Magnets_ Metals and Superconductors by dffhrtcv3

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									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




Gd3+ = f7
S = 7/2, L = 0, J = 0
i.e. is spin only!                eff  2 S (S  1)
eff = 7.94
Term symbol = 8S0
Er3+ = f11             mj       3       2       1       0       -1       -2   3



                                         The term state symbol is written
 S = 3/2                                 2S+1L
                                              J.
 L = mj = 6, J = 15/2, 13/2,
 11/2, 9/2                               Hund’s Rules:
 Term symbol = 4I15/2                    For less than half-filled shells,
 gj= 6/5 µeff = 9.58                     the smallest J term lies lowest;
                                         for more than half filled shells
                                         the largest J lies lowest.
  3 S ( S  1)  L( L  1)
g                             eff  g J J ( J  1)
  2       2 J ( J  1)

         L         0        1       2       3    4      5   6        7

         Symbol    S        P       D       F    G      H   I        K
2 Exam question 1 (2004) (b).




The gradient =1/C. This can be used to determine S from the
equation:
C = Ng2µB2S(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.
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


b) Ferromagnetic exchange: ST = nS

nS = 10 x 2 = 20.
  eff  2 nS (nS  1) B.M


                eff  2 20(21) =41 B
c) Non interacting (high temperature limit).
S = 2, n = 10

 eff  2 n[S (S  1)]

                 eff  2 10[2(3)]    = 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.
                         eff  2 1 / 2(3 / 2)

µeff = 1.73 µB
b)Ferromagnetic exchange: ST = nS            eff  2 nS (nS  1) B.M
nS = 3 x 1/2 = 3/2.

             eff  2 3 / 2(5 / 2) = 3.87 µB.



c) Non interacting (high temperature limit).
S = 1/2, n = 3
                    eff  2 n[S (S  1)]


                   eff  2 3[1/ 2(3 / 2)]    = 3.00 µB
4. Determine eff per mole of Cu2(OAc)4.2H2O. Apply a
diamagnetic correction to  and redetermine eff. Does it make
a difference?

         3k .T
eff            2.828 T                         3
                                 2.828 1.2 10  298
          N B2



 =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.
 eff    2.828 1.368103  298

= 1.806 µB per mole of dimer
Uncorrected = 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.

								
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