lecture8_2006_jrl - Today's Lecture 8) Wed, Oct 18: Bloch...

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October 1, 2004 Joanna R. Long 1 Today’s Lecture 8) Wed, Oct 18: Bloch Equations and Relaxation a. Transverse and longitudinal magnitization b. Mechanisms of relaxation c. Measuring relaxation
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October 1, 2004 Joanna R. Long 2 Individual magnetic moments: μ M Bulk Magnetization: T k B I I N M b 3 ) 1 ( 0 2 2 0 + = γ 0 B 0 B = μ M I ˆ μ- =
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October 1, 2004 Joanna R. Long 3 B M dt M d × = γ Case 1: At equilibrium in a magnet: 0 = dt M d Case 2: After a radiofrequency pulse moves M away from equilibirum: ) ( sin cos 2 2 0 0 y x y x M M M t M M t M M + = - = = ϖ This describes precession in the x-y plane, but there is no mechanism to return the magnetization back to equilibrium along z.
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October 1, 2004 Joanna R. Long 4 FTNMR 1) Sample is in the magnetic field at equilibrium (Case 1) nothing is happening 2) A strong rf field is applied for long enough to take the magnetization from the z-axis to the x (or y) axis 3) We observe the evolution in the x-y plane (Case 2) The signal is decaying as the system returns to equilibrium
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October 1, 2004 Joanna R. Long 5 A. S. Edison University of Florida Bloch Equations In order to allow the system to return to equilibrium, Felix Bloch made the following modifications to the basic equation d t dt t t t M M M B R M ( ) ( ) ( ) ( ( ) ) = × - - γ 0 Empirical modification in which a “relaxation matrix” R acts on magnetization that is different from the equilibrium state, M 0 ***Note: unfortunately in NMR, both relaxation and rotation matrices are sometimes denoted by R . Usually context will tell you which one you are looking at.
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October 1, 2004 Joanna R. Long 6 A. S. Edison University of Florida Bloch Equations d t dt t t t M M M B R M ( ) ( ) ( ) ( ( ) ) = × - - γ 0 This equation is easiest to understand broken into its matrix components. 1
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This note was uploaded on 06/07/2011 for the course BCH 6745 taught by Professor Staff during the Spring '08 term at University of Florida.

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lecture8_2006_jrl - Today's Lecture 8) Wed, Oct 18: Bloch...

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