Magnetism of Solids: Homework Solutions for Fe2+

In summary, the conversation discusses finding the mass ratio of MgO and Fe in a sample by plotting a graph of magnetic moment vs temperature. The combined graph shows a 1/T trend and the magnetic moment of the sample tends towards that of MgO as temperature increases. The equation for the curve is provided and the goal is to find the mass ratio.
  • #1
decerto
87
2

Homework Statement


N0Mdlnt.png


2. Homework Equations


##\mathcal{X}=\frac{\mu^2_BNg^2_j}{3k_BT}J(J+1)=\frac{C}{T}##

##M=\mathcal{X}H##

The Attempt at a Solution


[/B]
##Fe^{2+}## has a value 4 of J from hunds rules.

So I know what the curie factor for iron is

##M=\frac{m}{V}=\frac{HC}{T}##

##m=\frac{HVC}{T}##

I don't know how I am supposed to treat the sample, assuming that MgO has a temp independent, diamagnetic susceptibility means that the changing magnetic moment is just from the iron but I am not sure how to use this?
 
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  • #2
You will need to think around the subject for a bit to seek inspiration.
i.e. if you were to plot a graph of magnetic moment vs temp - what sort of curve would the MgO alone get you? What sort of curve for Fe aone? What sort of shape is the combined curve likely to be?
What happens to the magnetic moment of the sample as the temperature increases? Describe in terms of the relative moments of the MgO and the Fe.
 
  • #3
Simon Bridge said:
You will need to think around the subject for a bit to seek inspiration.
i.e. if you were to plot a graph of magnetic moment vs temp - what sort of curve would the MgO alone get you? What sort of curve for Fe aone? What sort of shape is the combined curve likely to be?
What happens to the magnetic moment of the sample as the temperature increases? Describe in terms of the relative moments of the MgO and the Fe.

Drawing the graph helped, thanks, the combined graph goes as 1/T and tends towards the magnetic moment of MgO as T increases.

What do you mean by "Describe in terms of the relative moments of the MgO and the Fe."?

Also what should I try to be working out, the susceptibility of Mg0, the volumes?

The equation for the curve I have is

##m_{total}=HV_{FE}\frac{C}{T}+HV_{MgO}\mathcal{X}_{MgO}##

##m_{total}=H(V_{FE}\frac{C}{T}+V_{MgO}\mathcal{X}_{MgO})##
 
  • #4
You are supposed to be working out the mass ratio...
 
  • #5
Simon Bridge said:
You are supposed to be working out the mass ratio...
I'm aware of that but I can't see how to get to it, I have a formula with volume in it due to the magnetization/magnetic moment relation which I don't know how to deal with.
 

1. What is the magnetic moment of Fe2+ in a solid?

The magnetic moment of Fe2+ in a solid varies depending on the specific composition and arrangement of the solid. However, in general, Fe2+ has a high magnetic moment due to its unpaired electrons. This means it is strongly attracted to magnetic fields and can exhibit ferromagnetic properties.

2. How does the magnetic moment of Fe2+ change with temperature?

The magnetic moment of Fe2+ can change with temperature due to thermal fluctuations affecting the alignment of its electrons. As the temperature increases, the magnetic moment may decrease or even disappear completely, depending on the strength of the magnetic field and the specific properties of the solid.

3. How does the crystal structure of a solid affect its magnetic properties?

The crystal structure of a solid can have a significant impact on its magnetic properties. For example, in a ferromagnetic solid, the atoms are arranged in a specific pattern that allows for strong alignment of magnetic moments, resulting in a strong overall magnetic field. In contrast, in an antiferromagnetic solid, the atoms are arranged in a way that cancels out magnetic moments, resulting in a weaker overall magnetic field.

4. How does the presence of impurities affect the magnetic properties of a solid?

The presence of impurities in a solid can have a significant impact on its magnetic properties. For example, if a non-magnetic element is introduced into a ferromagnetic solid, it can disrupt the alignment of magnetic moments and weaken the overall magnetic field. On the other hand, if a magnetic element is introduced into an antiferromagnetic solid, it can strengthen the overall magnetic field.

5. Can the magnetic properties of Fe2+ in a solid be manipulated?

Yes, the magnetic properties of Fe2+ in a solid can be manipulated through various methods. One way is by applying an external magnetic field, which can change the alignment of its magnetic moments. Another method is by changing the temperature, as discussed earlier. Additionally, changes in pressure or chemical composition can also affect the magnetic properties of Fe2+ in a solid.

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