EXPERIMENTAL TECHNIQUE OF MOSSBAUER SPECTROSCOPY

Q: What is electric quadrupole splitting ∆EQ?

57Fe of the quadrupole moment eQ in the absorber interaction with EFG (electric field gradient) is spherically symmetric. The resulting interaction also splits the excited state energy level into two lines; the splitting is known as electric quadrupole splitting ∆EQ.

Mossbauer’s studies of three quantities are known as hyperfine interaction. Three techniques are chemical (Isomer) shift (δ), Nuclear electric quadrupole splitting (∆E_Q), and Nuclear Zeeman splitting.

Table of Contents

CHEMICAL (ISOMER) SHIFT (δ)

The nuclear energy levels operate as both the source and the absorber in isomer shift, which is the electrostatic interaction between a solid’s nucleus and electrons given by,

\[\displaystyle \delta =\frac{{2\pi }}{5}z{{e}^{2}}\left[ {{{{\left| {{{\Psi }_{2}}\left( 0 \right)} \right|}}^{2}}-{{{\left| {{{\Psi }_{s}}\left( 0 \right)} \right|}}^{2}}} \right]\left( {R_{{ex}}^{2}-R_{{gd}}^{2}} \right)-----(1)\]

\[\displaystyle e=\text{ electronic charge}\]

\[\displaystyle \text{z = atomic number}\]

\[\displaystyle {{\text{R}}_{{ex}}}=\text{Radii of the nucleus in excited state}\]

\[\displaystyle {{\text{R}}_{{gd}}}=\text{Radii of the nucleus in ground state}\]

\[\displaystyle {{\left| {{{\Psi }_{2}}\left( 0 \right)} \right|}^{2}}=\text{electron density evaluted at the nucleus for the absorber}\]

\[\displaystyle {{\left| {{{\Psi }_{s}}\left( 0 \right)} \right|}^{2}}=\text{quantity of the source}\]

Only S orbital has a finite wave function at the nucleus, and P and d electron fading wave function at the nucleus. Here, isomer shifts appear due to only s electrons.

NUCLEAR ELECTRIC QUADRUPOLE SPLITTING (∆EQ)

In some cases, ⁵⁷Fe excited state has a nuclear spin > 1, and I =3/2. ⁵⁷Fe of the quadrupole moment eQ in the absorber interaction with EFG (electric field gradient) is spherically symmetric. The resulting interaction also splits the excited state energy level into two lines; the splitting is known as electric quadrupole splitting ∆E_Q.

e²Qq = Nuclear electric quadrupole coupling constant

Isomer Shift and Electric Quadrupole spitting ⁵⁷Fe Energy Level

NUCLEAR ZEEMAN SPLITTING

Another name for this splitting is known as Magnetic Hyperfine Splitting.

External nuclear Zeeman splitting results from magnetic field B’s splitting of nuclear energy levels.

Here, the metallic state of Fe has a large internal magnetic field of 30 T; this field also causes immense splitting.

Diagram depicts the combined effect of isomer shift (δ ≠ 0) and magnetic field (δ ≠ 0, B ≠ 0) on the Mossbauer spectrum of ⁵⁷Fe selection rule ∆m₁ = 0, ±1 gives six lines spectrum.