Cubic structure II

All common natural gas hydrates belong to the three crystal structures, cubic structure I (si), cubic structure II (sll), or hexagonal structure H (sH) shown in Figure 1.5. This chapter details the structures of these three types of hydrate and compares hydrates with the most common water solid, hexagonal ice Ih. The major contrast is that ice forms as a pure component, while hydrates will not form without guests of the proper size. 

Natural gas clathrate hydrates normally form either in the primitive cubic structure I, in the face-centered cubic structure II, or in the hexagonal structure H. 

Cubic structure I predominates in the earth s natural environments with small (0.4-0.55 nm) guests and cubic structure II generally occurs with larger (0.6-O.7 nm) guests in mostly man-made environments. Hexagonal structure H may occur in either environment, but only with mixtures of both small and the largest (0.8-0.9 nm) molecules. The smallest hydrated molecules (Ar, Kr, Oj and Nj) with diameters... 

As a rule, gas hydrates obtained under the P-T conditions close to those in the nearsurface have one of the three following structures cubic structure 1 (si), cubic structure II (sll) or hexagonal structure H (sH). Each of these structures has its own set of polyhedral cavities of different sizes. The better that the size and molecular shape of the guest... 

Figure 3 Cubic structure II clathrate hydrate, showing the two constituent cages, the space group, and typical lattice parameter.

Figure 4.25 Normal structures and the lamellar phase (a) normal micellar cubic structure (Ii), (b) normal hexagonal structure (Hj), (c) lamellar phase (L ), (d) normal bicontinuous cubic structure (Vi). Here a portion of the gyroid structure is sketched. The amphiphilic molecules form a bilayer film separating two continuous labyrinths of water. The amphiphilic film is a network with threefold node points, which defines the gyroid phase...

According to these authors all gas hydrates crystallize in either of two cubic structures (I and II) in which the hydrated molecules are situated in cavities formed by a framework of water molecules linked together by hydrogen bonds. The numbers and sizes of the cavities differ for the two structures, but in both the water molecules are tetrahedrally coordinated as in ordinary ice. Apparently gas hydrates are clathrate compounds. 

After crystal structure II was deduced, a definitive x-ray diffraction study of tetrahydrofuran/hydrogen sulfide hydrate was undertaken by Mak and McMullan (1965), two of Jeffrey s colleagues. The crystal consists of a face-centered cubic lattice, which fits within a cube of 17.3 A on a side, with parameters as given in Table 2.2a and shown in Figure 1.5b. In direct contrast to the properties of structure I, this figure illustrates how a crystal structure may be completely defined by the vertices of the smaller 512 cavities. Because the 512 outnumber the 51264 cavities in the ratio 16 8, only 512 are clearly visible in Figure 1.5b. 

The unit cell of pyrochlore can be considered as eight CaF2-type cells stacked as octants of a cube. There are two types of cells shown in Figure 6.21. They differ in the position of the oxygen vacancy and the relative positions of atoms A and B. Only two of the eight octants are shown to make it easier to visualize the relative positions of the three types of atoms. The octant on the lower left is type I and the other one is type II. There are four of each type, and they are not in adjacent cells. Atoms A and B are in ccp layers (a face-centered cubic structure) with oxygens in T layers. The type I cube has A ions located on face... 

There are 146 water molecules in the unit cubic cell of a structure II hydrate. Each cell has 16 small, pentagonal dodecahedral cages of... 

The gas hydrates occur in three types of structures, named type I, type n and type H. The type I has 512 and 51262 polyhedra associated by face-sharing in the ratio 1 3, whereas in type II, 512 and 5,264 polyhedra are combined by face-sharing in the ratio 2 1. These structures have cubic symmetry. The recently discovered type H [779] has hexagonal symmetry and is isostructural with the hexagonal clathrasil-dodecasil 7-H [780]. The host lattice contains 512, 435663 and a larger 51268 void which can accommodate larger organic molecules than the type II cubic structure. 

Thermogravimetric analysis of nickel(II) chloride hexa-hydrate shows that water evolution occurs from ambient temperatures (25°) to 66.6°. The resulting dihydrate is stable up to 133.3°, beyond which temperature further water loss occurs. Differential thermal analysis shows an endotherm at 53.9° related to the first dehydration step, and a second, strong endotherm at 118.9°, not accompanied by any weight loss, indicates the transformation of an octahedrally coordinated to a close-packed cubic structure. 

Carry out the LCAO energy-band calculation for nickel, in the face-ccntcred cubic structure. Use the same set of six orbitals per atom but now neglect all but nearest-neighbor interactions (second neighbors are 40 percent more distant). The analysis is the same as for the body-centered cubic structure, except that there are now twelve nearest neighbors, in directions 2 / (Oll), 2 " (101), 2 2(110), 2 (0lT), 2 > (101), 2- (lT0), and the negative of each of these. For each band, it may be helpful to make a table of I, in, and ii for each of the twelve neighbors, followed by the or other interatomic matrix element,... 

Fig. 4 Molecular structure of lyotropic liquid crystals. (A) lamellar (B) hexagonal (C) inverse hexagonal (D) cubic type I (E) inverse cubic type IV (F) cubic type II. (A, B, and D Adapted from Ref C Adapted from Ref E Adapted from Ref F Adapted from Ref. l)...

Manganese(II) sulphide can be prepared in three forms with, respectively, the wurtzite, zinc blende and rock salt structures. The greyish-pink precipitate, obtained when (NH4)7S is added to a solution of Mn + ion containing NH3 and NH4CI, is a mixture of the two cubic forms, one rose-red and the other green. MnSg, which occurs as hauerite, has a cubic structure. 

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