MagnetismOverview of magnetic materialsMagnetic objectsMagnetic field linesMolecular magnetism, example 1Paramagnetic gasesOrganic radicals are magneticZeeman splitting and NMRMetalsSlide 10Slide 11Slide 12Ferromagnets have a persistent moment, even without a magnetic fieldcM vs T for ferromagnetsThe math of magnetismUseful experimental quantityMoment per metal atomMagnetic susceptibility, cMSlide 19MagnetismOverview of magnetic materialsMagnetic objectsMagnetic field linesMolecular magnetism, example 1Paramagnets are attracted to magnetic fieldsParamagnetic gasesOrganic radicals are magneticZeeman splitting and NMRgap = g z Bg = Lande g-factor (~2 for eˉ)z = magnetic momentB = magnetic field strengthNuclear gap energy corresponds to radio frequenciesCertain nucleii have a magnetic spin, and are therefore active in NMR experimentsMetals•Many metals have unpaired electrons due to the high d-orbital degeneracy.n = 3 unpaired spinsS = 3/2 magnetic momentoctahedral Cr3+ has 3 d-electronsMetals•Multiple spin arrangements (HS, LS) are possible for a given number of d-electrons (in this case, 7 valence electrons).n = 3 unpaired spinsS = 3/2 magnetic momentn = 1 unpaired spinsS = 1/2 magnetic momenthalides < OHˉ < C2O42- < H2O < NCSˉ < py < NH3 < en < phen < NO2ˉ < CNˉ < COZeeman splitting and NMRgap = g z Bg = Lande g-factor (~2 for eˉ)z = magnetic momentB = magnetic field strengthNuclear gap energy corresponds to radio frequenciesCertain nucleii have a magnetic spin, and are therefore active in NMR experimentsparamagnet (disordered spins)ferromagnet (co-aligned spins)antiferromagnet (anti-aligned spins)Ferromagnets have a persistent moment, even without a magnetic fieldM vs T for ferromagnetsferromagneticparamagneticThe math of magnetismM – Molar susceptibilityeff – Effective momentB – Bohr magneton•Molar magnetic susceptibility, M•Magnetic susceptibility per mole–Why use “molar” and not the “gram” susceptibility?Useful experimental quantityMoment per metal atomS = total spin (1/2 per e ˉ)n = # unpaired eˉeff = moment in Bohr magnetons (B)g = magnetogyric ratio (Landé g-facor, ~2) B = 9.27 x 10-24 J / T)2()1(nnSSgeffeffMagnetic susceptibility, MM= measurable quantity (M / H)Can calculate eff from MCan calculate # of unpaired electrons from effTNkTkTNMeffBAMeffBeffAM997.733222(units are slightly fudged)(Curie Law – assumes no spin-spin interactions)Magnetic susceptibility, MSimple approximations break down when spins are not isolated from each otherTCTCkTNeffMeffBeffAM22223(Curie-Weiss law)(Curie
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