Magnetic susceptibility quadrupolar

The major sources of linebroadening such as chemical shift anisotropy, heteronuclear dipolar interaction, first-order quadrupolar interaction as well as magnetic susceptibility broadening, can be almost time-averaged to zero... 

Specific heat measurements on single crystals revealed a sharp peak at 7 K accompanied by two small anomalies at 4.6 and 7.6 K (Andres et al. 1978). It was conjectured that these anomalies are driven by quadrupolar interactions between the U ions. This mechanism can also account for anomalies in the magnetic susceptibility and the thermal expansion (increase of c/a ratio on cooling) observed at relevant temperatures on a single crystal by Ott et al. (1980). Dilution experiments on Uj Th Pdj point to an increase of jaeff/U atom for x > 0.9 reaching a value of 3.55/xB (Wemick et al. 1965). 

Conduction electrons in broad bands of s- and p-like character contribute to all three quantities (sp). The Landau orbital diamagnetism (L) of these electrons is frequently considered only in the free-electron approximation, and taken care of by introducing a factor of two thirds in front of jp, whilst represents only the core diamagnetism. More localized non-s-like electrons in narrow bands give temperature-dependent contributions. In addition to the spin part (d) of the susceptibility, which is noticeable at the nucleus via core polarization (and finally Fermi-contact interaction) or via dipolar interaction (dip), van Vleck type induced orbital contributions of the magnetic susceptibility lead to orbital (orb) contributions of K and l/T, and eventually also to quadrupolar contributions (Q) of l/Ti- In this chapter we will use the symbol a, (instead ofH , ) for the hyperfne coupling constant(s) (with units of Oep. or Oe/electron) in the equation... 

K = adiabatic compressibility Ap = molecular-field constant Aq = quadrupolar parameter /tb = Bohr magneton X = magnetic susceptibility >l/ =4f eigenfunction belonging to the m-fold level F ... 

The magnetization was only taken as an example. Many other properties (dielectric susceptibility, electric and thermal conductivity, molecular diffusion, etc.) are also described by second rank tensors of the same (quadrupolar) type Microscopically, such properties can be described by single-particle distribution functions, when intermolecular interaction is neglected. There are also properties described by tensors of rank 3 with 3 = 27 components (e.g., molecular hyperpolarizability Yijk) and even of rank 4 (e.g., elasticity in nematics, ATiju) with 3 = 81 components. Microscopically, such elastic properties must be described by many-particle distribution functions. 

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