Influence of sample rotation on the shape of the free induction decay

Sample rotation is commonly used in NMR as one of the methods which improve the effective homogeneity of magnetic fields. The magic angle spinning (MAS), the double rotation (DOR) and the dynamic angle spinning (DAS) can remove line broadening of an NMR spectrum in solids [1, 2]. It is generally assumed that the NMR spectrum of a rotating sample (in the case of isotropic liquids) is simply the orientationally averaged spectum [3]. Our calculations, which are presented below, show that the sample rotation can change the shape of free induction decay (FID) (and consequently NMR line). We discuss this fact because, as we shall show later, it can disturb the absolute evaluation of the measured relaxation time. The shape of the FID can be calculated from the well-known Bloch equation for the transverse component of the magnetization M (without diffusion) under following assumptions [4]: