Close-packed layers positions

The structure of layered compounds often can be described by the ABC notation, shown in conjunction with the sites between close-packed layers in Fig. 7.1. Given a close-packed layer of atoms, with atoms at positions we call A, there are three possible places to put the atoms of the next layer directly above the first layer (also in the A positions), or fitted into the interstices of the first layer, either in B or C positions. In this notation, a trigonal prism sandwich is denoted AbA, and an octahedral sandwich is AbC, where the uppercase letters denote the layers of chalcogen or oxygen, and the lowercase letters the layers of transition metal atoms. 

Draw a projection of a unit cell for both the hep and ccp structures, seen perpendicular to the close-packed layers (i.e., assume that the close-packed layer is the ab plane, draw in the v and / coordinates of the atoms in their correct positions and mark the third coordinate zas a fraction of the corresponding repeat distance c). 

Fig. 11.1. A close packed layer of atoms. A indicates the position of the atoms in this layer, B and C are possible positions for atoms in adjacent layers.

Figure 3.1. (a) Positions of atoms for one close-packed layer of spheres. (b) Positions for two layers in projection (c) three layers A, B, and C) in projection. 

The 2 4PTOT structure is an hep structure with eight (2 4) close-packed layers in the unit cell. The full sequence is P TBOcT PB T/i OcT/j. This full structure, shown in Figure 3.7, with all layers labeled is not known. Note that only the O sites (white balls) are in C sites. This accounts for the few known examples of a structure with full occupancy of O sites for an hep structure. Structures with only half of the O sites filled, or with only alternate layers occupied, avoid the interaction. When the O layers are omitted any hep structure has open channels along the C positions. 

Figure 4.18. Four cells of As showing the puckered layers. Positions of close-packed layers are shown.

Nitrogen atoms occur only at A positions and the projection of all N atoms in the unit cell in Figure 8.18a corresponds to a full close-packed layer. The Si atoms are near the centers of distorted tetrahedral arrangements of four N atoms, for example, Si at one-half has two N at one-half, one at 0 and one at three-quarters. For each double layer the N atoms fill 4/9 of the A sites and Si atoms fill 3/9 of the B or C sites. N atoms are in planar triangular NSi3 units. Other sites are more irregular. The notation for the double layer structure is 4JP3/9 4/9. 

Figure 9A.a shows a projection along c. The structure is similar to that of Pb3Li8 (Section 9.2.9) except it is based on a fee subcell and there are no Mo-Mo pairs. The Mo and A1 atoms are distributed among all sites with no close Mo-Mo neighbors. A close-packed layer normal to 111 of the pseudocell is shown in Figure 9.4b. Because of the 3 8 filling of layers, there are 33 layers repeating. Figure 9.4b shows positions of other layers by solid dots. The notation is 3 llP(m)(3 8).

Figure 9.4. (a) A projection of the Mo3A18 unit cell is viewed down the c axis. Mo atoms are the larger circles. (b) The arrangement of atoms in a close-packed layer of Mo3Al8. There are open circles for A1 and squares for Mo in this layer. The repeating positions are solid dots in the cell for 33 layers. 

NbRh is monoclinic with nine molecules per unit cell, a = 2.806, b = 4.772, c = 20.250 A, and (3 = 90.53°. Close-packed layers are stacked along c. Figure 9.7 shows a projection of A, B, and C positions. The A layer is shown by solid points and solid lines, B positions are joined by dotted lines, and C positions are joined by dashed lines. Each close-packed layer has equal numbers of Nb and Rh atoms, with rows of Nb and Rh atoms giving rectangular patterns for Nb or Rh. This is the pattern for L1/2 shown in Figure 3.11a. The unusual close-packed sequence is ABA BCB CAC, giving nine repeating layers and the notation 9Pi/2i/2(m). Odd sequences such at this... 

ZrGa2 is orthorhombic with four molecules per unit cell, a = 12.894, b = 3.994, and c = 4.123 A. It is a slightly distorted superstructure of close-packed layers. In the a direction there are three fee pseudocells. A close-packed layer normal to 111 of the pseudocell is shown in Figure 9.16. The sequence of close-packed layers is ABC, but actually ABC A B C A"B"C" because of changing environments causing by partial filling by Zr and Ga. Positions B, C, B, C, A", B", and C" are shown by solid dots. For the close-packed layer shown, one horizontal row is fully occupied by Ga and one-half occupied by Ga in the next two rows. In rows parallel to the other cell faces one row is filled... 

Figure 9.16. The view of a close-packed layer normal to 111 of the pseudocell of ZrGa2 is shown. Repeating positions of the other eight layers are shown by solid dots (B, C, B, C, B", C").

Figure 9.17. (a) A projection of the Mn2Au5 structure along the b axis is shown, circles are for Au and squares are for Mn. A face-centered subcell is outlined by dashed lines. (b) A close-packed layer of Mn2Aus (open circles and squares) and positions for the other 20 layers are shown by solid dots. 

Figure 9.18. A close-packed layer of the structure of Ga3Pt5 is shown (squares are for Pt and circles for Ga). Packing positions in the other two close-packed layers are shown as solid dots labeled B and C.

Figure 12.5. A projection of three closed-packed layer at the A, B and C positions.

Layered silicates reveal two types of filled close-packed layers of oxide ions. Those bonded to Al3+ or Mg2+ ions in octahedral sites are the usual close-packed layers, oxide ions form a network of hexagons with an oxide ion at the centers. The oxide layers forming the bases of tetrahedra have oxide ions which form smaller hexagons without oxide ions at the centers. This is also the pattern found for layers 2/3 filled, but those oxide layers in silicates are filled. For many of the layered silicates the repeating units, based on packing positions, requires stacking as many as three unit cells. 

In contrast to the imperfect dislocation discussed in the preceding paragraph, the Shockley partial dislocation (Fig. Q. 2b) is a mobile imperfect dislocation. A Shockley partial dislocation can be considered as a displacement of a portion of the atoms in one close-packed plane into a new set of positions. For example, in the close-packed layer sequence... ABCABC..., a portion of the atoms in, say, the B layer, are shifted to C sites. 

Figure 1 (a) A close-packed layer of equal sized spheres, (b) The layer labeled B is added below A and nests in the P positions shown in (c)... 

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