Structure types face-centred cubic

C (diamond), cF8-C, structural type Face-centred cubic, space group Fd3m, N. 227. 

The In cell may be considered a distortion of the Cu type, face-centred cubic, cell. The unconventional face-centred tetragonal cell (equivalent to the tI2 cell), corresponds to a = aJY = 459.8, c = c = 494.7 and c /a = 1.076. Protactinium has a similar structure, which however with a c/a value lower than one, can be considered a distortion of the body-centred cubic structure. 

We shall now discuss the method of crystal growth and the electronic properties of GaAs, a typical example of a III-V compound which is expected to become more useful than Si and Ge in the near future, concentrating on the relation between non-stoichiometry and physical properties. GaAs has a zinc blende type structure, which can be regarded as an interpenetration of two structures with face centred cubic lattices, as shown in Fig. 3.29. Disregarding the atomic species, the structure is the same as a diamond-type... 

The sequence ABCABC... having a cubic symmetry is shown in Fig. 3.21. It is the cubic (face-centred cubic) close-packed structure, also described as cF4-Cu type structure. 

Figure 3.21. The face-centred cubic close-packed structure (Cu type). On the left a block of eight cells is shown (one cell darkened). On the right a section of the structure is presented it corresponds to a plane perpendicular to the cube diagonal. Notice that the plane is the same presented on the left in Fig. 3.19. The sequence of the layers in this structure is shown in Fig. 3.20 in comparison with other close-packed elemental structures.

Notice, moreover, that one face-centred cubic cell of atoms X in which all the interstices are occupied (the octahedral by X and the tetrahedral by Z atoms) is equivalent to a block of 8 XZ, CsCl-type cells (see Fig. 3.31). This relationship (and others with other structures such as Li3Bi and MnCu2Al) should be kept in mind when considering, for instance, phase transformations occurring in ordering processes. 

The tI10-MoNi4 type is another superstructure based on face-centred cubic pseudo-cells. In the projection shown in Fig. 3.36, inside the true cell, the pseudo-cubic subcell (aps = 362 pm, cps = 356.4 pm) has been evidenced by dotted lines. Close-packed layers can be identified in this structure they are stacked in a 15 close-packed repeat sequence. 

A special case of long-period structure to be considered is the oI40-AuCu(II) type structure which has ID substitutional and displacive modulations (Fig. 3.41). We must first mention that ordering of the Au-Cu face-centred cubic (cF4-Cu type) solid solution, having a 50-50 atomic composition, re-distributes Cu and Au atoms... 

A traditional example of a Zintl phase is represented by NaTl which may be considered as a prototype of the Zintl rules. The structure of this compound (face centred cubic, cF16, a = 747.3 pm) can be described (see also 7.4.2.2.) as resulting from two interpenetrating diamond type lattices corresponding to the arrangements of the Na and T1 atoms respectively (Zintl and Dullenkopf 1932). Each T1 atom therefore is coordinated to other four T1 at a distance a)3/4 = 747.3)3/4 = 323.6pm which is shorter than that observed in elemental thallium (d = 341-346 pm in aTl, hP2-Mg type, CN = 6 + 6) and d = 336pm in /3 Tl, (cI2-W type, CN = 8). 

Their normal crystal structure, at ambient conditions, corresponds to the body-centred cubic cI2-W-type structure. At very low temperatures, the close-packed hexagonal hP2-Mg-type structure has been observed for Li and Na, while for Rb and Cs the face-centred cubic close-packed cF4-Cu-type structure is known at high pressure. No polymorphic transformation has been reported for potassium. 

The diamond structure, see Fig. 7.14 below, is a 3D network in which every atom is surrounded tetrahedrally by four neighbours. The eight atoms in the unit cell may be considered as forming two interpenetrating face-centred cubic networks. If the two networks are occupied by different atoms, the derivative cF8-ZnS (sphalerite) type structure is obtained. As a further derivative structure, the tI16-FeCuS2 type structure can be mentioned. These are all examples of a family of tetrahedral structures which have been described by Parthe (1964). 

The otherl4th group elements, Si, Ge and oSn have the diamond-type structure. The tI4- 3Sn structure (observed for Si and Ge under high pressure) can be considered a very much distorted diamond-type structure. Each Sn has four close neighbours, two more at a slightly larger and another four at a considerable larger distance. Fig. 7.13 shows the (3Sn unit cell. Lead, at ambient pressure, has a face-centred cubic cF4-Cu type structure. 

The section sequence of the cF24-Cu2Mg type structure is shown in Fig. 7.30. Face-centred cubic cF24-Cu4MgSn and cF24-AuBe5... 

Figure 1.24(c) shows a unit cell of a face-centred cubic structure. If a single atom is placed at each lattice point then this becomes the unit cell of the ccp (cubic close-packed) structure. Find the 100, 110, and the 111 planes and calculate the density of atoms per unit area for each type of plane. (Hint Calculate the area of each plane assuming a cell length a. Decide the fractional contribution made by each atom to the plane.)... 

Fig. 1.1 The three commonest elemental structure types (a) face-centred cubic, (b) hexagonal close-packed, and (c) body-centred cubic. From Wells (1986).

First preliminary variants of DDM were applied in the full-profile X-ray diffraction structure analysis of a series of new silica mesoporous materials and ordered nanopipe mesostructured carbons. DDM allowed stable back-ground-independent full-profile refinement of the structure parameters of these advanced nanomaterials, a result that was unattainable by any other method. To date, DDM has been applied to many various mesoporous and mesostructured substances. The structural parameters of a series of face-centred cubic (Fm3m), body-centred cubic Im3m), and two-dimensional hexagonal (pGmm) mesoporous silicates were determined by DDM from synchrotron XRD. A comprehensive structural analysis of mesoporous silicates SBA-16 (cage-type cubic Irriim), their carbon replicas, and silica/carbon composites was performed by applying DDM. The structure of MCM-48 mesoporous silicate materials was analysed in detail by DDM from different laboratory and synchrotron XRD data. The pore wall thickness of both as-made and... 

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