Bloch_eq_2010 - Pulse and FT NMR In practice bulk...

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Unformatted text preview: Pulse and FT NMR In practice bulk magnetization is observed For isolated spins behavior is according to classical Bloch equations dM/dt = γ M X B – (M z – M ) (1/T 1 ) – M x,y (1/T 2 ) Precession in a Static Field Torque on system with angular momentum (J) causes precession of the momentum vector. dJ/dt = T. Torque is given by M X B and M = γ J. Bloch equations give precession at ω = - γ B . dM/dt = γ M(t) X B 0 x y B J = M/ γ T dM x /dt = γ M y B dM y /dt = - γ M x B 0 dM z /dt = 0 i j k dM/dt = γ M x M y M z 0 0 B 0 Solution: M x (t) = M 0x cos(- γ B t) - M 0y sin(- γ B t) = M exp(-i γ B t) = M exp(i ω t) Spin precession is like precession of a gyroscope The Rotating Frame Simplifies Analysis of RF Pulses and Small Frequency Offsets ω 0 is very high (500 MHz x 2 π ) – differences due to chemical shifts etc. are small (ppm x 500 Hz x 2 π ) Therefore, use reference frame moving near ω ....
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Bloch_eq_2010 - Pulse and FT NMR In practice bulk...

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