Calculating Theoretical Landé Factor for Dy_2O_3 and Er_2O_3

In summary, The conversation is about an experiment on magnetic susceptibility of Dy_2O_3 and Er_2O_3 and the calculation of the theoretical Landé factor for the paramagnetic atoms in these salts. The Landé factor is defined as a relation between angular momentum and magnetic momentum and is calculated using the net quantum numbers for orbital momentum and electron spin. There is confusion about finding the correct values for these quantum numbers, and it is clarified that for Er3+ with 11 electrons in its 4f shell, the correct values are l=6 and s=3/2. The reason for this specific configuration is not easily understood and requires computer calculations. The summary ends with a correction for the total l value.
  • #1
kuengb
106
0
Hello everyone

I did an experiment about magnetic susceptibility of [itex]Dy_2O_3[/itex] and [itex]Er_2O_3[/itex]. For data evaluation I have to calculate the theoretical Landé factor for the paramagnetic atoms in these salts which is defined as
[tex]g_j=1+\frac{j(j+1)+s(s+1)-l(l+1)}{2j(j+1)} [/tex]
where l and s are the net quantum numbers for orbital momentum and electron spin respectively, j=l+s total angular momentum. The factor gives the relation between angular momentum and magnetic momentum.

The problem is: I don't completely understand how to find the correct values for l and s. That's how I understood it:

1)l is the sum of the l values for all electrons in non-filled orbitals, and s is the sum of the spin numbers (i.e. 1/2) of all unpaired electrons. For Erbium with configuration [itex](Xe)4f^{12} 6s^2[/itex] this would then be:12 electrons in the 4f orbital, hence l=12*3, and two unpaired electrons in that orbital, i.e. s=2*1/2. Does this make sense?

2)In the crystal structure of [itex]Er_2O_3[/itex], Erbium gives away three elecrons to Oxygen. Is it then reasonable to take the electron configuration of Terbium, which is three numbers below, for the above calculation? If not, how do I have to deal with this ionic bindings?

Thanks
Bruno
 
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  • #2
Er3+ has 11 electrons in its 4f shell (3 holes). These are the only ones you need to consider.
 
  • #3
Thank you. So, what I've written in 1) is correct, i.e. in this case l=11*3 and s=3/2 ?

Is there an easy way to understand why Er3+ has this particular configuration and not 4f9-6s2?

Regards
Bruno
 
  • #4
kuengb said:
Is there an easy way to understand why Er3+ has this particular configuration and not 4f9-6s2?
No, that requires computer calculations. But it is what the rare Earth's do (similar to the transition metals).

Your result for the total l is wrong, because one needs to add orbital moments vectorially. It is easiest to add the l_z components of the 4f-holes, and then one can see that l = maximum l_z = 3 + 2 + 1.
 

Related to Calculating Theoretical Landé Factor for Dy_2O_3 and Er_2O_3

1. What is the purpose of calculating the theoretical Landé factor for Dy2O3 and Er2O3?

The theoretical Landé factor is a measure of the strength of the magnetic moment of an atom or molecule. By calculating this factor for Dy2O3 and Er2O3, we can gain a better understanding of their magnetic properties and how they interact with external magnetic fields.

2. How is the theoretical Landé factor calculated for Dy2O3 and Er2O3?

The theoretical Landé factor is calculated using the formula: gJ = 1 + (J(J+1)+S(S+1)-L(L+1))/(2J(J+1)), where J, S, and L are the quantum numbers for total angular momentum, spin, and orbital angular momentum, respectively. These values can be determined from the electron configuration of the atoms in Dy2O3 and Er2O3.

3. What factors can affect the calculated theoretical Landé factor for Dy2O3 and Er2O3?

The calculated theoretical Landé factor can be affected by the presence of external magnetic fields, as well as the specific electronic structure and geometry of the atoms in Dy2O3 and Er2O3. Other factors such as temperature and pressure may also play a role.

4. How can the calculated theoretical Landé factor be used in practical applications?

The theoretical Landé factor can be used to predict and understand the behavior of Dy2O3 and Er2O3 in various magnetic fields, which can have practical applications in fields such as material science, electronics, and data storage. It can also help in the design and development of new magnetic materials with specific properties.

5. Are there any limitations to using the calculated theoretical Landé factor for Dy2O3 and Er2O3?

While the calculated theoretical Landé factor can provide valuable insights, it is important to note that it is a theoretical value and may not always accurately reflect the actual behavior of the atoms in Dy2O3 and Er2O3. Other factors, such as interactions with neighboring atoms and crystal structure, may also impact their magnetic properties. Experimental data should be used to validate the calculated values.

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