3 © 2012, K.S. Suslick Paramagnetic 1H NMR © 2012, K.S. Suslick Paramagnetic 1H NMR: Relaxation Time Paramagnetism derives from atoms, molecules, or ions possessing a permanent magnetic moment associated with unpaired electron spins (atoms or ions of the majority of transition metals and radicals). Paramagnetic polarization consists of the alignment of such magnetic dipoles which have random orientations under normal conditions. Paramagnetism is due to the presence of unpaired electrons in the material, so most atoms with incompletely filled atomic orbitals are paramagnetic, although exceptions such as copper exist. Due to their spin, unpaired electrons have a magnetic dipole moment and act like tiny magnets. Based on this picture, reasons for both diamagnetism and paramagnetism can be given: (i) As the magnetic moment is decreasing in the direction of the magnetic eld for both types of orbits, we expect the magnetization to drop with the magnetic eld. As shown in the example in Sec. 4.1, the drop is proportional to the magnetic eld. Paramagnetism and Diamagnetism Here we discuss the magnetic response of systems that do not feature (as opposed to, say, ferromagnets or superconductors) any order relevant to the interaction with the magnetic eld. We will con ne ourselves to the static response to a homogeneous magnetic eld. it (paramagnetism). If these effects happen for each "individual magnet" independently, they remain small. The corresponding magnetic properties of the material may then be understood from the individual behavior of the constituents, i.e. atoms/ions (insulators, semiconductors) or atoms/ions and free electrons (conductors), cf. section 8.3 as " paramagnetism " (displayed by a " paramagnetic material " ) in the case of χ > 0 and as " diamagnetism " (displayed by a " diamagnetic material " ) in the case of χ < 0. In the M - H curve this behavior is discriminated as a positive or negative slope, as shown in Figure 1.4 . Usually, a diamagnetic response toward an Quantum theory of paramagnetism What changes do we need to make to Langevin's classical theory ? i) detailed changes to the way in which the magnetic dipole moment is defined, The general definition is Using QM, the angular momentum L is quantised, and every electron is now specified by four quantum numbers (n l m l s) € m=m(L) SES # TOPICS LECTURE NOTES 1 Introduction. Coulomb's Law, Superposition. Energy of Charge Distributions ()2 Electric Field, Electric Flux, Gauss's Law Levo M = NH = Ms > 10 CL.-FOLD -zìo (OTE 0.5 Let) & Scanned with CamScanner . Title: Classical Langevin theory of paramagnetism Author: CamScanner Subject •Similar to free spins, if an atom has a magnetic moment , it can align along the magnetic field •Magnetization of a material with atomic density Nis (averaging included) •And susceptibility •Atom with orbital, spin and total angular momenta, L,S, and J = L+S , will have magnetic moment With Lindé g-factor Langevin atomic paramagnetism m PARAMAGNETISM Occurrence of electronic paramagnetism : • Atoms, molecules, & lattice defects with odd number of electrons ( S 0 ). E.g., Free sodium atoms, gaseous NO, F centers in alkali halides, organic free radicals such as C(C 6 H 5)3. • Free atoms & ions with partly filled inner shell (free or in solid), PARAMAGNETISM Occurrence of electronic paramagnetism : • Atoms, molecules, & lattice defects with odd number of electrons ( S 0 ). E.g., Free sodium atoms, gaseous NO, F centers in alkali halides, organic free r