Understanding Diamagnetic Materials: Key Properties and Uses

Diamagnetic materials are a class of substances that develop a weak, negative magnetization when placed in an external magnetic field. These materials are characterized by their tendency to repel a magnetic field due to the absence of permanent magnetic dipole moments in their atoms or molecules. Diamagnetism is a fundamental property observed in all materials, but it can be masked by stronger magnetic effects such as paramagnetism or ferromagnetism.

Definition and Origin of Diamagnetism

Diamagnetism arises when the orbital motion and spin of electrons in an atom or ion result in a net zero magnetic moment in the absence of an applied magnetic field. When an external field is applied, the electrons adjust their motions in such a way that an induced magnetic moment opposes the applied field, in accordance with Lenz’s Law.

The negative magnetization exhibited by diamagnetic materials is a result of this induced effect. The magnitude of diamagnetism is generally very weak compared to paramagnetism or ferromagnetism. The induced magnetic moments are always in the direction opposite to that of the external magnetic field.

Magnetic Susceptibility and Permeability

Diamagnetic materials are defined by a negative value of volume magnetic susceptibility ($\chi_v$), typically in the range of $-10^{-6}$ to $-10^{-5}$. These values reflect the weak and negative response to applied magnetic fields. The relative permeability ($\mu_r$) of diamagnetic materials is slightly less than one, commonly approximated as $\mu_r \approx 1 - 10^{-5}$.

The relationship between magnetic flux density $B$, applied magnetic field $H$, and magnetization $M$ is given by: $B = \mu_0 (H + M)$, where $\mu_0$ is the permeability of free space. For diamagnetic materials, $M$ is in the opposite direction to $H$, reducing the total $B$ inside the material.

Microscopic Explanation

On the atomic scale, electrons move in closed shells. In the absence of an external field, the orbital and spin magnetic moments cancel. When a magnetic field is applied, the electron orbits are modified, inducing a magnetic moment opposite to the field. This change in orbital motion is also referred to as the Larmor precession.

The net effect is a weak repulsion by a magnetic field. The diamagnetic susceptibility arises mainly from the closed-shell electrons, and its magnitude is proportional to both the number of such electrons and the square of their orbital radii.

Properties of Diamagnetic Materials

Diamagnetic materials display several characteristic properties that distinguish them from other magnetic types:

• Negative magnetic susceptibility, $\chi_v < 0$
• Relative permeability slightly less than unity
• Induced magnetization opposes applied field
• Repelled by external magnetic fields
• No permanent magnetic dipoles
• Induced effects vanish with external field removed
• Susceptibility is largely independent of temperature

Examples of Diamagnetic Materials

Common diamagnetic materials include bismuth, copper, silver, gold, lead, mercury, silicon, germanium, water, and the inert gases. Some organic compounds such as naphthalene and graphite also exhibit relatively strong diamagnetic behavior due to delocalized electrons.

Table: Relative Permeability ($\mu_r$) of Selected Diamagnetic Materials

For an extended list, refer to Diamagnetic Materials Overview.

Diamagnetism in Comparison with Other Magnetic Properties

Paramagnetic materials possess unpaired electrons and show a small positive susceptibility; they are attracted by magnetic fields. Ferromagnetic materials, such as iron and nickel, have large positive susceptibilities and exhibit spontaneous magnetization. Unlike these, diamagnetic materials lack unpaired electrons, and their magnetization is always negative and weak.

Diamagnetism is present in all materials, but in substances also exhibiting paramagnetism or ferromagnetism, the latter effects dominate and mask the diamagnetic response. For comparison between these types, see Properties Of Diamagnetic, Paramagnetic And Ferromagnetic Materials.

Mathematical Expression for Diamagnetic Susceptibility

The volume magnetic susceptibility ($\chi_v$) of a diamagnetic material may be expressed mathematically as:

$\chi_v = -\dfrac{\mu_0 N e^2 \langle r^2 \rangle}{6m_e}$

where $N$ is the number density of atoms, $e$ is the electron charge, $\langle r^2 \rangle$ represents the mean square radius of the electron orbit, $m_e$ is the mass of the electron, and $\mu_0$ is the permeability of free space. This expression shows that susceptibility is negative and independent of temperature.

Temperature Dependence

Diamagnetic susceptibility is essentially independent of temperature. This behavior contrasts with paramagnetic and ferromagnetic materials, which exhibit strong temperature dependence due to the thermal alignment of magnetic moments.

Heating or cooling a diamagnetic sample does not influence its susceptibility significantly. This property is useful in distinguishing diamagnetism from other types of magnetism in experiments.

Superconductors as Perfect Diamagnets

Superconductors are materials that, below their critical temperature, exhibit perfect diamagnetism, expelling all external magnetic fields from their interior. This phenomenon is known as the Meissner effect. In such a state, their magnetic susceptibility reaches $-1$, and the relative permeability approaches zero.

Superconductors do not allow magnetic fields to penetrate their bulk, making them ideal for magnetic levitation and shielding applications. For more on this topic, refer to the related content on Properties Of Solids.

Applications of Diamagnetic Materials

Diamagnetic materials find application in magnetic levitation, magnetic shielding, and precision weighing techniques. The weak repulsion from strong magnetic fields allows levitation of diamagnetic objects under highly controlled conditions, as observed with bismuth and pyrolytic graphite.

These materials are also used in magnetic resonance imaging (MRI) environments and for eliminating unwanted magnetic field influences in sensitive instruments. The study of diamagnetic effects contributes to understanding the electronic structure of atoms and molecules.

Identification and Measurement

Diamagnetic materials can be identified using techniques such as the Gouy balance method, where their weak repulsion from a magnetic field can be measured. When placed near a strong magnet, these materials move toward the region of weaker magnetic field intensity.

For reliable measurement, care must be taken to account for the weak magnitude of diamagnetic susceptibility, and to separate it from any paramagnetic or ferromagnetic contributions.

Key Distinctions and Summary

Diamagnetic materials are fundamentally different from paramagnetic or ferromagnetic substances due to the absence of permanent magnetic dipoles, negative susceptibility, and temperature-independent behavior. Their unique properties remain relevant in both theoretical and practical aspects of physics.

To further explore electromagnetic concepts and their applications in various phenomena, see Electromagnetic Induction And Alternating Currents.