Magnets, Metals and Superconductors Tutorial 1

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Magnets, Metals and SuperconductorsTutorial 1

• Dr. Abbie Mclaughlin
• G24a

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1. Determine the ground state configuration and
predict the effective magnetic moment for the
following Ln3 ions. Gd3, Er3
Gd3 f7 S 7/2, L 0, J 0 i.e. is spin
only! ?eff 7.94 Term symbol 8S0
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Er3 f11
The term state symbol is written 2S1LJ. Hunds
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 3/2 L ?mj 6, J 15/2, 13/2, 11/2,
9/2 Term symbol 4I15/2 gj 6/5 µeff 9.58
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2 Exam question 1 (2004) (b).
The gradient 1/C. This can be used to determine
S from the equation C Ng2µB2S(S1)/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.
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3a. 2 cyclic-Fe(OMe)(OAc)10 Fe2 d6 S 2 n
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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
b) Ferromagnetic exchange ST
nS nS 10 x 2 20. 41
?B
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c) Non interacting (high temperature limit). S
2, n 10 15.5 µB.
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.
µeff 1.73 µB
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b)Ferromagnetic exchange ST nS nS 3 x 1/2
3/2. 3.87 µB.
c) Non interacting (high temperature limit). S
1/2, n 3 3.00 µB
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4. Determine ?eff per mole of Cu2(OAc)4.2H2O.
Apply a diamagnetic correction to ? and
redetermine ?eff. Does it make a difference?
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.
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?eff
1.806 µB per mole of dimer Uncorrected 1.7 µB
per mole of dimer 0.1 difference. Its
important to correct if you want to be accurate.
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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.
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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 ? gt 0 it indicates ferromagnetic
interactions if ? 0 we have ideal Curie
behaviour and if ? lt 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.
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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.
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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.