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Magnets, Metals and Superconductors Tutorial 1

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 Ln 3+ ions. Gd 3+ , Er 3+. Gd 3+ = f 7 S = 7/2, L = 0, J = 0 i.e. is spin only!  eff = 7.94

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Magnets, Metals and Superconductors Tutorial 1

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  1. Magnets, Metals and SuperconductorsTutorial 1 Dr. Abbie Mclaughlin G24a

  2. 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

  3. Er3+ = 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 = 3/2 L = mj = 6, J = 15/2, 13/2, 11/2, 9/2 Term symbol = 4I15/2 gj= 6/5 µeff = 9.58

  4. 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.

  5. 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. =41 B

  6. 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

  7. 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

  8. 4. Determine effper 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.

  9. eff = 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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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