Magic angle
Encyclopedia
The magic angle is a precisely defined angle, the value of which is approximately 54.7356°. The magic angle is a root of a second-order Legendre polynomial, 
, and so any interaction which depends on this second-order Legendre polynomial vanishes at the magic angle. This property makes the magic angle of particular importance in solid-state NMR spectroscopy.
The magic angle θm is
where arccos and arctan are the inverse cosine and tangent functions respectively.
θm is the angle between the space diagonal of a cube and any of its three connecting edges, see image.
(NMR) spectroscopy, the dipolar coupling D in a strong magnetic field depends on the orientation of the internuclear vector with the external magnetic field by
Hence, two nuclei with an internuclear vector at an angle of θm to a strong external magnetic field, have zero dipolar coupling, D(θm)=0. Magic angle spinning
is a technique in solid-state NMR spectroscopy which employs this principle to remove or reduce dipolar couplings, thereby increasing spectral resolution.
.
Example: This artifact comes into play when evaluating the rotator cuff tendons of the shoulder. The magic angle effect can create the appearance of supraspinatus tendinitis.
, and so any interaction which depends on this second-order Legendre polynomial vanishes at the magic angle. This property makes the magic angle of particular importance in solid-state NMR spectroscopy.Mathematical definition
-
,
where arccos and arctan are the inverse cosine and tangent functions respectively.
θm is the angle between the space diagonal of a cube and any of its three connecting edges, see image.
Magic angle and dipolar coupling
In nuclear magnetic resonanceNuclear magnetic resonance
Nuclear magnetic resonance is a physical phenomenon in which magnetic nuclei in a magnetic field absorb and re-emit electromagnetic radiation...
(NMR) spectroscopy, the dipolar coupling D in a strong magnetic field depends on the orientation of the internuclear vector with the external magnetic field by
Hence, two nuclei with an internuclear vector at an angle of θm to a strong external magnetic field, have zero dipolar coupling, D(θm)=0. Magic angle spinning
Magic angle spinning
In nuclear magnetic resonance, magic angle spinning is a technique often used to perform experiments in solid-state NMR spectroscopy.By spinning the sample at the magic angle θm In nuclear magnetic resonance, magic angle spinning (MAS) is a technique often used to perform experiments in...
is a technique in solid-state NMR spectroscopy which employs this principle to remove or reduce dipolar couplings, thereby increasing spectral resolution.
Application to medical imaging: The magic angle artifact
The magic angle artifact refers to the increased signal on sequences with short echo time (TE) (e.g., T1 or PD Spin Echo sequences ) in MR images seen in tissues with well-ordered collagen fibers in one direction (e.g., tendon or articular hyaline cartilage). This artifact occurs when the angle such fibers make with the magnetic field is equal to.Example: This artifact comes into play when evaluating the rotator cuff tendons of the shoulder. The magic angle effect can create the appearance of supraspinatus tendinitis.