physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

and

chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...

, motional narrowing is a phenomenon where a certain

resonant frequency Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...

has a smaller

linewidth A spectral line is a weaker or stronger region in an otherwise uniform and continuous spectrum. It may result from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used ...

than might be expected, due to motion in an inhomogeneous system.''Solid state: nuclear methods''
by J. N. Mundy, section 6.2.1.1, page 441. The discovery of motional narrowing has been attributed to

Nicolaas Bloembergen Nicolaas Bloembergen (March 11, 1920 – September 5, 2017) was a Dutch- American physicist and Nobel laureate, recognized for his work in developing driving principles behind nonlinear optics for laser spectroscopy. During his career, he was a ...

during his thesis work in the 1940s

Example: NMR spectroscopy

A common example is

NMR Nuclear magnetic resonance (NMR) is a physical phenomenon in which atomic nucleus, nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field (in the near and far field, near field) and respond by producing ...

. In this process, the

nuclear spin Nuclear may refer to: Physics Relating to the nucleus of the atom: * Nuclear engineering * Nuclear physics * Nuclear power * Nuclear reactor * Nuclear weapon * Nuclear medicine *Radiation therapy *Nuclear warfare Mathematics * Nuclear space * ...

of an atom starts rotating, with the frequency of rotation proportional to the external

magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

that the atom experiences. However, in an inhomogeneous medium, the magnetic field often varies from point to point (depending, for example, on the

magnetic susceptibility In electromagnetism, the magnetic susceptibility (; denoted , chi) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the applied magnet ...

of nearby atoms), so the frequency of nuclear spin rotation is different in different places. Therefore, when detecting the resonant rotation frequency, there is a

(i.e., finite range of different frequencies) due to the variation in that resonant frequency from point to point. (This is called "

inhomogeneous broadening Homogeneous broadening is a type of emission spectrum broadening in which all atoms radiating from a specific level under consideration radiate with equal opportunity. If an optical emitter (e.g. an atom) shows homogeneous broadening, its spectra ...

".) However, if the atoms are

diffusing Molecular diffusion is the motion of atoms, molecules, or other particles of a gas or liquid at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid, size and density (or their product, ...

around the system, they will experience a higher magnetic field than average sometimes, and a lower magnetic field than average other times. Therefore, (in accordance with the

central limit theorem In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distributi ...

), the ''time-averaged'' magnetic field experienced by an atom has less variation than the ''instantaneous'' magnetic field does. As a consequence, when detecting the resonant rotation frequency, the linewidth is smaller (narrower) than it would be if the atoms were stationary. This is the motional narrowing effect.

Example: Electron spins in magnetically doped semiconductors

In magnetically doped semiconductors, the local magnetic field is determined by the magnetization of the dopant ions which are distributed statistically. The spin of charge carriers precesses in this field. The motional character enters the picture by the fact that the charge carriers diffuse through the semiconductor, and that the electron and hole spins thereby experience a varying local magnetization and variations of spin precession. The motional-narrowing effect was studied in optical pump/probe experiments, where mobile singlet

excitons An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force resulting from their opposite charges. It is an electrically neutral quasiparticle regarded as an elementary ...

were excited optically. The motional narrowing manifests in a peculiar temperature dependence of spin

dephasing In physics, dephasing is a mechanism that recovers classical physics, classical behaviour from a quantum physics, quantum system. It refers to the ways in which coherence (physics), coherence caused by perturbation decays over time, and the syst ...

: The dephasing becomes slower at higher sample temperature where the exciton velocity becomes larger and the excitons more quickly experience environments with different magnetization.

Example: Vibrational spectroscopy

A similar phenomenon occurs in many other systems. Another example is vibrational modes in a liquid. Each molecule of the liquid has vibrational modes, and the vibrational frequency is influenced by the positions of nearby molecules. However, if the nearby molecules reorient and move around fast enough, the vibration will essentially occur at an averaged frequency, and therefore have a smaller linewidth. For example, simulations suggest that the OH stretch vibration linewidth in

liquid water Water is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known living organisms ( ...

is 30% smaller than it would be without this motional narrowing effect."The Effects of Dissolved Halide Anions on Hydrogen Bonding in Liquid Water", J. D. Smith, R. J. Saykally, and P. L. Geissler, Journal of the American Chemical Society 129, 13847 (2007), .

References

{{Reflist Nuclear magnetic resonance Spectroscopy

Example: NMR spectroscopy

Example: Electron spins in magnetically doped semiconductors

Example: Vibrational spectroscopy

See also

References