Chimney-ladder structures

Composite crystals, in which the structure can be described as resulting from two or more substructures (related to two or more sets of three dimensional lattices) having different periodicity along at least one direction (chimney-ladder structures, vernier structures, misfit-layer structures, etc.). See the scheme presented in Fig. 3.42. 

A group of crystals show diffraction patterns in which two or more 3D lattices having periods commensurate or incommensurate to each other may be recognized. In other words, the crystal consists of two or more interpenetrating substructures (two or more different atom sets) with different periods at least along one direction (see Fig. 3.42). Names such as composite crystals, vernier structures, misfit-layer structures, and chimney-ladder structures have been used for this group of structures. 

Nowotny phases, chimney-ladder structures. The Nowotny chimney-ladder phases are an example in alloy field chemistry of composite structures. They are a series of intermetallic T X , compounds formed by transition metals T from the 4th to 9th groups with p-block elements X from the 13th to the 15th groups. 

Figure 3.43. Examples of chimney-ladder structures (b)-(d) and the reference oF24-TiSi2 type structure (a) presented in terms of a tetragonal pseudo-cell (12 atoms in the pseudo-cell). Notice that the metal atoms (black circles) form sequences of (3Sn like cells.

We consider incommensurate structures of the type which have two more or less independent, though modulated, sub-lattices derived from misfitting layers of two types, alternating regularly in the layer-stacking direction. These are the two-dimensional analogues of the so-called chimney-ladder structures (which are one-dimensional). 

The binary systems have been reinvestigated and ScMnj (MgZn2-type), ScjSi3 (MnjSi3-type) and ScSi (CrB-type) were confirmed, but Sc3Sij with the defect AlB2-type could not be obtained at 800°C. Similarly, one of the so-called Nowotny chimney ladder structures of the general formula Mn Si2 , was confirmed... 

In these phases, the unit cell (superstructure cell, super-cell) contains along the oaxis n pseudo-cells of T atoms and m interpenetrating pseudo-cells of X atoms. These phases (Nowotny phases) have been called chimney-ladder phases because they contain rows of atoms X (the ladder ), with variable interatomic spacing from one compound to another, which are inserted into channels ( chimneys ) in the T array. The T metals in all of the superstructures form a (3-Sn-like array (see Chapter 7) with the number of T metal atoms in the formula of the compound corresponding to the number of (3-Sn-like pseudo-cells stacked in the c direction of the super-cell. The arrangement of the atoms in these phases can be compared to that found in the structure of TiSi2. 

The fact that the electron concentration appears to play some role in the control of this family of structures was noted by Nowotny (Schwomma et al. 1964a, b, Jeitschko and Parthe 1967, Flieher et al. 1968a, b, Parthe 1969) and reported by Pearson (1972). The second rule, discernible in the electron diffraction of the T Xm Nowotny chimney-ladder phases, is the appearance, along the c-axis of a... 

Figure 3.44. Views, according to Fredrickson et al. (2004a, b), of the Ru2Sn3 structure type, an example of the chimney-ladder Nowotny phases. On the left, a lateral view of the Ru helix (black balls) and of the Sn helix (white balls). The periods of the two helices (cn and cm) are given together with the lattice parameter c.

A crystal structure which is composed of more than two sublattices, which are independent, though modulated, is named a vernier or chimney and ladder structure. If the dimension of each sublattice (named A, B, C,...) along the c-axis is supposed to be c, Cg, Cg,..., the unit length of the whole structure (supercell structure) along the c-axis is expressed as... 

Composite structures" (misfit-, intergrowth-, chimney ladder-. Vernier-structures)... 

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