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Magnetism in Chemistry. General concepts. There are three principal origins for the magnetic moment of a free atom: The spins of the electrons. Unpaired spins give a paramagnetic contribution. The orbital angular momentum of the electrons about the nucleus also contributing to paramagnetism.

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## Magnetism in Chemistry

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**General concepts**• There are three principal origins for the magnetic moment of a free atom: • The spins of the electrons. Unpaired spins give a paramagnetic contribution. • The orbital angular momentum of the electrons about the nucleus also contributing to paramagnetism. • The change in the orbital moment induced by an applied magnetic field giving rise to a diamagnetic contribution.**The molar magnetic susceptibility of a sample can be**stated as: • = M/H M is the molar magnetic moment H is the macroscopic magnetic field intensity**In general is the algebraic sum of two contributions**associated with different phenomena: = D + P D is diamagnetic susceptibility P is paramagnetic susceptibility**Curie paramagnetism**Energy diagram of an S=1/2 spin in an external magnetic field along the z-axis E = gmBH, which for g = 2 corresponds to about 1 cm-1 at 10000G**Brillouin Function**M = N SmnPn = N (m½P½ + m-½P-½) mn= -msgmB, Pn= Nn/N with S Nn**Brillouin Function**• Substituting for P we obtain the Brillouin function**Curie Law**where C = Ng2mB2/(4kB) is the Curie constant Since the magnetic susceptibility is defined as = M/H the Curie Law results:**vs. T plot**1/ = T/C gives a straight line of gradient C-1 and intercept zero T = C gives a straight line parallel to the X-axis at a constant value of T showing the temperature independence of the magnetic moment.**Curie-Weiss paramagnetism**q is the Weiss constant**Curie-Weiss paramagnetism**Plots obeying the Curie-Weiss law with a negative Weiss constant**Curie-Weiss paramagnetism**Plots obeying the Curie-Weiss law with a positive Weiss constant**Ferromagnetism**J positive with spins parallel below Tc**Antiferromagnetism**• J negative with spins antiparallel below TN**Ferrimagnetism**• J negative with spins of unequal magnitude antiparallel below critical T**Spin Hamiltonian in Cooperative Systems**This describes the coupling between pairs of individual spins, S, on atom i and atom j with J being the magnitude of the coupling**Magnetisation**Knowing how M depends on B through the Brillouin function and assuming that B = 0 we can plot the two sides of the equation as functions of M/T**SUPERPARAMAGNETS**• These are particles which are so small that they define a single magnetic domain. • Usually nanoparticles with a size distribution • It is possible to have molecular particles which also display hysteresis – effectively behaving as a Single Molecule Magnet (SMM)**Mn12**Orange atoms are Mn(III) with S = 2, green are Mn(IV) with S = 3/2

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