# Are ions without valence electrons diamagnetic

Paramagnetism is a manifestation of magnetism in matter. A Paramagnetmagnetizes itself in an external magnetic field in such a way that it intensifies the magnetic field inside. The magnetization is proportional to the magnetic field strength; the factor is determined by the magnetic susceptibility. Paramagnetism occurs in all materials whose atoms or molecules have a magnetic moment. In physics, all materials with positive magnetic susceptibility and without magnetic order are classified as paramagnetic.

### origin

As a model, one can imagine a paramagnetic sample made up of small bar magnets that rotate but cannot slip. If the sample is brought into a magnetic field, the bar magnets will preferentially align themselves in the direction of the magnetic field lines. An important feature here is that the bar magnets do not influence each other - they all align themselves independently of each other. The temperature causes a constant reorientation of the bar magnets, which means that a random arrangement is much more likely than an orderly one. Therefore, the stronger you want to align the magnets, the stronger the magnetic fields.

In physical terms: The cause of paramagnetic behavior lies in the alignment of the microscopic magnetic moments of a substance in a magnetic field. The individual magnetic moments are independent of one another. In contrast to ferromagnets, such an alignment is immediately destroyed again by thermal fluctuations after the magnetic field is switched off. The magnetization M. of the substance is proportional to the applied magnetic field H

With .

The greater the magnetic susceptibility χ of the substance, the easier it is to magnetize it. The susceptibility is therefore a measure of the strength of paramagnetism. Because of the simple relationship between susceptibility and relative magnetic permeabilityμr = χ + 1, the latter is also often taken as a measure.

One can often read that a very high susceptibility means that a sample is ferromagnetic. This statement is not entirely true. Although the susceptibility of ferromagnets is very high in many cases, the cause lies in the aforementioned coupling. Ferromagnets still show magnetization after switching off the magnetic field, the so-called remanence, while with paramagnets, as already mentioned, the magnetization disappears again after switching off the field.

### species

Classical consideration does not provide any explanation for the presence of the magnetic moments discussed above. However, these can be understood in terms of quantum mechanics. The important statement for magnetism is that the total angular momentum of an atomic state always with a magnetic moment is linked

.

It is G the Landé factor and μB. Bohr's magneton. The total angular momentum is made up of three components:

1. Spin and
2. Orbital angular momentum of the electrons as well
3. Nuclear spin of nucleons.

The magnetic moment associated with nuclear spin is - because of the significantly larger mass of the nucleons - too weak to be able to make a significant contribution to susceptibility. Therefore, this is not considered further in the following. It should be noted, however, that the magnetic moment of the nucleus is definitely measurable, which is used in medicine for magnetic resonance imaging (MRT) (this is why the procedure is also called magnetic resonance imaging).

The main contributions to susceptibility come from various sources, which are listed below. However, since there are always diamagnetic contributions to susceptibility, it is only an addition of all contributions that decides whether a substance is ultimately paramagnetic. However, if Langevin paramagnetism (see below) occurs, its contribution is usually dominant.

### Magnetic moments of atoms in the ground state (Langevin Paramagnetism)

The total angular momentum of an atom in the ground state can theoretically be determined using the so-called Hund's rules. Most important essence from this is that it is the total angular momentum

1. a closed shell and
2. a shell half full except for one electron

always added to zero. In all other cases the atom has a magnetic moment.

The temperature dependence of this contribution is determined by Curies law

is described C. the Curie constant (a material constant).

### Magnetic moments of the conduction electrons (Pauli paramagnetism)

Electrons can move practically freely in metals. Every electron has a magnetic moment - one expects a Curie-like contribution to the susceptibility. However, due to the Pauli principle, only the excited conduction electrons have the freedom to align their spin in the magnetic field. Their number is proportional to T / TF. (TF. is the Fermi temperature, another material constant):

.

However, a closer look shows that there is a dependency on the strength of the external magnetic field.

### Magnetic moments of atoms in excited states (Van Vleck Paramagnetism)

Even if the total angular momentum of an atom is zero in its ground state, this does not have to apply to excited states. At a finite temperature, some atoms are always in an excited state, so this contribution occurs in all substances. However, it is only of any appreciable size in molecular crystals; there it can even surpass Langevin's paramagnetism in strength. Calculating the size of this contribution is quite time-consuming, especially for molecules.

### Superparamagnetism

The magnetic properties of granular ferromagnetic solids depend on the grain size. When the grain size is reduced, the number of magnetic regions (Weiss region) per grain decreases. Below a critical size, it is energetically unfavorable to form several of these areas. So there is only one Weiss district per grain, i.e. H. all atomic magnetic moments of a grain are arranged parallel to one another. Below a further critical value, a stable alignment of the total magnetic moment is no longer possible at finite temperatures, since the energy required for remagnetization is less than the thermal energy. The solid as a whole now behaves paramagnetically with the peculiarity that the magnetic moments do not react individually, but in blocks to external magnetic fields. This particular form of paramagnetism is called Superparamagnetism designated.

### Alkali metals

The electron shell of the alkali metals consists of a noble gas configuration and an additional s-electron. According to Hund's rules, the atoms in their ground state have a magnetic moment. This is the first case (see above) that makes a strong contribution to susceptibility. The alkali metals are therefore paramagnetic.

### Alkaline earth metals

In contrast to the alkali metals, the alkaline earth metals have two s electrons and thus a closed lower shell. However, they belong to the group of metals and thus fall into the second case. With the exception of beryllium, this contribution outweighs the diamagnetic contribution, which means that the alkaline earth metals are weakly paramagnetic.

### Rare earth

The rare earths are among the technically most important materials for alloys in permanent magnets. The reason is that the crucial shell that is not fully occupied is inside the electron shell (f electrons) and therefore has no influence on the chemical properties of the atoms. Almost all rare earths are therefore paramagnetic (after the first case), but its strength varies. This makes them ideal candidates in alloys with ferromagnetic materials, which can be used to make very strong permanent magnets.

### Molecules

Since molecules often have a closed electron configuration and are not metals, they only show a contribution after the third case. Some examples of paramagnetic substances are:

### Magnetite

Magnetite (Fe3O4) normally shows ferrimagnetic behavior (ferrimagnetism).
With particle sizes which are smaller than 20 to 30 nm, superparamagnetic behavior is shown at room temperature. In the presence of an external magnetic field, all particles align themselves in the direction of this field. After removing the external field, the thermal energy is large enough that the mutual alignment of the particles relaxes and the magnetization approaches zero again.