The Knight shift is a shift in the

nuclear magnetic resonance Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with a ...

(NMR) frequency of a

paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...

substance first published in 1949 by the

UC Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public university, public land-grant university, land-grant research university in Berkeley, California. Established in 1868 as the University of Californi ...

physicist Walter D. Knight. For an ensemble of ''N'' spins in a magnetic induction field

\vec

, the nuclear Hamiltonian for the Knight shift is expressed in Cartesian form by:

=-\sum\limits_^

, where for the ''i''^th spin

_

is the

gyromagnetic ratio In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol , gamma. Its SI u ...

is a vector of the Cartesian nuclear

angular momentum operators In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum prob ...

, the

=\left( \begin
    &  &   \\
    &  &   \\
    &  &   \\
\end \right)

matrix is a second-

rank Rank is the relative position, value, worth, complexity, power, importance, authority, level, etc. of a person or object within a ranking, such as: Level or position in a hierarchical organization * Academic rank * Diplomatic rank * Hierarchy * H ...

tensor similar to the

chemical shift In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of ...

shielding tensor. The Knight shift refers to the relative shift ''K'' in NMR frequency for atoms in a metal (e.g. sodium) compared with the same atoms in a nonmetallic environment (e.g.

sodium chloride Sodium chloride , commonly known as salt (although sea salt also contains other chemical salts), is an ionic compound with the chemical formula NaCl, representing a 1:1 ratio of sodium and chloride ions. With molar masses of 22.99 and 35.45 g ...

). The observed shift reflects the local magnetic field produced at the sodium nucleus by the magnetization of the conduction electrons. The average local field in sodium augments the applied resonance field by approximately one part per 1000. In nonmetallic sodium chloride the local field is negligible in comparison. The Knight shift is due to the conduction electrons in metals. They introduce an "extra" effective field at the nuclear site, due to the

spin Spin or spinning most often refers to: * Spinning (textiles), the creation of yarn or thread by twisting fibers together, traditionally by hand spinning * Spin, the rotation of an object around a central axis * Spin (propaganda), an intentionally b ...

orientations of the conduction electrons in the presence of an external field. This is responsible for the shift observed in the nuclear magnetic resonance. The shift comes from two sources, one is the Pauli paramagnetic spin susceptibility, the other is the s-component wavefunctions at the nucleus. Depending on the electronic structure, the Knight shift may be temperature dependent. However, in metals which normally have a broad featureless electronic density of states, Knight shifts are temperature independent.

References

Nuclear magnetic resonance spectroscopy Chemical physics {{Spectroscopy-stub