1 protease (lkj7) (Prabu-Jeyabalan et al. 2002), Each monomer is shown in cyan and pink the substrate is shown in green, and the catalytic aspartic acids are highlighted in yellow...

Fig. 2.28 X-ray crystal structures of parallel sheet-forming and all-un//fce-/F -peptides 116 and 117 [10, 191]. Views along the parallel amide planes and crystal packing diagram show the parallel pleated sheet arrangement (view perpendicular to the amide planes).

When two metals A and B are melted together and the liquid mixture is then slowly cooled, different equilibrium phases appear as a function of composition and temperature. These equilibrium phases are summarized in a condensed phase diagram. The solid region of a binary phase diagram usually contains one or more intermediate phases, in addition to terminal solid solutions. In solid solutions, the solute atoms may occupy random substitution positions in the host lattice, preserving the crystal structure of the host. Interstitial soHd solutions also exist wherein the significantly smaller atoms occupy interstitial sites... 

The volume defect is somewhat more difficult to visualize in two dimensions. Let us suppose that a line defect has appeared while the crystal structure was forming. This would be a situation similar to that already shown in 3.1.3. where aline defect was shown. The compression-tension area of the defect has a definitive effect upon the growing crystal and causes it to deform around the line defect. This is shown in the following diagram ... 

This is shown in the following diagram. Note that a simple shift in unit cell dimension is all that is required for the crystal structure change to take place. 

---