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An introduction to Solid State NMR and its Interactions

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The quadrupole Interaction<br />

I1/2<br />

Electric coupling between the nuclear quadrupole moment Q<br />

<strong>and</strong> local electric field gradient V(r nuc<br />

) at the nucleus<br />

Quadrupolar Coupling Constant ( ~ MHz )<br />

C Q<br />

= eQ h V ZZ<br />

Quadrupolar asymmetry parameter<br />

First order<br />

C Q<br />

H 1 Q<br />

=<br />

6I2I−1 ×R Q ×T<br />

20<br />

20<br />

Second order (complex...)<br />

H Q 2 = 1 0<br />

C Q<br />

Q<br />

= V −V XX YY<br />

V iso<br />

=0<br />

V ZZ<br />

T 2,0=<br />

1 3 I 2 Z<br />

−I I1<br />

6<br />

6I2I−1 × ∑ l=0,2,4<br />

A l ∑ k=−l ,l<br />

B l k<br />

k<br />

D l , 0<br />

A l = f I Z 3 , I Z<br />

<br />

Second Order Quadrupolar Induced Shift !<br />

Q 2 =A 0 B 0 0 <br />

Isotropic shift

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