Magnetic behavior of metals

We quote here some basic results from the discussion of Appendix D the high-temperature and low-temperature limits of the susceptibility per unit volume are 

For typical values of in metals, (rs/ao) 2-6, we find that the temperature must be of order lO -lO K in order to satisfy this condition, which is too high to be relevant for any real solids. In the opposite extreme, at T = 0, it is natural to expect that the only important quantities are those related to the filling of the Fermi sphere, that is, the density n and Fermi energy ep. Using the relation between the density and the Fermi momentum fcp = 3k h, which applies to the uniform electron gas in 3D, we can rewrite the susceptibility of the free-electron gas at T = 0 as 

We specialize the discussion to models that provide a more detailed account of the magnetic behavior of metals. The first step in making the free-electron picture more realistic is to include exchange effects explicitly, that is, to invoke a Hartree-Fock picture, but without the added complications imposed by band-stmcture effects. We next analyze a model that takes into account band-structure effects in an approximate manner. These models are adequate to introduce the important physics of magnetic behavior in metals. 

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Spectroscopy and magnetism The optical and magnetic behavior of metal complexes can be tuned if their chemistry is understood. 

The focus of research on very mixed"-metal clusters has been on their synthesis and structure, and the limited physical measurements of these clusters have thus far been largely restricted to fluxionality and electrochemical investigations. Studies of ligand fluxionality are summarized in Section 111.A. and reports of electrochemical investigations are reviewed in Section Ill.B. The few reports of the magnetic behavior of these clusters are discussed in Section lll.C. 1., and theoretical studies are summarized in Section I1I.C.2. 

The limited magnetic measurements of very mixed -metal clusters are summarized in Table XIII. The magnetic behavior of some anti-ferromagnetic very mixed -metal carbonyl clusters (Fig. 82) has been studied by Pasynskii and eo-workers. Temperature dependences of the magnetic susceptibilities of Cr2Co(/t3-S)3(/i-SBu )(CO)2() -C3H4R)2l (R = H. Me) have been determined us-... 

Currently, holmium metal does not have much commercial application. However, because of its unusual magnetic properties, it is being used in research studies to explore the magnetic and alloying behavior of metals. 

In molecules, the interaction of surrogate spins localized at the atomic centers is calculated describing a picture of spin-spin interaction of atoms. This picture became prominent for the description of the magnetic behavior of transition-metal clusters, where the coupling type (parallel or antiparallel) of surrogate spins localized at the metal centers is of interest. Once such a description is available it is possible to analyze any wave function with respect to the coupling type between the metal centers. Then, local spin operators can be employed in the Heisenberg Spin Hamiltonian. An overview over wave-function analyses for open-shell molecules with respect to local spins can be found in Ref. (118). 

The multifaceted behavior of transition metal complexes calls for not only theoretical explanations within a common conceptual framework but also theoretical tools that are powerful enough to predict the chemical and magnetic behavior of open-shell transition metal ions. Specifically, one looks for theoretical methods to calculate geometries and relative energies for stable species and transition states as well as for methods that allow one to determine spectroscopic parameters with sufficiently predictive accuracy. 

A ligand field model has been used for the interpretation of the magnetic behavior of the Mo(R2Dtc)4 complexes (485). Extended Hiickel calculations compare the electron-donating characteristics of the dithiocarbamate ligand to other 1,1-dithio chelates. This calculation concluded that (1) there is more metal character in the lowest unoccupied MO in the dithiocarbamate complexes, and (2) there is more ligand character in the lowest unoccupied MO in the dithioacid complexes (485). This seems to be in agreement with the electronic spectra. 

Magnetic Methods. The preceding methods are destructive tests in that the restoration technique permanently alters the speciman. If improper conditions are applied in destructive tests, there is often no second chance to recover the number. Nondestructive methods are therefore especially attractive. Several promising, nondestructive approaches for serial number recovery from ferromagnetic alloys are based on the magnetization behavior of the metal. The potential of this method has been realized (15) but appears not to have been fully exploited. 

Most, but not all, of the observed magnetic behavior of the lanthanide hydrides fits in with the notion that the hydrogen-saturated metal lacks conduction electrons. The hydride of europium is an exception EuH186, the highest hydride that has been formed in this laboratory, has been shown (15) to be ferromagnetic below 25° K. This would ordinarily imply the existence of electrons in the con-... 

H20)Hg(0H)a+q and (HO)Hg(OH)aq species where two Hg—O bonds are shortened and the other four lengthened. Protonation of transition metal oxo complexes can affect the geometry and magnetic behavior of the compounds.40... 

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