Presented By - ANAMIKA BANERJEE, 115217

NUCLEAR QUADRUPOLE

EFFECT ON

MÖSSBAUER

SPECTROSCOPY

QUADRUPOLE EFFECT

All nuclei with a spin ≥ 1 possess an Electric Quadrupole moment which arises because the nuclei are not spherical.

Such nuclei, in fact, are shaped either like a

1. Cigar

2. Tangerine

.

Even if the charge density within the nucleus is constant , the distorted shape gives rise to a charge distribution which is non- spherical ; the electric quadrupole moment is a measure of the departure from sphericity , being positive for cigar shaped and negative for tangerine - shaped nuclei.For spherical nuclei (I = ½ or 0) the electric quadrupole moment is 0.

. The electric quadrupole moment interacts strongly with an applied electric field and if such a field has a pronounced gradient at the nucleus , the nuclear moment will try to follow this change.

MÖSSBAUER SPECTROSCOPY

Mössbauer spectroscopynamed after its discoverer RUDOLF MÖSSBAUER who received a Nobel Prize in 1961 for his work -

if the nucleus is bound in a crystal lattice, the whole crystal recoils rather than the individual nucleus. Due to the much greater mass involved in recoil, the energy of the emitted ray is very close to that of the difference in energy between the nuclear energy levels, and resonant absorption is possible.

EFFECT OF NUCLEAR QUADRUPOLE

MOMENT

.

It happens that the majority of Mössbauer nuclei have a non zero spin and, further, that most of them have half integral spins rather than integral spins.The spin of the excited state is invariably different from that in the ground state and so it follows that either or both of the nuclear states must involve a spin greater than ½ i.e. one or both will have a quadrupole moment and this will interact with the electric field gradient in the vicinity.

.

A fairly common situation is for the excited state nucleus to have I= 3/2 and the ground state I= 1/2 ; this is found , in 57 Fe, 119 Sn and 129 Xe.

In such a case, 4 possible orientations of the excited nucleus in an electric field along the vertical (z) direction.

Field(z)

-3/2

+3/2

+1/2

-1/2

4 allowed directions of a nuclear spin , I = 3/2

Fig. (A)

.

Since the angle which the cigar shaped nucleus makes with the field gradient is the same for Iz = +1/2 and the Iz = -1/2 states, these two states have the same energy in the field. Similarly, the Iz = ±3/2 states have the same energy, although this energy will be different from that of Iz = ±1/2.

The excited nuclear energy splits into two levels when an electric field gradient exists at the nucleus . With positive quadrupole moment of ±3/2 states are raised in energy and ±½ states are lowered.

.

Iz = 1/2

Iz = 3/2

No Field

Electric Field±3/2

±1/2

Fig. (B)

Fig. (C)

If the quadrupole moment is negative (tangerine shaped nucleus) the reverse is true.

SPECTRUM OF NITROPRUSSIDE [Fe(CN)5NO]2-

The splitting is small with normal electric field but in case of Nitroprusside ion the nuclear quadrupole effect is an observable effect. It should be noted that electric field causing the splitting here is not externally applied, but is inherent in the structure of the ion.

.

-1/2-5 0 +5

Cou

nts

s-1

mm s-

1

-5 +50

Cou

nts

s-1

mm s-

1

Comparing (A) and (B), we see that [Fe(CN)6]4 - is sufficiently symmetric so that there is no net field at Fe nucleus while replacement of one CN group by NO produces an internal field.

(A) ( B)

[Fe(CN)6]4 - [Fe(CN)5NO]2

-

∆EQ