Chapter 3 - Permanent magnets as energy materials

Question 1

What are the “soft” and “hard” magnetic materials? Give an example (schematic drawing) of typical M(H) curves for these type of magnets.

Answer 1

Soft magnetic materials are materials that have a low coercive field strength, and thus requires a lower field to flip the magnetization. Hard magnetic materials have a high coercive field strength, and thus requires a higher field to flip the magnetization.

Question 2

Name state of the art magnetic materials with the highest energy product |BH|_max. Analyze what limits their wider application as energy materials.

Answer 2

The highest energy product is found in compounds containing the rare earth element neodymium and dysprosium. For example the so called NEOMAX containing neodymium, iron and boron has a very high energy product.

The main concern for their wider application is that both Nd and Dy are not highly abundant. They are even regarded as critical, because of the high demand and the low availability.

Question 3

What are the straightforward approaches to predict magnetic properties? How does calculating the resulting spin moment help in the development of new magnets?

Answer 3

We can calculate the spin moment by using a simple formula, µ = g*sqrt(S(S+1)).

When there is an effect from the electrons in motion, giving rise to an orbital momentum, this too can produce a magnetic moment. In this case we can calculate using the formula: µ = sqrt(4S(S+1) + L(L+1)) where S is the spin quantum number and L is the orbital angular momentum quantum number.

Sometimes the orbital momentum is wholly or partially quenched, if the electric field on surrounding atoms or ions restrict the orbital motion of the electrons. Then the value can lie somewhere in between the two calculated values.

The resulting spin moment can then tell us something about the strength of the magnets (this should be investigated more, check Tilley).

Question 4

Explain what the driving forces responsible for the formation of the ferromagnetic domains are.

Answer 4

Dividing into ferromagnetic domains can reduce the magnetostatic energy. There is a trade-off here between energy of formation of domain walls, and the long-distance energy gain from having a opposite magnetization. (Look in Tilley for better explanation and update this).

Question 5

Analyze why the “Neo-Dy”-magnets play the dominant role in e.g. wind generators.

Answer 5

For generators, the resistance to demagnetization is critical. By introducing dysprosium in neodymium, the intrinsic coercivity is increased, and such magnets are therefore favorable (check the article on this for a better explanation).

Question 6

Why are permanent magnets advantageous in wind power production?

Answer 6

Because they can be operated efficiently at low revolution speeds, which are necessary for windmills to run at.

Question 7

Give some advantages of permanent magnet motors over induction motor.

Answer 7

It is more efficient, weighs less and is smaller in size.

Question 8

What is the physicist’s way of describing magnetism?

Answer 8

In terms of circulating currents in materials, that is motion of electrons.

Question 9

What is the engineer’s way of describing magnetism?

Answer 9

In terms of magnetic poles.

Question 10

Give a definition of a permanent magnet.

Answer 10

An inorganic solid that exhibit magnetic effects other than diamagnetism. In these materials there are some unpaired electrons in their outer valence shells. These electrons are usually located on metal cations, and can have both spin and orbital motion, which together generate a magnetic moment associated with the electrons.

Question 11

What classes of materials are mainly exhibiting permanent magnetic properties?

Answer 11

Compounds of transition metals and lanthanoids. Most of these elements contains unpaired d and f electrons.

Question 12

What is the definition of the magnetic induction, B? What is the unit it is measured in?

Answer 12

The magnetic induction is a material’s response to a magnetic field, H. [B] = T

Question 13

What is the definition of magnetization, M. What is the unit it is measured in?

Answer 13

Magnetization is the total magnetic moment per unit volume. It is measured in oersted ([M] = Oe).

Question 14

What is the definition of the magnetic susceptibility?

Answer 14

The susceptibility is the ratio of M to H.

Question 15

What is the permeability?

Answer 15

The permeability is the ratio of B to H.

Question 16

What is the intrinsic coercivity?

Answer 16

The intrinsic coercivity is the permanent magnet’s resistance to demagnetization.

Question 17

What is the customary figure of merit for a permanent magnet?

Answer 17

The energy product, |BH|_max. This quantity is twice the energy stored in the stray field created by the magnet.

Question 18

What is the Curie temperature?

Answer 18

The temperature above which the permanent magnetization cease to exist, since thermal fluctuations are enough to flip the magnetic dipoles.

Question 19

Why was the discovery of the ferrimagnetic hexagonal ferrites important?

Answer 19

Because they allowed to break the shape barrier. You no longer needed magnets that were horseshoe-shaped or bar magnets, but could have disk-like shapes. Before demagnetization would quickly occur due to shape related issues.

Question 20

Sketch the magnetic ordering in paramagnetic, antiferromagnetic, ferromagnetic and ferrimagnetic materials.

Answer 20

See slides.

Question 21

What is the Barkhausen noise?

Answer 21

When you look closely at a plot of magnetic induction (B) vs. an applied magnetic field (H), you see that the increase in magnetic induction is stepwise increased. This is due to the flipping of magnetic domains, which happens one at the time.

Question 22

What are the easy, medium and hard directions of magnetization? Give an example using bcc iron.

Answer 22

One axis is harder to magnetize than others. In bcc iron, it is hard to magnetize the iron by applying a field along the body diagonal. Along the cube edge, this will be easy. Along the face diagonal, this again is somewhere in between.