Magnets, Metals and Superconductors

Tutorial 1

Dr. Abbie Mclaughlin

G24a

1. Determine the ground state configuration and predict the effective magnetic moment for the following Ln3+ ions.

Gd3+, Er3+

L 0 1 2 3 4 5 6 7

Symbol S P D F G H I K

mj 3 2 1 0 -1 -2 3

)1(2 SSeff

Gd3+ = f7

S = 7/2, L = 0, J = 0i.e. is spin only!eff = 7.94Term symbol = 8S0

mj 3 2 1 0 -1 -2 3Er3+ = f11

The term state symbol is written 2S+1LJ.

Hund’s Rules:

For less than half-filled shells, the smallest J term lies lowest; for more than half filled shells the largest J lies lowest.

S = 3/2L = mj = 6, J = 15/2, 13/2, 11/2, 9/2Term symbol = 4I15/2

gj= 6/5 µeff = 9.58

L 0 1 2 3 4 5 6 7

Symbol S P D F G H I K

)1(2

)1()1(

2

3

JJ

LLSSg )1( JJg Jeff

2 Exam question 1 (2004) (b).

The gradient =1/C. This can be used to determine S from the equation:C = Ng2µB

2S(S+1)/3k

The value of can be determined from the 1/ vs T plot.This gives an indication of the strength and nature of the interactions between neighbouring molecules.

b) Ferromagnetic exchange: ST = nS

nS = 10 x 2 = 20.

=41 B)21(202eff

3a. 2 cyclic-[Fe(OMe)(OAc)]10 Fe2+ d6 S = 2 n = 10

a) Antiferromagnetic exchange ST = 0 or ½ depending on whether there is and even or odd number of electrons. There are 10 antiferromagnetic S = 2 ions, ST = 0

MBnSnSeff .)1(2

c) Non interacting (high temperature limit).S = 2, n = 10

= 15.5 µB.

)]1([2 SSneff

)]3(2[102eff

3b) [Cu3OCl4 (Mepy)4]Cu2+ d9, S = 1/2, n = 3

a) Antiferromagnetic exchange: ST = 0 or ½ depending on whether there is and even or odd number of electrons. There are 3 antiferromagnetic S = 1/2 ions, ST = ½.

)2/3(2/12eff

µeff = 1.73 µB

c) Non interacting (high temperature limit).S = 1/2, n = 3

= 3.00 µB

b)Ferromagnetic exchange: ST = nSnS = 3 x 1/2 = 3/2.

= 3.87 µB.

MBnSnSeff .)1(2

)]1([2 SSneff

)]2/3(2/1[32eff

)2/5(2/32eff

4. Determine eff per mole of Cu2(OAc)4.2H2O. Apply a diamagnetic correction to and redetermine eff. Does it make a difference?

TN

Tk

Beff

828.2.32

298102.1828.2 3

=1.7 µB per mole of dimer

Diamagnetic correction (for dimer)Cu = -11 X 10-6, OAc = -30 X 10-6, H2O = -13 X 10-6

Overall correction = -22 -120 -26 (X 10-6) = -168 X 10-6

M = dia + para para = M - dia =1.2 x 10-3 + 168 X 10-6 = 1.368 x 10-3.

29810368.1828.2 3 eff

= 1.806 µB per mole of dimerUncorrected = 1.7 µB = per mole of dimer 0.1 difference. It’s important to correct if you want to be accurate.

2 Exam question 1 (2004) (a).

What is meant by Curie behaviour? Give reasons why paramagnetic materials may deviate from Curie behaviour and explain what additional information can be extracted from such deviations.

The magnetic susceptibility, (M/H) is dependent on 1/T. =C/T.

As the temperature increases the increase in thermal energy gives rise to greater randomisation of the spin orientation and hence a smaller induced magnetisation.

The Curie constant C, comprises a series of fundamental constants and S, the spin quantum number. Thus from a plot of 1/ Vs T the value of S can be determined form the gradient.

Paramagnetic materials may deviate from Curie behaviour if:

a) there are local ferromagnetic or antiferromagnetic interactions between spins. The materials can then be described as Curie Weiss paramagnets.

= C/(T-)

When > 0 it indicates ferromagnetic interactions; if = 0 we have ideal Curie behaviour and if < 0 then it indicates antiferromagnetic interactions.

can be determined from a plot of 1/ vs T, which should be linear with an intercept on the T axis equal to . The larger the value of the greater the interaction between spins on neighbouring molecules.

Paramagnetic materials may deviate from Curie behaviour if:

b) If the material shows Van Vleck behaviour.

This occurs when there is thermal population of excited states whose magnetic behaviour is different to that of the ground state.

For example Eu3+. The ground state term is 7F0 hence the predicted µeff is 0 B.M. Observed values are typically in the range 3.3-3.5 B.M. at room temperature, although the value decreases upon cooling.

In the case of Eu3+ the separation of the ground state 7F0 and the first excited state is ca. 300cm-1. At room temperature there is enough thermal energy for the 7F1 state to be partially populated.

On cooling the 7F1 state becomes depopulated and the magnetic moment approaches 0 B.M. as T approaches 0 K when all the ions are in the 7F0 state.

However a second effect (temperature independent paramagnetism, TIP) is required to rationalize the data satisfactorily.