MAS of Second-Order Quadrupole Effects

1 MAS of second-order quadrupole effects. The same type of rotations using Wigner rotation matrices can be applied to the second-order effects as for the first-order interaction which leads to a second-order quadrupole energy of interaction such that 

For the normally observed central transition then, this frequency in the fast spinning limit is 

The centrebands produced under this limit will also have characteristic lineshapes even though the shapes will be very different from the static ones. The scale of the 

The residual second-order effect produces a linewidth which is a function of I and m and then 

This represents the speed that must be exceeded for MAS to cause even partial averaging of the second-order quadrupolar interaction, but fulfilling this condition does not mean that the fast spinning limit has been achieved. 

---