1. Introduction

Nuclear Magnetic Resonance (NMR) Spectroscopy is amongst the powerful techniques for the determination of molecular-level structure and dynamics. The wide range of application, accessible spin-active nuclides of all elements and the extremely high resolution under appropriate experimental conditions such that minor variation in the electronic environment of atoms shows observable different resonance frequencies hyped its importance.^[1]In late 1945, physicists successfully conducted NMR experiments on condensed phases for both solid and solutions which revealed that the better resolution and molecular structure information of great importance from the solution-state compared to solid-state. However, the  solid-state remained in preserved. Due to the accessible spin-active nuclides in all elements, Solid-state NMR can be applicable in wide areas from measuring membrane proteins, amyloid proteins, protein complexes in protein structural biology to measurements of cell wall matrices, organic, inorganic and hybrid materials and structural characterization of oxides.^[2]The Figure 1 shows illustrates the working mechanism of solid-state NMR based on spin active nuclei. The solid samples are added to the NMR probe which then is inserted into the superconducting magnet. The nuclear spin signal generated are then amplified and spectra's are formed.

 Figure 1. Schematics on the working mechanism of solid-state NMR. (Figure: Nea Möttönen, inspired by reference^[2]

2. Nuclear Spin Magnetization Concept

A magnetic moment is generated by the moving charge associated with the nucleus of non-zero magnetic quantum number I. The nuclear magnetic moment gets quantized to 2I + 1 direction due to strong magnetic field (B₀)  in the NMR experiment. There are two spin-states considered in nuclear spin magnetization. The γ (gamma) component is considered positive when aligned with the magnetic field  in low energy state and  is labelled as α (m_I= +1/2). The high energy state is labelled as β (m_I= -1/2) and the component is aligned opposite to the field.^[1]

However, the energies of the state are analyzed by the Zeeman effect which is expressed in terms of frequency in Equation mentioned below.

The energy difference transition between the state is based on the principle of NMR spectroscopy and can be calculated by following equation.

The obtained energy difference between the states is equal to the resonance frequency (V_NMR)  known as Larmor Frequency and the applied magnetic field is directly proportional to the Larmor frequency an in the equation mentioned below. 

^[1]

3. Magic- Angle Spinning

Magic-angle spinning is amongst the widely used technique used for high resolution spectrum. It has been used for the investigation of the zeolites and studies of chemical reaction on zeolites.^[3]In order to avoid the broadening of the spectrum of a solid-state sample high speed rotation about an axis which is inclined to the direction of the applied magnetic field (B₀) by magic angle (Ѳ_m)  of 54.7⁰ as shown in Figure 2.^[4]

Figure 2. Schematics showing magic angle spinning (MAS) of Ѳ_m= 54.7⁰ with reference to the magnetic field (B₀). (Figure: Nea Möttönen, inspired by reference ^[3])

The spinning rate of MAS should be equal or greater than the magnitude of the anisotropic interaction so that it can be averaged zero.^[5]The experiments are conducted in MAS NMR probes of 1cm length zirconia rotors which has spinning rates of 5-40kHz. The probes are equipped with dry air permitting the rotation of 2.5-7.0 mm in outer diameter.^[3]

The major factors that limits the maximum rotation of the rotor is the tensile strength of the rotor material and the speed of the sound gas that surrounds the rotor. The rotor material must have the properties to withstand the centrifugal forces generated by the high speed rotation.^[6]Incase of a cylinder rotor whose radius is R, spinning at ω and of density ρ, the pressure (P) on experinced by the surface can be calculated by following equation.^[6] 

4. References