Paramagnetic susceptibility temperature dependence

The YCOfiSne and YbCoeSns stannides are Pauli paramagnets, the temperature dependence of the susceptibility for other Co compounds follows the Curie-Weiss law (Skolozdra and Koretskaya 1984). 

Originally, Inoue and Shimizu (1980) regarded the alloys with paramagnetic collective d-electrons over the whole temperature range. Subsequently this model was used also for lanthanide-3 dTM alloys with ferromagnetic order in the collective electron system (Inoue and Shimizu 1984, 1986). The following two types of d-electron susceptibility temperature dependences were used ... 

The temperature dependence of the molar susceptibility of a paramagnetic substance follows the Curie-Weiss law (if the magnetic field is not too strong) ... 

The temperature dependence of the molar magnetic susceptibility (x) of an assembly of paramagnetic spins without interaction is characterized by the Curie behavior with x = C/T where C = /Vy2( 2.S (.S + l)/3k. It is a very common situation in the organometallic chemistry of radical species when the spin density is essentially localized on the metal atom. Since, in most cases, this atom is surrounded by various innocent ligands, intermolecular interactions are very weak and in most cases are reflected by a small contribution described by a Curie-Weiss behavior, with x = C/(T 0) where 0 is the Curie-Weiss temperature. A positive value for 0 reflects ferromagnetic interactions while a negative value — the most common situation — reflects an antiferromagnetic interaction. 

The partial orientation of the elementary dipoles in a paramagnetic solid is counteracted by thermal agitation, and it would be expected that at high temperatures the random motion of the atoms in the solid would cancel the alignment due to the magnetic field. The paramagnetic susceptibility would therefore be expected to vary with temperature. The temperature dependence is given by the Curie law ... 

Magnetic measurements of the 1 1 coordination complex of TTTA and Cu(hfac)2 3 revealed a ferromagnetic dimer with a weak interdimer antiferromagnetic interaction <2001JA3601, 2001POL1517>. Temperature dependence of the paramagnetic susceptibilities %-pT for 3 has been recorded over the range 1.8-350 K. 

Clark and Odell have found (39) that the susceptibility varies with temperature in a way that can be explained very well on the basis of temperature-dependent equilibria between diamagnetic and paramagnetic forms. This is valid equally for pyridine and for inert solvents. Thermodynamic quantities calculated from these measurements show that the paramagnetic forms have the lower enthalpies, and that there are relatively large increases of entropy on going from the paramagnetic to the diamagnetic forms. 

It was shown by Pierre Curie in 1895 that paramagnetic susceptibility is strongly dependent on temperature, and for many substances is inversely proportional to the absolute temperature. The equation... 

Transition-metal (dn) complexes with open shells belong to the class of paramagnetic materials their magnetic susceptibility is positive (the sample is attracted to the magnetic field) and is temperature dependent. At high enough temperatures and in small fields, the molar magnetic susceptibility normally obeys the Curie law... 

The Curie paramagnets [e.g., octahedral Fe(III) complexes] are rather rare, and the temperature dependence of the magnetic susceptibility requires more parameters, depending on the actual spacing of the low-lying energy levels. Let us enumerate the MPs associated with the SH formalism ... 

The first component xp is the paramagnetic susceptibility, which is due to the coupling of unpaired electrons with the magnetic field and is therefore absent for closed-shell molecules. When present it is much larger than the other two terms and is thus the predominant effect. xp is dependent on temperature and is particularly important in transition-metal chemistry. It will not be discussed further here. 

The magnetic susceptibility is thus a temperature-dependent property of a bulk substance. It is meaningless to specify the susceptibility of a single molecule or complex ion. For convenience, inorganic chemists prefer to answer the question How paramagnetic is this substance in terms of the magnetic moment peff defined by the relation ... 

The determination of n from measurement of peff is the most familiar application of magnetic susceptibility measurements to inorganic chemists. To the extent that the spin-only formula is valid, it is possible to obtain the oxidation state of the central atom in a complex. Thus an iron complex with a peff of 5.9B.M. certainly contains Fe(III) (high-spin d5) and not Fe(II). The diamagnetism of AgO rules out its formulation as silver(II) oxide, because Ag2+ has an odd number of electrons (d9) and should be paramagnetic it contains Ag(I) and Ag(III), in equal amounts. There are, however, a number of pitfalls, especially if reliance is placed on a single measurement at room temperature. The Curie law is rarely obeyed within the limits of experimental error. This means that the measured peff is somewhat temperature-dependent. A number of factors can be responsible for deviations from ideal Curie (or even Curie-Weiss) behaviour, and/or from the spin-only formula. 

Empirically, the temperature dependence of the susceptibility of paramagnetic materials (or, more accurately, / )ara = Xtotai — Ail) in l°w helds follows the Curie law... 

---