The factors that play an important role in the formation of transition metal nitrides are the difference in electronegativity between nitrogen and the other element forming the nitride, the size of the atoms, and the electronic bonding characteristics of these atoms.
2.4.1 Electronegativity
Electronegativity can be roughly defined as the tendency of an element to gain electrons and form negative ions. Table 2.6 shows the electronegativity of the transition metals and nitrogen, as well as their electronegativity difference. The electronegativity is calculated by Pauling and others [1, 2]. It should be noted that the electronegativity of an element is not a fixed value, and is dependent on its valence state. In Table 2.6, nitrogen has a higher electronegativity than any other element on the left. The difference in electronegativity between nitrogen and the other element forming a nitride is an important factor in the structure and electronic bonding of the transition nitrides that determines the nature of the compound.
The electronegativity of nitrogen is high while that of the transition metals is low (Table 2.6), resulting in ionic bonding because of the transfer of electrons from one atom to the other resulting in an electrostatic interaction. A qualitative relationship between the difference in electronegativity and the ionic character of the bond is well recognized;
the greater the difference, the greater the ionicity. In the case of TiN, the ionic bonding of TiN indicates a charge transfer from the titanium atom to the nitrogen atom, resulting in the formation of Ti+ and N- ions and, correspondingly, an electrostatic interaction. The ionic bonding is similar for the other nitrides of group IV (Zr and Hf) and lower for those of group V (Ta, V, Nb). Generally, in the ionic bonding, it is likely that the M-N bond is predominant due to the octahedral grouping of the metal atoms around the nitrogen atom. This grouping has six bonds to the six corners and, in forming the
mononitrides, the valence electrons of the nitrogen atom hybridize with the p-state metal atom, with likely d2sp3 hybridization, which is common for metals in group IV.
Table 2.6. Electronegativity and electronegativity difference between nitrogen and the transition metal nitrides [1].
The second factor controlling nitride formation is the atomic radius of the constituent elements. The radii of the elements of interest are listed in Table 2.7. It is important to be cautious when considering the radius of an element since the size of an atom is related to a wave function and it follows that no atom has a precise radius. The values presented in Table 2.7 are assumptions but they form an empirically useful set of values. Additionally, the radius of an atom may change depending on the hybridization.
It is interesting to note that nitrogen is one of the smallest atoms, and it is smaller than carbon. Table 2.7 also shows the type of nitride formed, i.e., interstitial (IS), covalent (C), or intermediate (IM). The transition metals of interest to us have a host lattice that is large enough for the nitrogen atom to fit in readily and thus form stable interstitial compounds.
Table 2.7. Approximate atomic radius of transition metals, nitrogen, and selected elements for reference [1].
2.4.3 Atomic Bonding
The other important factor governing the structure of nitrides is the nature of the bond between the nitrogen and the other element forming the compound. It is important to note that bonding, electronegativity, and atomic size are all interrelated. A bond, the attractive force that holds atoms or molecules together, is usually characterized by two factors: its length – determined by spectroscopic or diffraction techniques; and its strength - determined from quantitative measurements of the bond formation or dissociation energy. The type of bond is a function of the electronic configuration of the constituent elements, the orbital types, and the bond polarity. Generally, the shorter the bond the stronger the bond. The bonds in nitride compounds can be ionic, metallic, covalent or a combination of them.
The bonding of the transition metal nitrides of interest to us, interstitial nitrides, is not completely understood. Their characteristics and properties indicate that they are more than a simple solution of nitrogen atoms within the lattice of a transition metal.
Indeed, the differences between nitrides and host metals are significant and indicate the presence of metal to nitrogen (M-N) bonds with essentially no nitrogen to nitrogen bonds (N-N). The overall bonding scheme is a combination of these three types of bonding:
a. Ionic Bonding. Formed by transfer of valence electrons between two different atoms, giving a positive and negative ion, and producing an electrostatic attraction between these ions of opposite charge. A large difference in electronegativity favors ionic bonding. The best known ionic material is sodium chloride (NaCl).
b. Metallic Bonding. Here the atoms are considered to be ionized, with the positive ions arranged in the lattice positions. The electrons are delocalized; that is, they are able to move freely throughout the lattice. The bonding occurs by the electrostatic attraction between the electrons and the positive metal ions. Most metals can be considered as close packed arrays of atoms held together by these delocalized electrons.
c. Covalent Bonding. The major type between the metal d-state and the nitrogen p-state with some metal to metal interaction. The nature of a covalent bond is the sharing of electrons, rather than the transfers that takes place in ionic bonds.
Typically, two atoms share a pair of electrons.
The electronic configuration of the mononitrides, including band structure, density of states, and other bonding considerations, has been the matter of much research interest and is now relatively well known (as shown in later sections). As an example, Figure 2.10 presents an schematic of the bonding orbitals of TiN on the (100) crystallographic plane which is typical of transition metal nitrides. The nitrogen p orbitals and the titanium d orbitals form both and covalent bonds. The bonded overlapping titanium d orbitals indicate a certain degree of Ti-Ti interaction.
Figure 2.10. Planar view of the (100) plane of the bonding orbitals of TiN [1].
2.5 Properties of TiN, TaN and HfN