2. QUADRUPOLE
■ A distribution of electric charge or
magnetization consisting of four equal
monopoles, or two equal dipoles, arranged
close together with alternating polarity and
operating as a unit.
Picture courtesy…….
By Geek3 - Own work, CC BY-SA 4.0,
https://commons.wikimedia.org/w/index.php?curid=6352525
8
3. Electric quadrupole
■ The simplest example of an electric quadrupole consists of alternating positive and
negative charges, arranged on the corners of a square.The monopole moment (just
the total charge) of this arrangement is zero. Similarly, the dipole is zero, regardless of
the coordinate origin that has been chosen. But the quadrupole moment of the
arrangement in the diagram cannot be reduced to zero, regardless of where we place
the coordinate origin.The electric potential of an electric charge quadrupole is given
by
■ 𝑉𝑞 𝑅 =
1
4𝜋𝜀0
1
|𝑅|3 𝑖𝑗
1
2
𝑄𝑖𝑗 𝑛𝑖 𝑛𝑗
■ R is a vector 𝜀0 𝑖𝑠 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑝𝑒𝑟𝑚𝑖𝑡𝑡𝑖𝑣𝑖𝑡𝑦 𝑄𝑖𝑗is quadrupole moment 𝑛𝑖 𝑛𝑗is unit vector
4. QUADRUPOLE
■ To fully understand the quadrupole interaction we must first establish what a
quadrupole is. Quite simply, a quadrupole can be thought of as two dipoles. Unlike a
dipole however, the quadrupole will not couple to a symmetric field as the forces
and subsequent torques on the quarupole will cancel.
5. QUADRUPOLE
■ If there is an non-symmetric field there will be a force on the quadrupole, i.e., an
electric field gradient. We can then define the quadrupole moment as the tendency
of the quadrupole to rotate about an axis. Due to the 3D nature of a quadrupole it
may be described by a second rank tensor Q.
■ The quadrupole can then couple to an Electric Field Gradient (EFG) The electric
field gradient is denoted a V and is also described by a second rank tensor.
■ EFGs are generated in solids and liquids by the electrons in the sample.
6. QUADRUPOLE
■ Within the nucleus of an atom, the protons, and subsequent charge of the nucleus, can
be distributed symmetrically or asymmetrically. If the charge distribution is
symmetric, the spin,I, of the nucleus is 1/2 and the interaction of the nucleus with
electric field gradients is direction independent. However, if the charge distribution is
asymmetric I>1/2, and the electric field gradient can interact with the nucleus and
exhibit a torque on the nucleus.These nuclei are known as quadrupolar nuclei. It is
worth mentioning that the electric field gradient is generated by the electrons present
in the sample.Consequently, these nuclei exhibit a quadrupole moment, Q
■ . Figure 11: Charge distribution is spherical and non-spherical nuclei
7. Quadrupole moment, Q
■ Q can be considered a friction coefficient between rotations of the electric field of
the molecule. The larger the Q value, the more strongly the asymmetric nucleus will
interact with a non-uniform electric field gradient. This leads to a nuclear spin
reorientation in the nucleus. The exception is cubic symmetry (Td or Oh) where the
electric field gradient is symmetric resulting in no net effect on the non-spherical
nucleus.
8. Electric field gradient (EFG)
■ The electric field gradient (EFG) measures the rate of change of the electric
field at an atomic nucleus generated by the electronic charge distribution and the
other nuclei.
■ The EFG couples with the nuclear electric quadrupole moment of quadrupolar
nuclei (those with spin quantum number greater than one-half) to generate an
effect which can be measured using several spectroscopic methods, such as nuclear
(NMR), microwave spectroscopy, electron paramagnetic resonance (EPR,
ESR), nuclear quadrupole resonance (NQR), Mössbauer spectroscopy or perturbed
angular correlation (PAC). The EFG is non-zero only if the charges surrounding the
nucleus violate cubic symmetry and therefore generate an inhomogeneous electric
field at the position of the nucleus.
