NiAs (B8) structure

3.1.3. NiAs (B8) structure

The NiAs (B8) structure is represented by MmXn, where M is a metal ion and X is a B group element. X ions are in approximately close-packed layers which in turn are stacked in the ABAB…sequence and ðm , nÞ M ions are in octahedral coordination. This is in contrast to the NaCl (B1) structure in which the layers of the X ions are stacked in the ABCABC… sequence, where none of the octahedra shares faces.

Ideal NiAs structure has hexagonal symmetry. Each X ion is surrounded by six M ions at the corners of a trigonal prism. The axial ratio c/a varies from 1.22 to 1.97 for different compounds. For hexagonally close-packed spheres, the ideal axial ratio c/a is 1.633. A structure having a lesser value for this ratio is stabilized by cation–cation bonding through overlapping of d-orbitals (along the octahedra) and those in the bi-pyramidal interstices. Such compounds manifest metallic conductivity.

There are two crystallographic modifications of Fe-substituted NiAs (B8) structure, depending on whether Fe is in the Ni (normal B8) or in the As (inverse B8) sites. In normal B8 structure, the Fe atoms form chains along the c (the hexagonal) axis, the magnetic collapse is continuous and the transition is continuous because of the short Fe–Fe distance.

In inverse B8 structure, the transition is sudden and occurs at extreme pressure (.500 GPa).

3.1.3.1. Chemical bonding

In the NiAs structure, the axial ratio c/a becomes close to 1.63, when it assumes hcp structure. The structure is electrostatically unstable with respect to NaCl (B1) or CsCl (B2) structures but it is stabilized by appreciable covalent character of its bonding. Non-transition-metal compounds can have this structure under high P, T conditions. When the chemical bonds are appreciably covalent, the transition-metal ions tend to have six-coordination rather than four; hence, the NiAs structure occurs in preference to sphalerite or wurtzite structure. Thus, the NiAs structure stabilizes when the transition-metal ion is octahedrally coordinated and the bonding is dominantly covalent.

In an ideally close-packed hexagonal array c/a ¼ 1:633; an ion occupies the same space as in a cubic close-packed array but cation–cation distance along the c-axis of the hexagonal close-packed array is considerably shorter than the cation–cation distance in the cubic-packed array. Zemann (1958) computed the Madelung constant for the NiAs structure of various axial ratios. The maximum of these constant occurs for the NaCl structure. Thus, if electrostatic forces are the only interaction among the ions, the NaCl structure is more stable than the NiAs structure.

Anions having p3 and sp3 d2 orbitals favour the NaCl structure rather than the NiAs structure but some hybrid orbitals such as spd4 and pd5 have a trigonal-prismatic configuration. With a central X ion having sp3 hybrid orbitals, the distorted tetragonal orbitals “resonate” at the six positions by “pivoting around the central ion” (Pauling, 1961). Such ions which form quadrivalent bonds prefer trigonal prismatic sites.

This resonating quadricovalent bond of Pauling can explain the magnetic properties of the NiAs structure.

Structural Types of Major Phases 293In transition-metal compounds, two competing tendencies operate. Electrostatic forces among the ions tend to arrange the ions in the NaCl structure in order to lower the Coulomb energy of the system. The covalent bonds, on the other hand, tend to arrange the ions in the NiAs structure in order to lower the distortion energy (in the covalent bonds).

The covalency of the bonds is consequently determined by the choices between these two structures.

3.1.3.2. Hexagonal close packing and c/a ratio

The hcp metals are different from fcc and bcc metals in having an anisotropy parameter represented by the c=a ratio. The model of hard-sphere packing specifies the ideal values of the c/a ratio to be 1.633. Most of the hcp metals have axial ratios close to this value but there are some metals whose axial ratios are very different. The deviation from the ideal c=a value can be explained by the gain in the band-structure energy through lattice distortion.

With pressure, the variation of the axial ratio is continuous but there is a clear change in the slope of the volume dependence of the axial ratios at a common value of c/a ¼ p3ð¼ 1:732Þ: The hcp structure with c/a ¼ p3 has special symmetry both in real and reciprocal spaces. A number of hcp reciprocal lattice vectors are degenerate and have the same magnitude at c/a ¼ p3: The origin for the anomaly could be the topological transition of the Fermi surface of such materials. Further theoretical and experimental studies of this anomaly are highly desirable.

The most distorted hcp metals (namely Zn and Cd) manifest decrease in the axial ratios with pressure and approach the value of 1.59 in the pressure range 100–200 GPa.

The smallest axial ratio for hcp structure under pressure has been found in Ba(II), for which c/a ¼ 1:50 (at 12.6 GPa). Ba(II) transforms to Ba(IV) exactly when the axial ratio becomes 1.50. The hcp structure with c/a ¼ 1:50 attains high symmetry and also a number of reciprocal lattice vectors become degenerate. This remarkable decrease in the axial ratio with pressure can be related to the pressure-induced s–d electronic transition preceding phase II. The increased d-character of the valence electrons in phase II adopts directional bonding and may favour the distorted and anisotropic structure.

Réference: http://bookzz.org/dl/1067508/f892ae