Lattice hexagonal close-packed

Here, we have arranged the layers on a two-dimensional structure, even though the layers are arranged in three dimensional order. Note that only two crystallographic axes are indicated. We call this the natural stacking sequence because of the nature of the hexagonal close- packed lattice. 

Although the bond-orientational metrics defined above have proven useful for identifying numerous space-filling crystalline morphologies43 like face-centered cubic, body-centered cubic, simple cubic, and hexagonally close-packed lattices, they are inadequate for detecting order in systems that organize... 

The rhombohedral unit cells for rhodium and iridium trifluorides (44) contain two formula units. The structure can be related to the first structure type by considering anion positions, which here correspond to a hexagonal, close-packed array. There are no vacant anion sites and the cations occupy one-third of the octahedral holes. This leads to M—F—M angles of 132°, characteristic for filling adjacent, octahedral holes in a hexagonal close-packed lattice. Alternatively, the structure can be described as a linking of octahedra through all corners, but the octahedra are now tilted with respect to each other. 

The crystal structure of a-Cr203 is made up by a hexagonal close-packed lattice of oxide ions (sequence ABAB ) Two-thirds of the octahedral sites are occupied by Cr3+ ions. Possible idealized surface structures, based on the (001), (100), and (101) planes and the creation of surface sites in the form of coordi-natively unsaturated cations and anions on dehydroxylation of the surface, have been discussed by Burwell et al. (21) and by Stone (144). The (001) face is the most likely crystal plane to predominate in the external surface of well-crystallized a-Cr203 (145). A possible surface model that maintains the overall as well as the local electrical neutrality, as proposed by Zecchina et al. (145) for the dehydroxylated (001) face, is shown in Fig. 2a. It can clearly be seen that equal numbers of four- and five-coordinate Cr3+ ions are to be expected on this idealized surface. Dissociative chemisorption of water would lead to the formation of surface OH groups, as shown in Fig. 2b, for a partially hydroxylated model surface. In fact, on adsorption of D20, Zecchina et al. (145) observed OD-stretching fundamental bands at 2700 and 2675 cm-1, which were narrow and isolated. As evidenced by the appearance of a H20 bending band at 1590... 

Interstice filled by atom in layer A if third layer is added to cover this interstice, then. .ABAB... periodicity is formed hexagonally close-packed lattice (hep) of cannonballs is formed... 

Various schemes have been proposed for the classification of the different alumina structures (Lippens and Steggerda, 1970). One approach was to focus attention on the temperatures at which they are formed, but it is perhaps more logical to look for differences in the oxide lattice. On this basis, one can distinguish broadly between the a-series with hexagonal close-packed lattices (i.e. ABAB...) and the y-series with cubic close-packed lattices (i.e. ABCABC...). Furthermore, there is little doubt that both y- and j/-A1203 have a spinel (MgAl204) type of lattice. The unit cell of spinel is made up of 32 cubic close-packed O2" ions and therefore 21.33 Al3+ ions have to be distributed between a total of 24 possible cationic sites. Differences between the individual members of the y-series are likely to be due to disorder of the lattice and in the distribution of the cations between octahedral and tetrahedral interstices. 

The wurtzite form of ZnS, Figure 7-8(b, c), is much rarer than zinc blende, and is formed at higher temperatures than zinc blende. It also has zinc and sulfide each in a tetrahedral hole of the other lattice, but each type of ion forms a hexagonal close-packed lattice. As in zinc blende, half of the tetrahedral holes in each lattice are occupied. 

Chromium(III) oxide has a structure in which chromium ions occupy two thirds of the octahedral interstitial sites in a hexagonal close-packed lattice of oxygen ions. What is the if-electron configuration on the chromium ion ... 

For specificity, let us consider the application of these ideas to a-CraOa. Its crystal structure can be represented as a hexagonal close-packed lattice of oxide ions (the closed-packed layers of oxide ions alternate ababab. ..) in which two-thirds of the octahedral holes are filled with Cr3+ ions in a systematic fashion. Suppose the crystal to be cleaved in a close-packed plane in the presence of water. To preserve electrical neutrality, the oxide ions in this plane must be equally divided between the surfaces of the faces being formed. As a result, each Cr3+ in the layer below these oxide ions would be five-coordinate and in a square pyramidal configuration. Each ion would react with a molecule of water following which a proton would move from each adsorbed water molecule to an adjacent oxide ion. Thus, the outer face would consist of a close-packed layer of hydroxide ions. This is shown in Fig. 2. The basic point is that electrical neutrality and six-coordination can both be preserved by replacing what would be a plane of oxide ions in bulk by an equivalent plane of hydroxide ions at the surface. Similar ideas obtain on alumina. 

Okamoto et al. [34] studied the crystallization of iron(m) hydroxide gel, containing 15 to 22% water, precipitated from aqueous solution, using X-ray diffraction and Mossbauer spectra. The structure of this material is identified as a hexagonal close-packed lattice of oxygen in which the iron(III) ions are distributed in an almost random manner amongst the available octahedral voids. The kinetics of recrystallization to a-FeOOH were measured from Mossbauer spectra and shown... 

The powder pattern of zinc made with Cu A a radiation (Fig. 3-13) will serve to illustrate how the pattern of a hexagonal substance is indexed. Thirteen lines were observed on this pattern their sin 0 values and relative intensities are listed in Table 10-2. A fit was obtained on a Hull-Davey chart for hexagonal close-packed lattices at an approximate cja ratio of 1.87. The chart lines disclosed the indices listed in the fourth column of the table. In the case of line 5, two chart lines (10- 3 and 11-0) almost intersect at cja = 1.87, so the observed line is evidently the sum of two lines, almost overlapping, one from the (10 3) planes and the other from (11 -0) planes. The same is true of line 11. Four lines on the chart, namely, 20 0, 10 4, 21 -0, and 20 4, do not appear on the pattern, and it must be inferred that these are too weak to be observed. On the other hand, all the observed lines are accounted for, so we may conclude that the lattice of zinc is actually hexagonal close-packed. The next step is to calculate the lattice parameters. Combination of the Bragg law and the plane-spacing equation gives... 

The hexagonal close-packed lattice can be represented by Fig. 10-2, if c = = 1.633a. There is an atom at... 

Fig. 5.4 Unit cells of (a) a cubic close-packed (face-centred cubic) lattice and (b) a hexagonal close-packed lattice.

Yellowish metal, forms oxide film on exposure to moist air. Two cryst forms a-form, hexagonal close-packed lattice, d 6.77 cMorm, body-centered cubic lattice, forms at 800. d 6.64. mp 935", bp 3290" 90". E (aq) Pr1+/Pr —2.47 V (calc). Experimental reduction potentials (referred to a norma] calomel electrode) —1.875, —1.990 V Nod-dack, Brukl. Angew. Chem. 50, 362 (1937). 

The metal has a hexagonal close-packed lattice and resembles other transition metals such as iron and nickel in being hard, refractory (m.p. 1680°+10°, b.p. 3260°), and a good conductor of heat and electricity. It is, however, quite light in comparison to other metals of similar mechanical and thermal properties and unusually resistant to certain kinds of corrosion and has therefore come into demand for special applications in turbine engines and industrial chemical, aircraft, and marine equipment. 

The closest analogues of thiols, alkaneselenols R—SeH, were found to form well-packed monolayers on the Au(lll) surface. The structure of these layers was studied by X-ray diffraction. An oblique unit cell was revealed, indicating a distorted hexagonal close-packed lattice of selenol molecules . Benzeneselenol and diphenyl diselenide form identical monolayers on gold, as shown with STM microscopy. Monolayers of benzeneselenol do not have vacancy pits typical for thiolate monolayers, but show the presence of small islands of gold (20-200 A) which were absent before deposition . 

In part II, we have given the corundum structure. Often one considers that the oxygen atoms form a slightly distorted hexagonal close-packing lattice with metal atoms in some of octahedral holes. 

---