If two elements of quite different size and electronegativity are involved, they tend to form intermetallic compounds of well-defined composition. Atomic radii of the late 3d elements are about 125 pm. The atomic radii of rare-earths are around 180 pm. The 4f elements therefore occupy three times the volume of the 3d elements, and form intermetallic compounds, rather than solid solutions, with them. Intermetallics are often line compounds with a precisely defined composition, or else there is a very limited homogeneity range because they can tolerate little disorder of the constituent atoms. Some atomic radii are listed in Table 11.4, and the trends across the 3d, 4d, 5d, 4f and 5f are illustrated in Fig. 11.2.
Interstitial compounds form when a small atom with atomic radius < 100 pm, − boron, carbon or nitrogen − enters an octahedral interstitial site in a 3d metal or alloy. Hydrogen can also enter the structure of many rare earth elements and their compounds. At room temperature, the hydrogen forms an interstitial lattice gas of protons (H+) at room temperature, and produces a lattice dilation of approximately 7 × 106 pm3 per hydrogen atom. Dilation produces striking changes of the magnetic properties of iron alloys, where the exchange is particularly sensitive to interatomic spacing.
Another important class of magnetic materials are the ionic insulators. These are often oxides, where electron transfer from the metal fills the oxygen 2p shell, to create an O2− anion and leaves behind a positively charged metal cation with a partially filled d or f shell. Most oxide structures are based on dense-packed fcc or bcc oxygen arrays, with metallic cations occupying octahedral, and sometimes also tetrahedral interstices. Taking rO2− =140 pm, the radii of the cations which will just fit in octahedral (six-fold) and tetrahedral (four-fold) sites are ( √2 − 1)rO2− = 58 pm and (&32− 1)rO2− = 32 pm, respectively.
We see in Table 11.5 that most divalent and trivalent metal cations are bigger than this, so they tend to distort the oxygen lattice. Transition-metal fluorides are also ionic Ù‡nsulators, but the bonding in pnictides (compounds with N, P, As or Sb) and chalcogenides (compounds with S, Se and Te) is more covalent, which tends to raise the conductivity and reduce the cation moment from its spin-only value, and may destroy it entirely.
The d and f shells in ionic insulators have integral electron occupancy. The electron orbitals form narrow bands,which have a width W of about 2 eV for d shells and 0.2 eV for f shells. These bands are unable to conduct electricity, even when they overlap and the bands are not all completely full or empty. The point is that a conducting band has to include different instantaneous electronic configurations of the atoms, such as 3dn±1 as well as 3dn. For this, an electron must somewhere be transferred from one site to the neighbouring site, at an energy cost equal to Udd , which is the difference in ionization energy and electron affinity of the 3dn configuration in the solid. The value of Udd is a few electron volts, which must be less than the total bandwidth if electron transfer is to take place. Otherwise, when
Udd
--- > 1
W
the material is a Mott insulator, and the electrons stay put. The d–d electron correlations turn a material which would otherwise be a metal into an insulator. A competing charge transfer process in oxides is from the filled oxygen 2p shell to the 3d shell. The electronic excitation is then 2p63dn → 2p53dn+1, and the energy cost is εpd. When Udd > Upd > W, the oxide is a charge transfer insulator. The Mott insulators tend to be found at the beginning of the 3d series, where the 3d level lies high in the 2p(O)−4s(T) gap (T is a 3d transition metal), whereas the charge transfer insulators are found near the end of the series, where the 3d level lies near the top of the 2p(O) band. Figure 11.3 delineates the regions where metals or insulators are found.
Oxides are rarely perfectly stoichiometric, yet, unlike doped semiconductors, nonstoichiometric oxides remain insulating. Electrons in the dn±1 configurationswhich formin response to oxygen excess or deficiency are immobile. They create a local distortion of the ionic lattice, known as a polaron. For polarons to hop from one site to the next, they must have the thermal energy necessary
to overcome the energy barrier associated with the redistribution of the local lattice distortion.
Finally, there are a few materials whose magnetism does not fit the general picture of more-or-less localized d or f atomic moments, with interatomic Heisenberg exchange coupling. These include solid O2, which is a molecular antiferromagnet, some organic ferromagnets, and alloys like ZnZr2 whose component elements bear no atomic moment. No homogeneous liquids are known to order magnetically.
Magnetic order is a relatively low-temperature phenomenon. A histogram plot of Curie and Neel temperatures from a bibliography of magnetic materials (Fig. 1.8) shows that most order below room temperature. A Curie temperature greater than 500 K, needed for room-temperature applications, occurs in no more than about 20% of known magnetic materials. The record for a Curie temperature, TC = 1388 K, is held by cobalt.
For solid solutions of alloys of magnetic and nonmagnetic atoms, (TxN1−x ), the Curie temperature in mean field theory (5.26) should scale as ZT = Zx , where ZT is the number of magnetic neighbours and Z is the coordination number. However, ferromagnetic nearest-neighbour exchange interactions do not produce long-range ferromagnetic order below the percolation threshold xp. Weaker, longer-range interactions may lead to magnetic order at low temperature. Dilute alloys or compounds which contain less than 10% magnetic atoms cannot be expected to order magnetically at room temperature, if at all.
Reference: https://materials-sciences-algerien1970.blogspot.com/2019/11/magnetism-and-magnetic-materials.html
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